Express 45 as a product of its prime factors in index form

Answer:

t is less than or equal to 10

Step-by-step explanation:

At most means less than or equal to. The boat costs 6 an hour, so, 6t. He has a $8 off coupon, so, 6t-8 is less than or equal to 52. Add 8 on both sides and then divide by 6 to isolate t. t is less than or equal to 10 hours.

Answer:

it's I'd b yes so ya hope you do great

Step-by-step explanation:

Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

According to the statement seen in this question, the line segments RT and  ST are collinear to each other. Mathematically speaking, the length of the line segment ST can be found by using the following formula:

RT = RS + ST

ST = RT - RS

ST = 19 - 6

ST = 13

Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

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The graph of the water level, relative to the pier, at time t (in hours) can be represented by the formula f(t) = -8sin(πt/3) - 18, where f(t) denotes the water level in feet.

1. Given that at high tide, the water level is 10 feet below the pier, and at low tide, the water level is 26 feet below the pier.

2. The water level follows a sinusoidal behavior, indicating a sine function will be used to represent the graph.

3. Let's consider the sine function: y = A sin(B(t - C)) + D, where A represents the amplitude, B is the frequency, C is the horizontal shift, and D is the vertical shift.

4. Since the water level goes from 10 feet below the pier (high tide) to 26 feet below the pier (low tide), the amplitude of the sine function is (26 - 10) / 2 = 8.

5. The period of the sine function is the time it takes to go from one high tide to the next. Given that the first low tide occurs at t = 3, the period is 3 hours. Therefore, the frequency B = 2π / 3.

6. The horizontal shift C is 0 because the first low tide occurs at t = 3, and the starting point is at t = 0.

7. The vertical shift D is -18 because at t = 0, the water level is -18 feet.

8. Combining the information from steps 4, 5, 6, and 7, the formula for f(t) is f(t) = 8sin(πt/3) - 18, which represents the water level relative to the pier at time t in feet.

9. Sketching the graph using this formula will give a visual representation of the water level at any given time.

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Answer:

x = 10

Step-by-step explanation:

hope this helps :D

have a good day !!

Answer:

3rd option

Step-by-step explanation:

Given

4(x - 7) - 2(x + 1) = - 10 ← distribute parenthesis on left side

4x - 28 - 2x - 2 = - 10 ( collect like terms pn left side )

2x - 30 = - 10 ← equivalent equation

The efficiency of the power screw in raising the load is approximately 6976%.

The efficiency of a power screw can be calculated using the formula: Efficiency = (Ideal Mechanical Advantage / Actual Mechanical Advantage) x 100% To find the Ideal Mechanical Advantage (IMA) of the screw, we can use the formula:

IMA = (π / tan(α)) x (π / 2) x (D / P)

Where: π is the mathematical constant pi (approximately 3.14159) tan(α) is the coefficient of friction (given as 0.20) D is the major diameter of the screw (given as 19 mm) P is the pitch of the screw, which can be calculated as (25.4 mm / number of threads per inch) First, let's calculate the pitch: Number of threads per inch = 6

Pitch = 25.4 mm / 6 = 4.23 mm (approximately)

Now, we can substitute the values into the formula to find IMA:

IMA = (π / tan(α)) x (π / 2) x (19 mm / 4.23 mm)

Using the given coefficient of friction, we have:

IMA = (π / 0.20) x (π / 2) x (19 mm / 4.23 mm)

Simplifying the equation, we get:

IMA = 9.87 x 1.57 x 4.49

Calculating IMA, we find:

IMA ≈ 69.76

Now, we need to find the Actual Mechanical Advantage (AMA), which can be calculated using the formula:

AMA = Load / Effort

Where:

Load is the weight being lifted (given as 17.80 kN)

Effort is the force applied to turn the screw

Since the screw is being used to lift the load, the Effort is equal to the load.

AMA = 17.80 kin / 17.80 kin

AMA = 1

Now, we can calculate the efficiency using the formula:

Efficiency = (IMA / AMA) x 100%

Efficiency = (69.76 / 1) x 100%

Efficiency ≈ 6976%

The efficiency of the power screw in raising the load is approximately 6976%.

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The ordered triplet (x, y, z) or the following system of equations: x+3y + 2z = 1, 03x+y+5z=10, -2x-3y+z=7 is (-170/127, -89/127, 282/127).

Start with the first equation:

x + 3y + 2z = 1

Isolate x by subtracting 3y and 2z from both sides:

x = 1 - 3y - 2z

Substitute this expression of x into the second equation:

0.3x + y + 5z = 10

Substitute the value of x found in step 2 into this equation:

0.3(1 - 3y - 2z) + y + 5z = 10

0.3 -0.9y -0.6z + y + 5z = 10

0.1y + 4.4z = 9.7

y + 44z = 97

Solve for y by isolating it:

y = 97 - 44z

Substitute this expression of y into the first equation:

x + 3(97 - 44z) + 2z = 1

x + 291 - 132z + 2z = 1

Solve for x:

x = 130z - 290

Substitute this expression of x into the third equation:

-2(130z - 290) - 3(97 - 44z) + z = 7

-260z + 580 - 291 + 132z + z = 7

Solve for z:

127z = 282

z = 282/127

Substitute this value of z into the expression of y:

y = 97 - 44(282/127)

= -89/ 127

Substitute the values of z into the expression of x:

x = 130(282/127) - 290

= - 170/ 127

So the solution of the system of equations is: x = -170/127, y = -89/127, z = 282/127.

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Answer:

1. $19.91

Step-by-step explanation:

The problem that can arise from different styles and formats of quotations in terms of measurements or units is inconsistency and confusion.

If different suppliers or vendors quote prices based on different measurement units or quantities, it can make it difficult to compare and evaluate the offers accurately. It may lead to misunderstandings, errors in pricing, and challenges in making informed purchasing decisions. When quotations are based on different measurement units or quantities, it becomes challenging to compare them directly. For example, one supplier may provide a quotation based on cubic measurements, while another supplier may quote based on kilograms or the number of containers. This inconsistency can create confusion and make it difficult to determine which quotation offers the best value or meets the requirements of the buyer.

In such cases, it is essential to establish a common basis for comparison. This may involve converting the quotations to a standardized unit or quantity that is relevant to the buyer's needs. For example, if one supplier quotes based on cubic measurements and another based on the number of containers, the buyer may need to convert both quotations to a common unit, such as the cost per container or per cubic measurement, to make a fair comparison.

Without a standardized basis for comparison, it becomes challenging to assess the true costs and benefits of different quotations. It can lead to misunderstandings, as the buyer may assume a certain quantity or unit of measurement based on their expectations or previous experiences. This can result in errors in pricing, incorrect budgeting, and potentially selecting a supplier that may not be the most cost-effective or suitable option.

To avoid these problems, clear communication and clarification of the quotation requirements are crucial. Buyers should specify the preferred measurement units or quantities and ask suppliers to provide quotations based on those specifications. This helps ensure consistency, accuracy, and enables an informed evaluation of the quotations to make an appropriate purchasing decision.

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Answer:

Pop: 300 + 1200x (x represents the number of pop music bundles purchased)

Rock: 250 + 950z (z represents the number of rock music bundles purchased)

Answer:

Answered in the other one

Step-by-step explanation:

Answer:

371

Step-by-step explanation:

the nth term is 6n - 7

6(63) - 7

371

Answer:

Explanations:

From the table given, we can see that the value of y decreases by the same constant

The norms of the given functions are :

||p|| = √110 and ||q|| = √18.

To compute the norms ||p|| and ||q|| for the given functions p(t) = 6 + t and q(t) = 4 - 3t^2, with the inner product defined by evaluation at -1, 0, and 1, follow these steps:

Step 1: Evaluate p(t) and q(t) at the given points -1, 0, and 1.

For p(t) = 6 + t:
p(-1) = 6 + (-1) = 5
p(0) = 6 + 0 = 6
p(1) = 6 + 1 = 7

For q(t) = 4 - 3t^2:
q(-1) = 4 - 3(-1)^2 = 4 - 3 = 1
q(0) = 4 - 3(0)^2 = 4
q(1) = 4 - 3(1)^2 = 4 - 3 = 1

Step 2: Compute the norms ||p|| and ||q|| using the inner product.

For p(t):
||p|| = √(p(-1)^2 + p(0)^2 + p(1)^2) = √(5^2 + 6^2 + 7^2) = √(25 + 36 + 49) = √110

For q(t):
||q|| = √(q(-1)^2 + q(0)^2 + q(1)^2) = √(1^2 + 4^2 + 1^2) = √(1 + 16 + 1) = √18

Thus, ||p|| = √110 and ||q|| = √18.

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Answer: Mean  is the value obtained by dividing the sum of several quantities by their number; an average. Denoting the middle term of a series arranged in order of magnitude. The value which occurs most frequently in a set of data is known as the mode of the set of data.

Step-by-step explanation:

3)  since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.

(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:

Total payment A = Monthly installment * Number of installments

              = $375 * 36

              = $13,500

Therefore, Adrian paid a total of $13,500 over the course of 36 months.

(2) In the simple interest formula I = Prt, the letters used represent the following variables:

I: Interest (the amount of interest paid)

P: Principal (the initial amount, or in this case, the car worth)

r: Rate of interest (expressed as a decimal)

t: Time (in years)

(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:

r = (I / Pt) * 100

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Remi purchased approximately 150 pounds of pumpkins.

To find the number of pounds of pumpkins purchased by Remi, we can divide the total amount spent by the price per pound.

Let's assume that x represents the number of pounds of pumpkins purchased.

The total amount spent, $73.50, can be expressed as the product of the price per pound, $0.49, and the number of pounds purchased, x:

$73.50 = $0.49 × x

To solve for x, we divide both sides of the equation by $0.49:

x = $73.50 / $0.49 ≈ 150

Therefore, Remi purchased approximately 150 pounds of pumpkins.

By dividing the total amount spent by the price per pound, we found the quantity of pumpkins purchased.

In this case, Remi spent $73.50 and the price per pound was $0.49, resulting in the purchase of approximately 150 pounds of pumpkins. This information can be useful for budgeting, inventory management, and understanding consumer behavior at the local farm.

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The false statement among the given options is statement iv: "The sample means calculated from the samples of size 10 give a biased estimate of the true population mean compared with those from the samples of size 100."

Statements i, ii, and iii are true:
i. Each of the means calculated from the samples of size 100 is an unbiased estimate of the population mean. This is true because unbiased estimates are obtained when the sample mean is equal to the population mean on average.
ii. The standard deviation of the means calculated from the samples of size 10 is likely to be larger than the standard deviation of the means calculated from the samples of size 100. This is true because larger sample sizes tend to provide more precise estimates, resulting in smaller variability or standard deviation.
iii. Each of the means calculated from the samples of size 10 is an unbiased estimate of the population mean. This is true because unbiasedness is not dependent on sample size but on the sampling method itself.

Statement iv is false because the sample means calculated from samples of size 10 are unbiased estimates of the population mean, just like those calculated from samples of size 100. Unbiasedness is not influenced by sample size, but rather by the sampling method. The only difference is that the standard deviation of the means calculated from the samples of size 10 is expected to be larger than the standard deviation of the means calculated from the samples of size 100, as mentioned in statement ii.

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Answer:

Yes, they both have a volume of 423.9 inches cubed.

Step-by-step explanation:

Both cylinders have the same volume formula V=(pi)(r^2)(h)

d/2=r=3

h=15

so, (3.14)(9)(15)=423.9

The volume of each cylinder is 423.9

Answer:

The amount of 14 pairs of shorts is $ 103.25

Step-by-step explanation:

Given;

amount paid for 8 pairs of short, = $59.00

Then, a single pair short will cost ; $59.00 / 8 = $7.375

Buying at this rate, Amanda will pay the following amonut for 14 pairs.

The cost of 14 pairs of short is given as;

= 14 x $7.375

= $ 103.25

Therefore, the amount of 14 pairs of shorts is $ 103.25

Answer:

2:9 option b is the ans.

Answer: B and E

Step-by-step explanation:

Tip: 4:18 can be written in many ways, try dividing and multiplying 4 and 18 by different numbers so you can match the options

Divide 4 by 2 which gives you 2, do the same thing to 18 because in a ratio we do the same to both numbers

Doing so gives us 2:9, so this ratio is equal to 4:18

Now, multiply 4 by 2, do the same to 18 because we have to do the same thing to both sides of a ratio

Doing so gives us 8:36, this is equal to 4:18

So, the answer is 2:9 and 8:36 (B and E)

#1

\(\\ \tt\Rrightarrow -1/4(-8x+12y)\)

\(\\ \tt\Rrightarrow 2x-3y\)

#2

\(\\ \tt\Rrightarrow 36a-16\)

\(\\ \tt\Rrightarrow 4(9a-4)\)

To approximate the probability that fewer than 13 chips will be defective out of a random sample of 285, we can use the normal approximation to the binomial distribution with a correction for continuity.

First, we calculate the mean (μ) and standard deviation (σ) of the binomial distribution using the formula:

μ = n * p

σ = sqrt(n * p * (1 - p))

where n is the sample size and p is the probability of success (failure rate).

In this case:

n = 285

p = 0.055 (5.5% failure rate)

μ = 285 * 0.055 = 15.675

σ = sqrt(285 * 0.055 * (1 - 0.055)) = 4.142

Next, we use the normal distribution to approximate the probability of fewer than 13 defective chips. We standardize the value by calculating the z-score:

z = (x - μ) / σ

For x = 13:

z = (13 - 15.675) / 4.142 = -0.645

Using a standard normal distribution table or calculator, we find the cumulative probability for z = -0.645, which is approximately 0.259.

Therefore, the probability that fewer than 13 chips will be defective is approximately 0.259 (rounded to three decimal places).

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A NORMAL distribution is a symmetrical probability distribution with a bell-shaped curve. It is also called a Gaussian distribution or a normal curve. This distribution is often used in statistics to represent a large number of natural phenomena, such as the distribution of height, weight, or IQ scores in a population.

The first deviation of a NORMAL distribution includes 68.2% of the data. This means that if we were to take a random sample of data from a normally distributed population, about 68.2% of the data would be within one standard deviation of the mean.

The second deviation includes 95.4% of the data. This means that about 95.4% of the data would be within two standard deviations of the mean.

The third deviation includes 99.7% of the data. This means that about 99.7% of the data would be within three standard deviations of the mean.

It is important to note that while these percentages hold true for a NORMAL distribution, they may not apply to other types of distributions.

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the right answer is 12 and if you ever need more help just use the app mathaway

Answer:

Term-to-term rule: Adding one to the numerator and the denominator

10th term: 10/11

Step-by-step explanation:

Step-by-step explanation:

120 ft relate to 24 inches.

120/80 must be the same ratio as 24/model width.

120/80 = 3/2

so,

24/width = 3/2

48/width = 3

48 = 3width

width = 48/3 = 16 inches

1) The wavelength of A is equal to 6.98 × \(10^{-8}\)meters

2) The wavelength of B is equal to 3.45 × \(10^{-11}\) meters

Since we know that the wavelength = speed of light / frequency

The speed of light is 3.00 × \(10^8\) meters per second.

For light sample A with a frequency of 4.30 × 10^15 Hz can be calculated as;

wavelength of A = (3.00 ×  \(10^8\)  m/s) / (4.30 × 10^15 Hz)

wavelength of A = 6.98 ×  \(10^{-8}\) meters

For light sample B with a frequency of 8.70 × \(10^18\) Hz can be calculated as;

wavelength of B = (3.00 ×  \(10^8\) m/s) / (8.70 ×\(10^18\) Hz)

wavelength of B = 3.45 ×  \(10^{-11}\)  meters

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Answer:

18 and 9

Step-by-step explanation:

The numbers are x and 1/2x.

x + 1/2x = 27

3/2x = 27

x = 18 so the numbers of 18 and 9.

Answer:

\(16\pi\) \(cm^2\)

Step-by-step explanation:

Area of a circle is equal to \(\pi r^2\), where r is the radius

\(A=\pi r^2\)

A diameter is twice the length of the radius. (\(8/2\))

So the radius is 4 cm.

\(r^2=4^2=16\)

so the Area is \(16\pi\)