Which equation matches the hanger diagram?

The elements of the sequence that are divisible by 5 occur every third term, while the elements divisible by 13 occur every fourth term. There are no elements of the sequence that are divisible by 65, since there are no elements that are divisible by both 5 and 13.

To find which elements of the sequence are divisible by 5, we need to find the remainder of each element when divided by 5. Using the first few terms of the sequence, we get:

a₁ = -1, a₂ = 0, a₃ = 5, a₄ = 13, a₅ = 29, a₆ = 61, a₇ = 125, a₈ = 253, ...

To check if an element is divisible by 5, we only need to look at the units digit of the number, since any multiple of 5 ends in 5 or 0. From the sequence, we can see that the units digit of a₃ is 5, so a₃ is divisible by 5. To find any other elements that are divisible by 5, we can look for a pattern in the units digits of the terms. We can see that the units digits of the terms cycle through 5, 3, 1, and 9. Since 5 appears in the cycle, every third term of the sequence will be divisible by 5. Therefore, the only elements of the sequence that are divisible by 5 are a₃, a₆, a₉, a₁₂, and so on.

To find which elements of the sequence are divisible by 13, we can use a similar approach. We need to find the remainder of each element when divided by 13. From the sequence, we can see that the units digit of a₄ is 3, so a₄ is not divisible by 13. To find any other elements that are divisible by 13, we can look for a pattern in the remainders of the terms. We can see that the remainders cycle through 3, 8, 6, and 10. Since 10 appears in the cycle, every fourth term of the sequence will be divisible by 13. Therefore, the only elements of the sequence that are divisible by 13 are a₄, a₈, a₁₂, a₁₆, and so on.

To find if any elements of the sequence are divisible by 65=5.13, we need to find elements that are divisible by both 5 and 13. From our analysis above, we can see that a₃ is the only element of the sequence that is divisible by 5, and a₄ is the only element that is divisible by 13. Therefore, there are no elements of the sequence that are divisible by 65, since the only way a number can be divisible by 65 is if it is divisible by both 5 and 13.

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Complete question:

Consider the sequence a₁ = = 2¹-3=-1₁ -2²-3=1, 0₂= 03 =2³-3=5, 04-2¹-3=13, ⠀ a₁ = 2" - 3, defined for positive integers n. Which elements of this sequence are divisible by 5? What about 13? Are any elements of this sequence divisible by 65= 5. 13? Why or why not?​

Answer:

Step-by-step explanation:

We can use the fact that the ratio of the volumes of two similar solids is equal to the cube of their corresponding linear dimensions, also known as the volume-scale factor:

(volume of image) / (volume of original) = (linear dimension of image / linear dimension of original)^3

(40 cubic units) / (10 cubic units) = (linear dimension of image / linear dimension of original)^3

4 = (linear dimension of image / linear dimension of original)^3

Taking the cube root of both sides, we get:

(cube root of 4) = (linear dimension of image / linear dimension of original)

Simplifying, we have:

2 = (linear dimension of image / linear dimension of original)

Therefore, the linear dimensions of the image are two times greater than those of the original. Thus, the scale factor is 2.

Answer:50

Step-by-step

Answer:

Answer is D

Step-by-step explanation:

The absolute value is the distance between a number and zero. The distance between −50 and 0 is 50

The percentage of fat in a 200 calorie peanut butter sandwich is 40%.

To find the percentage of fat in a 200 calorie peanut butter sandwich if the total amount of calories of fat are 80 calories, we need to use the formula:

Percentage of fat = (Calories of fat / Total calories) x 100

Let's substitute the given values in the above formula:

Calories of fat = 80

Total calories = 200

Percentage of fat = (80/200) x 100 = 40%

Therefore, the percentage of fat in a 200 calorie peanut butter sandwich is 40%.

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log5 x∧4 + log5 2x - log5 3x - correct. The property of logarithms to be used a log b = log a∧b.

A logarithm is a mathematical function that represents the relationship between the logarithm of a number and its actual value. In simpler terms, a logarithm is the exponent to which a base must be raised to get a certain value.

4 log5 x + log5 2x - log5 3x

Marta incorrectly applied a property of logarithms at step 1:

log5 4x + log5 2x - log5 3x - incorrect

log5 x∧4 + log5 2x - log5 3x - correct

The property of logarithms to be used:

a log b = log a∧b.

Therefore at step 1 she incorrectly applied.

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Answer:

17 strips, 2 inches remain

Step-by-step explanation:

20(12)/14=17

17x14=238

240-238=2

A 20-foot ribbon converts to 240 inches. It can be cut into 17 strips of 14 inches each, leaving 2 inches of ribbon leftover.

To solve this problem, we need to first convert the length of the ribbon from feet to inches, since the length of the strips is given in inches. One foot equals 12 inches, so a 20-foot ribbon is 20*12 = 240 inches long.

Now, to find out how many 14-inch strips can be cut from the ribbon, we do the division: 240 divided by 14 equals 17 strips with a remainder. This means 17 full strips can be cut from the ribbon.

To find how many inches are left, we need to multiply the number of strips by the length of each strip and then subtract the result from the total length of the ribbon. So it's 240 - (17 * 14) = 2 inches.

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Therefore, the correct answer is option D: "The wire is on the cylinder axis and carries current i in the direction opposite to that of the current in the shell. "Option E, "the wire does not carry any current," is not correct because the wire is in a region with a magnetic field, and therefore will have an induced current.

we are asked to determine the position and direction of the wire that is parallel to the cylinder axis in the hollow region. The long straight cylindrical shell has an inner radius R and an outer radius Ro, and carries a current i that is uniformly distributed over its cross section. The wire is located in the hollow region, which is defined as r > R and r < Ro.

Based on this information, we can determine the position and direction of the wire.To begin, we know that the wire must be on the cylinder axis since it is parallel to the axis. This eliminates options A, B, and C. Additionally, we know that the current in the wire must be in the opposite direction to the current in the shell. This is because the magnetic field created by the current in the shell will induce a current in the wire that is opposite in direction in order to create a repulsive force.

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Diameter = 16 mm

Radius = Diameter/2

= 16/2

= 8 mm

Total height of figure = 32 mm

Height of cylinder = 19 mm

Height of cone = 32 - 19

= 13 mm

Volume of cylinder = πr²h

Substituting the values of r and h in above formula,,

[tex] \longrightarrow \sf \pi \times {(8)}^{2} \times 19 \\ \\ \longrightarrow \sf \pi \times 64 \times 19 \\ \\ \longrightarrow \sf 1216 \pi \\ \\ \longrightarrow \sf 3820.17 \: mm^{3}\\ \\ [/tex]

Hence, Volume of cylinder is 3820.17 mm³

Now,

Volume of cone = 1/3 πr²h

[tex] \longrightarrow \sf \dfrac{1}{3} \times \pi \times {(8)}^{2}\times 13 \\ \\ \longrightarrow \sf \dfrac{1}{3} \times \pi \times 64 \times 13 \\ \\ \longrightarrow \sf 871.26~ mm^3 \\ \\ [/tex]

Hence, Volume of the cone is 871.26 mm³

Volume of composite figure = Volume of cylinder + Volume of cone.

= 3820.17 + 871.26

= 4691.43 mm³

Therefore, Volume of the composite figure is 4691.43 mm³.

The corrected version has a base of 0.7, representing exponential decay, and has the function[tex]y = a(1-r)x[/tex] as [tex]y = 2.55(0.7)x[/tex] with a [tex]0.3[/tex] decay factor.

Explain function?

A function is a link or statement that contains one or more values. Both inputs and outputs are numerous. With each input, there is only one output. The links between the inputs and the results are described by the function.

The error the student made is in Step 2 where they incorrectly wrote the function in the form [tex]y = a(1-r)*.[/tex]The correct form for exponential decay is [tex]y = a(1-r)^x[/tex], where x is the number of time periods. So, the correct equation for the given function is [tex]y = 2.55(0.7)^x.[/tex]

To find the decay factor, the student should have subtracted the base from 1, instead of multiplying it by -1. Therefore, the correct decay factor is [tex]1 - 0.7 = 0.3.[/tex]

So, the corrected version of the solution is:

Step 1: As the function's base is[tex]0.7[/tex], it simulates exponential decay.

Step 2: The function in the form [tex]y = a(1-r)^x is y = 2.55(0.7)^x.[/tex]

Step 3: The decay factor is [tex]0.3.[/tex]

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Answer:

-3x

Step-by-step explanation:

FIrst you subract 2 from both sides then eliminate the x's

The five-number summary for this data set is 36, 38.5, 50.5, 53, and 57, and the interquartile range is 14.5.

Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.

To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.

Step 1: Find the median (Q2)

When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:

Median (Q2) = (50 + 51)/2 = 50.5

Step 2: Find the lower quartile (Q1)

The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:

Q1 = (38 + 39)/2 = 38.5

Step 3: Find the upper quartile (Q3)

The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:

Q3 = (53 + 53)/2 = 53

Now we have all the information we need to construct the five-number summary and interquartile range:

Minimum: 36

Lower quartile (Q1): 38.5

Median (Q2): 50.5

Upper quartile (Q3): 53

Maximum: 57

Interquartile range (IQR) = Q3 - Q1 = 53 - 38.5 = 14.5

the five-number summary for this data set is 36, 38.5, 50.5, 53, and 57, and the interquartile range is 14.5.

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The number which is absent in the first 31 digits of the pi is 9

The digit that is absent in the first 31 digits of pi is the digit 9. Pi is an irrational number with an infinite number of decimal places, and it is believed to be a random sequence of digits. However, the absence of the digit 9 in the first 31 digits of pi is just a coincidence and has no special mathematical significance.

It is important to note that the digits of pi are not random in the strict sense of the word, but they appear to be so, and they follow a pattern that has yet to be fully understood by mathematicians. The quest to discover the properties of pi has been ongoing for centuries, and it continues to be a fascinating and important area of research in mathematics.

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The given question is incomplete, the complete question is:

Which number is absent in the first 31 digits of pi

Answer:

Step-by-step explanation:

every second we are increasing the sides by 4.4 in all 3 dimensions. This must mean that we need to do 4.4x4.4x4.4 to get

85.184in^3 per second

Answer:

54 degrees

Step-by-step explanation:

180-126=54

Answer:

The cost price of each shirt is $8.

They mark up the shirts 25%, which means they increase the price by (25/100) * $8 = $2.

So, the selling price of each shirt becomes $8 + $2 = $10.

At the end of the year, they sell the shirts for 25% off, which means they reduce the price by (25/100) * $10 = $2.50.

Therefore, the selling price of each shirt after the discount becomes $10 - $2.50 = $7.50.

The profit made on each shirt sold at the end of the year is the difference between the selling price and the cost price, which is $7.50 - $8 = -$0.50.

Since the profit is negative, it means that the Spirit Club is making a loss of $0.50 on each shirt sold at the end of the year.

The score located at -3sx (standard deviation) from the mean in a normal distribution is 75. This is because in a normal distribution, the mean is the center and -3sx is three standard deviations away from the mean. Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.

To further explain, a normal distribution is a probability distribution characterized by a symmetrical bell-shaped graph, and it's determined by the mean and standard deviation of the dataset. In this case, the mean is 120 and the standard deviation is 15. Therefore, the data would have an average score of 120 and an average range of 30 (15 plus and minus from the mean). If the score is located at -3sx, it would be three standard deviations away from the mean and the score would be 75.

Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.

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Answer:1, -.66 repeating, 1.25

Step-by-step explanation  i turned them into decimals

24/8x-1/3= -1

-2/5x5/3= -.66 repeating

-5/6x-3/2= 1.25

The result is the t-statistic, which is used to compare the two samples.

The t-test is used to compare the means of two independent samples. The formula for the t-test is:

[tex]t = (x1 - x2) / √[s2/n1 + s2/n2][/tex],

where x1 is the mean of the first sample, x2 is the mean of the second sample, s2 is the variance of the two samples, and n1 and n2 are the sizes of each sample.

To calculate the t-test, first you need to calculate the mean for each sample. If the sample size is small (less than 30), then you should use the sample standard deviation.

Next, calculate the variance for each sample by taking the sum of the squared differences from the mean, and dividing by n-1 (where n is the sample size).

Finally, calculate the t-test statistic by substituting the means and variances into the formula above. The result is the t-statistic, which is used to compare the two samples.

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Answer:

The line y = 2 - 5/20 can be simplified to y = 2 - 1/4 = 7/4.

Substituting y = 7/4 into the equation of the circle, we get:

(x - 5)² + (7/4 + 1)² = 25

(x - 5)² + (15/4)² = 25

(x - 5)² = 25 - (15/4)²

x - 5 = ±√(25 - (15/4)²)

x = 5 ± √(25 - (15/4)²)

Simplifying, we get:

x = 5 ± √(400/16 - 225/16)

x = 5 ± √(175/16)

x = 5 ± (√175)/4

Therefore, the two intersection points are:

Left point: (5 - (√175)/4, 7/4)

Right point: (5 + (√175)/4, 7/4)

The probability that at least three students seek assistance in 10 days is approximately 0.117.

We can use the Poisson distribution to model the number of students who seek assistance in 10 days. Let X be the number of students who seek assistance in 10 days.

Then X follows a Poisson distribution with parameter λ=2.4, where λ is the mean number of students who seek assistance per day multiplied by 10 (the number of days).

Using the Poisson probability formula, we can calculate the probability of at least three students seeking assistance:

P(X ≥ 3) = 1 - P(X < 3) = 1 - [P(X=0) + P(X=1) + P(X=2)]

We can find that:

P(X ≥ 3) = 0.117

Therefore, the probability that at least three students seek assistance in 10 days is approximately 0.117.

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Answer:

To calculate the future value of an investment earning compound interest, we can use the formula:

FV = P(1 + r/n)^(nt)

where:

FV is the future value

P is the principal (starting amount)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

In this case, we have:

P = 6000

r = 0.18 (18% annual interest rate)

n = 12 (compounded monthly)

t = 8

Substituting these values into the formula, we get:

FV = 6000(1 + 0.18/12)^(12*8)

FV = 6000(1.015)^96

FV = 6000(3.045)

FV = 18270

Therefore, the future value of $6000 earning 18% interest, compounded monthly for 8 years, is $18,270.

The value of 50.7 / 7 is approximately equal to 7.24285714.

The given expression is 50.7 / 7.

Creating equal groupings or determining how many individuals are in each group after a fair distribution is the basic objective of division.

To simplify the expression, we need to perform the division operation.

In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

To solve this, we can perform the following steps:

First, we can write the given expression as:

50.7 ÷ 7

Then, we can perform the division operation as shown below:

50.7 ÷ 7

= 7.24285714 (rounded to 8 decimal places)

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A statement that must be true according to the dot plot include the following: A. the data is skewed left and shows that on half of the days, Darren received 11 or 12 e-mails from the customer.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

By critically observing the given dot plots which is used to illustrate the number of e-mails that Darren received from one of his customers each day for 14 days, we can reasonably infer and logically deduce that the data set is skewed left, which ultimately implies that that on half of the days (7 days), Darren received a total of 11 or 12 e-mails from this customer.

In conclusion, the dot plot is skewed left because it has a long tail on its left side and 7 days is the half of 14 days.

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A. The equation of the line is expressed as: y = (-5/2)x + 13.

B. The x-intercept of the equation is calculated as: 26/5.

A. We can use the point-slope form of a linear equation:

y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, to find the equation of a line passing through the point (4,3) with a slope of -5/2.

Substituting the values, we get y - 3 = (-5/2)(x - 4), which simplifies to y = (-5/2)x + 13 by expanding and adding 3 to both sides.

B. To find the x-intercept of the equation y = (-5/2)x + 13, we set y to 0 and solve for x. 0 = (-5/2)x + 13, which simplifies to x = 26/5 by multiplying both sides by -2/5 and adding (26/5) to both sides.

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A total of 5 glove prices meet the condition of having an absolute deviation from the mean of $8 or less.

To find the mean price, we need to sum up all the glove prices and divide by the total number of gloves.

Sum of glove prices = $55 + $42 + $28 + $39 + $82 + $25 + $40 + $32 + $45 + $38 + $52 + $34 = $512

Total number of gloves = 12

Mean price = Sum of glove prices / Total number of gloves = $512 / 12 = $42.67

To find the absolute deviation of each glove price from the mean, we subtract the mean from each price and take the absolute value.

Absolute deviation from mean for each glove = |Price - Mean price|

For example, for the first glove price of $55, the absolute deviation from the mean is |$55 - $42.67| = $12.33

We want the absolute deviation to be at most $8, so we need to find how many glove prices have an absolute deviation from the mean of $8 or less.

We can calculate the absolute deviation for each glove price and count how many are less than or equal to $8.

First row:

|$55 - $42.67| = $12.33

|$42 - $42.67| = $0.67

|$28 - $42.67| = $14.67

|$39 - $42.67| = $3.67

|$82 - $42.67| = $39.33

|$25 - $42.67| = $17.67

Out of the 6 glove prices in the first row, 2 have an absolute deviation from the mean of $8 or less.

Second row:

|$40 - $42.67| = $2.67

|$32 - $42.67| = $10.67

|$45 - $42.67| = $2.33

|$38 - $42.67| = $4.67

|$52 - $42.67| = $9.33

|$34 - $42.67| = $8.67

Out of the 6 glove prices in the second row, 3 have an absolute deviation from the mean of $8 or less.

Therefore, a total of 5 glove prices meet the condition

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The given condition is incomplete, the complete question is:

a baseball player wants to buy a new glove. the table shows the prices of several gloves. the player is willing to pay the mean price with an absolute deviation of at most $8. how many of the glove prices meet this condition?

The values of x is [tex]x < 39.5[/tex].

Given that the shopkeeper spends on rent and electricity is [tex]= 5x+14[/tex]

Spending of shopkeeper on rent [tex]= 3x-7[/tex]

So shopkeeper spends on electricity [tex]= (5x+14) - (3x-7) = 2x+21[/tex]

Given that amount the shopkeeper spends on electricity less than 100.

So suitable inequality,

[tex]2x+21 < 100[/tex]

[tex]2x < 100-21[/tex]

[tex]2x < 79[/tex]

[tex]x < 39.5[/tex]

All the values of [tex]x < 39.5[/tex].

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Answer:

4th degree

Step-by-step explanation:

When you are looking for the degree of an expression or equation, you just look for the biggest exponent.

Here, there is an

"x to the 4th power",

a "minus3 to the second power" and

a "9x" (which is a power of 1)

So the biggest exponent is 4...4th degree. That's it!