questions 7 and 8 please HELP!! solving steps would be nice

We can write the solution set as -

An inequality is used to compare two numbers or expressions.

Given is the linear inequality as -

|v| - 16 < - 5

The given linear inequality is -

|v| - 16 < - 5

|v| < - 5 + 16

|v| < 11

Now -

v < 11      {v > 0}

&

- v < 11      {v < 0}

v > - 11      {v < 0}

Therefore, we can write the solution set as -

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The best fit line is a straight line that reflects the best feasible estimate of the connection between two variables in a dataset in statistics and data analysis. The line is deemed to have the "best fit" since it minimises the difference between the observed data points and the line's anticipated values.

The method of least squares is the most often used approach for identifying the best fit line, which entails finding the line that minimises the sum of the squared differences between the observed data points and the corresponding predicted values on the line. This approach yields a linear equation of the form y = mx + b, where "m" represents the line's slope and "b" represents the y-intercept.

The best fit line may be used to anticipate the relationship between the variables in the dataset, as well as to detect any outliers or atypical data points that may be influencing the overall relationship. It is often used to evaluate data and create predictions in domains including as economics, engineering, and social sciences.

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The distance the submarine needs to travel to get to the destination is 15 feet.

Distance is a numerical measurement of how far apart two points or objects are in space. In mathematics, distance is typically measured using the Euclidean distance formula, which applies to points in two- or three-dimensional space.

The Euclidean distance between two points, (x1, y1) and (x2, y2), in a two-dimensional plane is given by the formula:

d = √[tex][(x2 - x1)^2 + (y2 - y1)^2][/tex]

where the symbol √ represents the square root function.

Similarly, the Euclidean distance between two points, (x1, y1, z1) and (x2, y2, z2), in a three-dimensional space is given by the formula:

d = √[[tex](x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2][/tex]

The distance between two points can be positive or zero, but it cannot be negative. Distance is an important concept in many areas of mathematics and science, such as geometry, physics, and engineering. It is also used in real-life applications, such as navigation, transportation, and sports.

There are other measures of distance used in different contexts, such as Manhattan distance or taxicab distance, which measure the distance between two points by the sum of the absolute differences of their coordinates, rather than the square of the differences as in Euclidean distance. Additionally, distance can be defined in different ways for objects other than points, such as for the distance between two lines or two planes in geometry.

To determine the distance the submarine needs to travel to get to the destination, we need to calculate the vertical distance between the submarine and the destination point.

The vertical distance is the difference between the destination point and the submarine's current position:

Distance = Destination Point - Submarine's Position

Distance = (-10.5 ft) - (4.5 ft)

Distance = -15 ft

Therefore, the distance the submarine needs to travel to get to the destination is 15 feet.

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Using the concept of proportions, the time it takes to type 100 words is approximately 33 minutes

Let's first break down the problem and identify the given information:

The time it takes to type on a page of paper is partly constant and partly inversely proportional to the number of words.

It takes 1 hour to type 180 words.

It takes 45 minutes to type 120 words.

To solve for the time it takes to type 100 words, we can use the concept of inverse proportionality:

Let x be the time it takes to type 100 words.

We know that the time it takes to type is inversely proportional to the number of words, so we can set up the proportion:

time / number of words = constant

Using the given information, we can write two equations for the constant:

1 hour = k * 180 words

45 minutes = k * 120 words

where k is the constant of proportionality.

Solving for k in each equation:

k = 1 hour / 180 words = 1/180 hour/word

k = 45 minutes / 120 words = 3/8 minutes/word

Since we want to express the time it takes to type 100 words in minutes, we need to convert the constant to minutes/word:

1 hour = 60 minutes, so k = 1/180 * 60 = 1/3 minutes/word

45 minutes = 0.75 hours, so k = 3/8 * 60 = 22.5 minutes/word

Now we can use the constant to find the time it takes to type 100 words:

time / 100 words = constant

Plugging in the values we found for the constant:

x / 100 = 1/3 or x / 100 = 22.5

Solving for x:

x = (1/3) * 100 = 33.33 minutes (or approximately 33 minutes)

x = 22.5 * 100 = 2250 minutes (or approximately 37.5 hours)

We can discard the second solution (37.5 hours) since it doesn't make sense in the context of the problem.

Therefore, it will take approximately 33 minutes to type 100 words.

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The value of weight of 76 kg when converted to pounds is  167.55112 pounds.

kilogram is the standard unit of mass in the International System of Units (SI), while pounds are a common unit of mass used in the United States and other countries.

To Know how to convert between different units of measurement is essential for accurate calculations and comparisons. convert 76kg to pounds, you can use the formula: 1 kilogram is equal to 2.20462 pounds.

Therefore, to convert 76kg to pounds, you would multiply 76 by 2.20462.

76  x 2.20462 =  167.55112 pounds

So, weight of 76kg is equivalent to  167.55112 pounds

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The number of times a number is multiplied by itself is known as the power or exponent. To calculate the power of a number, we use the exponent formula [tex]n^{p}[/tex] = n × n × n × ... × n, where n is the base number and p is the exponent. For example,[tex]4^{2}[/tex] = 16 and [tex]4^{3}[/tex]= 64.

The number of times a number is multiplied by itself is known as the power or exponent. For example, let's say we have the number 4. If we want to calculate 4 to the power of 2 ([tex]4^{2}[/tex]), we are essentially multiplying the number 4 by itself twice. This is written as 4 multiplied by 4, which is equal to 16. In mathematical notation, the calculation is written as [tex]4^{2}[/tex]  = 16.To calculate the power of a number, we can use the exponent formula: [tex]n^{p}[/tex] = n × n × n × ... × n

where n is the base number and p is the exponent. For example, if we want to calculate[tex]4^{3}[/tex] (4 to the power of 3), we would write the formula as 4 × 4 × 4 = 64. The corresponding mathematical notation is [tex]4^{3}[/tex] = 64.

In summary, the number of times a number is multiplied by itself is known as the power or exponent. To calculate the power of a number, we use the exponent formula [tex]n^{p}[/tex] = n × n × n × ... × n, where n is the base number and p is the exponent. For example,[tex]4^{2}[/tex] = 16 and [tex]4^{3}[/tex]= 64.

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Answer:

Mrs. Milton's car uses about 12 gallons of gasoline each week for her commute.

The booster club's lowest ticket price at which it can generate $3,600 in income is $20.

Its core idea is thought to be the figure is probably smallest equivalent fraction. Where to calculate the simplest form. Look for matching parameters in the denominator but also numerator. A uneven number can be checked to discover if it is a mathematical concept. A statement having two collinear and an equal sign in the middle is referred to as a mathematical model. Every variable's degrees are listed in lowest to highest in the general form of any equation. The model for a linear equation is x + b = 0. The general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Either conditional calculations or identities are categories for equations. An identity holds true for any real worth of the variables.

given

ticket price = p

total to make $3,600

the equation = 3600 = p(–4p+260) is the correct expression

lowest ticket price = 3600 = p(–4p+260)

= 3600 = -4p2 + 260p

= 4p2-260p + 3600

= 2p2 -130p + 1800

p2 - 65p + 900

(p-20 )(p-45)

p = 20

The booster club's lowest ticket price at which it can generate $3,600 in income is $20.

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Answer:

100-0.095x

Step-by-step explanation:

Answer:

c 90 degrees

Step-by-step explanation:

i took the test

Answer:

238000

Step-by-step explanation:

hope I did this right!!

Answer:

The total profit the company would make over the course of its first 14 years of operation is approximately $2,562,841.

Step-by-step explanation:

The profit of the company increased at a constant 20% per year. We can use the formula for the future value of an investment to calculate the profit for each year, where:

FV = PV x (1 + r)^n

FV is the future value of the investment

PV is the present value of the investment

r is the annual interest rate

n is the number of years

Using this formula, we can find the profit for each year:

Year 1: $140,000

Year 2: $168,000

Year 3: $201,600

Year 4: $241,920

Year 5: $290,304

Year 6: $348,364

Year 7: $418,037

Year 8: $501,644

Year 9: $601,972

Year 10: $722,367

Year 11: $866,840

Year 12: $1,040,208

Year 13: $1,248,250

Year 14: $1,497,900

To find the total profit over the course of the first 14 years, we can simply add up the profits for each year:

Total profit = $140,000 + $168,000 + $201,600 + $241,920 + $290,304 + $348,364 + $418,037 + $501,644 + $601,972 + $722,367 + $866,840 + $1,040,208 + $1,248,250 + $1,497,900

Total profit = $2,562,841 (rounded to the nearest whole number)

To determine whether the relation is a function, we need to check if each x-value is associated with only one y-value in the mapping diagram.

A mapping diagram is a picture of two circles that shows the connection between input and output values. Illustration of a mapping diagram. The x-values (inputs) in the image are converted to the associated y-values by drawing an arrow from one x-value to its corresponding y-value (outputs).

From the given mapping diagram, we can see that the x-value -8 is associated with the y-value -4, the x-value -5 is associated with the y-value -2, the x-value -1 is associated with the y-value -2, the x-value 1 is associated with the y-value -2, the x-value 12 is associated with both the y-value -4 and -2.

Since the x-value 12 is associated with two different y-values, the given relation is not a function. To be a function, each x-value must be associated with only one y-value in the mapping diagram.

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Answer: I think its C lmk if I'm wrong

Explanation:

After 54 days, 213.3 grams of protactinium will remain from the initial 488 grams.

In radioactive decay, the amount of material that remains after a given amount of time can be calculated using the equation A=A0e^-kt, where A is the amount remaining after time t, A0 is the original amount, k is the decay constant, and t is the elapsed time. In this problem, we are given that A0 = 488 grams, t = 54 days, and k = 0.0259. We can calculate the amount remaining after 54 days by plugging these values into the equation.

A = 488e-0.0259(54)

A = 488e-1.3926

A = 213.3 grams

In conclusion, after 54 days, 213.3 grams of protactinium will remain if 488 grams is initially present.

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The answer is (A) (11, 4).

Step-by-step explanation:  Given that two vertices of a right-angled triangle are A(5, 12) and B(11, 12).

We can plot the given points on the co-ordinate plane as shown in the attached figure.

We will then see that only the point C(11, 4) will lie exactly below the point B(11, 12). Also, the segment AB and BC are the legs of the triangle, AC is the hypotenuse.

The lengths of the three sides are

[tex]AB = 11 - 5 = 6\\\\BC = 12 - 4 = 8\\\\AC = \sqrt{AB^{2} +BC^{2} } = \sqrt{6x^{2}+8^{2} } = \sqrt{100} = 10[/tex]

Thus, the correct option is (A).

Take into consideration the solid that results from rotating the area enclosed by the provided curves about the x-axis. y = 2/7 x^2, y = 9/7 - x^2 . the volume of the solid is approximately 1.412 cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curves y = 2/7 [tex]x^{2}[/tex] and y = 9/7 - [tex]x^{2}[/tex] about the x-axis, we can use the method of disks or washers.

First, we need to find the limits of integration. The curves intersect when:

2/7[tex]x^{2}[/tex] = 9/7 - [tex]x^{2}[/tex]

Multiplying both sides by 7, we get:

2[tex]x^{2}[/tex] = 9 - 7[tex]x^{2}[/tex]

9[tex]x^{2}[/tex] = 9

[tex]x^{2}[/tex] = 1

x = ±1

Therefore, the limits of integration are x = -1 and x = 1.

Next, we need to express the curves in terms of y. Solving for x in each equation, we get:

x = ±√(7/2 y)

x = ±√(9/7 - y)

Using the method of disks, we can find the volume of the solid by integrating the areas of circular disks with radius y from y = 0 to y = 9/7.

The radius of each disk is given by the difference between the upper and lower curves evaluated at y:

r = √(9/7 - y) - √(7/2 y)

The area of each disk is given by:

A = π[tex]r^{2}[/tex]

Substituting for r, we get:

A = π [√(9/7 - y) - √(7/2 y)]

Expanding and simplifying, we get:

A = π [9/7 - y + 7/2 y - 2√(9/7 y)]

A = π [9/7 + 3/2 y - 2√(9/7 y)]

Integrating with respect to y, we get:

V = ∫[0, 9/7] π [9/7 + 3/2 y - 2√(9/7 y)] dy

V = π [(9/7) y + (3/4) - (4/9) [tex]9/7^{3/2}[/tex] [tex]y^{3/2}[/tex]] [0, 9/7]

V = π [81/28 - (64/81)  [tex]9/7^{3/2}[/tex]]

V ≈ 1.412

Therefore, the volume of the solid is approximately 1.412 cubic units.

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The percentage of full marks was obtained by D is (d) 60%.

What is percentage  ?

Let's start by using the given information to find out how many marks B, C, and D got in the exam.

We know that A got 10% less than B, so if A got 360 marks, then B got 10% more than that, which is:

B = 360 + 10% of 360

= 360 + 36

= 396

We also know that B got 25% more than C, so if B got 396 marks, then C got 25% less than that, which is:

C = 396 - 25% of 396

= 396 - 99

= 297

Finally, we know that C got 20% less than D, so if C got 297 marks, then D got 20% more than that, which is:

D = 297 + 20% of 297

= 297 + 59.4

= 356.4

So D got 356.4 marks out of 500. To find out what percentage of full marks D obtained, we can use the formula:

percentage = (marks obtained / full marks) x 100

Therefore, the percentage of full marks obtained by D is:

percentage = (356.4 / 500) x 100

= 71.28%

Rounded to the nearest integer, the answer is approximately 71%, which is closest to option (d) 60%. Therefore, the answer is (d) 60%.

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There are 20 ways to choose 2 letters from the set A, B, C, D, and E if the order of the choices is relevant

If the order of the choices is relevant, we are looking for the number of permutations of 2 letters chosen from a set of 5 letters. We can use the permutation formula to calculate this:

nPr = n! / (n - r)!

where n is the total number of items in the set (5 letters in this case), and r is the number of items we want to choose (2 letters in this case).

nPr = 5! / (5 - 2)!

nPr = 5! / 3!

nPr = 5 x 4 x 3 x 2 x 1 / (3 x 2 x 1)

Divide the numbers

nPr = 20

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The one important use of the regression line is to make predictions about the values of y for a given x-value, the correct option is A

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables. The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression.

We are given that;

The uses of regression line

Now,

The main purpose of a linear regression model is to find a linear equation of the formy^=mx+c

Here,

we can use the value of x to predict the value of y

Therefore, by regression line the answer will be A.

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Press fit is calculated by determining the required force to assemble two cylindrical parts, using the interference between them and their material properties.

Press fit is calculated by determining the amount of interference between two cylindrical parts and their material properties. The interference is the difference between the diameter of the shaft (male part) and the diameter of the hole (female part). The required force to assemble the parts is then calculated using the material properties of both parts and the amount of interference. The interference is typically expressed as a percentage of the shaft diameter, and the required force is expressed in pounds or newtons.

Calculating the press fit is important for ensuring that the parts are securely and correctly assembled, and for preventing excessive stress or deformation in either part. Press fit calculations are commonly used in mechanical engineering and manufacturing applications.

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Answer:

we can assume that m = 90% cause the square so the we know that all the angles add up to 180° so ad 30 +90 and then subtract you sum from 180 and that is the angle of x

Therefore, the value of the car after three years is approximately $9,484.

Percent is a term used to represent a fraction of 100. It is denoted by the symbol "%". Percentages are commonly used to express proportions, ratios or fractions in terms of parts per hundred. The word "percent" comes from the Latin phrase "per centum," which means "by the hundred." Percentages are commonly used in everyday life, such as in calculating taxes, discounts, interest rates, and in comparing statistics, among others.

Here,

The exponential decay model for the value of the car after ⁿ years can be written as:

v = 22500 * (0.75)ⁿ

where 22500 is the initial value of the car, and (0.75)ⁿ represents the value after ⁿ years with a 25% annual decrease.

To find the value of the car after three years, we can substitute n = 3 into the equation:

v = 22500 * (0.75)³

v = 22500 * 0.421875

v = 9484.375

Rounding this to the nearest dollar amount, we get:

v ≈ $9,484

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c²=a²+b²

(51)²=(24)²+b²

2601=576+b²

2601-576=b²

2,025=b²

√2025=√b²

b= 45

the length of the other leg of the triangle is 45 cm

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.

To find the volume of a triangular prism, you need to calculate the area of the triangular base and then multiply it by the height of the prism. First, calculate the area of the base by finding the length of the triangle's sides and then using the Heron's Formula. Then, multiply the area of the base with the height of the prism to get the volume of the triangular prism. For example, if the length of the sides of the triangle is 3, 4 and 5, then the area of the base is 6 and the height of the prism is 8, then the volume of the prism is 48.

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The length of the other leg of the triangle is 45 cm.

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.

To find the volume of a triangular prism, you need to calculate the area of the triangular base and then multiply it by the height of the prism. First, calculate the area of the base by finding the length of the triangle's sides and then using the Heron's Formula. Then, multiply the area of the base with the height of the prism to get the volume of the triangular prism. For example, if the length of the sides of the triangle is 3, 4 and 5, then the area of the base is 6 and the height of the prism is 8, then the volume of the prism is 48.

According to Pythagoras theorem.

c² = a²+b²

(51)² = (24)²+b²

2601 = 576+b²

2601-576 = b²

2,025 = b²

√2025 = √b²

b = 45

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55 kilograms is approximately equal to 121.2541 pounds.

A kilogram (symbol: kg) is the base unit of mass in the International System of Units (SI).

It is currently defined based on the fixed numerical value of the Planck constant, h,

Which is equal to 6.62607015 × 10-34 in the units of J·s.

A pound (symbol: lb) is a unit of mass used in the imperial and US customary systems of measurement.

The international avoirdupois pound (the common pound used today) is defined as exactly 0.45359237 kilograms.

To convert 55 kilograms to pounds,

We need to multiply the value in kilograms by 2.20462,

Since one kilogram is approximately equal to 2.20462 pounds.

Therefore,

55 kilograms multiplied by 2.20462 gives us:

55 kg x 2.20462 = 121.2541 pounds

(rounded to four decimal places)

So, 55 kilograms is approximately equal to 121.2541 pounds.

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The probability of at least one appearance in a 21-alternate period is 0.969803

(a) The appearance  rate is 10 passengers nanosecond , so the anticipated number of advents  in nanosecond is also 10. The probability of no advents  in one minute is given by the Poisson distribution with parameter lambda = 10:

P(X = 0) = [tex]e^{(-lambda)}[/tex] [tex]lambda^{0}[/tex] / 0! =  [tex]e^{(-10)}[/tex]* [tex]10^{0}[/tex] / 1! = 0.000045 (rounded to 6 decimal places)

Therefore, the probability of no arrivals in one-minute period is 0.000045.

(b) To compute the probability that three or fewer passengers arrive in one-minute period, we can use the cumulative distribution function (CDF) of the Poisson distribution:

P(X <= 3) = sum from i=0 to 3 of P(X = i)

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= [tex]e^{-10}[/tex] *[tex]10^{0}[/tex] / 0! + [tex]e^{(-10)}[/tex] * [tex]10^{1}[/tex]/ 1! + [tex]e^{(-10)}[/tex] * [tex]10^{2}[/tex] / 2! + [tex]e^{(-10) }[/tex]* [tex]10^{3}[/tex]/ 3!

= 0.010336 (rounded to 6 decimal places)

Therefore, the probability that three or fewer passengers arrive in one-minute period is 0.010336.

(c) The arrival rate is 10 passengers per minute, which is equivalent to 10/60 = 1/6 passengers per second. Therefore, the expected number of arrivals in a 21-second period is (1/6) * 21 = 3.5 passengers. The probability of no arrivals in a 21-second period is given by the Poisson distribution with parameter lambda = 3.5:

P(X = 0) = [tex]e^{(-lambda)}[/tex] * l[tex]lambda^{0}[/tex] / 0! = [tex]e^{(-3.5)}[/tex] * [tex]3.5^{0}[/tex]/ 1! = 0.030197 (rounded to 6 decimal places)

Therefore, the probability of no arrivals in a 21-second period is 0.030197.

(d) The probability of at least one arrival in a 21-second period is equal to 1 minus the probability of no arrivals:

P(at least one arrival) = 1 - P(no arrivals)

= 1 - 0.030197

= 0.969803 (rounded to 6 decimal places)

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The equation of the line that passes through the point (2, 1) and has a slope of -5/2 is y=(-5/2)*x+6.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=3x+4. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=3 and b=4.

The question gives:

Point : (2,1) , where x=2 and y=1

Slope= -5/2

From the  standard form of the linear equation ( y= mx+b) and the given point and the slope, you can write:

y=mx+b

1=-5/2*(2)+b , thus you can find b.

1=-5+b

-b=-5-1

-b=-6

b=6

If b=6 and m=-5/2, you can write the linear equation:

y=mx+b

y=(-5/2)*x+6

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The equation of line that models this is y = -5/2x + 6

The equation of a line is typically written in slope-intercept form, which is y = mx + b, where m is the slope of the line, and b is the y-intercept.

The slope (m) is a measure of how steep the line is, and it can be calculated using the formula:

y = mx + c

In the given question, the slope is -5/2 and the points are (2, 1)

Substituting the values into the formula of equation of line;

y = mx + c

1 = -5/2(2) + c

1 = -5 + c

c = 1 + 5

c = 6

The equation is y = -5/2 + 6

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Answer:

yes I know but how should I show u dude

Answer: look at the image for the answer and explanation

Step-by-step explanation:

The total amount spent when the 10 items are bought is $97.17.

The final temperature given the increase in temperature and the decrease in temperature is 18 degrees.

In order to determine if your friend has enough money to buy all the items, the total cost of the items have to be determined. The total cost is the sum of all the items bought.

here, we have,

Total cost = total cost of the first three items + total cost of the second three + total cost of the last three

Total cost = (3 x 15.99) + (3 x 10.40) + (4 x 4.50)

Total cost = $47.97 + $31.20 +18

Total cost = $97.17

An increase in temperature would be represented with a positive number. While, a decrease in temperature would be represented with a negative number. The final temperature can be determined by adding the temperature increase and decease together.

Final temperature = increase in temperature - decrease in temperature

Final temperature = 32 - 14 = 18 degrees

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The smallest pair of 4 digit numbers such that the difference between them is 303 and HCF is 101 are found to be 1010 and 1313.

The HCF is the highest common factor or in other words, the largest number by which two numbers can be divided. List the four-digit numbers that could be the HCF for 101 to begin.

101 x 10 = 1010

101 x 11 = 1111

101 x 12 = 1212

101 x 13 = 1313

These numbers now reveal two further numbers whose difference is 303.

1313 - 1010 = 303

The two smallest 4 digit numbers are 1010 and 1313 as a result.

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Complete question - Find the smallest pair of 4-digit numbers such that the difference between them is 303 and their HCF is 101.

86 centimeter is approximately equal to 33.8583 inches.

We may use the conversion factor of 1 inch = 2.54 cm to convert 86 cm to inches.

To obtain the corresponding measurement in inches, divide 86 cm by 2.54:

86 cm ÷ 2.54 inches = 33.8583 inches (rounded to four decimal places)

To comprehend this conversion, we must first realise that centimetres (cm) and inches (in) are both length units, but they are measured using distinct systems. Centimeters are part of the metric system, which is widely used in most nations worldwide, whereas inches are part of the Imperial system, which is widely used in the United States, the United Kingdom, and a few other countries.

The precise connection between the two measurement systems yielded the conversion factor of 1 inch = 2.54 cm. To translate a length from centimetres to inches, divide the value by 2.54, and to convert from centimetres to inches, multiply the value by 2.54.

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Answer:

Below

Step-by-step explanation:

Volume of a cone = 1/3  pi  r^2 h

      4125 pi             = 1/3 pi r^2 h

                       4125  = 1/3 r^2 h  <===if diameter =30  then radius = 15 units

                         4125 = 1/3 (15)^2 h

                            4125 / (1/3 * 15^2) = h = 55 units