If x -1/x=3 find x cube -1/xcube​

The value of length 's' is 44.3 cm

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

The measure of angle R = 180-( 48+29)

R = 180- 77

R = 103°

sinR/ r = sinS/s

sin103 / 58 = sin48/s

s × sin103 = 58 × sin48

s × 0.974 = 43.1

s = 43.1/0.974

s = 44.3 cm

therefore the value of length is is 44.3 cm

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Last week, the ratio of bananas sold to watermelons sold was 4 : 3.

This ratio means that for every 4 bananas sold, the number of watermelons sold was 3.

Since there were 48 bananas sold, we can find the number of watermelons sold by subtracting 12 from 48:

48 bananas - 12 = 36 watermelons

Now, we can determine the ratio of bananas sold to watermelons sold. The ratio would be:

Bananas : Watermelons = 48 : 36

To simplify this ratio, we can divide both numbers by their greatest common divisor (GCD), which in this case is 12:

48 ÷ 12 = 4
36 ÷ 12 = 3

So, the simplified ratio is:

4 : 3

This ratio means that for every 4 bananas sold, the number of watermelons sold was 3. In other words, out of every 7 fruits sold (4 bananas + 3 watermelons), 4 were bananas and 3 were watermelons. This provides an easy way to understand the proportion of each type of fruit sold at Jun's fruit stand last week.

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Jonana cut 24 pieces of 1/4 foot length from the 6-foot board

Let "x" be the number of pieces that Jonana cut.

Each piece is 1/4 foot long.

So, the total length of all the pieces is x * 1/4 = x/4 feet.

But the total length is also 6 feet.

So we can set up the equation:

x/4 = 6

Solving for x:

x = 24

Therefore, Jonana cut 24 pieces of 1/4 foot length from the 6-foot board.

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The solution to this system of equations are x = 7 and y = -3.

In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.

Given the following system of linear equations:

3y = 26 - 5x               .........equation 1.

6x + 7y = 21               .........equation 2.

Rewriting in standard form, we have:

5x + 3y = 26

6x + 7y = 21

By multiplying equation 1 by 6 and dividing by 5, we have:

6x + 3.6y = 31.2   .........equation 3.

By subtracting equation 3 from equation 2, we have:

3.4y = -10.2

y = -3.

x = (26 - 3y)/5

x = (26 - 3(-3))/5

x = 7

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The expression that represents the length of rope that needs to be lowered is 30 - -20

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

Using the above as a guide, we have the following:

Length of rope = helicopter - canyon

So, we have

Length of rope = 30 - -20

Evaluate

Length of rope = 50

Hence, the length of rope is 50 feet

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If all three conditions are met, then the two-sample t-test can be used to test the hypotheses.

For testing the hypotheses in part A, a two-sample t-test for independent means can be used to compare the mean speed of the baseball line drive using the old technique to the mean speed using the new technique. The conditions for the t-test are:

Independence: The 42 hits using the new technique should be independent of the hits using the old technique.

Normality: The speeds using the new and old techniques should be normally distributed. This can be checked by creating a histogram of the speeds and checking for a roughly bell-shaped curve.

Equal variances: The variance of the speeds using the new technique should be approximately equal to the variance of the speeds using the old technique. This can be checked by using a statistical test for equal variances, such as Levene's test.

If all three conditions are met, then the two-sample t-test can be used to test the hypotheses.

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The probability of the normal distribution with given mean and standard deviation representing average content in the selected bottles is smaller than 102.1 mL is equal to 0.9878.

Distribution of the sample means of a normal distribution ,

Mean μ = 101.5 mL

Standard deviationσ = 1.6 mL

sample size n = 36

For normal distribution,

Standard deviation of the sample means is,

σ/√n

= 1.6/√36

= 0.2667 mL

Probability that the average content in the selected bottles is smaller than 102.1 mL,

Standardize the sample mean using the formula,

z = (X- μ) / (σ/√n)

where X is the sample mean.

Substituting the values, we get,

⇒z = (102.1 - 101.5) / (0.2667)

⇒ z = 2.25

Using a standard normal distribution table ,

Probability of a z-score being less than 2.25 is approximately 0.9878.

Therefore, the probability that the average content in the selected bottles is smaller than 102.1 mL is approximately 0.9878.

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Answer:

Yes

Step-by-step explanation:

9/25

√9/√25 = 3/5 = 0.6

so it is a rational number because it has an integer as a denominator also because the decimal is not reoccurring

Answer: Yes

Step-by-step explanation:

Yes.

9/25 = .36  

Because the decimal stop it is rational

Only decimals that have no pattern and go on infinitely then it is irrational like [tex]\pi[/tex]  or √7   if you plug those into a calculator they go on forever and have no pattern

Answer:

mail

Step-by-step explanation:

skating Dinero broke 1p revision yahoo d10

The volume of the solid is 32/15 cubic units.

To find the volume of the solid, we need to integrate the area of each square cross section perpendicular to the x-axis over the interval [a, b], where a and b are the x-coordinates of the intersection points of f(x) and g(x):

First, we find the intersection points of the two functions:

x²+1 = 2x+1

x² - 2x = 0

x(x-2) = 0

x = 0 or x = 2

So, a = 0 and b = 2.

Next, we find the side length of each square cross section. Since the cross section is a square, the side length is equal to the difference between the y-coordinates of the functions f(x) and g(x) at each x:

Side length = f(x) - g(x) = (x²+1) - (2x+1) = x² - 2x

Finally, we integrate the area of each square cross section over the interval [0, 2] to get the volume of the solid:

V = ∫[0,2] (x² - 2x)² dx

V = ∫[0,2] (x⁴- 4x³ + 4x²) dx

V = [1/5 x⁵ - 1 x⁴ + 4/3 x³] [0,2]

V = (1/5 x⁵ - 1 x⁴ + 4/3 x³)|[0,2]

V = (1/5(2⁵) - 1(2⁴) + 4/3(2³)) - (1/5(0⁵) - 1(0⁴) + 4/3(0³))

V = (32/5 - 16/3)

V = 32/15

Therefore, the volume of the solid is 32/15 cubic units.

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The characteristics of the hyperbola with equation (x+12)²/36-(y-15)²/100=1 are:

Comparing the given equation with the standard form, we have:

(h, k) = (-12, 15)

a² = 36

b² = 100

Taking the square root of a² and b², we get:

a = 6

b = 10

c² = 36 + 100

c² = 136

c ≈ 11.66

The foci of the hyperbola are located at (-12, 15 + 11.66) and (-12, 15 - 11.66), which are approximately (-12, 26.66) and (-12, 3.34).

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The maximum rate of change occurs in the direction of this unit vector.

(a) To find the maximum rate of change of f at point P(1,0), we need to find the gradient of f at that point and then find its magnitude. The direction of maximum increase is given by the unit vector in the direction of the gradient.

The gradient of f is:

∇f(x,y) = <y cos(xy), x cos(xy)>

At point P(1,0), we have:

∇f(1,0) = <0, cos(0)> = <0, 1>

The magnitude of the gradient is:

||∇f(1,0)|| = sqrt([tex]0^2[/tex] +[tex]1^2[/tex]) = 1

Therefore, the maximum rate of change of f at point P is 1, and it occurs in the direction of the unit vector in the direction of the gradient:

u = <0, 1>/1 = <0, 1>

So the maximum rate of change occurs in the y-direction.

(b) To find the maximum rate of change of f at point P(8,1.3), we need to find the gradient of f at that point and then find its magnitude. The direction of maximum increase is given by the unit vector in the direction of the gradient.

The gradient of f is:

∇f(x,y,z) = <2x, 2y, 2z>

At point P(8,1.3), we have:

∇f(8,1.3) = <16, 2.6, 2(1.3)> = <16, 2.6, 2.6>

The magnitude of the gradient is:

||∇f(8,1.3)|| = sqrt[tex](16^2 + 2.6^2 + 2.6^2)[/tex]= sqrt(275.56) ≈ 16.6

Therefore, the maximum rate of change of f at point P is approximately 16.6, and it occurs in the direction of the unit vector in the direction of the gradient:

u = <16, 2.6, 2.6>/16.6 ≈ <0.963, 0.157, 0.157>

So the maximum rate of change occurs in the direction of this unit vector.

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The slope of the line that divides the region into two equal parts is 8/7.

We begin by finding the x-coordinates of the points where the parabola intersects the x-axis. Setting y = 0, we get:

[tex]2x - 7x^2 = 0[/tex]

x(2 − 7x) = 0

x = 0 or x = 2/7

Thus, the parabola intersects the x-axis at x = 0 and x = 2/7.

We want to find the slope of the line through the origin that divides the region bounded by the parabola and the x-axis into two regions with equal area.

Let's call this slope m.

We know that the area under the parabola from x = 0 to x = 2/7 is:

A = ∫[0,2/7] (2x − 7[tex]x^2[/tex]) dx

A = [[tex]x^2[/tex] − (7/3)[tex]x^3[/tex]] from 0 to 2/7

A = (4/21)

Since we want the line to divide this area into two equal parts, the area to the left of the line must be (2/21).

Let's call the x-intercept of the line h. Then the equation of the line is y = mx, and the area to the left of the line is:

(1/2)h(mx) = (1/2)mhx

We want this to be equal to (2/21), so we can solve for h:

(1/2)mhx = (2/21)

h = (4/21m)

The x-coordinate of the point of intersection of the line and the parabola is given by:

2x − 7[tex]x^2[/tex] = mx

Simplifying, we get:

[tex]7x^2 - (2 + m)x = 0[/tex]

Using the quadratic formula, we get:

[tex]x = [(2 + m) \pm \sqrt((2 + m)^2 - 4(7)(0))]/(2(7))[/tex]

x = [(2 + m) ± √(4 + 4m + [tex]m^2[/tex])]/14

x = [(2 + m) ± (2 + m)]/14

x = 1/7 or x = −(2/7)

Since we want the line to pass through the origin, we must choose x = 1/7, and we can solve for m:

[tex]2(1/7) - 7(1/7)^2 = m(1/7)[/tex]

m = 8/7

Therefore, the slope of the line that divides the region into two equal parts is 8/7.

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Answer: 135 and 45

Step-by-step explanation:

We can read off from these equations the gradients of the two lines: (3) and (-2).

Then we quote the trigonometric identity tan(A-B) = [tan(A)-tan(B)] / [1+tan(A)tan(B)]

Substituting tan(A)=3 and tan(B)=-2 gives tan(A-B) = [(3)-(-2)] / [1+(3)(-2)] = 5/-5 = -1

So A-B = 135°.

That is the obtuse angle between the two lines, so the acute angle is 45°.

To determine if x and y are proportional, we need specific values or a proportional relationship equation.

To determine whether x and y are proportional, we need to compare the ratio of their values. If the ratio of x to y remains constant as x and y vary, then they are proportional.

Mathematically, if x/y = k, where k is a constant, then x and y are proportional. However, without specific values or equations, it is not possible to ascertain their proportionality.

Without further information, we cannot determine whether x and y are proportional. Additional context, such as specific values or an equation relating x and y, is needed to make a conclusive statement about their proportionality.

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A. To obtain the position of EFGH, Johnny translated ABCD by 3 units to the right and 4 units up. To draw and label EFGH, simply shift each vertex of ABCD by this translation vector (3, 4).

B. Tom rotated ABCD by 90º clockwise about the origin, O, to get the position of IJKL. To draw and label IJKL, rotate each vertex of ABCD 90º clockwise around the origin. This can be achieved by switching the x and y coordinates of each vertex and negating the new x value.

C. Tony placed a smaller car, MNOP, on the coordinate plane. MNOP is a dilation of ABCD with its center at the origin and a scale factor of -0.5. To draw and label MNOP, multiply the coordinates of each vertex of ABCD by the scale factor -0.5, keeping the origin as the center.

Answer:

We know that Miranda ran 4 miles in 28 minutes. Let's set up the proportion:

4 miles / 28 minutes = x miles / 2 minutes

To solve for x, we can cross-multiply:

28 minutes * x miles = 4 miles * 2 minutes

28x = 8

Now, let's solve for x by dividing both sides of the equation by 28:

x = 8 / 28

x = 0.2857

Therefore, Miranda runs approximately 0.2857 miles in 2 minutes.

Answer:

Step-by-step explanation:

The best-supported statement by the information in the table is:

C. The fee at Bank K will always be greater than the fee at Bank F.

This is because for any given average daily balance, Bank K has a higher fee than Bank F. For example, for an average daily balance of less than $500, Bank F charges $8 while Bank K charges $12. Similarly, for an average daily balance between $500 and $750, Bank F charges no fee while Bank K charges $12. Therefore, the fee at Bank K will always be greater than the fee at Bank F.

The average rate of change of the function g(x)=6x from x=-1 to x=3 is found to be 6.

The function g(x) = 6x describes a relationship between x and the value of 6 times x. We want to find the average rate of change of this function from x = -1 to x = 3. The average rate of change tells us the average amount by which the function changes per unit of change in x over this interval.

In this case, by using the function g(x) = 6x and evaluating it for x = 3 and x = -1, a difference of 18 - (-6) = 24 is found. The difference in x's values is equal to 3 - (-1) = 4. We divide these to get an average rate of change of 6.

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Answer:3,15,18.

Step-by-step explanation:

6:1:5 total ratio =6+1+5=12 so you’ll take all the numbers at different times so 6 will be divided by 12 and multiplied by36 (6/12)36= 18so the first number is nine do the same thing for the next ratio (1/12)36=3 thirdly(5/12)36=15 now add the three numbers to check whether they sum up to36(18+3+15=36)

Approximately 378 people can fit in a passenger car with a length of 70 feet and a width of 9 feet.

To determine the number of people who can fit in a passenger car with a length of 70 feet and a width of 9 feet, we need to consider the available space inside the car and the amount of space required per person.

Assuming that the passenger car is a rectangular box shape, the volume of the car can be calculated as follows:

Volume of car = Length x Width x Height

Since we are only interested in the number of people who can fit in the car, we will assume a standard height of 6 feet for simplicity. Therefore, the volume of the car can be calculated as follows:

Volume of car = 70 feet x 9 feet x 6 feet

Volume of car = 3,780 cubic feet

Next, we need to determine the amount of space required per person. This can vary depending on the seating arrangement and the size of the individuals, but as a general rule, we can estimate that each person requires approximately 10 to 12 cubic feet of space in a seated position.

Assuming we use the lower end of that estimate and allocate 10 cubic feet of space per person, we can calculate the number of people who can fit in the car as follows:

Number of people = Volume of car / Space per person

Number of people = 3,780 cubic feet / 10 cubic feet per person

Number of people = 378 people

Therefore, if we assume a standard height of 6 feet and allocate 10 cubic feet of space per person, approximately 378 people can fit in a passenger car with a length of 70 feet and a width of 9 feet. However, it is important to note that this is just an estimate and the actual number of people who can fit in the car will depend on factors such as the seating arrangement and the size of the individuals.

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The region that contains viable solutions to the systems of inequalities is region H

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

This means that the region viable solutions to the systems of inequalities is the region below the inequallity line

In this case, the region is the region G

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The number of prizes Sam able to buy = 5

Given that;

Sam bought 1 prize for each 5 tickets

Which means he can buy 1 prize for 1 ticket

Since number of ticket Sam has = 5

Therefore he can buy

1 prize for 1 ticket

2 prizes for 2 tickets

3 prizes for 3 tickets

4 prizes for 4 tickets

5 prize4s for 5 tickets

Hence Sam can buy maximum 5 prizes.

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The class will use 20 yards of the 50-yard spool, leaving 30 yards of string leftover.

This leftover string could be used for future projects or saved for another occasion.

Lacey's class will use a total of 720 inches (30 inches per student x 24 students) of string for the candy necklaces.

To convert this to yards, we divide by 36 (since there are 36 inches in a yard). 720 inches ÷ 36 = 20 yards

It's important to note that when working with different units of measurement, it's necessary to convert them to the same unit before performing calculations.

In this case, we converted inches to yards in order to determine the amount of string used by the class. By doing so, we were able to determine how much string was leftover in yards, which is a more appropriate unit of measurement for a spool of string.

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It should be noted that f(25) represents the quantity of items sold when the price is $25. In other words, if the price of the item is $25, then f(25) gives the number of units that customers will buy.

Also, f⁻¹(30) represents the price at which q = 30 units will be sold. In other words, if the number of items sold is 30, then f⁻¹(30) gives the price at which these 30 units will be sold.

This quantity is also known as the inverse demand function, which gives the price as a function of quantity demanded. . f(25) represents the quantity of items that will be sold at a price of $25. This means that if the item is sold at a price of $25, the function f will return the number of items that will be sold.

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The statements true of the two-dimensional plane sections that could result from one of these slices made by Misha are B, C, D, E, and F.

A. False. The only two-dimensional plane sections that could result from slicing a cube with a plane are squares or rectangles, but not triangles.

B. True. A plane section that is square could result from one of these slices through the cube.

C. True. A plane section that is rectangular but not square could result from one of these slices through the cube.

D. True. A plane section that is triangular could result from one of these slices through the pyramid.

E. True. A plane section that is square could result from one of these slices through the pyramid.

F. True. A plane section that is rectangular but not square could result from one of these slices through the pyramid.

Therefore, the correct statements are B, C, D, E, and F.

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The property was not explicitly used in this example, but it is worth noting that adding 0 to any number leaves it unchanged (i.e., a + 0 = a).

The properties that were used to simplify the expression 4 + 3(9 + 2) into 37 are:

Distributive property: The expression was rewritten as 4 + (3 × 9) + (3 × 2) by distributing the 3 over the parentheses.

Associative property: The order of the terms (3 × 9) and (3 × 2) was rearranged without changing the result because of the associative property of multiplication.

Commutative property: The order of the terms 4, 27, and 6 was rearranged without changing the result because of the commutative property of addition.

Identity property: The property was not explicitly used in this example, but it is worth noting that adding 0 to any number leaves it unchanged (i.e., a + 0 = a).

The properties used to simplify the expression are Associative property of addition, Commutative property of addition, and Distributive property and Identity property of addition. Therefore, the correct option is A, C, E and F.

The properties used to simplify the expression are as follows.

1. Distributive property (E): 4 + 3(9 + 2) = 4 + (3 × 9) + (3 × 2)

This property is applied when a number is multiplied with the sum of two or more numbers. In this case, the number 3 is distributed over the numbers 9 and 2.

2. Identity property of addition (F): 4 + 27 + 6 = 4 + 6 + 27

This property states that adding zero to any number does not change its value. Although this property isn't explicitly shown in the given steps, it is implied by the fact that we can rearrange the terms in the addition without changing their value.

3. Commutative property of addition (C): 4 + 6 + 27 = 10 + 27

This property states that changing the order of numbers in an addition does not change the sum. Here, the numbers 4 and 6 were rearranged to make it easier to add them together.

4. Associative property of addition (A): (10 + 27) = 37

This property states that the grouping of numbers in an addition does not affect the sum. In this case, the parentheses are unnecessary since the numbers were already grouped correctly.

In summary, the properties used to simplify the expression are: A) Associative property of addition, C) Commutative property of addition, and E) Distributive property and F) identity property of addition.

Note: The question is incomplete. The complete question probably is: The real number properties can be used to simplify numerical expressions. in this section, you will identify which properties were used to simplify several expressions. Which properties were used to simplify the following expression? select all that apply.

4 + 3(9 + 2)

4 + (3 × 9) + (3 × 2)

4 + 27 + 6

4 + 6 + 27

10 + 27

37

A) associative property of addition B) associative property of multiplication C) commutative property of addition D) commutative property of multiplication E) distributive property F) identity property of addition G) identity property of multiplication

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(I) The new selling price per kilogram of the tomatoes is 0.4576.

(II) The percentage profit on the whole transaction is 24.77% if she threw away 5kg of bad tomatoes.

The new selling price is calculated as follows;

The cost per kilogram of the tomatoes is;

Cost per kg = Total cost / Total weight

Cost per kg = 52 / 130

Cost per kg = 0.4

Selling price per kg = Cost per kg + (Profit percentage x Cost per kg)

Selling price per kg = 0.4 + (0.3 x 0.4)

Selling price per kg = 0.52

The new selling price per kilogram is:

= Selling price per kg - (Reduction percentage x Selling price per kg)

= 0.52 - (0.12 x 0.52)

= 0.4576

The total revenue from selling the tomatoes is calculated as;

The woman sold half of the 130kg of tomatoes, = 130 / 2 = 65kg

Revenue = (amount sold x selling price per kg) + (amount left x new selling price per kg)

Revenue = (65 x 0.52) + (65 x 0.4576)

Revenue = 33.8 + 29.68

Revenue = 63.48

New total cost = Total cost / Total weight x (Total weight - Bad tomatoes)

New total cost = 0.4 x (130 - 5)

New total cost = 50.6

The profit on the whole transaction  is calculated as;

Profit = Total revenue - New total cost

Profit = 63.48 - 50.6

Profit = 12.88

The profit percentage on the whole transaction is calculated as;

Profit percentage = (Profit / Total cost) x 100%

Profit percentage = (12.88 / 52) x 100%

Profit percentage = 24.77%

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