What are all possible values of x that satisfy the inequality x3−8≥1?

The total area of the composite figure is 107/216 square yards.

What is Area?

Area is a measure of the size of a two-dimensional shape or surface. It is the amount of space inside the boundaries of a flat object, measured in square units such as square meters, square feet, or square inches.

To find the total area of the composite figure, we need to first convert the dimensions from inches to yards, since the given scale is in inches per yards.

Since 1 yard is equal to 3 feet, which is equal to 36 inches, we have:

The height of the triangle is 6/36 = 1/6 yards.

The base of the triangle is 9 times the height, which is 9/6 = 3/2 yards.

The length of the rectangle is 7/9 yards.

The width of the rectangle is 6/9 = 2/3 yards.

The area of the triangle is:

(1/2) x (1/6) x (3/2) = 1/8 square yards.

The area of the rectangle is:

(7/9) x (2/3) = 14/27 square yards.

Therefore, the total area of the composite figure is:

1/8 + 14/27 = 107/216 square yards.

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Answer:

The slope of a line parallel to Y-axis is zero.

the ticket price needs to be lowered by approximately $8.33 in order to fill all seats in the stadium.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, A baseball team plays in a stadium that holds 58,000 spectators. With the ticket price at $10, the average attendance at recent games has been 33,000.

Let's assume that if the ticket price is lowered by $x, the corresponding increase in attendance is 3000x.

Then, if the ticket price is lowered by $x, the new attendance will be:

33,000 + 3000x

We want to find the ticket price that will result in full capacity, which is 58,000 spectators.

So, we can set the new attendance equal to 58,000 and solve for x:

33,000 + 3000x = 58,000

3000x = 25,000

x = 25,000/3000

x ≈ 8.33

Therefore, the ticket price needs to be lowered by $8.33 to $1.67 in order to fill all seats in the stadium.

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Complete question:

A baseball team plays in a stadium that holds 58,000 spectators. With the ticket price at $10, the average attendance at recent games has been 33,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000. how much ticket price to be lowered so that all seats will be full?

Answer:The easiest way to do this is to just raise 10 to the negative value of the pH.  Thus, in this case hydrogen ion concentration would be 1x10-2.4.   However, one doesn't usually leave it that way, so you put it in to the more conventional form as

3.98x10-3 and this would be the hydrogen ion concentration.  If you take the negative log of this number (pH) you will get 2.4

Answer: $1.25

Step-by-step explanation:   Noah has $1.25 because since Noah has 50 cents, and you add on another 75, you get $1.50

Answer:

Noah has 50 cents initially and his mother gives him 3 quarters, which is 75 cents (3 quarters x 25 cents/quarter).

Therefore, in total, Noah has 50 cents + 75 cents = 125 cents.

In dollars, that is $1.25.

Therefore, John is incorrect, as buying a 2-liter bottle of orange juice is actually slightly more expensive per liter than buying a 1.5-liter bottle of cola.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

2.1.1 To determine how many packets of patties Julia should buy, we need to know the total number of patties needed for the school function. Let's assume that each person will eat one patty.

If there are 300 people attending the function, then Julia needs to buy:

300 x 1 = 300 patties

Each packet of patties contains 12 patties, so the number of packets needed can be calculated as follows:

300 patties ÷ 12 patties/packet = 25 packets

Therefore, Julia should buy 25 packets of patties.

2.1.2 To justify Julia's calculation, we can use algebra. Let's assume that the number of packets of patties she buys is x. We know that there are 12 patties in each packet, so the total number of patties is 12x. We also know that if she buys 42 packets, there will be a leftover of 4 patties.

This can be represented as the following equation:

12x + 4 = 42 x 12

Simplifying this equation:

12x = 500 - 4 = 496

x = 496/12 = 41.33 (rounded to two decimal places)

Since we can't buy a fractional number of packets, Julia would need to buy 42 packets of patties. This would give her a total of:

12 x 42 = 504 patties

She would then have 4 leftover patties, as calculated earlier. Therefore, Julia's calculation is correct.

2.2.1 To determine whether buying a 2-liter bottle of orange juice is cheaper than buying a 1.5-liter bottle of cola, we need to compare the price per liter of each drink.

For orange juice, the price per liter is:

R18.95 ÷ 2 liters = R9.475/liter

For cola, the price per liter is:

R14.50 ÷ 1.5 liters = R9.67/liter

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The given vertices don't form parallelograms.

A parallelogram is a quadrilateral with two pairs of parallel sides. In other words, opposite sides of a parallelogram are parallel and have the same length. Examples of parallelograms include rectangles, rhombuses, and squares.

Here we have

The coordinates of the vertices of quadrilateral LOVE are L (-2, -1), O(2, 1), V (5, 0), and E (-1, -3).  

Using the distance formula we can find the lengths of the sides as follows  

From L (-2, -1) and O(2, 1),

=> LO = √[ (2 + 2)² + (1 + 1)² ] = √20

From O(2, 1) and V (5, 0)

=> OV = √[ (5 - 2)² + (0 + 1)² ] = √10      d = √(x2 - x1)^2 + (y2 - y1)^2)

From V (5, 0) and E (-1, -3)

=> VE = √[(-1 - 5)² + (-3 - 0)²] = √45

From L (-2, -1) and E (-1, -3)

=> LE = √[(-1 +2 )² + (-3 + 1)²] = √5

Here LO ≠ OV ≠ VE ≠ LE

Therefore,

The given vertices don't form parallelograms.

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The measure of the angle ∠ADB of the parallelogram is m∠ADB = 49°

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented a ABCD

Now , the measure of ∠ACB = ( 13x - 16 )°

The measure of ∠ACB = ( 9x + 4 )°

And , the measures of the angles ∠ACB = measure of ∠ACB

On simplifying , we get

13x - 16 = 9x + 4

On simplifying , we get

4x = 20

Divide by 4 on both sides , we get

x = 5

So , the measure of m∠ACB = ( 9 ( 5 ) + 4 ) = 49°

The measure of m∠ADB = measure of m∠ACB ( alternate angles )

So , the measure of m∠ADB = 49°

Hence , the angles of the parallelogram are solved

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In the graph, the major axis is the horizontal axis, while the minor axis is the vertical axis.

An ellipse is a geometric shape that is a type of curve. In mathematics, an ellipse is defined as a set of points in a plane, such that the sum of the distances between any point on the curve and two fixed points is a constant which is known as foci.

To identify the major and minor axes of an ellipse, you can use both the graph and the equation of the ellipse.

Identify the major and minor axes using the graph: The major axis is the longest diameter of the ellipse, which passes through the center and touches the curve at two points called the vertices. The minor axis is the shortest diameter of the ellipse, which also passes through the center and touches the curve at two points called the co-vertices. On the graph, the major axis is the horizontal axis, while the minor axis is the vertical axis.

Identify the major and minor axes using the equation: The equation of an ellipse can be written in the standard form:

[tex]\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} = 1[/tex]

where the ellipse's center is (h, k), the semi-major axis' length is a, and the semi-minor axis' length is b. The semi-major axis is half the length of the major axis, while the semi-minor axis is half the length of the minor axis. Therefore, you can identify the major and minor axes by looking at the denominators of the terms that contain x and y in the equation. The larger denominator corresponds to the semi-major axis, while the smaller denominator corresponds to the semi-minor axis.

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Answer:

n = -24/7

Step-by-step explanation:

3 -7n = 27

-7n = 24         Subtract 3 from both sides

n = -24/7        Divided by -7 both sides

So, the answer is n = -24/7

Answer:

Below

Step-by-step explanation:

Subtract 3 from both sides of the equation THEN divide both sides of the equation by  - 7

Answer:

0.05%

Step-by-step explanation:

Answer: Here you go.

Step-by-step explanation:

To calculate the volume of excavation needed for the water line, we first need to calculate the cross-sectional area of the trench.

The trench has a width of 18 inches and a depth of 3 feet, or 36 inches. So the cross-sectional area of the trench is:

18 inches x 36 inches = 648 square inches

Next, we need to subtract the cross-sectional area of the water line from the cross-sectional area of the trench to get the area of the excavation. The water line has a 3.5 inch outside diameter, so the radius is 1.75 inches. The cross-sectional area of the water line is:

π x (1.75 inches)^2 = 9.62 square inches

The area of the excavation is therefore:

648 square inches - 9.62 square inches = 638.38 square inches

To convert square inches to cubic feet, we need to multiply by the length of the trench in feet. The length of the trench is 500 feet. So the volume of excavation needed for the water line is:

638.38 square inches x 500 feet = 1,909,140 cubic inches

To convert cubic inches to cubic feet, we divide by 12^3 (12 inches per foot, cubed):

1,909,140 cubic inches ÷ (12 x 12 x 12) = 11.04 cubic feet

Therefore, the volume of excavation needed for the water line is approximately 11.04 cubic feet.

The answer should be: x [tex]\geq[/tex] -10

1. The finance charge on the loan is $9,920.

2. The total deferred payment price of the airplane is $39,120.

To find the finance charge on the loan, we need to first determine the amount financed. George Bell made a 15% down payment on the airplane, so the amount financed is:

= $29,200 - (0.15)($29,200)

= $29,200 - $4,380

= $24,820

The total amount of payments made over the life of the loan is:

= $579/month x 60 months

= $34,740

The finance charge on the loan is:

= $34,740 - $24,820

= $9,920.

The total deferred payment price of the airplane is the sum of the down payment and the total amount of payments made over the life of the loan. The down payment is 15% of the purchase price which is:

= 0.15 * $29,200

= $4,380

The total amount of payments made over the life of the loan is:

= $579/month * 60 months

= $34,740

The total deferred payment price of the airplane is:

= $4,380 + $34,740

= $39,120.

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Answer:

Class A: 87, 93, 96, 88, 92, 90, 100, 93, 91, 96

Mean: 92.6

Median: 92.5

Mode: 93 and 96

Class B: 72, 69, 54, 66, 63, 74, 59, 64, 70, 68

Mean: 65.9

Median: 67

Mode: No mode or 0

Step-by-step explanation:

You're welcome.

Answer: Let's define the events:

A: a proposal is judged worthy of funding by the first panel

B: the decision to fund a proposal is reversed by the second panel

We want to find the probability of the intersection of events A and B (i.e., a worthy proposal is disapproved by both panels). We can use the formula:

P(A and B) = P(B|A) * P(A)

We know that P(A) = 0.22 (the probability that a proposal is judged worthy of funding by the first panel). We also know that when a proposal is judged worthy of funding by the first panel, the probability that the decision to fund is reversed by the second panel is 0.74 (i.e., P(B|A) = 0.74).

Plugging in these values, we get:

P(A and B) = 0.74 * 0.22 = 0.1628

Therefore, the probability that a worthy proposal is disapproved by both panels is 0.1628, or approximately 16.28%.

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = √24²+32² = √1600 = 40

find base angle Ф on the right:

Ф = sin⁻¹(32/40) = 53.13

find other base angle (sum of interior angles of a Δ is 180):

180 - 90 - 53.13 = 36.87

now you can use the Law of Sines to find z, x:

40/sin36.87 = z/sin53.13 = (x+24)/sin90

z = 40(sin53.13)/sin36.87 = 53.33

sin36.87(x+24) = 40(sin90)

x+24 = 40/sin36.87 = 66.66

x = 66.67 - 24 = 42.67

double check the answers:

y² + z² = (x+24)²

40² + 53.33² = (42.67 + 24)²

1600 + 2892 = 4444

4444 = 4444  answers are correct!

Answer:

520

Step-by-step explanation:

So you multiply 650 by 0.8 and you get 520. 0.8 is 80% but in a decimal form.

Answer:

Step-by-step explanation:

Let's assume that the first car used x gallons of gas during the week, then the second car used (75 - x) gallons of gas because the total gas consumption by both cars is 75 gallons.

The first car's fuel efficiency is 30 miles per gallon, so it traveled (30x) miles during the week.

The second car's fuel efficiency is 35 miles per gallon, so it traveled (35(75 - x)) miles during the week.

The total distance traveled by both cars is given as 2425 miles, so we can set up the equation:

30x + 35(75 - x) = 2425

Expanding the equation:

30x + 2625 - 35x = 2425

Simplifying:

-5x = -200

x = 40

Therefore, the first car used 40 gallons of gas during the week, and the second car used (75 - 40) = 35 gallons of gas during the week.

Answer: Car 1 used 40 gallons and car 2 used 35 gallons.

Step-by-step explanation: In this problem, we will use a system of equations to reach our answer. We can let x be the gallons consumed by the first car, and y be the gallons consumed by the second car(these are both for one particular week only). We know the total consumption of gas is 75 gallons so the gallons consumed by car 1 and car 2 have to add up to 75. We can then create the equation x+y=75. We know that car 1 has an efficiency of 30 miles per gallon and 35 miles per gallon for car 2. The miles produced by x gallons in car 1 can be represented by 30x=# of miles. we can use 35y = # of miles for car 2. We know the combined total of miles from both cars is 2425 so we can make the equation 30x+35y=2425 miles. Now that we have our equations, we can simply solve them to find our answers.

x+y=75

x=75-y                   Isolating a variable

30x+35y=2425    

30(75-y)+35y=2425            Substituting the variable we isolated

2250-30y+35y=2425

2250+5y=2425

5y=175

y=35

x+(35)=75

x=40

y=35 and x=40

Car 1 used 40 gallons and car 2 used 35 gallons.

Hope this helps!

Answer:

h [tex]\ge[/tex] 48

Step-by-step explanation:

This inequality states that the height h, must be either equal to 48 to greater than 48.

Answer: One possible expression that equals the target number (-2) using the given numbers (-1, -3, -5, -7, and -2) and basic arithmetic operations (+, -, *, /) is:

-3 * (-5) + (-7) - (-2) / (-1) = -2

Explanation:

-3 * (-5) = 15 (multiplication of -3 and -5 gives +15)

-7 - (-2) = -5 (subtracting a negative is the same as adding a positive, so -7 - (-2) = -7 + 2 = -5)

-2 / (-1) = 2 (dividing a negative number by a negative number gives a positive result, so -2 / (-1) = 2)

Therefore, 15 + (-5) + 2 = -2

Step-by-step explanation:

The length of the diagonal of the rectangle is AC = 17.69 units

The diagonal of a rectangle is calculated by the formula

From the Pythagoras Theorem , The hypotenuse² = base² + height² , and

Diagonal of a Rectangle = √ ( Length )² + ( Width )²

Given data ,

Let the rectangle be represented as ABCD

Now , the measure of side AB = 12 units

The measure of side BC = 13 units

Let the length be BC and the width be AB

where the diagonal of the rectangle is AC

Now , Diagonal of a Rectangle = √ ( Length )² + ( Width )²

On simplifying , we get

The diagonal of the rectangle AC = √ ( 12 )² + ( 13 )²

The diagonal of the rectangle AC = √ ( 144 + 169 )

The diagonal of the rectangle AC = √313

The diagonal of the rectangle AC = 17.69 units

Hence , the diagonal of the rectangle is 17.69 units

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The slopes of the points are computed below

The slope of any two points is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Using the above as a guide, we have the following slopes in set 2

For set 3, we have the following slope values

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The measures of the angles in the parallel lines is

m∠a = 97°

m∠b = 15°

m∠c = 68°

m∠d = 68°

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the two parallel lines be represented as l and m

Now , the transversal line is t

The measure of m∠a = 97° ( corresponding angles )

The measure of m∠d = 180° - 112° ( angles in a straight line = 180° )

So , the measure of m∠d = 68°

The measure of m∠c = measure of m∠d ( alternate interior angles )

So , the measure of m∠c = 68°

From the triangle formed by the intersection of lines ,

The measure of m∠b = 180° - ( a + d ) ( angles of a triangle = 180° )

So , the measure of m∠b = 180° - ( 97° + 68° )

The measure of m∠b = 15°

Hence , the measures of angles are solved

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Answer:

We should buy at least 19 bonds to have at least a 97% chance of getting 5 or more bonds that do not default.

Step-by-step explanation:

This problem can be solved using the binomial distribution, which can tell us the probability of getting a certain number of successes in a given number of trials, each with a certain probability of success. In this case, the trials are the bonds, the probability of success is 50% (the chance that a bond will not default), and we want to know how many bonds we need to buy to have at least a 97% chance of getting 5 or more successes.

Let X be the number of bonds that do not default. We want to find the smallest value of n (the total number of bonds we buy) such that P(X ≥ 5) ≥ 0.97.

Using the binomial distribution, we can calculate that the probability of getting exactly k successes out of n trials with a probability p of success is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n without regard to order.

To find P(X ≥ 5), we can calculate the probabilities of getting 5, 6, 7, 8, 9, or 10 successes and add them up:

P(X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

We want this probability to be at least 0.97, so we can set up the following inequality:

P(X ≥ 5) ≥ 0.97

P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) ≥ 0.97

We can then use a spreadsheet or a binomial probability table to find the smallest value of n that satisfies this inequality. For example, using Excel's BINOM.DIST function, we can enter the following formula in a cell:

=BINOM.DIST(4,n,0.5,TRUE) + BINOM.DIST(5,n,0.5,TRUE) + BINOM.DIST(6,n,0.5,TRUE) + BINOM.DIST(7,n,0.5,TRUE) + BINOM.DIST(8,n,0.5,TRUE) + BINOM.DIST(9,n,0.5,TRUE) + BINOM.DIST(10,n,0.5,TRUE)

where n is the number of bonds we want to buy, and TRUE indicates that we want to calculate the cumulative distribution function (CDF) up to the given value of k.

We can then use Excel's Goal Seek tool to find the smallest value of n that makes this formula equal to 0.97. For example, if we set the target value to 0.97 and the "Set cell" to the formula cell, and we vary the "To value" of n, Goal Seek finds that the smallest value of n that satisfies the inequality is 19. Therefore, we should buy at least 19 bonds to have at least a 97% chance of getting 5 or more bonds that do not default.

Answer: A great white shark can grow up to 20 feet in length, while a horn shark can grow up to 3 feet in length. Therefore, a great white shark is 17 feet larger than a horn shark.

Bamboo sharks can grow up to 5 feet in length. Therefore, to equal the length of a great white shark, you would need 4 bamboo sharks (since 4 x 5 = 20).

Step-by-step explanation:

The probability of someone pulling 1-10 in consecutive order from a bad that contains 10 balls labelled 1-10 is 1/3628800.

An event's probability is a numerical representation of how likely it is that the event will take place. In mathematical notation, it is written as a number between 0 and 1, or as a percentage between 0% and 100%. The higher an event's probability, the more likely it is to occur.

In a sample space, there is a probability of 1 for each event. The probability formula states that the ratio between the number of favourable outcomes and the total number of outcomes determines the likelihood that an event will occur. Sets are used in the terminology of probability theory. A set is a grouping of various things.

It is said that there are 10 balls in a bag, labelled 1-10.

Now,

The number of ways the ball labelled 1 is picked is 1

The number of ways the ball labelled 2 is picked is 2

So the number of ways a ball labelled certain number is picked is 1.

Now there is no replacement.

So the total number of balls decreases by 1 when 1 ball is taken.

Then,

The probability of choosing the ball numbered 1 = 1/10

The probability of choosing 2 = 1/9

The probability of choosing 3 = 1/8

.

.

.

the probability of choosing 10 = 1

Total probability of choosing the balls in consecutive order = 1/10 * 1/9 * 1/8 *.......* 1/2*1/1 = 1/10! = 1/3628800.

Therefore the probability of someone pulling 1-10 in consecutive order from a bad that contains 10 balls labelled 1-10 is 1/3628800.

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The number of ducks in a farm are 20 and the number of pigs in a farm are 8.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, in a farm there are 28 animals and combined they have 72 legs.

Let the number of pigs be p and let the number of ducks be d.

Here, p+d=28 ------(i)

4p+2d=72 -------(ii)

From equation (i), p=28-d

Substitute p=28-d in equation (ii), we get

4(28-d)+2d=72

112-4d+2d=72

112-72=2d

d=20

Substitute d=20 in equation(i), we get

p+20=28

p=8

Therefore, the number of ducks in a farm are 20 and the number of pigs in a farm are 8.

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Answer:

19

y = 6x - 11 it says the input is 5 so you input 5 as x

y = 6(5) - 11

y = 30 - 11

y = 19