Which of the following are examples of rational numbers? Select all that apply.
√4+√16
√5 +√36
√9+√24
2* √4
√49 • √81
3√12

Answer:

s < [tex]\frac{1}{7}[/tex]

Step-by-step explanation:

8s + 8 < s + 9

7s + 8 < 9

7s < 1

s < [tex]\frac{1}{7}[/tex]

Answer:

the answer is c(t)=x2 +3

Step-by-step explanation:

because if u insert every x value in x place u will get the 2nd coordinate or y value so it is the correct equation

The total amount of water Keisha drinks in 12 days is 12 + 18 = 30 quarts.

Algebra is a branch of mathematics that involves using letters and symbols to represent numbers and quantities in mathematical equations and formulas. It includes a variety of topics, such as solving equations, manipulating expressions, working with functions and graphs, and studying abstract structures such as groups and rings.

At its core, algebra is about understanding the relationships between numbers and how they can be manipulated using various operations such as addition, subtraction, multiplication, and division. Algebraic expressions can be used to model real-world situations and solve problems in fields such as physics, engineering, and finance.

To find the total amount of water Keisha drinks in 12 days, we need to add up the amounts of water she drinks each day:

1 1/2 + 2 1/4 + 2 + 1 1/2 + 1 3/4 + 1 1/2 + 1 1/4 + 2 + 2 1/4 + 1 1/2 + 2 + 1 1/2

We can simplify the mixed numbers by converting them to improper fractions:

3/2 + 9/4 + 2 + 3/2 + 7/4 + 3/2 + 5/4 + 2 + 9/4 + 3/2 + 2 + 3/2

Then we can add the fractions together:

(3/2 + 3/2 + 3/2 + 2 + 2 + 2) + (9/4 + 7/4 + 5/4 + 9/4 + 3/2 + 3/2)

Simplifying the sum of the whole numbers, we get:

12

Simplifying the sum of the fractions, we get:

(18/4 + 14/4 + 10/4 + 18/4 + 6/4 + 6/4) = 72/4 = 18

So the total amount of water Keisha drinks in 12 days is:

12 + 18 = 30 quarts.

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The complete  question is:

For 12 days, Keisha keeps track of how much water she drinks per day. 1 1/2 quarts, 2 1/4 quarts, 2 quarts, 1 1/2 quarts, 1 3/4 quarts, 1 1/2 quarts, 1 1/4 quarts, 2 quarts, 2 1/4 quarts, 1 1/2 quarts, 2 quarts, 1 1/2 quarts. What is the total amount of water that Keisha drinks the 12 days?

Rewriting 11,000,000 as a power of 10 using scientific notation is: 1.1 * 10⁷

A number is written in scientific notation whenever a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 * 10^8.

Now, we want to write the number 11000000 as a power of 10. Using the concept of scientific notation, we have:

11000000 = 1.1 * 10⁷

That is the final expression of the given number as a power of 10

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The solution of the expression is x = (-1 ± i√3)/2 and the domain of the expression is all values of x l x ≥ 0 (option c).

The given equation is -x² = √x. To solve this equation, we need to isolate x on one side of the equation. We begin by squaring both sides of the equation to eliminate the radical:

(-x²)² = (√x)²

x⁴ = x

Now we have a quartic equation, which we can solve by factoring:

x(x³ - 1) = 0

We can further simplify this equation by factoring the cubic term using the difference of cubes formula:

x(x - 1)(x² + x + 1) = 0

From this factorization, we can see that the solutions are x = 0, x = 1, and the solutions of the quadratic factor x² + x + 1 = 0. To find the solutions of the quadratic, we can use the quadratic formula:

x = (-1 ± √1 - 4(1)(1))/2(1)

x = (-1 ± i√3)/2

Therefore, the solutions to the equation -x² = √x are x = 0, x = 1, and x = (-1 ± i√3)/2.

Now let's consider the domain of the solutions, which is determined by the inequality x ≥ 0. This inequality means that the solutions must be greater than or equal to 0. We can see that x = 0 and x = 1 satisfy this inequality.

For the solution x = (-1 ± i√3)/2, we can see that it does not satisfy the inequality x ≥ 0 because it is negative. Therefore, the solutions to the equation -x² = √x in the domain x ≥ 0 are x = 0 and x = 1.

Finally, let's consider the inequality x ≤ 0. This inequality means that the solutions must be less than or equal to 0. We can see that x = 0 satisfies this inequality. However, x = 1 and x = (-1 ± i√3)/2 do not satisfy this inequality. Therefore, the solutions to the equation -x² = √x in the domain x ≤ 0 are x = 0.

Hence the correct option is (c).

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Complete Question:

Solve the expression -x² = √x . And identify the domain of the expression,

A. all values of x

B. all values of x l x ≥ 1

C. all values of x l x ≥ 0

D. all values of x l x ≤ 0

The numbers that could be added to 1/12 to make the sum greater than 1/2 are 9/24 and 4/9.

To make the sum greater than 1/2, we need to find the number that, when added to 1/12, gives a result greater than 1/2.

1/2 is the same as 6/12, so we need to find the number that, when added to 1/12, gives a result greater than 6/12.

1/12 + 5/12 = 6/12, which is not greater than 1/2.

1/12 + 9/24 = 1/12 + 3/8 = 11/24, which is greater than 1/2.

1/12 + 1/3 = 1/12 + 4/12 = 5/12, which is not greater than 1/2.

1/12 + 4/9 = 3/36 + 16/36 = 19/36, which is greater than 1/2.

Therefore, the numbers that could be added to 1/12 to make the sum greater than 1/2 are 9/24 and 4/9.

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Answer:

You just need to create an expression with the variables then add them together to get the total income: 7e + 13n

Answer:

So, the possible width of the banner would be 9 feet or less, since we have assumed a maximum total trim of 50 feet. If the width exceeds 9 feet, the total trim required would exceed the available trim of 50 feet. Therefore, the possible widths of the banner are 9 feet or less.

Step-by-step explanation:

Given:

Length of the banner (L) = 16 feet

Total trim available (T) = 50 feet

The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (Length + Width)

In this case, the perimeter of the banner would be equal to the total trim available, since the trim goes all the way around the banner.

So, we can set up the equation as follows:

2 * (L + w) = T

Plugging in the given values:

2 * (16 + w) = 50

Simplifying the equation:

32 + 2w = 50

2w = 50 - 32

2w = 18

w = 18 / 2

w = 9

Answer: The First Graph and the Last Graph

Step-by-step explanation:

So all of these are inverses of a function. But as for how do you tell if the inverse is a function...

Well, it has to pass the test that all functions have to pass: the Vertical Line Test.

Any time you draw a vertical line down a graph, it should ONLY PASS THROUGH ONE POINT.

Your pictures are a little blurry, but as far as I can tell, Graph 1 is pretty linear, and a vertical line drawn would only intersect one point on the graph.

The second one however... well it seems pretty obvious why the vertical line test wouldn't work there. A vertical line drawn on the right half would intersect two points, which does not pass the test.

Same thing for Graph 3.

Graph 4 looks like it would pass the vertical line test. I cannot see the section on the y-axis that well, but it looks like it doesn't double back on itself.

Just check them with the Vertical Line Test! It's really useful for figuring out if something's a function or not.

Answer: See Below

Step-by-step explanation:

A slope of 0 simply means a straight line. Since we want the point (8,0), we need to shift our graph to the right 8. Therefore, the equation would be...

x = 8

Answer:

5

Step-by-step explanation:

6.5 / x = 1.3

multiply by x on each side to cancel it out

6.5 = 1.3x

/1.3   /1.3

x = 5

1.3 x 5 = 6.5

According to operations in maths, -8 - 12 is solved by adding the two numbers together and maintaining the negative sign, which will give us: -20.

Operations in mathematics are often guided by these rule listed below:

minus + plus = minus

minus + minus = minus

minus × minus = plus

minus × plus = minus

Thus, if we are given the expression, -8 - 12, applying the second rule stated above, we will have:

-8 - 12 = -20

This means we are adding two negative numbers together, which will give us the negative value of their sums.

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The maximum profit will be $87,000.

To find the quantity of things that will augment the benefit, we want to find the vertex of the parabola addressed by the given capability.

The vertex of a parabola in the form of[tex]y = ax^2 + bx + c[/tex] is located at the point [tex](-b/2a, c - b^2/4a)[/tex].

So for the function [tex]P(x) = -3x^2 + 12x + 75,[/tex] the coefficient of [tex]x^2[/tex] is -3, the coefficient of x is 12, and the constant term is 75.

Therefore, the number of items that will maximize the profit is:

x = -b/2a = -12 / 2(-3) = 2

The second derivative test is something we can use to make sure that this is a maximum. The vertex is a maximum when the second derivative of P(x) is -6, which is negative.

Since x is in thousands, the maximum profit occurs when 2,000 items are produced, and the maximum profit is:

[tex]P(2) = -3(2)^2 + 12(2) + 75 = 87[/tex]

Hence, the business will boost its benefit by making 2,000 things, and the most extreme benefit will be $87,000.

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Answer:

Step-by-step explanation:

You want to know the number of panels and posts needed for a 40 ft fence comprised of 8 ft panels, with a post between panels and at each end of the fence.

The number of panels needed is ...

  (40 ft)/(8 ft/panel) = 40/8 panels = 5 panels

The 5 panels will have 2 ends and 4 spaces, requiring 2 + 4 = 6 posts.

  o ---- o ---- o ---- o ---- o ---- o

The width of the path is 24 meters.

Let's call the width of the path "x".

The dimensions of the inner rectangle (the lawn without the path) are 46m by 34m. The dimensions of the outer rectangle (the lawn with the path) are (46+2x) by (34+2x).

Area of path = Area of outer rectangle - Area of inner rectangle

425m² = (46+2x)(34+2x) - (46)(34)

Simplifying and solving for x:

425m² = (2x+46)(2x+34)

425m² = 4x² + 80x + 1564

4x² + 80x - 1161 = 0

We only want the positive value for x, so:

x = (-80 + 272) / 8

x = 24m

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According to the concept of inequality, the maximum value of A is obtained when a = 2 and c = 28.

Let's assume that each minute of advertising attracts 40,000 viewers and each minute of comedy attracts 45,000 viewers. Therefore, the total audience (in thousands) that can be reached is given by:

A = 40a + 45c

Firstly, we know that the total time allotted for advertising and comedy cannot exceed 30 minutes. Therefore, we can rewrite the inequality as:

a + c ≤ 30

Solving for c, we get:

c ≤ 30 - a

Now, we can substitute this expression for c in the equation for A:

A = 40a + 45c

A = 40a + 45(30 - a)

A = 1350 - 5a

To maximize A, we need to find the value of a that will result in the maximum value of A. Taking the derivative of A with respect to a and setting it equal to zero, we get:

dA/da = -5 = 0

a = 0

This does not make sense, as a cannot be zero. Therefore, we need to check the endpoints of the interval [2,4] to see if they give a maximum value for A.

When a = 2, we get:

A = 40(2) + 45c

A = 80 + 45c

Substituting c = 30 - a, we get:

A = 80 + 45(30 - 2)

A = 80 + 1350

A = 1430

When a = 4, we get:

A = 40(4) + 45c

A = 160 + 45c

Substituting c = 30 - a, we get:

A = 160 + 45(30 - 4)

A = 160 + 1215

A = 1375

This means that the producer should allocate 2 minutes for advertising and 28 minutes for the comedy program in order to maximize the number of viewers.

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Answer:

3568 or 3567

Step-by-step explanation:

42820 divided by 12

The type of skewness that can be observed in an histogram are positive and negative skewness.

An histogram can display both positive and negative skewness.

A positive skew means that the tail of the histogram is longer on the positive side of the distribution, indicating that there are more data points with smaller values, and fewer data points with larger values.

A negative skew, on the other hand, means that the tail of the histogram is longer on the negative side of the distribution, indicating that there are more data points with larger values, and fewer data points with smaller values.Read more about histogram at

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Angles complementary to ∠BEA are ∠BED and ∠ABE.

Angles supplementary to ∠BFC are ∠AFB and ∠EFC.

Angle supplementary to ∠CAE is ∠FCD.

Complementary angles are defined as two angles whose sum is 90 degrees.

Complementary angles sum up to 90 degrees.

Supplementary angles are those angles that sum up to 180 degrees.

Therefore, the sum of the angles is 180 degrees.

Let's find the angles that are supplementary or complementary to the highlighted angles.

Therefore,

Angles complementary to ∠BEA are ∠BED and ∠ABE.

Angles supplementary to ∠BFC are ∠AFB and ∠EFC.

Angle supplementary to ∠CAE is ∠FCD.

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Answer:

-4. my answers need to be 20 characters+ soooo

The expected value of X is 7, and the standard deviation of X is 2.42 respectively.

The average of X's potential values is the expected value of X. We must first determine the sum of all potential x values multiplied by each value's associated probability before we can determine the expected value.

Calculate the expected value of X

Expected value = (2×(1/36)) + (3×(2/36)) + (4×(3/36)) + (5×(4/36)) + (6×(5/36)) + (7×(6/36)) + (8×(5/36)) + (9×(4/36)) + (10×(3/36)) + (11×(2/36)) + (12×(1/36))

Expected value = 7

Calculate the variance of X

Variance = (2-7)2×(1/36) + (3-7)2×(2/36) + (4-7)2×(3/36) + (5-7)2×(4/36) + (6-7)2×(5/36) + (7-7)2×(6/36) + (8-7)2×(5/36) + (9-7)2×(4/36) + (10-7)2×(3/36) + (11-7)2×(2/36) + (12-7)2×(1/36)

Variance = 5.83

Calculate the standard deviation of X

Standard deviation = √(variance)

Standard deviation = 2.42

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Complete Question:

Consider the roll of two dice. Let X be a random variable representing the sum of the number of dots appearing on each of the dice. The probabilities of each possible value of X are as follows:

x             P(x)

2            1/36

3            2/36

4            3/36

5            4/36

6            5/36

7            6/36

8            5/36

9            4/36

10           3/36

11            2/36

12            1/36

Determine the expected value and standard deviation of X.

1. Chicken became the key product that drove the creation of the Interstate Highway System, which led to the dominance of American trucks in the US truck market.

2. A party may want to impose a tariff to protect domestic industries from foreign competition or to generate revenue for the government.

3. A party is usually trying to protect domestic industries, but a tariff on automobiles would hurt both domestic consumers who would pay higher prices and foreign producers who would face reduced demand.

4. Competition encourages innovation by providing incentives for companies to improve their products and services to stay ahead of their rivals; American trucks stayed the same because they faced little competition due to protectionist policies.

5. Foreign companies tried to get around American-imposed tariffs on automobiles by establishing factories in the US, forming joint ventures with American companies, or exporting through third countries.

6. The methods used to get around tariffs can be efficient in the short term, but they may not be sustainable or desirable in the long term as they can lead to trade imbalances and undermine the competitiveness of domestic industries.

7. Tariffs can be used as a bargaining chip to negotiate better trade deals, but they should be imposed judiciously and only as a last resort to avoid damaging the economy and harming consumers.

1. In the podcast, chicken is cited as the reason why American trucks dominate the truck market in the United States.

This is because in the 1960s, the government imposed regulations on the trucking industry that limited the amount of weight a truck could carry.

To get around these regulations, the industry started using smaller trucks to transport goods, which were often not strong enough to handle the weight.

However, they found that if they put chicken on the back of the trucks, the weight of the cargo would distribute more evenly and the smaller trucks could handle the load.

This led to the development of the modern pickup truck, which is now a staple of the American automobile market.

2. Parties may want to impose tariffs for various reasons, such as to protect domestic industries and jobs from foreign competition, to raise revenue for the government, or to level the playing field in international trade.

Two specific reasons for imposing tariffs could be to protect national security interests or to address unfair trade practices by other countries.

3. Tariffs are usually imposed to protect domestic industries and jobs, and the parties that are being protected are typically the producers of the goods or services in question.

However, tariffs can also harm consumers who may have to pay higher prices for imported goods or may have fewer choices in the marketplace. For example, if a tariff is imposed on automobiles, domestic car manufacturers may benefit, but consumers may have to pay more for cars, and foreign automakers may lose market share.

4. Competition encourages innovation by creating incentives for companies to improve their products or services to gain a competitive advantage.

In the case of American trucks, the lack of competition may have contributed to their lack of innovation over the years. Since they dominated the market, there was little pressure to improve or innovate, and as a result, they have largely stayed the same.

However, the rise of foreign competition in recent years has led American truck manufacturers to invest more in innovation to stay competitive.

5. Foreign companies have tried to get around American-imposed tariffs on automobiles in various ways, such as by moving production to countries not subject to the tariffs, by exporting parts and assembling them in the United States, or by lobbying the government for exemptions or tariff reductions.

6. The methods used by foreign companies to get around tariffs may not be efficient for the economy as a whole because they can lead to higher costs and inefficiencies in the supply chain.

However, they may be necessary for individual companies to remain competitive in the short term.

Ultimately, a more efficient solution would be to address the root causes of the trade imbalances that lead to tariffs in the first place.

7. A tariff can be used as a bargaining chip by threatening to impose tariffs on imports from a country unless they make concessions in trade negotiations.

While this can be an effective strategy in certain situations, it can also lead to a trade war and harm both economies.

In general, tariffs should be used sparingly and as a last resort, and efforts should be made to address underlying trade issues through diplomacy and negotiation.

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Answer:

first one is 18 second one is 45

Step-by-step explanation:

add 18 and 45 to get 63

area is 63

Answer:

Step-by-step explanation:

Let X be the number of adults who had their faces painted.

Therefore, the number of kids who had their faces painted is 8*X.

Given that 56 kids had their faces painted, we can write an equation as:

8*X = 56

Solving for X:

X = 7

So, there were 7 adults who had their faces painted and 56 kids who had their faces painted.

Altogether, there were 7 + 56 = 63 people who had their faces painted.

To express 1/4 as an equivalent fraction with a different denominator, we need to find a common multiple of 4 and the desired denominator.

Let's say we want to express 1/4 as an equivalent fraction with a denominator of 12. To do this, we can multiply both the numerator and denominator of 1/4 by 3, which gives us:

1/4 x 3/3 = 3/12

So 1/4 is equivalent to 3/12 when the denominator is 12.

In general, to express a fraction a/b as an equivalent fraction with a different denominator c, we can multiply both the numerator and denominator by the same value that makes b equal to c.

This is because when we multiply both the numerator and denominator by the same value, we are essentially multiplying the fraction by 1, which does not change its value.

For example, to express 2/5 as an equivalent fraction with a denominator of 15, we can multiply both the numerator and denominator by 3, which gives us:

2/5 x 3/3 = 6/15

Therefore, 2/5 is equivalent to 6/15 when the denominator is 15.

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The standard deviation of the sample mean weight will decrease by a factor of √2, so the answer is C) It will decrease by a factor of 2. The mean of the sample mean weight will remain unchanged, so the answer is E) It will remain unchanged. It is a correct statement, and it is a result of the Central Limit Theorem, so the answer is C) It is a correct statement, and it is a result of the Central Limit Theorem.

When the sample size is doubled, the standard deviation of the sample mean weight decreases by a factor of √2 according to the formula σ/√n, where σ is the standard deviation of the population and n is the sample size. So, The correct answer is C).

The mean of the sample mean weight is an unbiased estimator of the population mean and is not affected by the sample size. Therefore, doubling the sample size will not change the mean of the sample mean weight.  So, The correct answer is E).

The Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the underlying distribution of the population. Therefore, the statement is correct and a result of the Central Limit Theorem.  So, The correct answer is C).

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The lateral surface-area of the cone with dimensions 12 cm height and 5 cm radius is 65π cm² using the formula πrl.

What is surface-area?

The overall surface area of a solid shape, item, or three-dimensional figure.It can have a flat or curved surface. Cone and cylinder surfaces are curved, but those of solid structures like the cube and cuboid have flat surfaces. The surface area of the cube is provided by 6 times side times side, which equals the area of each face side times side. The cube and cuboid have 6 faces, 12 equal edges, and 8 corners or vertices.

Given that the dimensions of cone:

Radius(r)=5 cm

Height(h) = 12 cm

slant height l =[tex]\sqrt{r^{2} +h^{2} }[/tex]

                      =[tex]\sqrt{(5)^{2} +(12)^{2} }[/tex]

                      =[tex]\sqrt{25+144}[/tex]

                      =[tex]\sqrt{169}[/tex]

                      =13 cm

Slant height (l) = 13 cm

lateral area of cone= πrl.

                                =π (5) (13)

                                =65 π cm²

The lateral surface area of cone=65 π cm²

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The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

To determine if the function f(x) = (x+3)/(x²-9) is continuous at x=3, we need to check if the limit of the function exists as x approaches 3 from both the left and the right, and whether this limit is equal to the value of the function at x=3.

First, we can check the limit as x approaches 3 from the left:

lim x→3- f(x) = lim x→3- (x+3)/(x²-9) = (-3)/(0-) = ∞

Next, we can check the limit as x approaches 3 from the right:

lim x→3+ f(x) = lim x→3+ (x+3)/(x²-9) = (6)/(0+) = ∞

Since both one-sided limits are infinite, the limit as x approaches 3 does not exist.

Therefore, the function f(x) = (x+3)/(x²-9) is not continuous at x=3.

The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

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Answer:

17/12

Step-by-step explanation:

What is the missing number in [_] -3/4=2/3?

Let the missing number be x

We have

x - 3/4 = 2/3

x = 2/3 + 3/4

x = 8/12 + 9/12

x = 17/12

So, the missing number is 17/12