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The function f(x)=√x with f:R→R is injective and surjective but not bijective.

Injective (or one-to-one): f(x) is injective, which means that if f(x1) = f(x2), then x1 = x2. In other words, if the square root of x1 is equal to the square root of x2, then x1 and x2 are equal.

Surjective (or onto): f(x) is surjective, which means that for every y in the codomain (R), there exists an x in the domain (R) such that f(x) = y. In other words, the square root of any real number can always be expressed as a real number.

Bijective: f(x) is not bijective. The square root function is not bijective because it is not defined for negative values of x.

Function: A function f is a function if for every x in the domain of f, there is exactly one y in the codomain of f such that f(x) = y. In other words, each x in the domain is mapped to exactly one y in the codomain.

In the case of f(x) = √x, it is a function. For every x in the domain of f, which is [0,∞), there is exactly one y in the codomain of f, which is [0,∞), such that f(x) = y.

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Answer:

System of equations:

20x + 30y = 650

x + y = 25

Time underwater = 10 hours

Time at the surface = 15 hours

Step-by-step explanation:

Let x = time underwater at 20 km/h.

Let y = time on the surface at 30 km/h.

speed = distance/time

distance = speed * time

distance underwater: 20x

distance on the surface: 30y

total distance: 650

20x + 30y = 650

total time: x + y

total time: 25

x + y = 25

20x + 30y = 650

x + y = 25

20x + 30y = 650

-20x - 20y = -500

--------------------------------

          10y = 150

              y = 15

x + y = 25

x + 15 = 25

x = 10

Answer:

53/3

Step-by-step explanation:

3(x^2+2)-3y                   Evaluate when x = 2 & y = 2/3

3(2² + 2) - 3(2/3)

3(4 + 2) - 3(2/3)

3(6) - 3(2/3)

18 - 3(2/3)

18 - 6/18

18 - 1/3

54/3 - 1/3

53/3

So, the answer is 53/3

Answer:

Negative

Step-by-step explanation:

When you multiply a negative number by a positive number then the product is always negative.

Answer:

Y = -94

Step-by-step explanation:

130 - y = 224     -subtarct 130

-y = 94        -multiply by -1

y = -94

Hope this helps. Pls give brainliest.

Answer:

y = -94

Step-by-step explanation:

130 - y = 224

subtract 130 from both sides

130 - 130 - y = 224 - 130

-y = 94

u want y not -y so divide both sides with "-"

y = -94

The probability that a CD will last less than 3 years is approximately 86.65%.

The probability can be determined using the standard normal distribution. Given that the CD's lifespan follows a normal distribution with a mean of 4 years and a standard deviation of 0.8 years, we need to find the z-score for 3 years. The z-score formula is calculated as (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

For 3 years, the z-score is (3 - 4) / 0.8 = -1.25. Using a standard normal distribution table or a calculator, we can find that the probability corresponding to a z-score of -1.25 is approximately 0.1056 or 10.56%.

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The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Risk probability is the level of probability that an investment will not produce the expected gain.

Risk probability refers to the likelihood that an investment will not generate the expected returns. It is an important concept in investment analysis and decision-making.  When making investment decisions, it is crucial to assess the potential risks involved. Risk probability helps us evaluate the likelihood of an investment not meeting our expectations. It provides an estimate of the chances of experiencing a loss or not achieving the desired level of gain.

For example, let's say you are considering investing in stocks. Before making a decision, you would analyze various factors such as market trends, company performance, and economic indicators. By assessing the risk probability, you can determine the likelihood of the investment not producing the expected returns. Also understanding the risk probability, investors can better manage their investment portfolios and make more informed decisions.

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The set of points at which the function f(x, y) = xy/(8ex − y) is continuous is the set of all points (x, y) such that 8ex ≠ y.

To determine the set of points at which the function is continuous, we need to check if the limit of the function exists and is equal to the value of the function at that point.

Taking the limit of the function as (x,y) approaches (a,b) gives:

lim_(x,y)→(a,b) f(x,y) = lim_(x,y)→(a,b) xy/8ex-y

Using L'Hopital's rule, we can find that the limit is equal to \(ab/8e^(b-a)\).

The function is continuous for all points (a,b) in \(R^2\).

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Given differential equation is y"-9y'+20y=0We can write this equation asy²-9y+20y=0Here, a = 1, b = -9, and c = 20Now, we have to find the roots of this equation.

Now, let us find the value of the discriminant. b²-4ac= (-9)²-4(1)(20)= 81-80= 1Since the value of the discriminant is greater than zero, therefore, we have two real and distinct roots for this equation.Roots are given by the quadratic formula.x= (-b±√(b²-4ac))/2aOn substituting the values of a, b, and c we get,x = (9±√1)/2Now,x1= 5x2= 4/1These roots give two linearly independent solutions as follows: y1=e^5t and y2=e^4tTherefore, the general solution to the differential equation is:y=c1e^5t+c2e^4tWhere c1 and c2 are constants.

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The given differential equation is y"-9y'+20y=0.

Let us use the characteristic equation to solve this differential equation.

The characteristic equation of y"-9y'+20y=0 isr² - 9r + 20 = 0.

Solve for r by factoring the characteristic equation(r - 5)(r - 4) = 0. 

Therefore, r = 5 and r = 4.

Thus, the general solution of the differential equation y"-9y'+20y=0 isy(x) = c₁e⁴x + c₂e⁵x

where c₁, c₂ are constants.

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The dimensions of the container of least cost are 15 inches by 15 inches by 3 inches, and the least cost of the container is $990.

Let the side of the square base of the rectangular container be x, and the height be y. The volume of the container can be expressed as xy² = 2250. From this, we can solve for x in terms of y using x = (2250/y²) as shown in equation (1).

Next, let's consider the cost of the sides (C). The cost of the sides is directly proportional to the surface area of the sides of the container, which is given by 2xy + 4y². Therefore, we can express the cost of the sides as C = k(2xy + 4y²) in equation (2), where k is a constant.

Since we are looking for the dimensions of the container of least cost, we need to minimize the cost function. To do this, we can differentiate the cost function with respect to y and set it equal to zero. This will give us the critical point where the cost is minimized.

Differentiating C with respect to y, we get dC/dy = 2k(x + 4y). Setting this equal to zero, we have 0 = 2k(x + 4y). Simplifying this equation, we get y = x/4 as shown in equation (3).

From equations (1) and (3), we have x = 15 and y = 3 inches. Therefore, the dimensions of the container of least cost are 15 inches by 15 inches by 3 inches.

To find the total cost, we calculate the cost of the top and bottom of the container (2xy) which is $2(15²) = $450, and the cost of the sides (4y²) which is $3(4*15*3) = $540. The total cost is the sum of these costs, which is $450 + $540 = $990.

In conclusion, the dimensions of the container of least cost are 15 inches by 15 inches by 3 inches, and the least cost of the container is $990.

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Answer:

Step-by-step explanation:

3×3=9 + 1 = the ten

10×3=30 +1= the 31

31 time three equal 93 plus One equal 94

94 time three equal 282 + 1 = 283

283 × three equal 846 + 1 equal 847

a equal 283.5

b equal 847.5

Answer: 2

Step-by-step explanation:

Answer: 2

_________

_________

_________

On solving the provided question, we can say that the spherical balloon's initial radius is 7 cm.; the final radius is 14 cm. ratio =  (7/14) ^2 = 1:4

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle.

The spherical balloon's initial radius is 7 cm.

The final radius is 14 cm.

ratio =

(7/14) ^2 = 1:4

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No, volume and radius are not the same. Volume is the measure of the amount of space within a three-dimensional object, while radius is the measure of the distance from the center of a circle or sphere to its outer edge.

Volume and radius are two different measures of a three-dimensional object. Volume is the measure of the amount of space within a three-dimensional object, and is calculated by multiplying its length, width, and height together. On the other hand, radius is the measure of the distance from the center of a circle or sphere to its outer edge. It is one-half of the diameter, which is the distance from one side of the circle or sphere to the opposite side. Volume and radius are not the same, as they measure different properties of a three-dimensional object. Volume is an indication of the amount of space within a three-dimensional object, while radius is an indication of the distance from the center of a circle or sphere to its outer edge.

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Answer:

∠ ABE = 46°

Step-by-step explanation:

Since BE bisects ∠ ABC , then

∠ EBC = ∠ ABE, substitute values

4x - 6 = 2x + 20 ( subtract 2x from both sides )

2x - 6 = 20 ( add 6 to both sides )

2x = 26 ( divide both sides by 2 )

x = 13

Thus

∠ ABE = 2x + 20 = 2(13) + 20 = 26 + 20 = 46°

The sampling distribution of the sample mean is the probability distribution of the mean of the sample.

The sampling distribution of the sample mean is the probability distribution of the mean of the sample. This distribution is important because it allows us to make inferences about the population mean based on the sample mean. The distribution is also important because it allows us to quantify the variability of the sample mean.

The mean of the sampling distribution is equal to the population mean. This is because the mean is a measure of central tendency and the sampling distribution is a representation of the population.

The standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size.

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Answer:

The answer is  

20x + 17.5

Step-by-step explanation:

Multiply the 5 by the numbers inside the parenthesis.

5 x 4x

5 x 3.5

Answer:

see below

Step-by-step explanation:

3, 12, 48, 192

We are multiplying by 4 each time  (12/3 =4)

The 5th term

192 *4 =768

The 6th term

768 *4 =3072

The th term

3072 *4 =12288

To find the common ratio, take the second term and divide by the first

2/4 = 1/2

The common ratio is 1/2

Problem 1

---------------------------

Explanation:

The first term is a = 3 and the common ratio or multiplier is r = 4. We start with 3 and multiply each term by 4 to get the next one. The nth term of this geometric sequence is

a(n) = a*(r)^(n-1)

a(n) = 3*(4)^(n-1)

Plug in n = 7 to get the seventh term

a(7) = 3*(4)^(7-1)

a(7) = 3*(4)^6

a(7) = 3*4096

a(7) = 12288

====================================================

Problem 2

----------------------

Explanation:

To find the common ratio, we pick any term but the first one and divide it over its previous term

r = common ratio

r = (second term)/(first term) = 2/4 = 1/2 = 0.5

r = (third term)/(second term) = 1/2 = 0.5

r = (fourth term)/(third term) = 0.5/1 = 0.5

Each term is cut in half to get the next one.

The option that rewrite the expression 1 / 3 + 2  / 5 using commutative law of addition is D.

The commutative property of addition states that a change in the order of the numbers being added does not affect the sum. In other words, when the order of a sum of values is changed, the commutative property of addition states that the sum of the numbers does not affect the sum of the numbers.

Therefore, let's use the commutative law of addition to rewrite 1 / 3 + 2  / 5.

Hence,

\(\frac{1}{3} + \frac{2}{5} = \frac{2}{5}+\frac{1}{3} = \frac{6+5}{15} = \frac{11}{15}\)

Therefore, the answer is D.

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Answer:

There's nothing to answer to that question, can you be specific.

Step-by-step explanation:

Answer:

it is a dotted line, because of the < symbol. If there is no line under < then it is dotted, but if there is a line under the < symbol it will be solid

Step-by-step explanation:

The value of the function at the right endpoint of the rectangle is 5 +6k/n.

In the question above;

Th width of the interval is said to be  (5 -2) = 3.

So, the width of one of n parts of it = 3/n

To solve for the differences that exist between the left end point of the interval and the value of  x at the right end of the k-th rectangle, one can say that:

 k·(3/n) = 3k/n

Note that the value of x at shows the point of  difference added to the interval's left end and thus it will be:  2 + 3k/n

Therefore, the value of the function for the value of x will be:

 f(2 +3k/n) = 2(2 +3k/n) +1  = (4 +6k/n) +1

 = 5 +6k/n

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Answer:

Step-by-step explanation:

The experimental probability of the cube landing on three is 1/10.

Answer:

Step-by-step explanation:

-1 divided by x

1 - x

X - 1

Answer:

d.

Step-by-step explanation:

Answer:

option c I guess - "It increases exponentially "

Answer:

Step-by-step explanation:

In a survey, a group of students were asked their favorite sport. eighteen students chose “other” sports, while 37.5% chose football, and 40% chose baseball. how many students chose football

Answer:

In a survey, a group of students were asked their favorite sport. eighteen students chose “other” sports, while 37.5% chose football, and 40% chose baseball. how many students chose football

Step-by-step explanation:

The dashed blue curve represents the normal distribution with the greater standard deviation.

The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

Considering the format of the normal curve, we have that a flatter curve, with lower peak, will have a higher standard deviation, hence the dashed blue curve represents the normal distribution with the greater standard deviation.

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