. which interval describes all values of x for which the function f(x) = 2 sin–1(2x) is defined?

The distance the water balloon traveled over 1.5 seconds using the data georgia’s brother collected is attached below.

A distance-time graph, also known as a displacement-time graph or position-time graph, is a graphical representation that shows the relationship between the distance traveled by an object and the time it takes to travel that distance.

Using the information gathered by Georgia's brother, we can plot the points on a coordinate plane to graph the distance the water balloon travelled during a period of 1.5 seconds.

The data points provided are as follows:

Time (s)     Distance (m)

0.25              0.3

0.5                1.2

0.75              2.8

1.0                4.9

1.25              7.7

1.5               11.0

Plotting these points on a graph with time on the x-axis and distance on the y-axis, we get the graph attached.

The water balloon's route over 1.5 seconds is depicted on a graph. As time increases, the distance traveled by the balloon also increases. The graph shows a curved line, indicating that the distance traveled is not constant but increases at a varying rate.

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It will take 19.44 years for the decay rate of 137Cs to decrease to 10^7 decays per second.

The decay rate of 137Cs is given by the formula:

A = A0 * e^(-λt)

Where A is the decay rate, A0 is the initial decay rate (10^10 decays per second), λ is the decay constant (ln(2)/30.1 years) and t is the time in years.

To calculate the time, t, required for the decay rate to decrease to 10^7 decays per second, we solve for t and substitute the given values into the equation:

[tex]t = (ln(A0/A))/λ\\t = (ln(10^10/10^7))/(ln(2)/30.1)\\t = 19.44 years[/tex]

Therefore, it will take 19.44 years for the decay rate of 137Cs to decrease to 10^7 decays per second.

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For given expression, solution will be y=(t-1)/(1+t).

What are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

Given expression is t^2dy/dt-t=1+y+ty

After differentiation : As (d/dx) (x^n ) = nx^{n-1}

2t-t=1+y+ty

t-1=y(1+t)

y=(t-1)/(1+t)

for y(1)=2

2+2t=1-t

3t=-1

t=-1/3

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Answer:

A data type is an attribute associated with a piece of data that tells a computer system how to interpret its value

Step-by-step explanation:

Data types categorize data and specify its nature, amount characteristics, and behavior. It decides how data is handled within a computer system in terms of storage and manipulation.

Data types categorize data and specify its nature, characteristics, and behavior. It is a crucial part of every data structure and computer language. Primitive data types and complex data types are the two basic divisions of data types. Basic types like numbers, characters, booleans, and strings are examples of primitive data types. Arrays, objects, and records are examples of sophisticated data types that are more complex. Data types specify how information is handled and stored by computer systems. Size, precision, and range are a few examples of the unique qualities that each data type possesses. The arithmetic, comparison, and logic operations that can be carried out on the data are also determined by the data types.

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A scale of 1:900,000 is 36 times smaller than a scale of 1:24,000.

This can be expressed mathematically as a ratio: 1:900,000 = 1:24,000 / 36. To calculate the scale factor between two maps, divide the denominator of the larger scale by the denominator of the smaller scale. In this example, the scale factor is 36.

A scale of 1:900,000 means that one unit on the map represents 900,000 units of the same type in the real world. For example, one centimeter on the map could represent 900,000 centimeters in real life, or 9 kilometers. A scale of 1:24,000 would mean that one unit on the map represents 24,000 units of the same type in the real world. For example, one centimeter on the map could represent 24,000 centimeters in real life, or 0.24 kilometers.

The scale factor is the number that is used to compare the size of one map to another. In this example, a map with a scale of 1:900,000 is 36 times smaller than a map with a scale of 1:24,000. This means that the features on the 1:900,000 map are 36 times smaller than the same features on the 1:24,000 map. Therefore, the 1:900,000 map is not as detailed as the 1:24,000 map.

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The probability of exactly two babies being born deaf is approximately 0.037, or 3.7%.

The probability of exactly two babies being born deaf in a sample of 1,000 babies from healthy baby nurseries can be calculated using the binomial distribution.

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

       (n choose k) = n! / (k! * (n-k)!)

       For this problem:

       n = 1000 (number of babies surveyed)

       k = 2 (number of deaf babies)

       p = 2/1000 (probability of a baby being deaf in a healthy baby nursery)

P(X = 2) = (1000 choose 2) * (2/1000)² * (998/1000)^998

P(X = 2) = 999000 * 4 * (998/1000)⁹⁹⁸

P(X = 2) = approximately 0.037

So the probability of exactly two babies being born deaf in a sample of 1,000 babies from healthy baby nurseries is approximately 0.037, or 3.7%.

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The best describe each of the sets of lines or points will be coplanar, equidistant, and collinear. Then the correct options are B, C, and E.

An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two factors determine a line, two points are transparently collinear. If the points are in a line, then the points are collinear points.

Let A, B, C, and D be the collinear points. Then the condition of the collinear will be

AB + BC + CD = AD

The collinear points lie in the same plane. Then the points are coplanar too.

From the graph, the distance between points E, H, and J will be the same.

The best describe each of the sets of lines or points will be coplanar, equidistant, and collinear. Then the correct options are B, C, and E.

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The algebraic expression representing the length of the desk as a function of the width is given as follows:

L = W + 6.

The two variables in the context of this problem are given as follows:

The length is 6 inches greater than the width of the desk, hence the algebraic expression representing the length of the desk as a function of the width is given as follows:L = W + 6.

The problem asks for the algebraic expression representing the length of the desk as a function of the width.

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By vertical angles theorem, ∠1≅∠3 and ∠2≅∠4. Therefore, option B is the correct answer.

Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.

From the given figure,

By vertical angles theorem, we have

Angle 1 and angle 3 are congruent.

Angle 2 and angle 4 are congruent

Therefore, option B is the correct answer.

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When 80 kg is converted to lbs it will be equal to 176.36980975 pounds (lb).

        Here in this case,

        80kg x 2.20462

         = 176.36980975 pounds.

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Answer:

456.9 inches

Step-by-step explanation:

We can use the law of sines to find c:

c = (a / sin C) = (270 inches / sin 164°)

To find the sine of an angle in degrees, we can use a scientific calculator or a trigonometry table. Rounding to the nearest 10th of an inch, c = approximately 456.9 inches.

Answer: It's 534.7

Step-by-step explanation:

I sacrificed my chance of getting it right to see the answer. It's right That I guarantee. btw brainiest, please?

Answer:2.12

Step-by-step explanation:

The correct option is "will be centered around p, the true population proportion."

Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.

Given that, the students select their random samples and plot the results on a dot plot, the dots, represent the sample proportions obtained by the students,

Since, the dots are representing the sample proportions, we know,

The population proportion is equal to the mean of the sampling distribution of the sample proportion.

Hence, the correct option is "will be centered around p, the true population proportion."

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Answer:

D

Step-by-step explanation:

1. Find which of these 4 (four) has a y-intercept of positive 4, in this case, B and D. Recall, that the y-intercept means when X is 0 (zero) what is the value of Y?

2. Find the slope of B and D
The formula to find slope is change in y/change in x (Y/X)

B:

X: 0 - 4 = -4
Y: 4 - 0 = 4

4/-4 = -1

D:

X: 0 - -4 = 4

Y: 4 - 0 = 4

4/4 = 1

Using commutative property of addition, a + b = b + a, Therefore, 39 + 67 = 67 + 39, Hence the missing number is 67.

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The average value is the intersection point between the function and the line, which is at (0,1+C).

The average value of a function on an interval can be calculated using the following formula: Average Value = (1/b-a)∫a b f(x)dx. In this case, the function is f(x) and the interval is [0,1]. To calculate the average value, we must first calculate the integral of the function on the given interval. The integral of f(x) is nx^n-1 + C, where C is a constant. Using the fundamental theorem of calculus, we can evaluate the integral from 0 to 1 to be 1 + C.

The average value of the function on the given interval is then (1/1-0)∫0 1 (1+C)dx, which simplifies to 1+C. Therefore, the average value of the function on the given interval is 1 + C.

Graphically, the average value of the function on the given interval can be seen by plotting the graph of the function, which is a parabola with a vertex at (0,0), and a line at y=1+C. The average value is the intersection point between the function and the line, which is at (0,1+C).

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Conditional statements using the theme of the real number system:

Conditional statements in if-then form:

Conditional statements are statements in logic and mathematics that assert the truth of a statement based on certain conditions. They are usually written in the form "if P, then Q", where P is a condition and Q is a conclusion that follows from P. Conditional statements are used to make decisions or test certain conditions in programming, mathematics, and everyday life.

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The height of the tree is obtained as  27.7 m

We have to note that in the solution of the problem that the tangent of the angle is going to come in to play. The tangent if one of the trigonometric ratios and the other ratios are the cos and the sine.

We know that the tangent of the angle is;

tan 36 = opposite/adjacent

Opposite of the angle = x + 5

(Where x is the height of the tree)

Adjacent of the angle = 45 m

We would then have that;

tan 36 = x + 5/45

45 tan 36 = x + 5

x = (45 tan 36) - 5

x = 27.7 m

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The second derivative of a(x) is larger than the second derivative of b(x) for the given x values.

The second derivative of a function with respect to x is the rate of change of the first derivative with respect to x. The second derivative of a function measures the "curvature" of the graph. In the case of the two functions shown, the blue line represents a(x) and the pink line represents b(x). By looking at the graph, we can see that the first derivative of a(x) is steeper than that of b(x). Therefore, the second derivative of a(x) will be larger than the second derivative of b(x). This can be seen by looking at the graph and noting that the blue line has a greater curvature or "bend" than the pink line. In other words, the second derivative of a(x) is larger than the second derivative of b(x) for the given x values.

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The exponents of the values are;

1) 343

2) 9

3) 32

4) That the nth root of a and raise to the power of m

The laws of exponents are a set of rules for performing arithmetic operations with exponential expressions. They include:

Product rule: For any real numbers a, b and positive integers m, n, (am)(bn) = a^m * b^n.

Quotient rule: For any real numbers a, b and positive integers m, n, (a^m)/(a^n) = a^(m-n).

Power rule: For any real number a and positive integers m, n, (a^m)^n = a^(mn).

Zero exponent rule: For any real number a, a^0 = 1.

Negative exponent rule: For any real number a ≠ 0 and positive integer n, (1/a^n) = a^(-n).

Exponent of a power rule: For any real numbers a, b and positive integers m, n, (a^m)^n = (a^n)^m.

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Answer:240!

16 xs 15 = 240

Step-by-step explanation:

Answer: 240

Step-by-step explanation:

16 x 15 = 240 :)

Answer:

Factors

Step-by-step explanation:

To find the roots of a polynomial, [factors] help the process of finding them

Total area of the enclosed figure is given as  66 sq. units.

The quantity of unit squares that cover a closed figure's surface is its area. Square units like cm2 and m2 are used to measure area. A shape's area is a two-dimensional measurement.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The common ways to depict square units, which are the same as areas, are square inches, square feet, etc.

The space around by a shape's perimeter or boundary is known as its area. Using particular mathematical methods, we may determine the area of shape for various geometric forms.

In the shape there is 2 triangles and 3 rectangle

Area of the bottom triangle = 1/2 * 3*4 = 6 sq. units

Area of the top triangle = 1/2 * 4*2 = 4 sq. units

Area of the bottom rectangle = 8*3 = 24 sq. units

Area of the middle rectangle = 8*3 = 24 sq. units

Area of the top rectangle = 4*2 - 8 sq. units

Total area of the enclosed figure is given as 6+4+ 24+ 24+ 8 = 66 sq. units.

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The correct graph that shows a line on the scatter plot that fits the data is the one with a line drawn through the points (1,7 and 2,6).

In mathematics, a graph is a visual representation of a set of objects, called vertices or nodes, that are connected by lines or arcs, called edges or links. Graphs are commonly used to represent and analyze relationships between different entities, such as people, places, or things.

here, we have,

The vertices in a graph can represent anything, such as cities on a map, people in a social network, or molecules in a chemical reaction. The edges between vertices represent the connections or relationships between them. For example, in a social network graph, the edges might represent friendships between people, while in a transportation network, the edges might represent roads or train tracks connecting different cities.

Graphs are used in many areas of mathematics and science, including computer science, physics, biology, and social science. They are a powerful tool for analyzing and visualizing complex systems and relationships, and have many practical applications, such as in route planning, network analysis, and social network analysis.

The correct graph that shows a line on the scatter plot that fits the data is the one with a line drawn through the points (1,7 and 2,6).

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9.53 fertilizer bags are required to cover a lawn that is rectangular and is 260 feet by 120 feet.

The nitrogen fertilizer type known as urea is inexpensive. This is as a result of its high nitrogen content and the ensuing low costs of storage and transportation.

When all that is required for a soil fertility program is nitrogen, urea can be the best fertilizer to use.

Finding the location of the lawn is the first stage.

Area: 110 feet by 260 feet.

28600 square feet.

Calculating how many bags of fertilizer to purchase is the next step.

Bags = Area x 3,000 feet

Bags: 28600 feet / 3000 feet

9.53 bags total are in the bag.

Inconclusion 9.53 sacks of fertilizer should be bought to cover a lawn that is rectangular and measures 260 feet by 120 feet.

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Answer:

25

Step-by-step explanation:

$50

Cost=$6

Selling price=$8

Profit=$8-$6=$2

50/2=25

The volume of the region will be 4/3 cubic unit with the help of integration.

What is integration?

Integration is the calculation of an integral. Integrals in maths are used to find many useful quantities such as areas, volumes, displacement, etc. When we speak about integrals, it is related to usually definite integrals. The indefinite integrals are used for antiderivatives. Integration is one of the two major calculus topics in Mathematics, apart from differentiation(which measure the rate of change of any function with respect to its variables).

Definite Integral

An integral that contains the upper and lower limits then it is a definite integral. On a real line, x is restricted to lie. Riemann Integral is the other name of the Definite Integral.

A definite Integral is represented as:

∫f(x)dx from a to b.

Indefinite Integral

Indefinite integrals are defined without upper and lower limits. It is represented as:

∫f(x)dx = F(x) + C

Where C is any constant and the function f(x) is called the integrand.

Now,

For volume

Integrate y=1-x^2 for x=-1 to 1.

volume=1-x^2.dx

V=x-x^3/3

=1-1/3+1-1/3

=2-2/3

Hence,

          Volume=4/3 cubic unit

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Team A needs to sell 255 bags of popcorn to reach their goal of $100.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Team A will sell the bags of popcorn for $0.50 each.

Team B will sell the cotton candy for $0.75 per stick.

Let the number of bags of popcorn sold by Team A be "x".

So, the total cost for the popcorn machine rental and supplies is

= $15 + 0.05x.

To reach their goal of $100

$100 = 0.5x - ($15 + 0.05x)

$100 = 0.5x - $15 - 0.05x

$115 = 0.45x

x = $115 / 0.45

x = 255 bags of popcorn

Thus, Team A needs to sell 255 bags of popcorn.

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