What are numbers using exponents are called?

Answer:

108

Step-by-step explanation:

The statement is true. Simple random sampling is a method of selecting a sample from a larger population in which every member of the population has an equal chance of being selected for the sample.

This method is associated with a high degree of generalizability because it ensures that the sample is representative of the population. When a sample is representative of the population, the findings from the sample can be generalized to the entire population with a high level of confidence.

Simple random sampling is considered to be one of the most reliable and unbiased methods of sampling, making it a popular choice in many research studies.

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The arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

In mathematics, an expression or mathematical expression is a combination of terms both variables and constants. For example -

2x + 4y + 5z

4y + 2x

Given are the expressions as given in the questions.

{a} -

5 - 9 = - 4

{b} -

8 - 8 = 0

{c} -

- 1 + 12 = 11

{d} -

- 12 + 12 = 0

{e} -

- 2 + 4 + 3

5

{f} -

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

Therefore, the arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

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{Complete question -

Calculate the following:

a) 5-9

b) 8-8

c) -1 + 12

d) -12 + 12

e) -2 +4+3

f) -4-3+2-1}

Answer:

true

Step-by-step explanation:

a parallelogram has 2 congruent consecutive sides then it is a square

A) There are 12 elements in the sample space.

B) The required probability is 1/4 or 0.25.

C) Yes, the events are mutually exclusive.

Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty

Part(A)

An experiment consists of first rolling a die and then tossing a coin.

Thus the sample space is:

(1,H), (2,H) (3,H) (4,H) (5,H), (6,H)

(1,T), (2,T) (3,T) (4,T) (5,T), (6,T)

Hence, there are 12 elements in the sample space.

Part(B) Let A be the event that either a 2, 3 or 4 is rolled first, followed by landing a head on the coin toss.

Now consider the above sample space. There are 3 possible case in which 2, 3 or 4 is rolled first, followed by landing a head on the coin toss.

i.e (2,H) (3,H) (4,H)

The required probability is: P(A)= 3/12 = 1/4 = 0.25

Hence, the required probability is 1/4 or 0.25.

Part(C)

Mutually exclusive, means that they cannot occur at the same time.

From part (B) Event A = (2,H) (3,H) (4,H)

Let B be the event that a number less than 2 is rolled, followed by landing a head on the coin toss.

Thus, the Event B = (1,H).

Therefore, Event A and B can't be occur at the same time as P(A and B)=0.

Hence, yes, the events are mutually exclusive.

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The 98% confidence interval for the population mean (μ) is approximately (2.711, 3.009).

1: Identify the given data

Sample size (n) = 150 students

Sample mean (x) = 2.86

Population standard deviation (σ) = 0.78

Confidence level = 98%

2: Find the critical z-value (z*) for a 98% confidence level

Using a z-table or calculator, you'll find that the critical z-value for a 98% confidence level is 2.33 (approximately).

3: Calculate the standard error (SE)

SE = σ / √n

SE = 0.78 / √150 ≈ 0.064

4: Calculate the margin of error (ME)

ME = z* × SE

ME = 2.33 × 0.064 ≈ 0.149

5: Construct the confidence interval

Lower limit = x - ME = 2.86 - 0.149 ≈ 2.711

Upper limit = x + ME = 2.86 + 0.149 ≈ 3.009

The 98% confidence interval is approximately (2.711, 3.009).

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Answer:

C. 244,596 gal

Step-by-step explanation:

To determine the number of gallons of water that a swimming pool holds, you can use the following formula:

gallons = cubic feet * 7.48

Plugging in the given volume of 32,700 cubic feet, you get:

gallons = 32,700 cubic feet * 7.48

= 244,596 gal

Therefore, the swimming pool holds approximately 244,596 gallons of water.

The Area of Trapezium is 50, 267 mm².

We have,

base 1 = 224 mm

base 2 = 77 mm

Height = 334 mm

Now, Area of Trapezium

= 1/2 (Sum of parallel side) x height

= 1/2 (224 + 77) x 334

= 1/2 x 301 x 334

= 50, 267 mm²

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The slope of the line is -(1/2)

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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To find the directional derivative of the function \(\(f(x, y) = e^x \cos y\)\) at the point (0, 0) in the direction indicated by the angle \(\(\theta = \frac{\pi}{4}\),\)the directional derivative of\(\(f(x, y)\)\) at (0, 0) in the direction of \(\(\theta = \frac{\pi}{4}\)\) is \(\(\frac{\sqrt{2}}{2}\).\)

First, we find the gradient of \(\(f(x, y)\)\) by taking the partial derivatives with respect to x and y:

\(\(\frac{\partial f}{\partial x} = e^x \cos y\) and \(\frac{\partial f}{\partial y} = -e^x \sin y\).\)

Next, we evaluate the gradient at the point (0, 0):

\(\(\nabla f(0, 0) = \left(e^0 \cos 0, -e^0 \sin 0\right) = (1, 0)\).\)

To obtain the unit vector in the direction of \(\(\theta = \frac{\pi}{4}\)\), we use the components of \(\(\theta\)\) as the coordinates of the vector:

\(\(\mathbf{u} = (\cos \theta, \sin \theta) = \left(\cos \frac{\pi}{4}, \sin \frac{\pi}{4}\right) = \left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)\).\)

Finally, we compute the dot product between\(\(\nabla f(0, 0)\)\) and \(\(\mathbf{u}\)\) to find the directional derivative:

\(\(\nabla f(0, 0) \cdot \mathbf{u} = (1, 0) \cdot \left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right) = \frac{\sqrt{2}}{2}\).\)

Therefore, the directional derivative of f(x, y) at (0, 0) in the direction of\(\(\theta = \frac{\pi}{4}\) is \(\frac{\sqrt{2}}{2}\).\)

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Equation of the tangent line to the curve  \(xe^{y} + ye^{x} = 5\) at5 the point (0,5) is y = - (\(e^{5}\) + 5)x + 5.

Given curve is,

\(xe^{y} + ye^{x} = 5\)

We will differentiate both sides with respect to x,

\(\frac{d}{dx}\)\([xe^{y} + ye^{x} ]\) = \(e^{y} + xe^{y}\frac{dy}{dx} + e^{x}\frac{dy}{dx} + ye^{x}\) = 0

⇒ \(\frac{dy}{dx}\) \([xe^{y} + e^{x} ] = - [e^{y} + ye^{x} ]\)

⇒ \(\frac{dy}{dx}\) = \(- \frac{e^{y}+ye^{x} }{xe^{y}+e^{x} }\)

We have to find the equation at point (0,5).

Therefore substituting values of x and y,

that is x = 0 and y = 5.

\(\frac{dy}{dx} = - \frac{e^{5}+(5)e^{0} }{(0)e^{5} + e^{0} }\)

    = \(- \frac{e^{5} + 5}{1}\)

\(\frac{dy}{dx}\)  = - [\(e^{5}\) + 5] = gradient

Therefore the equation of tangent line is

(y - y1) = [m(x - x1)]

where m is the gradient

⇒ y - 5 = - [(\(e^{5}\)+5)(x - 0)]

⇒  y = - (\(e^{5}\) + 5)x + 5

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Solution:

Using the formula;

B=p(1+r)t

Where B = balance, p = principal, r = rate, t = time p= 30, r= 10%= 0.1, t=1

B=30(1+ 0.1)1

Answer= 33$

Answer:

3.14

Step-by-step explanation:

area=pi times the square of radius

1^2 = 1 x 3.14=3.14

The currents i1, i2, and i3 are 10 A, 10 A, and 10 A, respectively. The currents i1, i2, and i3 can be found using the following equations:

i_1 = \frac{v_1}{r_1} = \frac{100}{1} = 10 A

i_2 = \frac{v_2}{r_2} = \frac{100}{1} = 10 A

i_3 = \frac{v_3}{r_3} = \frac{100}{1} = 10 A

where v1, v2, and v3 are the voltages across the resistors r1, r2, and r3, respectively.

The currents i1, i2, and i3 are all equal to 10 A because the resistors r1, r2, and r3 are all equal to 1 ohm. Therefore, the current will divide equally across the three resistors.

The currents i1, i2, and i3 are the currents flowing through the resistors r1, r2, and r3, respectively. The currents are found by dividing the voltage across the resistor by the resistance of the resistor.

The voltage across a resistor is equal to the product of the current flowing through the resistor and the resistance of the resistor. The resistance of a resistor is a measure of the opposition that the resistor offers to the flow of current.

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Answer:

\(11xy+4x^{2} t\)

Step-by-step explanation:

1. Collect Like Terms

\((7xy+4xy)+(-x^{2} t+5x^{2} t)\\\)

2. Simplify.

\(11xy+4x^{2} t\)

Answer: A. 6

Step-by-step explanation: if you go from -2 to 6 you go 8 spaces. You go from -2 to 0 which is 2 spaces, and they 6 more spaces to get to 6.  If you went to -9 you are going 7 spaces.  and to 0 you go 2 spaces, and -1 you go one space. So, the furthest is positive 6.

Hope this helps ^_^

A. 6 is farthest from the number line.

A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals.

Given a number 2 on the number line and we had to find which one is farthest. Since,

The difference between numbers is directly proportional to the distance between two numbers in the number line.

Hence,  -2 -6 = -8

-2-0 = -2

-2-(-1) = -1

-2 - (-9) = 7

Therefore, 6 will be the farthest number from two in the number line.

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Answer:

Have an amazing night/day!

Step-by-step explanation:

14 i think ill edit if im wrong

Answer:

The ratio would be 65:1 since they mow 65 lawns in 1 hour. I hope this helps! :)

On solving the provided question we can say that - Therefore, by equation models 25 strawberries are supplied as the necessary number of strawberries to be consumed by the buddy.

A model of a situation in the form of an equation employing constants and variables is referred to as an equation model. Mathematicians use the terms "simplifying" and "simplification" to refer to the operations and interpretations done to make a function or statement simple or easier to grasp.

so

suppose  the number of strawberries he eat  = x,

and now

his friend eat = 5x - 25

x\(Put x = 10\)

his friend eat = 50 - 25 = 25

Therefore, 25 strawberries are supplied as the necessary number of strawberries to be consumed by the buddy.

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So the maximum number of edges in an undirected graph with 100 vertices is 4950.

In an undirected graph, each edge connects two vertices, and as such, it is counted twice, once for each vertex it connects. Therefore, the total number of edges in the graph is the sum of the degrees of all vertices, divided by 2.

In a complete graph with n vertices, every vertex is connected to every other vertex, except itself, and so the degree of each vertex is n-1 (it is connected to n-1 other vertices). Therefore, the total number of edges in the graph is:

n * (n-1) / 2

Substituting n = 100, we get:

100 * 99 / 2 = 4950

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The expression evaluates to true regardless of the values of p and q, we can conclude that (p ∨ q) → (q → q) is a tautology.

To verify that (p → [q → (p ∧ q)]) is a tautology, we can use substitution rules and laws of logic.

1. Start by assuming p is true and q is true.
2. Substitute these values into the expression: (true → [true → (true ∧ true)])
3. Evaluate the innermost expression first: (true ∧ true) = true
4. Substitute this result back into the expression: (true → [true → true])
5. Evaluate the second innermost expression: (true → true) = true
6. Substitute this result back into the expression: (true → true)
7. Evaluate the remaining expression: true

Since the expression evaluates to true regardless of the values of p and q, we can conclude that (p → [q → (p ∧ q)]) is a tautology.

Now, let's use this result to show that (p ∨ q) → (q → q) is also a tautology.

1. Start by assuming (p ∨ q) is true and q is true.
2. Substitute these values into the expression: true → (true → true)
3. Evaluate the innermost expression first: (true → true) = true
4. Substitute this result back into the expression: true → true
5. Evaluate the remaining expression: true

Since the expression evaluates to true regardless of the values of p and q, we can conclude that (p ∨ q) → (q → q) is a tautology.

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Answer:

\(y=0\)

Step-by-step explanation:

\(y+25=25 \\ \\ y=25-25 \\ \\ y=0\)

Answer:

\( \sf \: y = 0\)

Step-by-step explanation:

Given equation,

→ y + 25 = 625 ÷ 25

Now the value of y will be,

→ y + 25 = 625 ÷ 25

→ y + 25 = 25

→ y = 25 - 25

→ [ y = 0 ]

Hence, the value of y is 0.

Answer:

answer is a

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the 2/3x represents how much it will increase while the -1 represents the y-intercept

Answer:

moonano

Step-by-step explanation:

Answer:

5:46pm

Step-by-step explanation:

6:32 - :46 =

6:00 = :46 - :32 = :14

6:00 = 5:60

5:60 - :14 = :60 - :14 = :46

5:46

The minimum value of the function f(x) =0. 9x2+3. 4x-2. 4 is -3.77 and its parabolic curve is upward because of its minimum value.

Let's consider the equation of a function.

f(x) = \(0.9x^{2} + 3.4x -2.4\)

Now, divide each and every element and assume that a, b, and c are coefficients of the function given.

a: 0.9

b: 3.4

c: -2.4

The sign of the coefficient of a determines the exposure of the parabola. Since a >  0, the parabola is open upwards and has a minimum value.

We can find the "x" of the vertex using the following expression.

x(v) = -b/2a = -3.4/(0.9)

x(v) = -3.77

We can find the "y" of the vertex by replacing this x in the equation

y(v) = 0.9(-3.77)² + 3.4(-3.77) -2.4

y(v)  = -2.42

The minimum value of the function is -3.77

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