Please help me with this problem

Answer:125

Step-by-step explanation:

The formula for the associative property of multiplication is (a × b) × c = a × (b × c).

This is further explained below.

Generally, The associative property is a feature that certain binary operations have in mathematics. This property indicates that the outcome of an expression will not change even if the parentheses are rearranged in the expression.

Associativity is a legitimate rule that may be used to substitute expressions in logical proofs when working with propositional logic.

In conclusion, (a times b) times c equals a times (b times c), and this is the formula for the associative property of multiplication.

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Answer:

G(x) = 3x +2

Step-by-step explanation:

I do not know what the problem is asking for, but if it's asking for the function, here you go.

Answer:

shbdhsjdcjsvdbssegehehhehehejrjehe

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

Answer:

Reduce 9/4 to lowest terms

94 is already in the simplest form. It can be written as 2.25 in decimal form (rounded to 6 decimal places).

Step-by-step explanation:

If Gas prices are typically marked up for holiday travel. If the prices are marked up 10% and the regular price is $2.45,  the price after the mark-up is $2.70.

Frist step is to find the marked-up price using this formula

Markup price = Markup percentage × Regular price

Let plug in the formula

Markup price = 10% × $2.45

Markup price = $0.245

Now  let find the price after markup  using this formula

Price after markup = Regular price + Markup price

Let plug in the formula

Price after markup = $2.45 + $0.245

Price after markup = $2.695

Price after markup = $2.70 ( Approximately)

Therefore $2.70 is the price after marked-up.

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Answer:

(2,0)

Step-by-step explanation:

I think that the answer

The value of the expression, \(\sqrt[90]{100}\) is given using logarithms as approximately 1.0525

The logarithm of a number, a, is the value, y, to which a base number, b, is to be raised to give the number x as follows;

\(log_ba = y\)

\(\therefore b^y = a\)

The evaluation of the the expression, \(\sqrt[90]{100}\), can be performed as follows;

Let x represent the value, \(\sqrt[90]{100}\), we have;

x =  \(\sqrt[90]{100}\)

\(\sqrt[90]{100} = 100^{\frac{1}{90} }\), which gives;

\(x= 100^{\frac{1}{90} }\)

Taking the logarithm to base 10 of both sides gives;

\(log_{10}x = log_{10}100^{\frac{1}{90} }\)

\(log_{10}x = log_{10}100^{\frac{1}{90} } = \dfrac{1}{90}\cdot log_{10}100^\)

\(log_{10}x = \dfrac{1}{90}\cdot log_{10}100=\dfrac{1}{90}\times 2 = \dfrac{1}{45}\)

\(x = antilog\left(\dfrac{1}{45} \right)\approx 1.0525\)

Therefore; x =  \(\sqrt[90]{100}\) ≈ 1.0525

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The distance between given point A and point B on the graph is 3√2 units.

Hence the correct option is (A).

We know that the distance between two points having coordinates (a, b) and (c, d) is = √((c - a)² + (d - b)²).

From the given graph we can see that,

the coordinates of the point A = (-2, -1)

the coordinates of the point B = (1, 2)

So the distance between the point A and point B is given by,

= √((1 - (-2))² + (2 - (-1))²)

= √((1 + 2)² + (2 + 1)²)

= √(3² + 3²)

= √(9 + 9)

= √18

= 3√2 units

Hence the correct option will be (A).

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Answer:

143.44 degrees

Step-by-step explanation:

T=36+(190-36)e^(-0.12*3)

Answer:

The answer is 7 socks.

Step-by-step explanation:

To ensure one matching pair, you need to pull out 4 socks. If none of the first three match, the fourth one will guarantee a matching pair.

You will then need to pull out 3 more socks, for a total of 7 socks, to ensure two matching pairs.

Answer:

48 percent

Step-by-step explanation:

12 divided by 25 gets you .48 which can be expressed as 48%

Answer:

48%

Step-by-step explanation:

1. Change 12/25 to a fraction with a denominator of 100

25 x 4=100

12 x 4=48

2. Find the percent

48/100= 48%

Answer:

option 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = \(\frac{0-(-2)}{4-0}\) = \(\frac{0+2}{4}\) = \(\frac{2}{4}\) = \(\frac{1}{2}\)

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = \(\frac{1}{2}\) x - 2 ← equation of line

The value of x in the equation x + 5 = 7 is 2

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, the equation is:

x + 5 = 7

Collect the like terms

x = 7 - 5

x = 2

Therefore, x is 2.

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Answer:

x = 2

Step-by-step explanation:

Given equation,

→ x + 5 = 7

Now the value of x will be,

→ x + 5 = 7

→ x + 5 - 5 = 7 - 5

→ [ x = 2 ]

Hence, the value of x is 2.

An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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Answer:

D

Step-by-step explanation:

The total water usage in the water park, in scientific notation is 1.41 × \(10^{6}\) gallons of water.

To express the total gallons of water used in the water park, including the additional water used by the new ride, we can use scientific notation.

The initial water usage in the park is given as 5.9 × \(10^{5}\) gallons of water.

The water usage of the new ride is stated as 820,000 gallons.

To find the total water usage after adding the new ride, we need to add the initial water usage to the water usage of the new ride:

5.9 × \(10^{5}\) + 820,000

To perform this calculation, we need to convert the water usage of the new ride to scientific notation:

820,000 = 8.2 × \(10^{5}\)

Now, we can add the two values:

5.9 × \(10^{5}\) + 8.2 × \(10^{5}\)

When adding values in scientific notation, we need to ensure that the exponents are the same. In this case, both values have an exponent of 5, so we can simply add the coefficients:

5.9 + 8.2 = 14.1

Therefore, the total water usage in the water park, including the new ride, can be expressed in scientific notation as 1.41 × \(10^{6}\) gallons of water.

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Therefore, the  solution of given equation is x<48.84. Therefore the correct option is option a .

An equation is a mathematical expression of the type A=B that is used to determine values or solutions. Typically, equations incorporate variables (unknowns). x + 4 = 14, where x is a variable, is an illustration of an equation. The objective is to identify the value of x that causes the equal (=) sign to be true. In this case, the answer is x = 10.

Here,

The given inequality is

11.22x + 200 <  347.96

We need to solve the above inequality for x.

Add 200 on both sides.

11.22x - 200+ 200 < 347.96 +200

11.22 <547.96

Divide both sides by 11.22.

11.22x/11.22 < 547.96/ 11.22

x< 48.8377896613

x < 48.84

Therefore the  solution of given equation is x<48.84. Therefore the correct option is option a .

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Answer:

300.94 sq.m

Step-by-step explanation:

A solid in the shape of cylinder with two hemisphere to each of its ends.

Finding, the Curved surface area of cylinder

Calculate the height of cylinder

Height of cylinder = 11 m

Now, we have

Height of cylinder = 11 m

Radius of cylinder = 7 / 2 = 3.5 m

Using Formula :-

Curved surface area of cylinder = 2× π × r × h

Substitute the values

Curved surface area of cylinder = 2π× 3.5m×11m.

Using the value of π = 3.14

Curved surface area of cylinder =2×3.14× 3.5m × 11 m.

multiply, we get.

Curved surface area of cylinder = 241.78 m².

Finding curved surface area of hemisphere

Using Formula

Curved surface area of hemisphere = 2 × π × r²

substitute the values into the formula

Curved surface area of hemisphere = 2 π × ( 3.5 )²

Evaluate the exponent

Curved surface area of hemisphere =2π×12.25m².

Using value of π = 3.14

Curved surface area of hemisphere = 2 × 3 14 × 12.25 m ²

multiply , we get

Curved surface area of hemisphere = 76.93 m².

Total area of capsules = Curved surface area of cylinder + 2 (Curved surface area of hemisphere)

Total surface area of capsules = 241.78 m²+ 2 × 76.93 m².

Total surface area = 241.78m² + 153.86m².

Subtract and finally we get

Total surface area = 395.64 m ²

Answer:

The coordinate of \(Z\) is 13.36.

Step-by-step explanation:

According to the statement, we have the following information:

\(\frac{XY}{XZ} = \frac{5}{12}\) (1)

\(\frac{YZ}{XZ} = \frac{7}{12}\) (2)

\(X = 0.4\) (3)

\(Y = 5.8\) (4)

From (2), we have the following expression:

\(YZ = \frac{7}{12}\cdot XZ\)

\(Y-Z =\frac{7}{12}\cdot (X-Z)\)

\(Y - Z = \frac{7}{12}\cdot X -\frac{7}{12}\cdot Z\)

\(Y-\frac{7}{12}\cdot X = Z-\frac{7}{12}\cdot Z\)

\(\frac{5}{12}\cdot Z = Y-\frac{7}{12}\cdot X\)

\(5\cdot Z = 12\cdot Y-7\cdot X\)

\(Z = \frac{12}{5}\cdot Y-\frac{7}{5}\cdot X\) (5)

If we know that \(Y = 5.8\) and \(X = 0.4\), then the coordinate of \(Z\) is:

\(Z = \frac{12}{5}\cdot (5.8)-\frac{7}{5}\cdot (0.4)\)

\(Z = 13.36\)

The coordinate of \(Z\) is 13.36.

The measures represent a 7-point Likert scale.

Interval scales are numerical scales in which the difference between any two adjacent points is the same.

Examples of interval scales include temperature (in Celsius or Fahrenheit), standard IQ scores, and dates.

Ordinal scales are numerical scales in which the difference between any two adjacent points is not necessarily the same.

Examples of ordinal scales include rankings (e.g., 1st, 2nd, 3rd, etc.), letter grades (A, B, C, etc.), and Likert scales (e.g., strongly agree, agree, neutral, disagree, strongly disagree).

Ordinal scales allow for the ranking of items, but the distances between points on the scale are not necessarily equal.

Interval scales, on the other hand, measure the distance between points on the scale and the difference between any two points is the same.

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If we let Z = 3 - X, then Z is another exponential random variable with mean 1 that is negatively correlated with X.

Let Y = 2 - X, where X is an exponential random variable with mean 1.

To show that Y is negatively correlated with X, we need to show that Cov(X,Y) < 0.

Cov(X,Y) = E[XY] - E[X]E[Y]

Since X and Y are both exponentially distributed with mean 1, we have:

E[X] = 1, E[Y] = 2 - E[X] = 1

E[XY] = E[X(2-X)] = 2E[X] - E[X^2] = 2 - Var(X)

Var(X) = E[X^2] - (E[X])^2 = 1 - 1^2 = 0

Therefore, Var(X) = 0, which means that E[XY] = 2, and Cov(X,Y) = E[XY] - E[X]E[Y] = 2 - 1*1 = 1 > 0.

Since Cov(X,Y) > 0, we know that Y is positively correlated with X. To find a random variable that is negatively correlated with X, we can use Y = 3 - X instead.

Therefore, if we let Z = 3 - X, then Z is another exponential random variable with mean 1 that is negatively correlated with X.

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The student who consults 3 books spends 637 minutes on a research paper based on the line of best fit if the equation of the line of best fit is y = 70.28x + 425.77 option (D) is correct.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

\(\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}\)

We have:

Kevin gathered data from his classmates about the number of books they consulted and the total time they spent on a research paper.

The line of best fit is:

y  = 70.28x + 425.77

Plug x = 3 in the line of best fit:

y  = 70.28(3) + 425.77

y = 21.084 + 425.77

y = 636.61 minutes ≈ 637 minutes

Thus, the student who consults 3 books spends 637 minutes on a research paper based on the line of best fit if the equation of the line of best fit is y = 70.28x + 425.77 option (D) is correct.

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To evaluate the iterated integral ∭W fdV, where f(x, y, z) = xz + y^2 + z^2 and W is the bottom half of a sphere with radius 6, we can use spherical coordinates. The integral can be expressed as ∫AB ∫CD ∫EF ρ^2 sin(ϕ) f(ρ, ϕ, θ) dρ dϕ dθ, and the limits of integration need to be determined based on the geometry of the region.

In spherical coordinates, the integral ∭W fdV can be written as ∫AB ∫CD ∫EF ρ^2 sin(ϕ) f(ρ, ϕ, θ) dρ dϕ dθ, where ρ represents the radial distance, ϕ represents the polar angle, and θ represents the azimuthal angle.

Since W is the bottom half of a sphere with radius 6, the limits of integration need to be determined accordingly. The radius, ρ, varies from 0 to 6, as it represents the distance from the origin to the surface of the sphere. The polar angle, ϕ, ranges from 0 to π/2, as we are considering the bottom half of the sphere. The azimuthal angle, θ, can span the full range of 0 to 2π.

To evaluate the integral, we substitute the function f(ρ, ϕ, θ) = ρz + y^2 + z^2 into the integral expression and calculate the iterated integral ∫AB ∫CD ∫EF ρ^2 sin(ϕ) (ρz + y^2 + z^2) dρ dϕ dθ using the determined limits of integration. The resulting value will be the evaluation of the integral.

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Answer:

5.28

Step-by-step explanation:

we use the formula

H²=B²+P²

and we will get the answer

branliest if it is helpful

Answer:

Angle BXY

using pythogoras theory which is

hyp*2= opp*2 +adj*2

hypothenus being the longest part of the angle BX=?

Step-by-step explanation:

hyp= 4.2*2+ 3.2*2

hyp*2 =17.64 + 10.24

hyp*2 = 27.88

hyp =√27.88

hyp=5.28...Ans

note *2...square

Answer:

75%

Step-by-step explanation:

the percentage amount of the drink that mike drank is calculated by dividing the total drink by the amount drank. In this case that is 8/32 which gives us 0.25 or 25%.

In order to find the amount Mike has left you simply subtract the amount drank from the 1 as 1 is equal to 100% or the amount mike had at the begining.   In this case 1-0.15= 0.75 or 75%.

OR

you can also solve this by subtracting tha amount drank by the total then dividing the remaining drink by the total amount of the drink. In this case that would look like:

32-8= 24

24/32= 0.75

A. square root property

\(3x^2-192=0\\x^2-66=0\\x^2=66\\x= -\sqrt{66} or \sqrt{66}\)

it has one value with x which is x^2 and it cn be easily solved without having to factorise, quadratic formula cant be used as it need ax^2+bx+c=0 format

B. factorising

\(x^2-x-6=0\\x^2+2x-3x-6=0\\(x+2)(x-3)=0\\x+2=0 and x-3=0\\x= -2 \\x= 3\)

i just felt like this was easier to factorise than the other 2 options left

C. Completing the square

\(x^2-6x-7=0\\(x-3)^2=0\\x= -1\\x= 7\)

same reason personal preference

D- Quadratic

\(x^2-17x-7=0\\x=\frac{-(-17)+\sqrt{(-17)^2-4(1)(-7)} }{2(1)} \\x=\frac{-(-17)-\sqrt{(-17)^2-4(1)(-7)} }{2(1)}\\x=17.4\\x=-0.402\)

the 17 kinda threw me off and i didnt wanna get on factorising or doing completing the square so quadratic formal

The curve that passes through (4, 5) and has a slope of 3√x at each point is given by y = (\(2x^{3/2}\) + 5 -  2\((4)^{3/2}\)

To find the curve that passes through (4, 5) and has a slope of 3√x at each point, we can integrate the derivative of y with respect to x, which gives us the original function y(x):

\(\frac{dy}{dx}\) = 3√x

Integrating both sides with respect to x, we get:

y = (\(2x^{3/2}\)) + C

where C is a constant of integration.

We can use the point (4, 5) to solve for C:

5 = 2\((4)^{3/2}\) + C

C = 5 - 2\((4)^{3/2}\)

Substituting this value of C, we get the final equation for the curve:

y =  (\(2x^{3/2}\)) + 5 -  2\((4)^{3/2}\)

Therefore, The curve that passes through (4, 5) and has a slope of 3√x at each point is given by y = (\(2x^{3/2}\) + 5 -  2\((4)^{3/2}\)

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