find the value of 6^-3​

Answer:

x = 4.6439

Step-by-step explanation:

2^x =25

Take the log of each side

log  2^x = log 25

We know that log a^b = b log a

x log 2 = log 25

Divide each side by log 2

x = log 25  / log 2

x =4.643856

Rounding to 4 decimal places

x = 4.6439

Answer:

x = 4.6439

Step-by-step explanation:

\(2^{x} =25log 2^x = log 25\\log 2 = log 25x = log 25 / log 2\\x =4.643856\\x = 4.6439\)

In business calculus, the term "functions" refers to mathematical relationships that associate inputs (typically denoted as x) with corresponding outputs (typically denoted as y). Functions can represent various aspects of business operations, such as revenue, cost, profit, demand, and supply.

The concept of "limits" in calculus deals with the behavior of a function as the input approaches a particular value. It determines the value that the function approaches or tends to as the input gets arbitrarily close to a specified value. Limits are essential for analyzing the behavior of functions near certain points, understanding rates of change, and evaluating derivatives and integrals.

"Continuity" of a function refers to its smooth and unbroken nature, without any abrupt jumps, holes, or vertical asymptotes. A function is continuous if its graph can be drawn without lifting the pen from the paper. Continuity ensures that small changes in the input correspond to small changes in the output, which is crucial for reliable analysis and prediction.

For example, consider the function f(x) = 2x + 1. This linear function represents a business scenario where x represents the number of units sold, and f(x) represents the total revenue generated. The limit of f(x) as x approaches 2 is 5, indicating that as the number of units sold approaches 2, the total revenue approaches $5. Since f(x) = 2x + 1 is a linear function, it is continuous across its entire domain.

Learn more about functions, limits, and continuity in calculus here:

brainly.com/question/29297331

#SPJ11

Answer:

x = 0.5

graph is shown in image

Step-by-step explanation:

The value of {x} is equivalent to 7.

Given is a triangle ΔXYW.

The median of a triangle is a bisector of the angle. Median is found to be joining the vertex of the triangle with the opposite side of the triangle. So, we can write -

m∠1 = m∠2

(2x + 9) = (4x - 5)

2x + 9 = 4x - 5

14 = 2x

x = 7

Therefore, the value of {x} is equivalent to 7.

To solve more questions on triangles, visit the link below -

brainly.com/question/12413243

#SPJ1

The random variable follows a continuous uniform distribution between 20 and 50.

The continuous uniform distribution is a probability distribution where all values within a specified range are equally likely to occur. In this case, the random variable follows a continuous uniform distribution between 20 and 50. To calculate the probabilities for this distribution, we can use the properties of the uniform distribution.

P(x ≤ 25):

To find this probability, we need to calculate the proportion of the range from 20 to 50 that lies below or equal to 25. Since the distribution is uniform, the probability is equal to the ratio of the length of the range below or equal to 25 to the length of the entire range.

Length of the range below or equal to 25 = 25 - 20 = 5

Length of the entire range = 50 - 20 = 30

P(x ≤ 25) = (Length of the range below or equal to 25) / (Length of the entire range) = 5 / 30 = 1/6 ≈ 0.1667

Therefore, P(x ≤ 25) is approximately 0.1667 or 16.67%.

P(x ≤ 30):

Using a similar approach, we calculate the probability of the range below or equal to 30.

Length of the range below or equal to 30 = 30 - 20 = 10

P(x ≤ 30) = (Length of the range below or equal to 30) / (Length of the entire range) = 10 / 30 = 1/3 ≈ 0.3333

Therefore, P(x ≤ 30) is approximately 0.3333 or 33.33%.

P(24 ≤ x ≤ 35):

To find this probability, we need to calculate the proportion of the range from 20 to 50 that lies between 24 and 35.

Length of the range between 24 and 35 = 35 - 24 = 11

P(24 ≤ x ≤ 35) = (Length of the range between 24 and 35) / (Length of the entire range) = 11 / 30 ≈ 0.3667

Therefore, P(24 ≤ x ≤ 35) is approximately 0.3667 or 36.67%.

P(x = 28):

Since the continuous uniform distribution is continuous, the probability of a single point is zero. Therefore, P(x = 28) is equal to zero.

In summary:

P(x ≤ 25) ≈ 0.1667 or 16.67%

P(x ≤ 30) ≈ 0.3333 or 33.33%

P(24 ≤ x ≤ 35) ≈ 0.3667 or 36.67%

P(x = 28) = 0

These probabilities are calculated based on the assumption that the random variable follows a continuous uniform distribution between 20 and 50.

Learn more about random variable here

https://brainly.com/question/14356285

#SPJ11

Answer:

hi

Step-by-step explanation:

srry

Answer:

Below.

Step-by-step explanation:

A = 1/2bh for a triangle.

36 = 1/2b(12)

36 = 6b

----    ----

6        6

b = 6

Answer:

1st answer

Step-by-step explanation:

\(f(g(x)) = f(4x)=(4x)^2-8(4x)+4\\=16x^2-32x+4\)

He argues that teachers and administrators often label students based on their behavior, appearance, or other factors, which can have a profound impact on students' self-perceptions and future opportunities.

Theoretical perspectives are perspectives that sociologists use to help them better understand and explain human social behavior.

These perspectives encompass various theories and approaches to the study of education.

The following is an overview of three major theoretical perspectives and their associated classic studies of education:

Functionalism perspective

The functionalist perspective is a theoretical approach that views society as a complex system composed of various parts that work together to maintain social order.

Functionalism is also known as structural functionalism.

According to functionalists, education plays an important role in society by providing students with necessary skills and knowledge to become productive members of society.

Classic study of education:

Durkheim's study of education in "The Division of Labor in Society."

In this classic study, Durkheim argues that education serves a crucial function in socializing young people into shared cultural values, beliefs, and norms.

According to symbolic interactionists, education is a process of social interaction in which students learn to make sense of the world around them.

Classic study of education: Becker's study of labeling in "Becoming a Marijuana User.

"In this classic study, Becker demonstrates how schools play an important role in shaping student identities.

For more related questions on administrators:

https://brainly.com/question/31843645

#SPJ8

Answer: 108 degrees.

Step-by-step explanation:

I think this is how you solve it:

A circle has a total of 360 degrees.

Having 5 equally placed sensors with a certain detection angle means that the sensors form a regular pentagon.

Finding the measure of the interior angles of a regular pentagon can be found using the formula

(180(n-2))/n, with n being the number of vertices of the polygon.

180(5-2)/5 ; 180(3)/5 ; 540/5 = 108

I think this means the detection angle is 108 degrees. Hope this helps!

If you get it wrong I'm terribly sorry T-T

Answer:

\(512x^3\)

Step-by-step explanation:

\((8x)^3 = 8^3x^3 = 512x^3\)

Answer:

\(x=110^o\)

Step-by-step explanation:

If AB = AD, then you have that triangle ABD is an isosceles triangle (it has two equal sides). If it is isosceles, then the angles opposite to angles those equal sides must be equal. Then angle ADB = \(35^o\). and by the property of all internal angles of a triangle have to add to \(180^o\), we get that:

\(x=180^o-35^o-35^o=110^o\)

Answer:

x = 110 degrees, y = 49 degrees.

Step-by-step explanation:

We have adjacent isosceles triangles here, so

x = 180 - 2(35) = 110 degrees, and

2y  + 82 = 180

so y = (180 - 82) / 2 = 49 degrees.

Answer:

\(\mbox{\large {-\dfrac{5y^2z^4}{x^3}}}\)

Step-by-step explanation:

We have the following expression and asked to simplify

\(\dfrac{\left(-5x^{-3}y^2\right)}{z^{-4}}\)

Using the exponent rule: x⁻a = 1/xᵃ we get x⁻³ = 1/x³

Using the exponent rule 1/x⁻ᵃ = xᵃ we get 1/z⁻⁴ = z⁴

The resultant expression becomes:
\(-\dfrac{5y^2z^4}{x^3}\)

This cannot be simplified any further since the variables are different

Answer:

20. is B (second one)

21. is A (first one)

Step-by-step explanation:

Answer:

46=p x 98 because 46 is the product of multiplying the percentage(p) to 98

156+97 because subtracting a negative number is the same as adding

The solution of the system of equation is (-7, -2).

The system of the equations;

\(\rm y^2 + x^2 = 53 \\\\y -x = 5\)

From equation 1

\(\rm y -x=5\\\\y = 5+x\)

Substitute the value of y in equation 1

\(\rm y^2+x^2=53\\\\(5+x)^2+x^2=53\\\\25+x^2+10x+x^2=53\\\\2x^2+10x+25-53=0\\\\2 x^2 + 10x - 28 = 0 \\\\Divide \ by \ 2 \ both \ side \ the \ equation\\\\x^2 + 5x - 14 = 0\\\\x^2-7x+2x-14=0\\\\x(x-7) + 2(x-7) =0\\\\(x-7) \ (x+2)=0\\\\x-7=0 \ \ x = 7\\\\x +2 =0 \ \ x=-2\)

The value of x= 2 is rejected because x = 2 not satisfy the equation.

Substitute 2 for the value of x in equation II

y − x = 5

y – 2 = 5

y = 5 +2

y = 7 (x =2, y =7) … Not included in the options

If x = -7

Substitute the value of x = -7 in the equation

\(\rm y -x=5\\\\y - (-7)=5\\\\y +7= 5\\\\y = 5-7\\\\y = -2\)

Hence, the solution of the system of equation is (-7, -2).

To know more about System of Equation click the link given below.

https://brainly.com/question/1495351

Answer:

− 3 = − 14

Step-by-step explanation:

Hope this helps !

If Fidel has a rare coin worth $550 and its value increases by 10% each decade, we can calculate the value of the coin after a certain number of decades by applying the compound interest formula.

The compound interest formula is given by:

A = P(1 + r)^n

Where:

A is the final amount (value of the coin after n decades)

P is the initial amount (value of the coin)

r is the interest rate per period (in decimal form)

n is the number of periods (in this case, the number of decades)

In this case, the initial amount (P) is $550 and the interest rate per decade (r) is 10% or 0.1 (in decimal form).

Let's calculate the value of the coin after 1 decade:

A = 550(1 + 0.1)^1

A = 550(1.1)

A = $605

After 1 decade, the value of the coin would be $605.

Similarly, we can calculate the value of the coin after multiple decades. For example, after 2 decades:

A = 550(1 + 0.1)^2

A = 550(1.1^2)

A = $665.50

After 2 decades, the value of the coin would be $665.50.

You can continue this calculation for any number of decades to determine the value of the coin.

Learn more about decade here:

brainly.com/question/28494826

#SPJ11

Answer: C=0

Step-by-step explanation:

expand \(5\left(2c-3\right)\) : \(10c-15\)

expand \(3\left(3c\:-\:5\right)\) : \(9c-15\)

\(10c-15=9c-15\)

add 15 on both sides

\(10c-15+15=9c-15+15\)

simplify

\(10c=9c\)

\(\mathrm{Subtract\:}9c\mathrm{\:from\:both\:sides}\)

\(10c-9c=9c-9c\)

simplify

\(c=0\\\)

Answer:

C=0

Step-by-step explanation:

Hope it helps.

Answer:

B,AD

Step-by-step explanation:

BECAUSE I SAY IT

Yes, it is reasonable to conclude that the mean income of those selecting Plan B is larger. The p-value for the two-sample t-test is 0.012, which is less , This means that there is a statistically significant difference between the mean incomes of the two groups.

The two-sample t-test is a statistical test used to compare the means of two independent groups. In this case, the two groups are the subscribers to Plan A and the subscribers to Plan B. The null hypothesis is that the mean incomes of the two groups are equal. The alternative hypothesis is that the mean income of the Plan B subscribers is larger.

The p-value for the two-sample t-test is 0.012. This means that there is a 1.2% chance of getting a difference in means as large as the one observed in the sample if the null hypothesis is true. In other words, the probability of observing this difference by chance is very low.

Therefore, we can reject the null hypothesis and conclude that there is a statistically significant difference between the mean incomes of the two groups.

The mean income of the Plan B subscribers is $61,000, which is $4,000 more than the mean income of the Plan A subscribers. This difference is relatively large, and it is statistically significant. Therefore, we can conclude that the mean income of those selecting Plan B is larger.

Here are some additional details about the two-sample t-test:

To know more about value click here

brainly.com/question/30760879

#SPJ11

The given expression 3d - 4 is a linear expression.

Given that,
To classify the expression 3d - 4.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the linear function, cubic function, etc. ax+b is a polynomial.

Here,
Given expression 3d - 4, which only contains one variable d and one constant 4, or exponent to the variable is also 1 implies the expression is linear expression.

Thus, the given expression 3d - 4 is a linear expression.

Learn more about function here:

brainly.com/question/21145944

#SPJ1

After answering the presented question, we can conclude that As a equation result, eliminating the $40 wage from the set would have no effect.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

The information is expressed as follows:

665 occupations pay between $15 and $20 per hour.

One employment pays $40 per hour.

The average pay across all 666 roles would be:

\($$\frac{665\times($15+$20)+1\times$40}\\{666} = $17.56$$\\\)

With all 666 occupations included, the median salary would be $17.50, which is the halfway between the 333rd and 334th lowest incomes.

If the $40 pay is removed from the list, we are left with 665 occupations with rates ranging from $15 to $20. The new mean would be as follows:

\($$\frac{665\times($15+$20)}\\{665} = $17.50$$\)

Because there are an odd number of earnings, the new median would likewise be $17.50, and the midpoint would still be the 333rd lowest wage.

As a result, eliminating the $40 wage from the set would have no effect.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

The skip interval should be 40 if the sampling frame has 2000 names and the desired sample size is 50.

Systematic sampling is a type of sampling which uses the probability method where researchers select members of the group or population at a regular interval.

To determine the skip interval, it is necessary to first determine the sample size. Then the skip interval can be determined by dividing the total population by the target/desired sample size. Therefore;

skip interval = population / target sample size

Substituting the given values;

skip interval = 2000 / 50

skip interval = 40

Hence, the skip interval is calculated to be 40 if the frame has 2000 names and the desired sample size is 50.

To learn more about systematic sampling; click here:

https://brainly.com/question/14333907

#SPJ4

The angles formed by the bisector are equal in measure, adjacent, supplementary, form a linear pair, and are congruent.

When a line bisects an angle, it divides the angle into two equal parts. The resulting angles have several properties

They have equal measures: The two angles formed by the bisector have the same degree measurement.

They are adjacent: The two angles share a common side and vertex.

They are supplementary: The sum of the two angles formed by the bisector is 180 degrees.

They form a linear pair: The two angles, together with the adjacent angle on the other side of the bisector, form a straight line or a linear pair.

They are congruent: The two angles formed by the bisector are congruent to each other.

These properties are useful in solving problems involving angle bisectors in geometry.

Learn more about bisector here

brainly.com/question/2478436

#SPJ4

I have solved the question in general, as the given question is incomplete.

The complete question is:

What are some properties of the angles formed by the bisector?

Answer:

the correct answer is that it's true :)

The rate of change of the surface area when the radius is 12 cm is approximately -0.033 cm^2 per minute.

To find the rate of change of the surface area when the radius is 12 cm, follow these steps:

1. Find the relationship between the volume (V) and the radius (r) of the sphere. The formula for the volume of a sphere is V = (4/3)πr^3.

2. Differentiate V with respect to time (t) to find the rate of change of volume (dV/dt): dV/dt = 4πr^2(dr/dt).

3. We know the rate of change of volume (dV/dt) is -5 cm^3 per minute (gas is escaping, so the rate is negative). Plug this value into the equation: -5 = 4π(12^2)(dr/dt).

4. Solve for the rate of change of the radius (dr/dt): dr/dt = -5/(4π(12^2)).

5. Find the relationship between the surface area (A) and the radius (r) of the sphere. The formula for the surface area of a sphere is A = 4πr^2.

6. Differentiate A with respect to time (t) to find the rate of change of surface area (dA/dt): dA/dt = 8πr(dr/dt).

7. Plug in the known values (r = 12 cm and dr/dt from step 4) into the equation: dA/dt = 8π(12)(-5/(4π(12^2))).

8. Simplify and calculate the rate of change of the surface area: dA/dt ≈ -0.033 cm^2 per minute.

So, the rate of change of the surface area when the radius is 12 cm is approximately -0.033 cm^2 per minute.

Learn more about "surface area": https://brainly.com/question/16519513

#SPJ11

Rate of change of the surface area when the radius is 12 cm and the gas is escaping at a rate of 5 cm³/min is approximately -0.65 cm²/min.

We are given that the rate of gas escaping the spherical balloon is 5 cm³/min. This means that the rate of change of volume, dV/dt, is -5 cm³/min (since the volume is decreasing).

The formula for the volume of a sphere is:

V = (4/3)πr³

Differentiating with respect to time, we get:

dV/dt = 4πr²(dr/dt)

where dr/dt is the rate of change of the radius with respect to time.

Solving for dr/dt, we get:

dr/dt = (dV/dt) / (4πr²)

Substituting the given values, we get:

dr/dt = (-5 cm³/min) / (4π(12 cm)²) = -0.00215 cm/min (Note that the negative sign indicates that the radius is decreasing.)

Now, we need to find the rate of change of surface area, dA/dt. Using the formula for the surface area of a sphere, A = 4πr², we can differentiate with respect to time using the chain rule:

dA/dt = dA/dr * dr/dt

where dA/dr is the rate of change of surface area with respect to the radius.

Differentiating A = 4πr² with respect to r, we get:

dA/dr = 8πr

Substituting the given value, we get:

dA/dr = 8π(12 cm) = 301.59 cm²

Finally, substituting both values into the chain rule equation, we get:

dA/dt = (301.59 cm²) * (-0.00215 cm/min) ≈ -0.65 cm²/min

Therefore, the rate of change of the surface area when the radius is 12 cm and the gas is escaping at a rate of 5 cm³/min is approximately -0.65 cm²/min.

learn more about 'volume':https://brainly.com/question/31226103

#SPJ11

Answer: I think it took Andre 70 minutes

Step-by-step explanation:

Answer:

A.) Andre B.) 70 min

Step-by-step explanation:

A.) the key words are that it took andre 175% of Jada's time

B.)just take Jadars time 40 and multiply it by 175% or 1.75 as for the digram show Jadars as 100% and Andres as an extra 175% sorry i cant realy draw one right now

Answer:

a. The coordinates of the first train are (-12,6).  The coordinates of the second train are (20,35).

b. The slope of the line for the first train is \(-\frac{1}{2}\).  The slope is neither horizontal or vertical.  It slopes diagonally downward from left to write since the slope is negative.  In slope-interdept form, it is written as \(y=-\frac{1}{2} x\).  In standard form, it is written as \(x+2y=0\).   The slope of the line for the second train is \(\frac{7}{4}\).  The slope is neither vertical or horizontal.  It slopes diagonally upward from left to right since the slope is positive.  In slope-intercept form, it is written as \(y=\frac{7}{4}x\).  In standard form, it is written as \(-7x+4y=0\).

c. The equarion of a line in slope-intercept form of the new track would be \(y=-\frac{1}{2} x+2\).

Step-by-step explanation:

a.  The way to find the coordinates is either to picture a coordinate grid in your head or to have one out in front of you for a visual.  The first train travels 12 miles west, or 12 units to the left (-12), and 6 miles north, or 6 units up (6).  On a coordinate plane, that would be marked as (-12,6).  The second train travels 20 miles east, or 20 units to the right (20), and 35 miles north, or 35 units up (35).  On a coordinate plane that would be marked as (20,35).  This means that the coordinates of the first train would be (-12,6), and the coordinates of there second train would be (20,35).

b. The way to find slope is to find \(\frac{delta "x"}{delta "y"}\).  "Delta" means "the change in".  The equation would be \(m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\).  So, let's find the slope of the first train's travel path.  We'll use the origin, (0,0), and the stopping point, (-12,6), as our coordinates to find the slope.  \(\frac{0-6}{0-(-12)}=\frac{0-6}{0+12}=\frac{-6}{12}=\frac{-1}{2}=-\frac{1}{2}\).  That makes the slope of the first train's travel path to be (-1/2).  Now, let's find the slope of the second train's travel path.  We'll use the origin, (0,0), and the stopping point, (20,35), as our coordinates to find the slope.  \(\frac{0-35}{0-20}=\frac{-35}{-20}=\frac{35}{20}=\frac{7}{4}\).  That makes the slope of the second train's travel path to be (7/4).  They want to know the equation of the travel path line in slope-intercept form and in standard form, and what the line looks like.  To start off, any vertical line would be undefined, and that would be if the slope was a fraction with a denominator of zero, which doesn't occur for either train path.  A horizontal line  would be if the slope was zero itself and the trains were not moving, but the trains are moving, so that's not possible either.  The way to determine theway a slope is diagonally is to look at whether the slope is positive or negative.  The first train's path slopes negatively, so it moves diagonally downward from left to right, or diagonally upward from right to left (both the same thing).  The second train's path slopes positively, so it moves diagonally upward from left to right, or diagonally downward from right to left.  Finally, the equations for this part of the question.  For both trains, the origin is the y-intercept, so the y-intercept does not have to be written in the slope-intercept equation.  The slope-intercept form of an equation of a line is \(y=mx+b\) where "m" is the slope and "b" is the y-intercept.  The "b" value is 0, so that will not be written.  The slope for the first train is (-1/2), so the slope-intercept form of the first train's travel path is y=(-1/2)x.  The slope of the second train is (7/4), so the slope-intercept form for this train's path is y=(7/4)x.  As for standard form, subtract the "mx" value from both sides, and set the equation equal to 0. Also, get rid of any fractions. So, for the first train, standard form would be x+2y=0.  And for the second train, standard form would be -7x+4y=0.

c.  Parallel means having the same slope but a different y-intercept.  The second train station would be placed two miles north, or two units up, from the first train station.  The first train station is at (0,0), so the second train station would be placed at (0,2).  That makes 2 the y-intercept for if the first train had taken the second train station's travel route.  The slope for the intitial route was (-1/2), so that will stay the same.  Therefore, the equation of thr route taken if the first train had come out of the second train station, if it was already built, would be y=(-1/2x)+2.

The theoretical probability is given by 1 over the number of hobbies.

If there is a total of 8 hobbies, the probability of a student having a specific hobby is:

The experimental probability is given by the number of students with that hobby over the total number of students. If 3 students have the hobby roller skating among the 24 students surveyed, the probability is:

The required polynomial is given as \(4x^4y^4 + 8/3x^5y^4 + 14/3x^4y^3 + 16/3x^3y^2\).

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.

Here,
According to the question,
\(=(6xy^2+4x^2y+7xy+8)(2/3x^3y^2)\\= 4x^4y^4 + 8/3x^5y^4 + 14/3x^4y^3 + 16/3x^3y^2\)

Thus, the required polynomial is given as \(4x^4y^4 + 8/3x^5y^4 + 14/3x^4y^3 + 16/3x^3y^2\).

Learn more about polynomial functions here:

https://brainly.com/question/12976257

#SPJ2