What is 17 = 3x + 2 ?

The solution to the equation for x is x = 1/6[e^2]

from the question, we have the following parameters that can be used in our computation:

ln 9+ln 4x^2=4

Combine the natural logarithm

So, we have the following representation

ln(9 * 4x^2) =4

This gives

ln(36x^2) = 4

Take the exponent of both sides

36x^2 = e^4

Divide both sides by 36

x^2 = 1/36[e^4]

Take the square roots

x = 1/6[e^2]

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Answer:

I think there are 6 Tricycles in the shop.

Step-by-step explanation:

There is 3 wheels in a tricycle and 18 divided by 3 is 6.

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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Answer:

lesser x =-4

greater x =1/2

Answer: The property sold for $5,870.41.

Step-by-step explanation:

Let x be the selling price of the property.

Then, gross commission = 6.5% of x = 0.065x

listing salesman received = 12% of ( 0.065x)  = 0.12 (0.065x) = 0.0078 x

Balance = x - ( 0.065x) -  (0.0078 x)

= (1+0.065-0.0078)x

= 1.0572x

Scott received = 45% of (1.0572x)

=0.45 (1.0572x)

= 0.47574x

Now, \(0.47574x=2,792.79\)

\(\Rightarrow\ x=\dfrac{2792.79}{0.47574}\\\\\Rightarrow\ x=5870.41\)

Hence, the property sold for $5,870.41.

The positive integer +10 represents a gain of 10 yards on the football play.

A gain of 10 yards on the football play signifies that a team has improved on their position in the game.

Assuming they started from 0 the are along the positive direction of the axis by 10 units or yards.

Hence the integer to represent this is given by +10 a positive integer of 10 units.

Integer examples include positive, negative, and zero. The word "integer" means "whole" or "intact" in Latin. As a result, integers do not contain fractions or decimals.

Neither negative numbers nor all whole numbers are regarded as integers. This indicates that when negative numbers are added to whole numbers, an assortment of integers is the outcome. A number without a decimal or fractional element is called an integer, and it can consist of both positive and negative integers, including zero.

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One that does not belong to other three fraction is  -6/8.

To determine which of these fractions doesn't belong with the other three, we need to compare them and look for any differences or similarities. One way to do this is to convert the fractions to a common denominator, which in this case would be 8.

-3/4 can be rewritten as -6/8 (multiply the numerator and denominator by 2), and -5/8 is already in the form of 5/8.

Now we can compare all four fractions:

-6/8, 5/8, -5/8, -5/8

We can see that three of the fractions have -5/8 in common, while the other fraction (-6/8) is different. Therefore, the answer to the question is -6/8.

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Note: The question given is incomplete. Here is the complete question.

Question: Which one doesn't belong with the other three? -3/4-5/8 -6/8 5/8

Answer:

400

Step-by-step explanation:

Answer:

≈ 19.63 in³

Step-by-step explanation:

volume of cylinder = πr²h

here, r = 1 in and h = 6.25 in

πr²h ≈ 19.63 in³ because r is in in and h is in in, in² * in = in³

Answer:

c. -14

Step-by-step explanation:

is the highest number out of all of them

Answer: 5

Step-by-step explanation:

You  can only have real outputs for a root when that root is 0 or higher because you can never take the square root of a negative number

\(f(x) = \sqrt{x-5} +2\)              >Under the root must be 0 or greater

x-5 = 0

x= 5

so x must be 5 or greater

The wholesale price isn't given, suppose the wholesale price is $5

Answer:

$6.25 ; 1441.8 pesos

Step-by-step explanation:

Number of items purchased = 24

Wholesale price of item = x

To obtain a 25% profit, the sales price would be :

Wholesale price = wholesale price + 25% of wholesale price

(x = x + 0.25x) per unit

For 24 items :

24x + 0.25 * 24x

Unit wholesale price = 5

24(5) + 0.25*24(5)

= $150

Hence, sale price per unit will be :

$150 / 24

= $6.25

Total profit in pesos :

1 dollar = 48.06 pesos

Total profit = $150 - 24(5) = $150 - $120 = $30

$30 = (30 * 48.06) = 1441.8 pesos

Step-by-step explanation:

dy/dx

= d/dx [x / (1 - x²)]

= [(1 - x²)(1) - (x)(-2x)] / (1 - x²)²

= (1 + x²) / (1 - x²)².

When dy/dx = 1, (1 + x²) / (1 - x²)² = 1.

=> 1 + x² = 1 - x²

=> 2x² = 0, x = 0.

Also when x = 0, y = (0) / [1 - (0)²] = 0.

Hence the coodinates is (0, 0).

Jose can plow 7.5 acres of land in an hour. it will take Jose 12 minutes to plow 1.5 acres of land.

To calculate how long will it take Jose to plow 1.5 acres of land, we can use the following steps:

1: Determine the number of acres Jose can plow per minute. Dividing 7.5 acres by 60 minutes will give us the number of acres Jose can plow in 1 minute:7.5 ÷ 60 = 0.125 acres/minute

2. Determine the number of minutes it will take Jose to plow 1.5 acres of land. To calculate the number of minutes, we can divide the number of acres by the acres Jose can plow in 1 minute: 1.5 ÷ 0.125 = 12 minutes

Therefore, it will take Jose 12 minutes to plow 1.5 acres of land.

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Answer:

64 degrees

Step-by-step explanation:

since x is corresponding to 64, they are congruent.

Answer:

x = 64

Step-by-step explanation:

x and 64° are corresponding angles and are congruent , then

x = 64

a) Since the triangles are congruent, and ΔABC is congruent to ΔDEF, segments AB and DE have the same value. Therefore, you can use algebra to solve for x when using the knowledge that (12 - 4x) is equal to (15 - 3x).

To solve:

12 - 4x = 15 - 3x

12 = 15 + x

-3 = x

Therefore, x is equal to -3.

b) To find the value of AB, plug in the value of x found in part a).

12 - 4x

12 - 4(-3)

12 - (-12)

12 + 12 = 24

Thus, segment AB is equal to 24.

c) As shown in part b), plug in the value of x found in part a) to find the value of segment DE.

15 - 3x

15 - 3(-3)

15 - (-9)

15 + 9 = 24

Thus, segment DE is also equal to 24.

We can confirm the knowledge of the equal side lengths because the triangle are congruent. This means that all the side lengths in the triangle are the same, which is confirmed when algebraically plugging in the value of x to solve for the values of the segments AB and DE.

I hope this helps!

Answer:

Step-by-step explanation

wow, never seen this before

Answer:

Step-by-step explanation:

Answer:

Degrees = Radians x 180/π

or

Degrees = 57.2958  x radians

Step-by-step explanation:

1 radian = 180/π degrees

1 radian = 57.2958 degrees

Multiply radians by this factor of 57.2958  to get the equivalent measure in degrees

π radians = 180°

2π radians = 360° which is the number of degrees in a circle

For anything greater than 2π radians you will have to subtract 360°

For example, 7 radians using the formula is 7 x (57.2958  ) ≈ 401.07°

But this still falls in the first quadrant, so relative to the x-axis it is
401.07 - 360 = 41.07°

Take 2 points from the graph in order to find slope

for example I take (2,4) and (-2,-2)

\(m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{ - 2 - 4}{ - 2 - 2} \\m = \frac{ - 6}{ - 4} \\ m = \frac{6}{4} \\ = \frac{3}{2} \)

slope is 3/2

Answer:

Kiran's Aunt will be 32

Step-by-step explanation:

When Kiran was born her/his Aunt would be 17 as the problem says, so just add 15 to 17 to make 32; therefore Kiran's Aunt is 32 years old when Kiran is 15 years old. :)

Answer:

She would be 32 years old.

Step-by-step explanation:

Hope this helps.

uniform distribution are (3) P(X > 0.5) = (1 - 0.5) / (1 - 0) = 0.5. (4) P(X > 0.7 | X > 0.2) = 0.3 / 0.8 = 0.375.

Uniform distribution is a continuous probability distribution that is characterized by a constant probability density function between two parameters. In this case, the parameters for the uniform distribution X are 0 and 1.

To verify if uniform distribution has memoryless property, we need to check if the probability of an event occurring in the future is independent of the time that has already passed. The memoryless property states that the conditional probability of an event occurring in the future given that it has not occurred in the past is the same as the unconditional probability of the event occurring in the future.

For Question 3, we need to find the probability that X is greater than 0.5. Since X follows a uniform distribution between 0 and 1, the probability can be calculated as the area under the curve of the probability density function between 0.5 and 1. Therefore, P(X > 0.5) = (1 - 0.5) / (1 - 0) = 0.5.

For Question 4, we need to find the probability that X is greater than 0.7 given that X is greater than 0.2. Using Bayes' theorem, we can calculate this as follows:

P(X > 0.7 | X > 0.2) = P(X > 0.7 and X > 0.2) / P(X > 0.2)

Since X follows a uniform distribution, we can simplify this as:

P(X > 0.7 | X > 0.2) = P(X > 0.7) / P(X > 0.2)

Using the formula for a uniform distribution, we can calculate the probabilities as:

P(X > 0.7) = (1 - 0.7) / (1 - 0) = 0.3
P(X > 0.2) = (1 - 0.2) / (1 - 0) = 0.8

Therefore, P(X > 0.7 | X > 0.2) = 0.3 / 0.8 = 0.375.

In conclusion, we can verify that uniform distribution has memoryless property because the conditional probability of an event occurring in the future given that it has not occurred in the past is the same as the unconditional probability of the event occurring in the future.

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the approximate area of the base of the paint can is 53.5 square centimeters.by using Volume formula is Base Area × Height

To find the approximate area of the base of the paint can, we can use the formula for the volume of a cylinder:

Volume = Base Area × Height

We are given the volume (535 cubic centimeters) and the height (10 cm). We need to solve for the Base Area. Rearranging the formula to solve for Base Area, we get:

Base Area = Volume ÷ Height

Now, substitute the given values:

Base Area = 535 cubic centimeters ÷ 10 cm

Base Area ≈ 53.5 square centimeters

So, the approximate area of the base of the paint can is 53.5 square centimeters.

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The approximate area of the base of the can is 53.5 square centimeters

From the question, we have the following parameters that can be used in our computation:

Volume = 535 cubic centimeters of paint

Height of container = 10 cm

The area of the base of the can is calculated as

Base area = Volume/Height

Substitute the known values in the above equation, so, we have the following representation

Base area = 535/10

Evaluate

Base area = 53.5

Hence, the base area is 53.5 square centimeters

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It will take 6 years for the enrollment at both schools to be equal.

To solve this problem, we need to set up an equation to represent the enrollment at both schools over time.

From the problem it can be deduced that

For Central Middle School:

Nichols Middle School

set these two equations equal to each other and solve for x:

800 + 75x = 890 + 60x

Simplifying the equation

15x = 90

Dividing both sides by 15, we get:

x = 6

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Answer:

8.7

Hope this helps <3

Have a great day!

The key is to check whether the given side measures satisfy the triangle inequality theorem or not, if yes then we can create a unique triangle, if no then no triangle can be created, and if the given measures are the perimeter of a triangle, we can create many triangles.

When given three side measures of a triangle, the following scenarios can occur:

Unique triangle: If the three side measures given are the lengths of the three sides of a triangle and they satisfy the triangle inequality theorem, then we can create a unique triangle. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

No triangle: If the three side measures given do not satisfy the triangle inequality theorem, then it is not possible to create a triangle with those side lengths.

Many triangles: If the three side measures given are the perimeter of a triangle, and we are allowed to vary the lengths of the three sides of the triangle within a certain range, then we can create infinitely many triangles.

Example: A triangle with perimeter 12cm, we can create a unique triangle with sides 3,4,5, or we can create many triangle with sides (2,5,5), (4,4,4),(3,4,5) and so on.

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a function that transforms the parent root function with a horizontal compression by a factor of 5 and a downward shift of 10 units is: \(f(x) = \sqrt[n]{5x} -10\)

The function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the another variable).

A function is described as a relationship between a group of inputs and one output each. A function is, to put it simply, a connection between inputs in which each input is connected to exactly one output.

Parent root function is given by:

\(f(x) = \sqrt[n]{x}\)

According to rules-

Combining these 2 transformation gives us the function: \(f(x) = \sqrt[n]{5x} -10\)

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The mean of the recorded times for the 8 participants to solve the puzzle is 20.6 seconds. The median is 20.1 seconds. The 5-number summary consists of the minimum value (15.2 seconds), the first quartile (18.3 seconds), the median (20.1 seconds), the third quartile (22.7 seconds), and the maximum value (29.4 seconds). The box plot visually represents this data distribution. The sample variance is approximately 13.01 seconds squared, and the sample standard deviation is approximately 3.61 seconds.

To find the mean, we sum up all the recorded times and divide by the number of participants: (15.2 + 18.3 + 19.3 + 19.7 + 20.1 + 21.9 + 22.7 + 29.4) / 8 = 164.6 / 8 = 20.6 seconds.

To find the median, we arrange the times in ascending order and locate the middle value. In this case, the middle value is the 4th number: 19.7 seconds. Therefore, the median is 20.1 seconds, which is the average of the two middle values.

The 5-number summary helps summarize the data distribution. The minimum value is 15.2 seconds, the first quartile is 18.3 seconds (the median of the lower half of the data), the median is 20.1 seconds, the third quartile is 22.7 seconds (the median of the upper half of the data), and the maximum value is 29.4 seconds.

A box plot visually represents the 5-number summary. It consists of a rectangular box (with lines at the first quartile, median, and third quartile) and "whiskers" extending to the minimum and maximum values. The box represents the interquartile range (IQR), which contains the middle 50% of the data.

To calculate the sample variance, we need to find the squared deviation from the mean for each time and average the squared deviations. The deviations from the mean are as follows: (-5.4, -2.3, -1.3, -0.9, -0.5, 1.3, 2.1, 8.8). Squaring each deviation gives us: (29.16, 5.29, 1.69, 0.81, 0.25, 1.69, 4.41, 77.44). Summing these squared deviations gives us 120.54 seconds squared. Finally, we divide this sum by (n-1) to get the sample variance: 120.54 / (8-1) ≈ 13.01 seconds squared.

The sample standard deviation is the square root of the sample variance. Taking the square root of 13.01 seconds squared gives us approximately 3.61 seconds.

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Answer:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a right triangle to represent the situation:

        |\

        | \

   h    |  \   9 ft

        |   \

        |    \

        |     \

        -------

        6 ft

Here, h represents the height on the wall where the ladder touches. We want to find the angle of elevation θ.

Using the right triangle, we can write:

sin(θ) = h / 9

cos(θ) = 6 / 9 = 2 / 3

We can solve for h using the Pythagorean theorem:

h^2 + 6^2 = 9^2

h^2 = 9^2 - 6^2

h = √(9^2 - 6^2)

h = √45

h = 3√5

So, sin(θ) = 3√5 / 9 = √5 / 3. We can solve for θ by taking the inverse sine:

θ = sin^-1(√5 / 3)

θ ≈ 37.5 degrees

Therefore, to the nearest tenth of a degree, the angle of elevation the ladder makes with the ground is 37.5 degrees.

Farmer Ed has 3,000 meters of fencing and wants to enclose a rectangular plot that borders on a river.The largest area that can be enclosed is 750,000 square meters.

To get the largest area that can be enclosed, we have to find the dimensions of the rectangular plot. Let's assume that the width of the rectangle is x meters.The length of the rectangle can be found by subtracting the width from the total length of fencing available:L = 3000 - x. The area of the rectangle can be found by multiplying the length and width:Area = L × W = (3000 - x) × x = 3000x - x²To find the maximum value of the area, we can differentiate the area equation with respect to x and set it equal to zero.

Then we can solve for x: dA/dx = 3000 - 2x = 0x = 1500. This means that the width of the rectangle is 1500 meters and the length is 3000 - 1500 = 1500 meters.The area of the rectangle is therefore: Area = L × W = (3000 - 1500) × 1500 = 750,000 square meters. So the largest area that can be enclosed is 750,000 square meters.

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