The figures below are similar. Find the length of the missing side.
90
10
7
Х
36
4
14
126
X=

Answer:

\(6x -2\frac{1}{2}\)

Step-by-step explanation:

\(4x + \frac{1}{2} + 2x - 3\)              Addition of like terms

\(6x + \frac{1}{2} - 3\)                      Addition of content terms  

\(6x -2\frac{1}{2}\)

The Multiplication property of equality refers to a mathematical concept that states that if two quantities are equal, then multiplying both sides of an equation by the same number will still result in an equal equation.


To understand and apply the multiplication property of equality, you can follow these steps:

1. Identify the given equation or problem that involves multiplication.
2. Determine the desired outcome or solve for a specific variable.
3. Use the multiplication property of equality to simplify or solve the equation.
  - If you multiply both sides of the equation by the same number, the equation will still hold true.
4. Simplify both sides of the equation by performing the multiplication.
5. Continue solving or simplifying the equation until you obtain the desired solution or value.

Remember, it's important to work through the problem step by step and show your work. This will help you understand the concept and ensure accuracy in your answers. If you're having trouble with a specific problem, feel free to ask for assistance by providing the equation or problem details.

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A statement which describes a translation that would produce ΔDEF from the pre-image of triangle ΔABC include the following: A. To the right five units, and up two units.

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Next, we would determine the translation rule as follows;

ΔABC → ΔDEF = (2 + 5, 1 + 2) = D (7, 3)

ΔABC → ΔDEF = (4 + 5, 4 + 2) = E (9, 6)

ΔABC → ΔDEF = (4 + 5, 1 + 2) = F (9, 3)

Therefore, the translation rule is given by this mathematical expression ΔABC → ΔDEF = (x + 5, y + 2). This ultimately implies that, triangle ABC (ΔABC) was translated by five units to the right and up two units in order to produce triangle DEF (ΔDEF).

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Given :

Ruth wants to buy a skateboard for $44.

She has $100 in her account. She spent $11.36 to buy stationary.

She also wants to buy some comic books for $3.72 each.

To Find :

The maximum number of comic books, n, that Ruth can buy so that she has enough money left to buy the skateboard.

Solution :

Money left after buying skateboard and stationary is :

Money left = $(100 - 11.36 - 44)

Money left = $44.64

Number of comic she can buy is :

\(n = \dfrac{44.64}{3.72}\\\\n = 12\)

Therefore, she can buy a maximum of 12 books.

Hence, this is the required solution.

Answer:

12

Step-by-step explanation:

c = 11.05 ≈ 11 cm. When the diagonal length for the rectangular prism is given is to the nearest whole unit, the correct answer is B.

A quantity known as length has the ability to calculate approximate distance between two areas. In addition to height the breadth, it creates an object's length. Children will learn about length in math lessons to help them solve practical challenges both inside and outside of the classroom. the length or width that is possible to measured; a thing's greatest or longest dimension. 10 feet in length. Table of Metric units, Metric System Table: The length characteristic. The quantity or measurement between two points is the definition of length. In other words, a geometric arrangement or object's largest two or highest three dimensions.

given

Start by calculating the length of the base's diagonal using the Pythagorean theorem:

a² + b² = c²

Fill in the equation with the length and width:

8² + 3² = c²

64 + 9 = c²

73 = c²

c ≈ 8.54 cm

Using our estimated diagonals for the base and the height, we can now determine the prism's diagonal's length. Apply the same formula:

(8.54)² + 7² = c²

73 + 49 = c²

122 = c²

√122 = c

c = 11.05 ≈ 11 cm. When the diagonal length for the rectangular prism is given is to the nearest whole unit, the correct answer is B.

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The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.

An equation is an expression that shows the relationship between two or more variables and numbers.

The area of big sector = (60/360) * π(10)² = (50π /3) cm²

Area of small sector = (60/360) * π(x)² = (x²π /6) cm²

Unshaded area = (x²π /6) cm²

Shaded area = (50π /3) - (x²π /6) = (100π - x²π) /6

Shaded area = unshaded area

(100π - x²π) /6 = (x²π /6) cm²

x = 7.07

The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.

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The length of x in the sector is 7.08 cm.

area of a sector = ∅ / 360 × πr²

where

Therefore,

area of a sector = 60 / 360 × π × 10²

area of a sector = 60 / 360 × π × 100

area of a sector = 6000 / 360 π

Hence,

area of the unshaded portion = 6000 / 360 π ÷ 2 = 6000π / 720 =  26.1666666667 = 26.2 cm

Hence,

26.2 = 60 / 360 × 3.14 × x²

x² = 26.2 / 0.52333333333

x = √50.0637261552

x = 7.07557064836

x = 7.08 cm

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Answer:

Step-by-step explanation:

Let's verify:

This is less than $100, so the answer is no

Answer:

n=170

Step-by-step explanation:

add 27 to 143

then the equation is n=170

Answer:

B

Step-by-step explanation:

Answer:

0.16666666666 is the answer of two thirds take away one half.

Answer:

A

Step-by-step explanation:

if it's not I'm sorry but that is the most logical answer:)

9514 1404 393

Explanation:

1) 2x^2 -5x -3 = 0 . . . . standard form equation

To convert this to factored form, you can look for factors of the product (2)(-3) that have a sum of -5. It can help to start by listing the ways that -6 can be factored. Since we want the sum of factors to be negative, we want to have larger negative factors.

  -6 = (1)(-6) = (2)(-3)

The sums of these factor pairs are -5 (what we want) and -1 (not relevant). We can call these factors p=1 and q=-6.

If a = 2 is the leading coefficient of our standard form quadratic, we want to use these factors in the form ...

  (ax +p)(ax +q)/a . . . . . factored form of the quadratic

  (2x +1)(2x +(-6))/2 . . . .fill in the values we know

  (2x +1)(x -3) . . . . . . .  factor 2 from the second binomial

So, the factored form of the quadratic equation is ...

  (2x +1)(x -3) = 0 . . . . factored form equation

__

2) f(x) = x^2 +7x +10 . . . . standard form quadratic function

Using the thinking process described above, we are looking for factors of 10 that have a sum of 7. We know those are 2 and 5. So, the factored form of the function is ...

  f(x) = (x +2)(x +5) . . . . . . factored form quadratic function

The leading coefficient is 1, so we have no further work to do.

Roots, x-intercepts, zeros

The graph attached below shows this function crosses the x-axis when x=-2 and x = -5. These values of x are variously called "roots", "x-intercepts", and "zeros" of the function. They are values for which the factors and the function are zero. (x+2=0 when x=-2, for example)

Solutions

Often, we are interested in solving the equation ...

  f(x) = 0

For that equation, the solutions are the zeros or x-intercepts or roots. The graph attached also shows solutions for ...

  f(x) = 4

Those solutions are x = -6 and x = -1. The function value is not zero for these values of x, so the roots, x-intercepts, or zeros are not solutions to this equation.

Answer:

when we roll two dice, the possibility of getting number 4 is (1, 3), (2, 2), and (3, 1).

Step-by-step explanation:

The probability of rolling two dice and getting a sum of 4 is 1/12. Let's find how likely we get a sum of 4 when we roll two dice simultaneously. So, when we roll two dice there are 6 × 6 = 36 possibilities. So....when we roll two dice, the possibility of getting number 4 is (1, 3), (2, 2), and (3, 1).

The probability that the sum of the faces is 4, given that the first die rolled is odd will be 1/18.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences. Then the probability is given as,

P = (Favorable event) / (Total event)

If two dice are rolled. The sample for the two dice is given as,

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

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

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

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

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

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

The probability that the sum of the faces is 4, given that the first die rolled is odd is calculated as,

P = 2/36

P = 1/18

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The situation in which it is safe to employ t-procedures is described by option (c) where both samples are approximately normal.

option (c) is identified as the situation where it is safe to use t-procedures.

t-procedures are appropriate when certain assumptions are met, including the assumption of normality of the population or sample distributions. Option (c) states that both samples are approximately normal, which fulfills this requirement. This means that the data in both samples have a symmetric bell-shaped distribution, allowing t-procedures to be used for hypothesis testing or confidence interval estimation.

Options (a), (b), and (d) describe scenarios where either one or both samples are moderately skewed or contain outliers, which violates the assumption of normality. Skewness and outliers can impact the validity of t-procedures, making them less reliable. Therefore, these options do not fulfill the requirement for safely employing t-procedures.

Option (e) states that it is safe to use t-procedures in more than one of the situations above. However, based on the analysis provided, only option (c) meets the criteria of having both samples approximately normal, making it the only situation where t-procedures can be safely employed.

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Answer:

70

Step-by-step explanation:

Step 1:

a² + b² = c²

Step 2:

56² + 42² = 4900

Step 3:

4900 ÷ 70 = 70

Answer:

70

Hope This Helps :)

Answer:

-3(2) = -6

Step-by-step explanation:

Simply multiply -3 and 2 to check his answer.

Answer:

-6 = -3*2

Step-by-step explanation:

–6 ÷ 2 = -3

Multiply each side by 2

–6 ÷ 2*2 = -3*2

-6 = -3*2

Answer: 12.5

Step-by-step explanation: 2times 12.5 is 25

Answer:

5 days

Step-by-step explanation:

To find out this question, we can subtract the amount she wants to get, 25, by the amount she has, 15:

25 - 15 = 10

So, Jomaya wants to save up $10, and because she saves $2 every day, we can divide:

10 / 2 = 5

So, it will take Jomaya 5 days to save $25

Hope this helps :)

Answer:

you dont have enough information

Step-by-step explanation:

A box contains five cards lettered A,A,B,C,D. If one card is selected at random from the box and NOT replaced, what is the probability that Jill will draw an A and then a C?​

step 1

Find the probability that Jill draw an A

P=2/5

step 2

Find the probability that jill draw a C

P=1/4

therefore

the probability that Jill will draw an A and then a C is

P=(2/5)(1/4)

P=2/20

Answer:

6.4

Step-by-step explanation:

70.4/11

= 6.4

Assuming that the number of moles of solute in a solution follows a normal distribution, the distribution of molarity can be approximated as normal with mean µ and standard deviation σ.

Assuming that the number of moles of solute in a solution follows a normal distribution, the distribution of molarity (M) can also be approximated as normal.

Let n be the number of moles of solute and V be the volume of the solution in liters. Then the molarity M is given by:

M = n/V

Using the rules of propagation of errors, we can find the variance of M in terms of the variances of n and V as:

Var(M) = Var(n)/V^2 + (n^2/ V^4) * Var(V)

Assuming that the variance of the number of moles of solute and the variance of the volume are known, we can use the above formula to calculate the variance of the molarity.

Once we have the mean and variance of the molarity, we can approximate its distribution as normal using the following parameters:

- Mean: µ = E(M)

- Standard deviation: σ = sqrt(Var(M))

Therefore, the distribution of molarity M is approximately normal with mean µ and standard deviation σ.

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Answer:

Step-by-step explanation:

4x+8<2x+2

Subtract 2x from both sides.

4x+8−2x<2

Combine 4x and −2x to get 2x.

2x+8<2

Subtract 8 from both sides.

2x<2−8

Subtract 8 from 2 to get −6.

2x<−6

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

x<  

2

−6  

Divide −6 by 2 to get −3.

x<−3

Hope this helps :)  

Pls make brainliest :3  

And have an amazing day <3

Answer: x < -3

Step-by-step explanation:

The total cost of each utility eliminating 450 tons of pollution is $180,000.

To calculate the total cost for each utility to eliminate 450 tons of pollution, we need to multiply the cost per ton of pollution elimination by the number of tons each utility needs to eliminate.

For People's Electric, the cost of eliminating one ton of pollution is $400. So, to eliminate 450 tons, the total cost would be 450 tons * $400/ton = $180,000.

For Municipal Energy, the cost of eliminating one ton of pollution is $350. Again, to eliminate 450 tons, the total cost would be 450 tons * $350/ton = $157,500.

Therefore, the total cost for each utility to eliminate 450 tons of pollution is $180,000 for People's Electric and $157,500 for Municipal Energy.

The cost calculation is based on the given information that each utility is provided with 450 pollution permits by the government. These permits allow them to legally produce a ton of pollution. By setting a limit on the number of permits, the government aims to reduce pollution by half. The utilities have the option to trade permits with each other.

In this scenario, People's Electric has a higher cost of eliminating pollution per ton compared to Municipal Energy ($400 vs. $350). It means that People's Electric would find it more expensive to reduce pollution through internal measures like investing in cleaner technology or implementing environmental initiatives. On the other hand, Municipal Energy has a lower cost, indicating that they have relatively more cost-effective methods for pollution reduction.

Given these costs, it is more beneficial for People's Electric to purchase permits from Municipal Energy rather than eliminating the pollution themselves. By purchasing permits, People's Electric can meet the pollution reduction target at a lower cost. Conversely, Municipal Energy can generate additional revenue by selling their permits.

This permit trading mechanism allows for cost efficiency in achieving the government's pollution reduction goal. The total cost for each utility is determined by multiplying the cost per ton of pollution elimination with the number of tons they need to eliminate.

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Answer:

8.778 or 8.8

Step-by-step explanation:

20% of 43.89 is 8.778

math: 43.89*(20/100) = 8.778

To determine the number of ways Samantha can arrange her mathematics books and computer science books on the shelf, we can use the concept of permutations.

1. First, we'll arrange the 3 mathematics books in the first 3 positions. Since Samantha has 7 mathematics books to choose from, she can arrange them in 7P3 ways:
7P3 = 7! / (7-3)! = 7! / 4! = 7 x 6 x 5 = 210 ways

2. Next, we'll arrange the 2 computer science books in the last 2 positions. Since Samantha has 5 computer science books to choose from, she can arrange them in 5P2 ways:
5P2 = 5! / (5-2)! = 5! / 3! = 5 x 4 = 20 ways

3. Now, we need to multiply the number of ways to arrange the mathematics books by the number of ways to arrange the computer science books since these are independent events:
Total ways = 210 (mathematics books) x 20 (computer science books) = 4200 ways

So, Samantha can arrange her 7 mathematics books and 5 computer science books in 4200 different ways, with the first 3 positions occupied by math books and the last 2 by computer science books.

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The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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The mean value of the radius (r) at which you would find the electron, given the H atom wave function is 100(r), is 0.

The wave function of an electron in the hydrogen atom, denoted by Ψ, describes the probability distribution of finding the electron at different positions around the nucleus. In this case, the given wave function is 100(r), where r represents the radius.

To calculate the mean value of the radius, we need to evaluate the integral of r multiplied by the absolute square of the wave function, integrated over all possible values of r. However, the wave function 100(r) does not provide a valid description of the hydrogen atom's electron distribution. The wave function should be normalized, meaning that the integral of the absolute square of the wave function over all space should equal 1. In this case, the given wave function lacks normalization.

Since the wave function is not properly normalized, we cannot accurately calculate the mean value of the radius. Without normalization, the probability distribution described by the wave function does not provide meaningful information about the electron's position.

In summary, based on the given wave function, the mean value of the radius cannot be determined without proper normalization of the wave function. A properly normalized wave function is necessary to obtain accurate information about the electron's position.

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The probability that a die will land on an even number at least once when rolled twice is 3/4.

To find the probability that a die will land on an even number at least once when rolled twice, we can use complementary probability.

Step 1: Identify the complementary event.
The complementary event to landing on an even number at least once is that the die lands on odd numbers both times.

Step 2: Calculate the probability of the complementary event.
There are 3 odd numbers (1, 3, and 5) on a standard 6-sided die. So, the probability of landing on an odd number in one roll is 3/6 or 1/2.
For two rolls, the probability of landing on odd numbers both times is (1/2) * (1/2) = 1/4.

Step 3: Calculate the probability of the original event using complementary probability.
The probability of landing on an even number at least once is 1 - the probability of the complementary event,

which is 1 - 1/4 = 3/4.

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The sample tensile strength of fiber specimens will be greater than 75.75 psi in 43.25 percent of cases.

Z-score: Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean. Standard deviation is essentially a reflection of the amount of variability within a given data set.

given that a synthetic fiber used in manufacturing carpet has a tensile strength that is normally distributed with a mean 75.5 psi and standard deviation 3.5 psi

z = (raw score - mean) / (sample standard deviation - standard deviation)

n = 6; mean=75.5 psi; standard deviation=3.5 psi.

For (greater than) > 75.75,

z = (75.75 - 75.5) / (3.5 ÷√6) = 0.17

P(z > 0.17) = 1 - P(z < 0.17) = 1 - 0.5675 = 43.25%

The sample tensile strength of fiber specimens will be greater than 75.75 psi in 43.25 percent of cases.

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