Which graph shows the solution to the inequality |x+3|<2?

Answer:

x = -2, y = 3

Step-by-step explanation:

Given equations are,

4x + 5y = 7 ---------(1)

3x - 2y = -12 ----------(2)

Multiply equation (1) by 3

12x + 15y = 21 ------(3)

Multiply equation (2) by (-4)

-12x + 8y = 48 --------(4)

Now add equations (3) and (4),

(12x + 15y) + (-12x + 8y) = 21 + 48

(12x - 12x) + (15y + 8y) = 69

23y = 69

y = 3

From equation (2),

3x - 2(3) = -12

3x - 6 = -12

3x = 6 - 12

x = -2

Therefore, x = -2 and y = 3 will be the answer.

Answer:

What is the solution to this system of equations?

\(4x +5y = 7\)

\(3x-2y=-12\)

The solution is ✔ \((-2,3)\) .

You can form 56,800 possible teams from a pool of 16 eligible engineers by selecting a total of 3 team members.

The total number of teams can be calculated using combination formula. The combination formula is nCr where n is the total number of items and r is the number of items you want to choose.

In this case, n = 16 and r = 3. Hence, the number of possible teams:

This means you can form 56,800 unique teams by choosing 3 engineers out of 16 eligible engineers. The combination formula helps in finding the number of possible combinations when the order does not matter, which is the case here as the order of engineers in a team does not matter.

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Answer:

Step-by-step explanation:

You didn't give your options, but it doesn't matter. We'll find all the possibilities and then you can pick it from your list.

When I teach this in Algebra 2, I call it the "the c over d thing" and all my students know EXACTLY to what I am referring. "c" is the constant and "d" is the leading coefficient. The combination of c/d give you the possibilities of roots for the polynomial. There are no real roots that a polynomial can have other than the possibilities we find when we do the c/d thing.

Our c is a 20.  All the factors of 20 are as follows (notice that we have both the positive and negative factors):

20: ±1, ±2, ±4, ±5, ±10, ±20

Our d is a 3.  All the factors of 3 are as follows (again, both the + and the -):

3: ±1, ±3 and that's it for 3.

c/d is as follows. Make sure you put ever c over every d!!!:

c/d: ±\(\frac{1}{1}\), ±\(\frac{2}{1}\), ±\(\frac{4}{1}\), ±\(\frac{5}{1}\), ±\(\frac{10}{1}\), ±\(\frac{20}{1}\), ±\(\frac{1}{3}\), ±\(\frac{2}{3}\), ±\(\frac{4}{3}\), ±\(\frac{5}{3}\), ±\(\frac{10}{3}\), ±\(\frac{20}{3}\)

Those are all the possibilities for your roots for that polynomial. As long as the roots are real (and they won't always all be real!), there are no roots but these.

Answer:

its D on edge

Step-by-step explanation:

The statement ''The z-score follows a normal distribution with u = 1 and o=0, which is known as the standard normal distribution.'' is false because the standard normal distribution has a mean (μ) of 0 and a standard deviation (σ) of 1, not the other way around. The z-score is a measure of how many standard deviations a value is from the mean in a normal distribution.

The statement is incorrect. In a standard normal distribution, the mean (μ) is equal to 0 and the standard deviation (σ) is equal to 1, not the other way around. The z-score is a measure of how many standard deviations a particular value is from the mean of a normal distribution.

A standard normal distribution is a specific type of normal distribution with a mean of 0 and a standard deviation of 1. It is often used as a reference distribution for statistical calculations and hypothesis testing.

The z-score allows us to standardize values from any normal distribution and compare them to the standard normal distribution.

Therefore, the correct statement is: The z-score follows a normal distribution with μ = 0 and σ = 1, which is known as the standard normal distribution.

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Answer:

x = -166, y = 34

Step-by-step explanation:

5(x+2y) - 3 = 3x+5

4(x-3y) - 50 = -33y

Open both equations

5x+10y - 3 = 3x+5

2x+10y = 8

4x-12y - 50 = -33y

4x+21y = 50

Now multiply -2 on both sides of 1st equation.

(easier to add both equations.)

-4x+-20y = -16

4x+21y = 50

Add both equations

x cancels out

y = 34

plug y back into other equation to find x

2x + 340 = 8

2x = -332

x = -166

Answer:

y = 34, x = -166

Step-by-step explanation:

Let's simplify the first equation.

5(x + 2y) - 3 = 3x + 5

We can multiply the 5 out:

5x + 10y - 3 = 3x + 5

Now let's isolate x on one side, although you can choose to isolate y if you want to. Subtract 3x on both sides:

2x + 10y - 3 = 5

Add 3 on both sides and subtract 10y on both sides.

2x = 8 - 10y

Divide 2 on both sides.

x = 4 - 5y

Now to the next equation!

4(x - 3y) - 50 = -33y

Multiply 4 out:

4x - 12y - 50 = -33y

Add 12y and 50 on both sides.

4x = -21y + 50

Now divide 4 on both sides!

x = -5.25y + 12.5

Now we have these equations:

x = 4 - 5y

x = -5.25y + 12.5

Therefore 4 - 5y = -5.25y + 12.5

Once again let's isolate the variable. Let's add 5.25y on both sides and subtract 4 on both sides:

0.25y = 8.5

Now multiply by 4 on both sides to bring y's coefficient to 1:

y = 34

Let's substitute the y value into the equation x = 4 - 5y to get x = 4 - 136 = -132

The probability of observing a sample proportion (p) of 0.11 or less, given a population proportion (p) of 0.14 and a sample size (n) of 148, can be determined using the binomial distribution formula. The probability can be calculated using an Excel spreadsheet or other statistical software.

In this case, the probability is approximately 0.0003. This means that the chance of obtaining a sample proportion of 0.11 or less, given a population proportion of 0.14 and a sample size of 148, is very low. The probability value indicates that such an outcome is highly unlikely to occur by chance alone. It suggests that the observed sample proportion significantly deviates from the population proportion, indicating a potential difference between the sample and the population.

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Answer:

35/49 - 3/7 = 2/7

(Brainliest please!!!)

The object fell from a height of approximately 7.057 meters above the ground.


We can solve this problem using the equations of motion for a freely falling object. The equation we’ll use is:
H = (1/2) * g * t^2
Where h is the initial height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time taken to travel the last distance. Rearranging the equation, we get:

H = (24.0 m) + (1/2) * (9.8 m/s^2) * (1.20 s)^2
Calculating this expression, we find that h is approximately 7.057 meters. Therefore, the object fell from a height of approximately 7.057 meters above the ground.

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The required value of x is 22 degrees for the given figure.

Adjacent angles are a sort of additional angle. Adjacent angles share a common side and vertex, such as a corner point. Their points do not overlap in any manner.

As we know that supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.:

According to the given figure, it can be written as follows:

2x + 24 + 6x - 20 = 180

8x + 4 = 180

8x = 180 - 4

8x = 176

x = 176/8

x = 22

Therefore, the required value of x is 22 degrees for the given figure.

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The complete question is as follows:

Find the value of x for the below figure.

First, let's write the distance formula:

Probably we should draw the points to get an image of what we have:

Then, we can calculate the distance between each point, so that we find out if all the sides are equal or different.

Since we have 2 pairs of sides with the same dimension, then we assume that it is a rectangle or a paralelogram.

We can get the slope of two lines in order to know if they are perpendicular or they have certain angle between each other.

Since the slopes are reciprocal and have different sign, we asure that both lines are perpendicular, therefore, we are talking about a rectangle.

Answer:

24

Step-by-step explanation:

6×5=30

6*4=24

you have to find more then half which would be 3:6 so it's more then 15 but less then 30

Answer:

5.00

Step-by-step explanation:

5.00

=======================================================

Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

--------------

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

Answer:

I'm gonna go a little out of order.

To determine b, find where the line crosses the y-axis. If it's positive, put it as " + " and if it's negative, put it as " - ".

To determine m, find two points on the line that are directly on the number. Example, choose (4, 1) instead of (4.1, 5.2). Go up/down and left/right (while making sure to count) until you reach the second number. going up and right will be considered positive while down and left are considered negative.

Using rise/run, put your number for up/down as a numerator over your left/right, which will be a denominator.

Insert m and b and you're good to go!

Answer:

Does this help

Step-by-step explanation:

A coordinate grid has two perpendicular lines, or axes, labeled like number lines. The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the x-axis and y-axis intersect is called the origin.

Answer:

horizontal

Step-by-step explanation:

9514 1404 393

Answer:

  Africa

Step-by-step explanation:

In order, from lowest to highest, the low points are ...

  Antarctica < Asia < Africa < North America < South America < Europe < Australia

The lower continent on your answer choices list is Africa.

The numerical limits for a D grade are 57 and 76. Rounded to the nearest whole number, these limits are 57 and 76 .

The letter grades for a psychology professor are assigned on a test based on the following scheme:

A is given to the top 10% of scores, B is given to scores below the top 10% but above the bottom 64%, C is given to scores below the top 36% but above the bottom 17%, D is given to scores below the top 83% but above the bottom 6%, and F is given to the bottom 6% of scores.

Given that scores on the test are normally distributed with a mean of 69.2 and a standard deviation of 7.7, we need to find the numerical limits for a D grade. The area to the left of the D grade is the area from the bottom 6% to the top 83%. Therefore, the z-score for the bottom 6% is -1.56 and the z-score for the top 83% is 0.94.

Using these z-scores, we can calculate the limits of the D grade

The lower limit of the D grade is given by:

Lower limit = mean + z-score × standard deviation

Lower limit = 69.2 + (-1.56) × 7.7

Lower limit = 56.98

The upper limit of the D grade is given by: Upper limit = mean + z-score × standard deviation

Upper limit = 69.2 + 0.94 × 7.7

Upper limit = 76.13

Therefore, the numerical limits for a D grade are 57 and 76. Rounded to the nearest whole number, these limits are 57 and 76.

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The mean of this probability distribution is 1.55.

To find the mean of a probability distribution, we need to multiply each possible value by its corresponding probability, and then add up these products. So, the mean is:

mean = (0)(0.19) + (1)(0.37) + (2)(0.16) + (3)(0.26) + (4)(0.02)
    = 0 + 0.37 + 0.32 + 0.78 + 0.08
    = 1.55

Therefore, the mean of this probability distribution is 1.55.

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Given:

The mean of the data set is 2.5.

We are asked to calculate the mean absolute deviation (MAD) of the data set.

Formula for MAD:

MAD = ∑ | xi - μ | / n

Where:

μ = Mean of the data set

xi = Data points

n = Number of data points

Calculation for MAD:

Data set: 1, 2, 3, 4, 5

Step 1: Find the deviations of each data point from the mean.

Data point Deviation from mean

1 -1.5

2 -0.5

3 -0.5

4 -1.5

5 -2.5

Step 2: Find the total deviation (absolute value).

Total deviation (absolute value): 1.5 + 0.5 + 0.5 + 1.5 + 2.5 = 6

Step 3: Calculate the mean absolute deviation (MAD).

MAD = Total deviation / Number of data points = 6 / 5 = 1.2

Rounded to the nearest tenth:

MAD ≈ 1.2

Therefore, the mean absolute deviation (MAD) of the given data set is 1.2 (rounded to the nearest tenth).

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Answer:

10 9/64

Step-by-step explanation:

To answer this, multiply '1 3/8 miles' by '7 3/8.'  

The improper fraction form of '1 3/8' is 11/8, and that of 7 3/8 is 59/8.

Multiplying 11/8 by 59/8, we get 649/64, or (as a mixed number) 10 9/64

Answer:

3,696

Step-by-step explanation:

7x24x22 equals 3,696

24x7=168

168x22=3,696

We are given that fifteen boys and fifteen girls entered a drawing for four free movie tickets. We want to find the probability that all four tickets were won by girls.

To solve this problem, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:

The total number of outcomes represents all the possible ways to choose four winners from the thirty participants (boys and girls). We can calculate this using the combination formula:

C(30, 4) = 30! / (4!(30 - 4)!) = 27,405

Here, C(n, r) represents the combination of choosing r objects from a set of n objects.

Favorable outcomes:

We want to determine the number of ways to select all four winners from the group of fifteen girls. This can also be calculated using the combination formula:

C(15, 4) = 15! / (4!(15 - 4)!) = 1365

Probability calculation:

The probability is the ratio of the favorable outcomes to the total number of outcomes. So, we divide the number of favorable outcomes by the total number of outcomes:

P(Girls winning all four tickets) = 1365 / 27,405

Simplifying the fraction, we find:

P(Girls winning all four tickets) = 1 / 20

Therefore, the probability that all four tickets were won by girls is 1/20.

In summary, out of all the possible combinations of selecting four winners from the thirty participants, only one out of every twenty combinations will result in all four tickets being won by girls.

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Answer:

Step-by-step explanation:

2

Same amount of money can buy 95 dinners after 12 years.

Inflation is a decrease in the purchasing power of money, reflected in a general increase in the prices of goods and services in an economy.

Given,

Purchasing power of a fixed quantity of money decreases by 5% every year

It can buy 175 frozen dinners today,

Principal value P = 175 frozen dinners

Rate of decrease R = 5% = 0.05

Time n = 12 years

Equation for the future value

A = P (1- R)ⁿ

Frozen dinners that can be bought in 12 years with same amount

A = 175 ( 1 - 0.05 )¹²

A = 175 (0.95)¹²

A = 175 × 0.540360088

A = 94.5630154 ≈ 95

Hence, 95 frozen dinners can be bought after 12 years with same amount of money.

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Answer:

C

Step-by-step explanation:

arc length is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × \(\frac{80}{360}\) ( r is the radius of the circle )

     = 2π × 7 × \(\frac{8}{36}\)

     = 14π × \(\frac{2}{9}\)

     = \(\frac{28\pi }{9}\) ≈ 9.8 ft ( to 1 decimal place )

The function in the random library that generate a random integer from 0 to the parameter value inclusive is random.randint() function

Functions are another key idea in programming because they let you put a piece of code that performs a specific purpose inside a specified block and then call that code whenever you need it with a single, brief command rather than repeatedly typing the same code.

Code units that are "self contained" and carry out a particular purpose are called functions. Typically, functions "take in," "process," and "return" data and results. Once a function has been developed, it may be utilized countless times.

From the above definition, we get that

The  function in the random library will generate a random integer from 0 to the parameter value inclusive is  random.randint() function

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Therefore, we have indirectly proven that if n is an odd number, and its negation is false, then the original statement "if n is an odd number" is true.

To construct an indirect proof of the statement "if n is an odd number," we assume the negation of the statement, which is "n is not an odd number" or "n is an even number."

In an indirect proof, we aim to derive a contradiction from this assumption. Therefore, we will show that assuming n is an even number leads to a contradiction.

Assume n is an even number. By definition, an even number can be written as 2k, where k is an integer.

Since n is an even number, we can write it as n = 2k for some integer k.

Now, we can consider the parity of n. If n is an even number, it can be divided by 2 without a remainder, which means n is divisible by 2.

However, this contradicts the initial assumption that n is an odd number. By definition, an odd number cannot be divided by 2 without a remainder.

Since assuming n is an even number leads to a contradiction, we can conclude that the negation of the statement "n is not an odd number" is false.

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The expression equivalent to\(-4x^2 + 2x - 5(1 + x)\)  is \(4x^2 + 8x + 5.\)

This expression matches the form \(x^2 + x + c,\) where c = 5.

To simplify the given expression \(-4x^2 + 2x - 5(1 + x)\) and make it equivalent to the expression \(x^2 + x + c,\) where c is a constant term, we need to perform some algebraic operations.

First, let's distribute the -5 to the terms inside the parentheses:

\(-4x^2 + 2x - 5 - 5x\)

Next, we can combine like terms:

\(-4x^2 + (2x - 5x) - 5 - 5x\)

Simplifying further:

\(-4x^2 - 3x - 5 - 5x\)

Now, let's rearrange the terms to match the form \(x^2 + x + c:\)

\(-4x^2 - 3x - 5x - 5\)

To make the leading coefficient positive, we can multiply the entire expression by -1:

\(4x^2 + 3x + 5x + 5\)

Now, we can combine the x-terms:

\(4x^2 + 8x + 5\)

So, the expression equivalent to \(-4x^2 + 2x - 5(1 + x)\) is \(4x^2 + 8x + 5.\)This expression matches the form \(x^2 + x + c,\) where c = 5.

It's important to note that the original expression and the equivalent expression have different coefficients and constants, but they represent the same mathematical relationship.

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Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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An unnormalized relation refers to a table in a relational database that contains more than one row. This means that there are duplicate rows in the table, which violates the rules of normalization.

Normalization is a process in database design that aims to eliminate data redundancy and ensure data integrity. It involves breaking down a database into multiple tables and defining relationships between them. By doing so, we can efficiently store and retrieve data while minimizing inconsistencies.

In an unnormalized relation, duplicate rows can lead to various problems. For example, it can result in data inconsistencies, as updating one instance of a row may not reflect changes in other duplicate rows. Additionally, it can cause unnecessary storage and maintenance overhead.

To normalize an unnormalized relation, we need to identify the functional dependencies in the table and create separate tables for related data. This helps organize the data and reduces redundancy.

In summary, an unnormalized relation is a table in a relational database that has duplicate rows. It is important to normalize such relations to ensure data integrity and efficiency.

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