Insert parentheses so that the expression has a value of 67: 3×5+6×2+1

Final answer:

In mathematics, while a data set can have more than one mode if multiple values share the highest frequency, there is usually only one mean. The mode refers to the most common value, and the mean is the arithmetic average. Statistical tools often help calculate these measures of center.

Explanation:

Yes, there can be more than one mean or mode in a math problem. The mode is the most frequently occurring value in a data set, and a data set can have multiple modes if there are several values with the same highest frequency. When a data set has two modes, it is known as bimodal. In contrast, while there can be more than one solution to an equation (such as in quadratic equations), there is typically only one mean for a given data set. The mean is calculated by adding all the values together and dividing by the number of values. However, the mean can be influenced by skewed data or outliers more than the median or mode.

The measures of center like mean, median, and mode are critical in statistics for summarizing data. They provide different perspectives on the central tendency of the data. The mean is the arithmetic average, the median is the middle value when the data set is ordered, and the mode shows the most frequently occurring value(s). In analyzing data, statistical software or graphing calculators are often used to efficiently calculate these measures of center.

When considering the relationship between the shape of a distribution and the measures of center, typically, the mean is most affected by skewness and outliers. A skewed distribution will pull the mean toward the long tail while the median tends to resist the influence of outliers and skewed data. Mode, being the most frequent value, doesn't necessarily indicate skewness but can reveal frequency patterns within the data set.

7360/3680 = 2

3680/1840 = 2

920/2= 460

 month 5 sales will be 460

The equation can be written as x+4=x^2 is \sqrt{x+4} =x, where x>0.

[tex]\sqrt{x+4} =x[/tex]

If we square both sides of the equation

We can rid of the exponent on the right side and add a square root to

x + 4.

[tex]\sqrt{x+4}=x[/tex]

Squaring on both sides we have,

The square root of a number is that factor of a number that when multiplied by itself gives the original number.

[tex](\sqrt{x+4}})^2=x^2[/tex]

x+4=x^2

Therefore, The equation can be rewritten as x + 4 = x^2.

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The real interest rate that Sally pays the credit card company is 8% a year.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

We are given that;

Balance = $10,000

Interest rate = 17 percent

Now,

The real interest rate is the interest rate that has been adjusted to remove the effects of inflation. According to 1, it can be calculated as:

Real interest rate = nominal interest rate - inflation rate

In this case, the nominal interest rate is 17% and the inflation rate is 9%. Plugging these values into the formula, we get:

Real interest rate = 17% - 9%

Real interest rate = 8%

Therefore, by the given interest the answer will be 8% a year.

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Answer:

[tex]x+11[/tex]

Step-by-step explanation:

In order to simplify this:

[tex]x+15-4[/tex]

You just need to substract like terms:

[tex]15-4=11[/tex]

Hence, the simplified is expression is:

[tex]x+11[/tex]

This represents a line which intercepts with the y-axis at 11 and with the x-axis at -11. I attached you the graph.

The simplified form of the expression is x + 11.

To simplify the expression "x + 15 - 4", you just need to do the addition and subtraction operation:

x + 15 - 4 = x + 11

Simplifying an expression means to make it as easy to understand as possible. This can involve combining like terms, removing unnecessary parentheses, and using the distributive property.

In the expression x + 15 - 4, the like terms are x and 15. These terms can be combined to give x + 11. The parentheses around the 15 are unnecessary, so they can be removed. The simplified expression is x + 11.

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Answer:

[tex]2x^3-11x^2+16x-3[/tex]

Step-by-step explanation:

We have been given an expression [tex](x-3)(2x^2-5x+1)[/tex]. We are asked to find the product of our given expression.

Upon using distributive property, we will get:

[tex]x(2x^2-5x+1)-3(2x^2-5x+1)[/tex]

[tex]x*2x^2-x*5x+x*1-3*2x^2-3*-5x-3*1[/tex]

[tex]2x^3-5x^2+x-6x^2+15x-3[/tex]

Upon combining like terms, we will get:

[tex]2x^3-5x^2-6x^2+15x+x-3[/tex]

[tex]2x^3-11x^2+16x-3[/tex]

Therefore, the product of our given expression would be [tex]2x^3-11x^2+16x-3[/tex].

Answer:

50%

Step-by-step explanation:

The next table display all possible outcomes.

penny | dime

head   | head  

head   | tail

tail       | head

tail       | tail

If each single outcome is equally likely and there are 4 options , then all outcomes has a probability of 1/4 = 0.25 or 25%. The probability of getting one head and one tail is 50% because it's obtained by two outcomes.

To solve the given system of equations using elimination, multiply the first equation by 2 to make the coefficients of 'x' the same in both equations. Then solve for 'x' and substitute the value into the first equation to solve for 'y'. The solution is x = -8 and y = -11.

To solve the given system of equations using elimination, first multiply the first equation by 2 to make the coefficients of 'x' the same in both equations.

10x = -50 + 10y

Next, subtract the equation obtained in step 1 from the second equation.

10y = 42 + 2x - (-50 + 10y)

Simplify the equation and solve for 'x'.

x = -8

Substitute the value of 'x' into the first equation to solve for 'y'.

5(-8) = -25 + 5y

y = -11

Therefore, the solution to the system of equations is x = -8 and y = -11.

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The German invasion of Poland on September 1st 1939 caused Britain to declare war on Germany two days later, starting the war.

The value of the given expression is 133.

Simplification involves taking complicated mathematical expressions and simplifying them. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given expression 73+3(23−13)2 is termed as E and will be solved as below:-

Use the concept of PEMDAS. Here, the PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

E = 73+3(23−13)2

E = 73 + 3 ( 10 ) 2

E = 73 + 6 ( 10 )

E = 73 + 60

E = 133

Therefore, the value of the given expression is 133.

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A triangle with sides of lengths x^2-1, 2x, and x^2+1 is a right triangle as confirmed by the Pythagorean theorem. By squaring these lengths and simplifying the resulting equation, it's shown that the squares of the lengths of the two shorter sides sum up to the square of the length of the longest side.

To prove that a triangle with sides of lengths x^2-1, 2x, and x^2+1 is a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Therefore, if x^2-1 and 2x are two sides of the triangle and x^2+1 is the hypotenuse, then the equation becomes:

(x^2-1)^2 + (2x)^2 = (x^2+1)^2

If this equation is true, then we have a right triangle. Let's simplify the equation:

x^4 - 2x^2 + 1 + 4x^2 = x^4 + 2x^2 + 1

After simplifying, we get that 2x^2 equals 2x^2, which confirms that we indeed have a right triangle.

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8 divided by 97 equals 0.082

I stopped after getting the 2, so not sure what the next number would've been

( I didn't use a calculator)

The conjecture is true; by determining the pattern of increasing differences between consecutive numbers (increasing by 3), we can conclude that adding 12 to the last number, 13, gives us the next number in the sequence, which is 25.

The conjecture that the next number in the sequence -5, -2, 4, 13 is 25 can be tested by looking at the pattern of how the numbers are increasing. To do this, let's look at the differences between the numbers:

We see that the differences between the numbers are increasing by 3 each time (3, 6, 9). Therefore, if we continue this pattern, the next difference should be 9 + 3 = 12. If we add 12 to the last number in the sequence, 13, we get:

13 + 12 = 25

Therefore, the conjecture is true. The next number in the sequence is indeed 25.

Answer:

The answer is 2.

Step-by-step explanation:

In order to determine the value of the expression, we have to know about absolute value function.

The absolute value function is a function that only change the sign into positive and maintain the values. It is represented by " | x | " where x can be any number.

For example, if [tex]x=-2[/tex]

[tex]|x|=|(-2)|=2[/tex]

In this case, we have the next values:

[tex]a=5\\b=-3\\\\|a|-|b|\\|5|-|(-3)|\\5-3\\2[/tex]

Finally, the value of the expression is 2.