8.52 > 8.18
Which is the greatest number.

No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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The type of triangle is an obtuse triangle.

A triangle is a 3-sided polygon.Every triangle has three sides and three angles, some of which may be the same. When the angles are thesame, the triangle is called an equilateral triangle.

An obtuse triangle is a type of triangle in which one of it's angles is more than 90°.

An acute triangle is a type of triangle in which none of it's angles is UpTo 90°

Also a right triangle is a type of triangle in which one of the angles is exactly 90°.

Therefore since one of the angles is 110 and it is greater than 90°, the angle is an obtuse triangle.

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The residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5 μm/min is equals to the -2 μm/min.

The residual for each observation in statistics is the difference between predicted values of y (dependent variable) and observed values of y. That is Residual= observed y value − predicted y.

Here, cupric chloride is used to etch circuit boards. The linear regression equation is, y = 2 + (1/5)x

where, x = temperature in °C

y = etching rate in μm/min

Observed value of etching rate of cupric chloride = 5 μm/min for 25°C

To determine the estimated or predicted value of etching rate of cupric chloride, we substite x = 25, in the above linear equation, y = 2 + (1/5)x

=> y = 2 + (1/5)× 25

=> y = 7

So, Predicted Value = 7 μm/min

Observed Value = 5 μm/min.

Residual = Observed Value - Predicted

= 5 - 7 = -2

Hence, required value is -2 μm/min.

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Complete question:

Calculating and interpreting residuals You might need: Calculator Alexander uses cupric chloride to etch circuit boards. He recorded the room temperature, in °C, and the etching rate, in μm/min of the cupric chloride. After plotting his results, Alexander noticed that the relationship between the two variables was fairly linear, so he used the data to calculate the following least squares regression equation for predicting the etching rate from the room temperature: y = 2 + 5/x, What is the residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5 μm/min. ? Show Calculator

Answer:

its B

Step-by-step explanation:

Hey there! I'm happy to help!

Let's write this equation out.

2/3+1/3x=2x

We want to get all of the variables on the left side and all the numbers on the right side so we can see what number x is equal to. First, Let's subtract 2/x from both sides.

2/3+1/3x-2x=0

We subtract 2/3 from both sides.

1/3x-2x=-2/3

We combine our x values.

-5/3x=-2/3

We divide both sides by -5/3.

x=-5

Have a wonderful day and keep on learning! :D

Answer:

B. 10 km. per minute

Step-by-step explanation:

A unit rate is a ratio that is over 1. 10 km. per minute is describing how many km. in one minute. A unit rate can then be used to predict ratios further in a sequence by multiplying the minutes with the 10 km.

Hope that helps!

Answer:

b

Step-by-step explanation:

According the question The approximate probability that more than 200 out of 500 people will be against increasing taxes is approximately 0.0114 or 1.14%.

Given:

- Sample size (n) = 500

- Probability of being against increasing taxes (p) = 0.35

- Probability of being in favor of increasing taxes (q) = 1 - p = 0.65

Mean (μ) and standard deviation (σ) of the binomial distribution:

\(\[\mu = n \cdot p = 500 \cdot 0.35 = 175\]\)

\(\[\sigma = \sqrt{n \cdot p \cdot q} \approx \sqrt{500 \cdot 0.35 \cdot 0.65} \approx 10.95\]\)

To find the probability of more than 200 people being against increasing taxes, we can use the normal approximation to the binomial distribution. Let's calculate the Z-score:

\(\[Z = \frac{{X - \mu}}{{\sigma}} = \frac{{200 - 175}}{{10.95}} \approx 2.28\]\)

Using a standard normal distribution table or calculator, we find that the probability of \(Z > 2.28\) is approximately 0.0114.

Therefore, the approximate probability that more than 200 out of 500 people will be against increasing taxes is approximately 0.0114 or 1.14%.

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The pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²

A pentagonal prism is a prism that has two pentagonal bases like top and bottom and five rectangular sides.

Given that, the volume of a pentagonal prism is 360 in³, with a height of 3 inches,

We need to find the area of the base,

We know that, the volume of a pentagonal prism is =

V = 1/4 √(5(5+2√5)·a²h

Where a is the base edge and h is the height,

360 = 1/4·3 √(5(5+2√5)·a²

1/4·√(5(5+2√5)·a² = 120

Since, the base of a pentagonal prism is a pentagon, and the area of a pentagon = 1/4 √(5(5+2√5)·a²

And we have,

1/4 √(5(5+2√5)·a² = 120

Therefore, the base area is 120 in²

Hence, the pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²

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Based on the graph,

At,

f(2) = 1 (1)

f(9) = 6 (2)

At f(2) = 1,

At f(9) = 6 ,

Equate them to find b, a = a,

Let's find a at f(2) = 1 and the seventh root of 6,

Let's now complete the equation.

The product (5+6)(5-4) can be found using the FOIL method, which stands for First, Outer, Inner, Last. , the product of (5+6)(5-4) is equal to 5.

First, we multiply the first terms of each binomial: 5 multiplied by 5, which gives us 25.

Outer, we multiply the outer terms: 5 multiplied by -4, resulting in -20.

Inner, we multiply the inner terms: 6 multiplied by 5, giving us 30.

Lastly, we multiply the last terms: 6 multiplied by -4, which equals -24.

To find the final product, we combine the results: 25 - 20 + 30 - 24. Simplifying further, we have 5.

Therefore, the product of (5+6)(5-4) is equal to 5.

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Counting from point M (0 unit) on this number line, we can logically deduce that point H is located at -7.

A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.

In Mathematics, there are six (6) common types of numbers and these include the following:

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length. Also, the negative numerical values are positioned at the left from zero while the positive numerical values are positioned at the right from zero.

Note: Each of the tick represents 1 unit.

Therefore, counting from point M (0 unit) on this number line, we can logically deduce that point H is located at -7.

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The missing values are derived from the graph as follows:

3 ) 7, 14, 21, 28, 35

4) 3, 7, 10, 14, 17

5) 1, 21, 10, 49, 19

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

In order to solve for the above values, the best way is to spot the function that exists in the graph which is given as:

F(y) = 3.5x

In the first table, where x = 2

y= 3.5 *2

= 7

This iteration goes on and on and is consistent for all the values.

In the second table,

Where F(y) is known, for example 10.5, then x is derived as:

10.5 = 3.5x (divide both sides by 3.5)

x = 3

This iteration goes on and on and is consistent for all the values.

In the third table, we simply swap the values back and forth using the function F(y) = 3.5x to derive all values.

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Answer:

Do it your self

Step-by-step explanation:

Answer:

A. -3

Step-by-step explanation:

The y-axis is the one going up and down (vertical). The line touches the y-axis at (0,-3)

Around 433.63 would be the correct answer

Answer:is there any choices?

Step-by-step explanation:

Answer:

\(y = 1500 * 1.09^t\)

Step-by-step explanation:

\(\text{It should be clear that the rate of change is non-linear}\)\(\text{, meaning that we can express the function in the following manner}\)

\(\text{y = a * b^t, where a is the initial value and b is the rate of change and t is how}\)\(y = a * b^t,\) \(\text{where a is the initial value and b is the rate of change and t is how many years.}\)

\(\text{Well, year 0 is the rate of change so we can say that a = 1500}\)

\(\text{Next, we divide any two consecutive year balances to find our rate of change:}\)

\(1635/1500 = 1.09\)

\(\text{Therefore, our equation looks like this:}\)

\(y = 1500 * 1.09^t\)

Answer:

y = 1.09^t * 1500

Step-by-step explanation:

After each year, the balance(y) is multiplied by 1635/1500 or 1.09.

From this information, we know that y = 1.09^t * 1500

Answer:

$500

Step-by-step explanation:

100-12=88

88/100=440/x

88x=100(440)

88x=44000

/88.  /88

x=500

hopes this helps

(0,3) , (4,0) are two solution of equation 3x + 4y = 12.

An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two parts, separated by an equal sign (=), with the expressions on either side representing the same value.

Given Linear equation in two variables:

3x + 4y = 12 ----( 1 )

Substitute x = 0 , in equation ( 1 ) ,

3 × 0 + 4y = 12

=> 4y = 12

=> y = 12/4

y = 3

Therefore ,

( x , y ) = ( 0 , 3 )

Substitute y = 0 in equation ( 1 ) ,

3x + 4 × 0 = 12

=> 3x = 12

=> x = 12/3

x = 4

Therefore,

( x , y ) = ( 4 , 0 )

Required two solutions are ( 0 , 3 ) , ( 4 , 0 )

Therefore, (0,3) , (4,0) are two solution of equation 3x + 4y = 12.

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Given:

Required:

To find the limit value of the given function.

Explanation:

Cancel out the same terms from the numerator and denominator.

Now apply the limit.

Final Answer:

The limit value of the given function is

Answer: Let x be the number of race entries. In order to raise at least $55,000, we must have 45x + 17,900 ≥ 55,000 −45x ≥ −37,100 x ≤ -37,100/45 x ≤ 824.44 Therefore, the charity needs 824 or more race entries to raise at least $55,000.

Answer:

D.) 14/9

Step-by-step explanation:

Remove parenthesis and add

8/9 + 2/3

Get LCD of 9

8/9 + 6/9 = 14/9

f(x) = {x, if x < 0

x^2, if x >= 0

This function is defined by two pieces: the formula x for x < 0, and the formula x^2 for x >= 0. The "jump" or change in formula occurs at x = 0.

A) From the given graph we see that, step function has 4 pieces. B) The step function is composed of 3 intervals: (0, 1), [1, 2), [2, 3), and [3, ∞). C) Point is not included in a function, it is indicated by an open circle.

A function that is defined by various equations or formulae on various intervals or portions of its domain is known as a piecewise function. To put it another way, a piecewise function is a function made up of several functions that have been "stitched" together.

A piecewise function is defined on a particular interval or collection of intervals for each piece. A "jump" or change in the formula used to describe the function is commonly indicated by vertical lines that separate the intervals when different parts of the function are described.

A) From the given graph we see that, step function has 4 pieces.

B) The step function is composed of 3 intervals: (0, 1), [1, 2), [2, 3), and [3, ∞).

C) When a point is not included in a function, it is indicated by an open circle; when a point is included in a function, it is indicated by a closed circle.

D) Because each input (weight) translates into exactly one output (postage cost), this is a function. In other words, no two weights that are different from one another have the same shipping price.

E) Because each piece of this piecewise function can be represented by a linear equation of the form y = mx + b, where m and b are constants, the pieces of this piecewise function are linear.

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Answer:

4/12

Step-by-step explanation:

i am not good at this but i will try☺

Answer:

30%

Step-by-step explanation:

To find the percentage of something we decide the amount of things we want to find the percentage off by the total amount of things and then multiply the product by one hundred.

Apple: 4

Total fruit: 12

So,

4/12 = 0.3

The percentage of apples:

30%

Answer: hola

Step-by-step explanation:

The probability that the coin will show tails at least once is 0.56.

To find the probability that the coin will show tails at least once, you can sum the probabilities of getting 1, 3, or 4 tails, as shown in the table:

Probability of 1 tail: 0.25
Probability of 3 tails: 0.25
Probability of 4 tails: 0.06

Now, add these probabilities together:

0.25 + 0.25 + 0.06 = 0.56

So, the probability that the coin will show tails at least once is 0.56.

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I hope it helps you ❤️❤️❤️

Answer:

Step-by-step explanation:

let r be the radius of the circle.

→ We know that in circle , the length of an arc

and the corresponding central angle are proportional.

180 corresponds to πr

120 corresponds to 10π

Then

\(\frac{\uppi r}{180} =\frac{10\uppi }{120}\)

\(\Longrightarrow r=\frac{180\times 10\pi }{120\pi } =\frac{180}{12} =15\)

The correct answer is D. $2.75 / $3.24

To determine how much you should expect to pay for gas in Philadelphia versus Cleveland, we need to compare the transportation expenses in both cities. Based on the given data, the transportation expenses are as follows:

Philadelphia: $117

Cleveland: $106

To calculate the expected gas prices, we need to consider the transportation expenses relative to the national average. The formula to find the expected gas price is:

Expected Gas Price = National Average * (Transportation Expense / National Average)

National Average for gas = $2.59

For Philadelphia:

Expected Gas Price in Philadelphia = $2.59 * ($117 / 92) ≈ $3.30

For Cleveland:

Expected Gas Price in Cleveland = $2.59 * ($106 / 78) ≈ $3.51

Comparing the expected gas prices, we find that:

A. $3.03 / $2.75: This option does not match the expected gas prices in Philadelphia and Cleveland.

B. $1.95 / $2.59: This option does not match the expected gas prices in Philadelphia and Cleveland.

C. $2.34 / $2.75: This option does not match the expected gas prices in Philadelphia and Cleveland.

D. $2.75 / $3.24: This option matches the expected gas prices in Philadelphia and Cleveland.

Therefore, the correct answer is:

D. $2.75 / $3.24

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Answer:

AB is parallel to AC

Step-by-step explanation:

the product of the gradients of perpendicular line should be -1

AB=2/3

AC=-3/2

2/3*-3/2=-1

=-1

The correct statement is,

⇒ AB is perpendicular to AC.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

Points are,

A(0, 0), B(3, 2), and C(−2, 3),

Now, We can find slopes as;

AB = (2 - 0) / (3 - 0)

AB = 2/3

AC = (3 - 0)) / (- 2 - 0)

AC = - 3/2

Hence, AB is perpendicular to AC.

Thus, The correct statement is,

⇒ AB is perpendicular to AC.

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