A pitcher holds 8 and one half cups of orange juice and I pour all of the juice evenly into six different glasses. How many cups of juice will there be in each glass?

Final answer:

Triangles A (right obtuse triangle) and B (equilateral scalene triangle) and D (right equilateral triangle) are impossible to draw because their defined characteristics contradict the specific angles and sides that a triangle must have to fit those definitions.

Triangle C (acute isosceles triangle) and E (right scalene triangle) are possible according to the definitions of their angles and sides.

Explanation:

When classifying triangles, the definition of each type of triangle must be considered to determine if it is possible to draw them based on their angles and sides. Here are the classifications:

A right triangle has one 90-degree angle.

An obtuse triangle has one angle greater than 90 degrees.

An acute triangle has all angles less than 90 degrees.

An equilateral triangle has three sides of equal length and three angles each measuring 60 degrees.

A scalene triangle has all sides of different lengths and, correspondingly, all angles are different.

An isosceles triangle has two sides of equal length and two angles that are equal.

Using these definitions:

A right obtuse triangle (A) is impossible because a triangle cannot have a right angle (90 degrees) and an obtuse angle (greater than 90 degrees) at the same time.

An equilateral scalene triangle (B) is impossible because an equilateral triangle has all sides equal, while a scalene triangle has all sides of different lengths.

An acute isosceles triangle (C) is possible as it can have two equal angles that are both acute, and the third angle also being acute.

A right equilateral triangle (D) is impossible because in an equilateral triangle all angles must be 60 degrees, which does not allow for a 90-degree angle.

A right scalene triangle (E) is possible because it can have one 90-degree angle and two other angles that are different from each other and both less than 90 degrees, with corresponding sides being of different lengths.

Answer:

0.004

Step-by-step explanation:

2.704 - The value of the digit 2 is 2 ones, or 2.

2.704 - The value of the digit 7 is 7 tenths, or 0.7.

2.704 - The value of the digit 0 is 0 hundredth, or 0.00.

2.704 - The value of the digit 4 is 4 thousandths, or 0.004.

Final answer:

To earn the prize of 1800 points from the rewards club, you would need to send 360 texts, as you get 5 points for each text.

Explanation:

The problem requires us to find out the number of texts needed to be sent to earn enough points for a prize from the cell phone company's rewards club. Since you receive 15 points for every 3 texts sent, and you need a total of 1800 points for the prize, the calculation is as follows:

First, determine how many points are awarded for one text message by dividing 15 points by 3 texts, which equals 5 points per text.

Next, find out how many texts are needed for 1800 points by dividing 1800 points by 5 points per text, giving us 360 texts.

Therefore, you need to send 360 texts to earn 1800 points and get the prize.

Answer:

Step-by-step explanation:

These angles are equal due to the property of corresponding angles. If there are two parallel lines being intersected with a transversal that means the angles are equal. 3 and 5 are equal because they are alternate interior angles. 4 and 6 are also alternate interior angles.

find 2 numbers when multiplied by each other = 100

sqrt(100) = 10

since the equation has a minus sign

 the answer would be (x+10)(x-10)

The allowance saved by Mike after expenditure will be equal to $43.

Equations are mathematical expressions that have two algebraic symbols on either side of the equal (=) sign.

The equality of the left and right expressions serves as an illustration of this relationship. An easy equation to remember is the left side equals the right side.

As per the data provided in the question,

Let the allowance saved by Mike is x.

Amount received on birthday = $25

And amount left = $34

Then, the equation will be,

(x + 25)/2 = 34

Solve the equation for x,

x + 25 = 38

x = 38 - 25

x = $43

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Mike had saved $43 from his allowance money before receiving $25 for his birthday and spending half of the total amount, leaving him with $34.

Mike initially had a certain amount of allowance money saved. After receiving $25 for his birthday, he then went to a toy store and spent half of his total money. Post-purchase, he has $34 remaining. To find out how much allowance money Mike had originally saved, we need to determine what half of his total money is.

We know that:

Mike has $34 left after spending half his money.

Therefore, before spending, Mike had $34 (the amount left) times 2.

$34 x 2 = $68 was the total amount Mike had before spending.

Since he received $25 for his birthday, the allowance money he had saved before his birthday was $68 - $25.

$68 - $25 = $43 was the amount Mike had saved from his allowance.

The measurement of 84.8 centimeters in scientific notation is represented as 8.48 x 10² centimeters.

To express the length of an object measured as 84.8 centimeters in scientific notation, we need to place the decimal after the first non-zero digit and count the number of places the decimal has moved. Here, the decimal moves two places to the left, so the exponent will be 2. Therefore, the length in scientific notation is 8.48 x 10² centimeters.

The length of 84.8 centimeters can be written in scientific notation as 8.48 × 101 cm.

To convert the given measurement to scientific notation, move the decimal point to the right until there is only one non-zero digit to the left of the decimal point. Count the number of places you moved the decimal point and use it as the exponent of 10. In this case, we moved the decimal point one place to the right, so the exponent is 1.

Final answer:

The measurement of 84.8 centimeters in scientific notation is 8.48 x 10¹ cm.

Explanation:

The length of the object in scientific notation is 8.5 x 10¹ cm.

Here's the breakdown:

Identify the significant digits: In 84.8 centimeters, both the "8" and the "4" are significant, as they contribute to the precision of the measurement. The trailing "8" is also significant because it's between two significant digits.

Move the decimal: Count the positions from the leading significant digit ("8") to the right until you reach the rightmost significant digit ("8"). In this case, there are 0 positions.

Write the exponent: Since the decimal didn't move, the exponent of 10 will be 0, but we typically write it explicitly as 10⁰.

Combine the coefficient and exponent: Combine the leading significant digit ("8") with the decimal and multiply by 10 raised to the adjusted exponent: 8.5 x 10⁰.

Therefore, the length of the object in scientific notation is 8.5 x 10¹ cm.

Answer: A. 51.9, 52, 49, 6

Step-by-step explanation:

The given data : 49, 49, 54, 55, 52, 49, 55

[tex]{\text{Mean =}\dfrac{\text{Sum of observations}}{\text{Number of observations}}[/tex]

[tex]{\text{Mean =}\dfrac{363}{7}=51.8571428571\approx51.9[/tex]

For Median , first we arrange observations in order.

49, 49, 49, 52, 54, 55, 55

Median = Middlemost observation = 52

Mode = Most repeated observation = 49

Range = Maximum number -Minimum number

[tex]=55-49=6[/tex]

Final answer:

The percent of decrease in Aaron's score from 92 to 84 is calculated by finding the difference, dividing by the original score, and multiplying by 100, which gives approximately 8.7%.

Explanation:

To calculate the percent of decrease in Aaron's score, we first find the difference in scores, then divide by the original score, and finally multiply by 100 to get the percent change. Aaron's score decreased from 92 to 84. So, the difference is 92 - 84 = 8. The percent decrease is then (8 ÷ 92) × 100, which approximates to 8.6956521739%. Rounded to two decimal places, the closest answer is 8.7%. Therefore, the correct option is 8.7.

Following are the calculation to the points:

Given:

x= 3

To find:

points=?

Solution:

Using slop formula:

[tex]\to y= mx+c[/tex]

Then [tex]x = 3[/tex], the function's value is [tex]4[/tex].

Its slope is  [tex]\frac{1}{5}[/tex] and the y-intercept is [tex]3 \frac{2}{5}[/tex].

Therefore, in slope-intercept form (with the unknown value of x)

It is

[tex]\to f(x)=\frac{1}{5} + 3 \frac{2}{5}\\\\\to f(x)=\frac{1}{5} + \frac{17}{5}\\\\\to f(x)=\frac{1+17}{5} \\\\\to f(x)=\frac{18}{5} \\\\[/tex].

Therefore the final answer is "[tex]\frac{18}{5}[/tex]".

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