Answer:
[tex].06 = \frac{6}{100} = \frac{3}{50} [/tex]
a square and a rectangle have the same perimeter.the square has a side length of 8xunits.the rectangle has a length of 5x+8 and a width of 10 units .what will be the perimeter of both square and rectangle
The area of the ice surface of a skating rink is about 221 yd2. The rink is about the shape of a rectangle where the ice-surface width is 4 yd longer than its length. Find the dimensions of the surface
"The dimensions of the ice surface are approximately 25 yd in length and 29 yd in width.
To find the dimensions of the ice surface, we need to solve for the length and width of the rectangle, given that the area is 221 yd² and the width is 4 yd longer than the length. Let's denote the length of the rink as l and the width as w. We can then set up the following equations based on the given information:
1. The area of a rectangle is given by the product of its length and width, so we have:
[tex]\[ l \times w = 221 \][/tex]
2. The width is 4 yd longer than the length, so we have:
[tex]\[ w = l + 4 \][/tex]
Now we can substitute the second equation into the first equation to express the area solely in terms of the length I:
[tex]\[ l \times (l + 4) = 221 \][/tex]
Expanding the equation, we get:
[tex]\[ l^2 + 4l = 221 \][/tex]
Rearranging the terms to set the equation to zero, we have a quadratic equation:
[tex]\[ l^2 + 4l - 221 = 0 \][/tex]
To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring, we look for two numbers that multiply to -221 and add up to 4. These numbers are 13 and -17. So we can rewrite the equation as:
[tex]\[ (l + 17)(l - 13) = 0 \][/tex]
Setting each factor equal to zero gives us two possible solutions for l:
[tex]\[ l + 17 = 0 \quad \text{or} \quad l - 13 = 0 \] \[ l = -17 \quad \text{or} \quad l = 13 \][/tex]
Since a negative length does not make sense in this context, we discard l = -17 and take l = 13 yd as the length of the rink.
Now we can find the width w by adding 4 yd to the length:
[tex]\[ w = l + 4 \] \[ w = 13 + 4 \] \[ w = 17 \][/tex]
However, we made a mistake in the factoring process. The correct factors of 221 that add up to 4 are 17 and 13, not -17 and 13. The correct length should be 13 yd, and the width should be:
[tex]\[ w = l + 4 \] \[ w = 13 + 4 \] \[ w = 29 \][/tex]
Therefore, the correct dimensions of the ice surface are 13 yd in length and 29 yd in width.
In a six-sided dice game, a prize is won if the arithmetic mean of number rolled is 3.25-3.75. In a second game, a prize is won if the arithmetic mean is more than 4.5. In which game would you rather roll the dice 20 times or 200 times
For rolling the dice 200 times, the same logic applies. Regardless of the number of rolls, the game with the higher probability of winning, which is the second game, is preferred.
To determine which game is more favorable for rolling the dice, we need to calculate the expected value for each game. The expected value represents the average outcome of rolling the dice.
For the first game, the possible outcomes are integers between 1 and 6. The arithmetic mean should be between 3.25 and 3.75 to win a prize. So, we need to find the probability of rolling numbers that satisfy this condition.
Let's denote [tex]\( p_1 \)[/tex] as the probability of winning the first game. To find [tex]\( p_1 \)[/tex], we calculate the probability of rolling numbers between 13 and 18 (inclusive) since the sum of these numbers falls within the range of 3.25 to 3.75.
[tex]\[ p_1 = \frac{6}{6^2} = \frac{1}{6} \][/tex]
For the second game, we need the arithmetic mean to be more than 4.5. This means the sum of the numbers should be more than [tex]\( 4.5 \times 6 = 27 \)[/tex]. Since the maximum sum of rolling six dice is 36, all outcomes satisfy this condition.
Let's denote [tex]\( p_2 \)[/tex] as the probability of winning the second game. Since all outcomes are favorable, [tex]\( p_2 = 1 \)[/tex].
Now, we calculate the expected values for each game:
[tex]\[ E_1 = p_1 \times \text{Prize amount for game 1} \][/tex]
[tex]\[ E_2 = p_2 \times \text{Prize amount for game 2} \][/tex]
Given that the prize amount is the same for both games, we can compare the expected values directly.
For rolling the dice 20 times:
[tex]\[ E_1 = \frac{1}{6} \times \text{Prize amount} \][/tex]
[tex]\[ E_2 = 1 \times \text{Prize amount} \][/tex]
Since [tex]\( \frac{1}{6} \)[/tex] is less than 1, it's better to choose the game with the higher probability, which is the second game.
For rolling the dice 200 times, the same logic applies. Regardless of the number of rolls, the game with the higher probability of winning, which is the second game, is preferred.
The complete question is:
In a six-sided dice game, a prize is won if the arithmetic mean of number rolled is 3.25-3.75. In a second game, a prize is won if the arithmetic mean is more than 4.5. In which game would you rather roll the dice 20 times or 200 times
how do you get the percent of 20% off 7.12
3/7x + 4 = -1/2
explain pls
Karleigh walks 5/8 mile to school every day. How far does she walk to school in 5 days?
____________________
What force would be required to accelerate a 1,100 kg car to 0.5 m/s2?
Answer:550(N)
Step-by-step explanation:
Answer:
550 N
Step-by-step explanation:
I got the answer right.
A scale drawing of a house addition shows a scale factor of 1 in. = 3.3 ft. Josh decides to make the house addition smaller, and he changes the scale of the drawing to 1 in. = 1.1 ft. What is the change in the scale factor from the old scale to the new scale? Help Please!!
The change in the scale factor from the old scale to the new scale is option A; 3 to 1.
What is Scale?The ratio used to depict the relationship between the dimensions of a model or scaled figure and the corresponding dimensions of the real figure or object is called the scale. On the other hand, a scale factor is a value that is used to multiply all of an object's parts in order to produce an expanded or decreased figure.
Given, A scale drawing of a house addition shows a scale factor of 1 in. = 3.3 ft.
Since Josh decides to make the house addition smaller,
he changes the scale of the drawing to 1 in. = 1.1 ft.
Old: 1 inch = 3.3 feet.
New: 1 inch = 1.1 feet.
Old; 3.3 / 1.1 = 3.
New; 1.1 / 1.1 = 1
The change in the scale factor from the old scale to the new scale is option A; 3 to 1.
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Lemonade is sold in 2 L bottles how many millimeters are in a 2 L bottle of lemonade
Hey Siri has to water towers one tower hold 7.35×10 to the fifth power gallons of water in the other tower holds 9.78×10 to the fifth power gallons of water what is the combined water capacity of a two Towers
Final answer:
To find the combined capacity of the two water towers, you add their capacities together by summing the significant figures and keeping the exponent the same. The result is a combined water capacity of 17.13×105 gallons.
Explanation:
The question involves adding two large numbers that are expressed in scientific notation. To find the combined water capacity of the two water towers, we simply add the quantities together. The first tower holds 7.35×105 gallons, and the second tower holds 9.78×105 gallons.
To combine these:
Add the significant figures (the numbers before the exponent): 7.35 + 9.78.
Calculate this sum: 7.35 + 9.78 = 17.13.
Since both powers of ten are the same (105), you can keep the exponent as is.
Combine the significant figures with the exponent to get the final answer: 17.13×105 gallons.
This is the total combined water capacity of the two towers.
Use completing the square to solve for x in the equation (x-12)(x+4)=9.
a. x = –1 or 15
b. x = 1 or 7
c. x=4+√41
d. x=4+√73
Answer:
The correct answer is
D
Help me with 1-6 please
the market value of Christine and genes home is 275,000 the assessed value is 230,000 the annual property tax rate is 17.50 per $1,000 Us in value what is the property tax on their home
To calculate the property tax on Christine and Gene's home, multiply the tax rate of 0.0175 (converted from $17.50 per $1,000) by the assessed value of $230,000. The annual property tax on their home would be $4,025.
Explanation:The student is asking how to calculate the property tax on Christine and Gene's home. To calculate this, you need to use the assessed value of the property and the property tax rate. Here is the step-by-step calculation:
Property tax rate = $17.50 per $1,000 of assessed value.Assessed value of the home = $230,000.To find the property tax, convert the tax rate to a decimal by dividing by 1,000, resulting in 0.0175 ($17.50 / $1,000).Multiply the resulting decimal by the assessed value: Property tax = 0.0175 * $230,000.The calculation is:
Property tax = 0.0175 * $230,000 = $4,025
Therefore, the annual property tax on their home is $4,025.
ana tiene 5000000 en una cuenta bancaria. le dan un interes de 3.2%, ¿cuanto dinero trndra dentro de 2 meses y 10 dias ( todos los meses tienes 30 dias)
please help with 7,8,9
The length of an equilateral triangle is increased by 7 inches, so the perimeter is now 36 inches. Find the original length of each side of the equilateral triangle.
Which best summarizes the Pythagorean theorem
The Pythagorean theorem, usually applied in right-angled triangles, states the square of the hypotenuse equals the sum of the squares of the other two sides. This can be summarized by the equation: a² + b² = c². It is a fundamental principle in geometry.
Explanation:The Pythagorean theorem is a mathematical principle that applies specifically to right-angled triangles. The theorem, credited to the ancient Greek philosopher Pythagoras, stipulates that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship can be represented by the equation: a² + b² = c², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
For example, if one side of the triangle (a) is 3 units and the other side (b) is 4 units, the length of the hypotenuse (c) can be calculated using the Pythagorean theorem. The calculation would be set as follows: 3² + 4² = c². When solved, it results in c = √(3² + 4²) = √(9 + 16) = √25 = 5 units. Therefore, the length of the hypotenuse in this case is 5 units.
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the volume of the sphere is 500/3 pie cubic units . what is the value of X?
How do you do this problem? It isn't C is all I know.
In the living world, there is a great deal of genetic variation. The genetic information of dogs differs from the genetic information of cats. The genetic information of plants differs from the genetic information of bacteria. Your genetic information differs from your father's genetic information, and so on.
I'm having trouble answering this question and the 2/3 confuses me
Simplify to create an equivalent expression.
(4+2k)⋅6+3k =
To simplify the expression (4+2k)⋅6+3k, distribute 6 to both terms inside the parentheses and combine like terms.
Explanation:To simplify the expression (4+2k)⋅6+3k, we need to distribute the 6 to both terms inside the parentheses:
(4⋅6) + (2k⋅6) + 3k
Simplifying further, we have:
24 + 12k + 3k
Combining like terms, we get:
24 + 15k
So, the simplified expression is 24 + 15k.
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The length of the legs in a right triangle are 14 in and 22 in. Find the length of the hypotenuse. Round your answer to the tenths place.
tell whether the measure can be the side lengths of a triangle. if so classify the triangle as acute obtuse or right
Using the Triangle Inequality Theorem and the Pythagorean theorem, we can determine if a given set of measures can form a triangle, and if so, what type of triangle (acute, obtuse, or right) it is. We find that measures a) 4,7,9; b) 10,13,16; c) 8,8,11; d) 9,12,15 and f) 4.5,6,10.2 can all form triangles, but e) 5,14,20 cannot. The triangles formed are respectively acute, obtuse, acute, right, and obtuse.
Explanation:Triangular Side Lengths and IdentificationIn the discipline of Mathematics, specifically Geometry, we use the Triangle Inequality Theorem and the Pythagorean theorem to determine if given measures can constitute the sides of a triangle and also classify the triangle. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be larger than the length of the third side. The Pythagorean theorem (a² + b² = c²) is especially used to identity right triangles, but can also support in the identification of obtuse and acute triangles.
4,7,9 - These lengths can form a triangle. Since 4² + 7² > 9², the triangle is acute.10,13,16 - These lengths can form a triangle. However, since 10² + 13² < 16², the triangle is obtuse.8,8,11 - These lengths can form a triangle. Since 8² + 8² > 11², the triangle is acute.9,12,15 - These lengths can form a triangle. As 9² + 12² = 15², this is a right triangle.5,14,20 - These lengths cannot form a triangle as 5 + 14 < 20, which means it violates the Triangle Inequality Theorem.4.5,6,10.2 - These lengths can form a triangle. As 4.5² + 6² < 10.2², it is an obtuse triangle.Learn more about Triangle Classification here:https://brainly.com/question/4028542
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How do I add fractions with different denominations?
To solve the equation 3x−2=4x−1 3 x − 2 = 4 x − 1 , Veronica graphs the functions f(x)=3x−2 f ( x ) = 3 x − 2 and g(x)=4x−1 g ( x ) = 4 x − 1 on the same set of coordinate axes.
Which statement describes the solution of the equation 3x−2=4x−1
The solution of the equation is the y-coordinate of the ordered pair where the graphs of the two functions intersect.
The solution of the equation is the y-intercept of the linear equations.
The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.
The solution of the equation cannot be found graphically. Veronica should solve the equation algebraically.
If angle c = 90° , c= 17, and a= 15, then b =
A property sells for $620,000 two years after it was purchased. If the annual appreciation rate was 4%, how much did the original buyer pay for the property (round to the nearest $1,000)?
The original purchase price of the property, after accounting for 4% annual appreciation over two years with a final selling price of $620,000, is approximately $573,000 when rounded to the nearest $1,000.
Explanation:The question involves finding the original price of a property given its final selling price after a period of annual appreciation. To calculate the original purchase price, we need to use the formula for compound appreciation in reverse, known as discounting. Since the appreciation is 4% per year for two years and the final selling price is $620,000, the original purchase price (P) can be found using the formula:
P = Final Price / (1 + rate of appreciation)^number of years
So, substituting the given values, we get:
P = $620,000 / (1 + 0.04)^2
Now, calculate the denominator:
(1 + 0.04)^2 = 1.0816
And then divide by the final price:
P = $620,000 / 1.0816
P = $573,029.94
When rounded to the nearest $1,000, the original purchase price is approximately $573,000.
Find both unit rates. 1435 points scored in 25 games + Brainliest!!
Write the following equation in standard form: x^5+2x^3+6x+1/5
Answer:
[tex]x^5+2x^3+6x+\frac{1}{5}[/tex]
Step-by-step explanation:
We have been given an equation [tex]x^5+2x^3+6x+\frac{1}{5}[/tex]. We are asked to write our given equation in standard form.
We know that to write an equation in standard form, we need to write the degree terms in descending order.
Upon looking at our given equation, we can see that all terms are in descending order of degree, therefore, our given equation is already writen in standard form.