Eleven is decreased by twice a number. Represent this statement using an algebraic expression.
1. 11x-2
2. 2x+11
3. 11-2x
4. 2x-11

Answer:

61.27

Step-by-step explanation:

Using the quadratic equation f(x) = -16[tex]x^2[/tex] + 70x + 10, which models the height of the baseball, we apply the quadratic formula to find that the ball is in the air for approximately 4.438 seconds before it lands back on the ground if not caught.

The student asks how long a baseball remains in the air during practice using a quadratic equation that models the height of the baseball after a certain number of seconds. The equation provided is f(x) = -16[tex]x^2[/tex] + 70x + 10, which models the height in feet of the baseball after x seconds. To determine the time the baseball is in the air, we need to find when the ball returns to the ground level (when f(x) = 0).

We can solve this quadratic equation using the quadratic formula: x = (-b ± [tex]\sqrt{(b^2 - 4ac)) / (2a)}[/tex], where a is -16, b is 70, and c is 10. Plugging in these values, we get two solutions for t (time), and we choose the positive time value at which the height becomes zero again, indicating that the ball has landed back on the ground.

The use of the quadratic formula yields t = 4.438 seconds and t = -0.138 seconds. We discard the negative time value as it is not physically relevant to the problem, and thus the baseball is in the air for approximately 4.438 seconds before it lands back on the ground if it's not caught.

Addison should put 1.2 pounds of fruit salad into each of the 10 containers for the fundraiser.

To find out how much fruit salad Addison should put in each container, we need to first calculate the total weight of the fruit she brought, which is 5 pounds of oranges plus 7 pounds of cherries, equaling 12 pounds of fruit in total.

Then, to distribute this equally among 10 containers, we divide the total weight of the fruit by the number of containers:

[tex]\[ \frac{12 \text{ pounds}}{10 \text{ containers}} \]\[ = 1.2 \text{ pounds per container} \][/tex]

So, Addison should put 1.2 pounds of fruit salad into each container.

Final answer:

The probability of rolling a prime number on a six-sided die is 1/2 or 50%, since there are three prime numbers (2, 3, 5) out of six possible outcomes.

Explanation:

The probability of rolling a prime number on a six-sided cube labeled with the numbers 1 through 6 can be determined by identifying which numbers on the cube are prime. Prime numbers are numbers that are only divisible by 1 and themselves. On a six-sided die, the prime numbers are 2, 3, and 5.

Since there are 6 faces on the die, the total number of possible outcomes when you roll it once is 6. The event of rolling a prime number includes three outcomes: rolling a 2, rolling a 3, or rolling a 5. So, the probability, P, of rolling a prime number is determined by dividing the number of favorable outcomes (rolling a 2, 3, or 5) by the total number of possible outcomes.

The calculation for the probability is therefore P(Prime) = Number of prime faces / Total number of faces = 3/6. This simplifies to 1/2, which means that the probability of rolling a prime number is 1/2, or 50%.

We can conclude that if you roll the die only a few times, the law of large numbers may not hold, and the experimental probability may not closely align with the theoretical probability of 1/2, but over many rolls, it would generally converge to this value.

Answer:

11.55

Step-by-step explanation:

Exactly 1 of these triangles can fit inside this rectangle.

The sentence that is true is exactly 1 of these triangles can fit inside this rectangle. To understand why, let's analyze the dimensions of the triangle and the rectangle. Suppose the base of the triangle is 4 units and the height is 3 units. If the length of the rectangle is also 4 units and the width is 3 units, the triangle will perfectly fit inside the rectangle. However, if the length or width of the rectangle is different from the corresponding dimensions of the triangle, it will not be possible to fit the triangle inside the rectangle without overlapping.

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Answer:

We have to convert the measurement in square meters. Therefore 120 sq. feet = 120×0.093 = 11.148 sq. meters.

Answer: D.)51,200

Step-by-step explanation:

Hi, to answer this question we have to multiply the number of attendants (64,000) by the percentage amount of supporting home team (80/100)

64,000 x (80/100) = 51,200

51,200 people were supporters of the home team.

The correct option is D).

Feel free to ask for more if needed or if you did not understand something.

Answer:

Step-by-step explanation:

your answer is x>37

The vertex of a parabola is the minimum or the maximum point of the parabola

The equation of the parabola is given as:

The x-coordinate of the vertex is calculated using:

[tex]x = -\frac{b}{2a}[/tex]

So, we have:

[tex]x = -\frac{12}{2 \times 1}[/tex]

[tex]x = -\frac{12}{2}[/tex]

[tex]x = -6[/tex]

Substitute -6 for x in f(x)

[tex]f(-6) = (-6)^2 + 12(-6) + 27[/tex]

[tex]f(-6) =-9[/tex]

So, the vertex of the parabola is (-6,-9)

Let x = 0.

So, we calculate f(0) as follows:

[tex]f(0) = (0)^2 + 12(0) + 27[/tex]

[tex]f(0) = 27[/tex]

This means that f(x) passes through (0,27)

See attachment of the parabola

Read more about parabolas at:

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Final answer:

To find the area of the banner with a given perimeter of 72 inches and a width that is 1/3 its length, we first determine the length to be 27 inches and the width to be 9 inches, leading to an area of 243 square inches.

Explanation:

To solve the problem, let's denote the length of the rectangular banner as L inches and the width as W inches. We're given that the perimeter is 72 inches and that the width is 1/3 its length, hence W = 1/3 * L. The formula for the perimeter of a rectangle is 2L + 2W = 72.

Substituting the value of W in terms of L into the perimeter equation gives 2L + 2(1/3 * L) = 72. Simplifying this equation: 2L + 2/3L = 72, or (6/3)L + (2/3)L = 72, which simplifies to (8/3)L = 72. By solving this equation, we find that L = 27 inches. Therefore, W = 1/3 * 27 = 9 inches.

Finally, the area of the rectangle, which is Length × Width, can now be calculated as 27 inches × 9 inches = 243 square inches.

Answer:

[tex]136 \: {km}^{2} \div 8 \: km = 17 \: km[/tex]

To find the width of Bill's rectangular pool, set up an equation with 'x' as the width, resulting in x(x + 60) = 1600. Solving this quadratic equation, the width of the pool is found to be 20 feet.

The question asks us to determine the width of Bill's backyard swimming pool given that the pool's length is 60 feet longer than its width and the surface area of the water is 1600 square feet. To solve this, we can set up an equation where the width of the pool is x feet and the length is x + 60 feet. Because surface area is found by multiplying the length by the width for a rectangular object, our equation is x(x + 60) = 1600.

Now, solve for x:

We can solve this quadratic equation by factoring or using the quadratic formula. In this case, the equation factors nicely:

Setting each factor equal to zero gives us:

Since a negative width doesn't make sense for a physical object, we discard x = -80 and the width of the pool is 20 feet.