a baseball coach uses a pitching machine to simulate pop flies during practice. the quadratic function f(x)=-16x^2+70x+10 models the height in feet of a baseball after x seconds. how long is the baseball in the air if the ball is not caught?
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.
Explanation: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.
Volume of Composite Shapes, i need help again
What is 136 sq km divided by 8 km?
Answer:
[tex]136 \: {km}^{2} \div 8 \: km = 17 \: km[/tex]
What is probability of rolling a prime number cube with sides labeled 1-6
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.
followed your directions @ninc and I got this, but I don't think it's right
the length of bill's backyard swimming pool is 60 ft longer than the width if the pool. The surface area of the water is 1600 square ft. What is the width of the pool?
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:
x^2 + 60x = 1600x^2 + 60x - 1600 = 0We can solve this quadratic equation by factoring or using the quadratic formula. In this case, the equation factors nicely:
(x + 80)(x - 20) = 0Setting each factor equal to zero gives us:
x + 80 = 0 or x - 20 = 0x = -80 or x = 20Since a negative width doesn't make sense for a physical object, we discard x = -80 and the width of the pool is 20 feet.
Ramona is asked to draw a tree using a scale of 1 inch:3 meters.She draws a 4-inch tree.How tall is the tree?
This figure consists of a rectangle and a quarter circle.
What is the perimeter of this figure?
Use 3.14 for π .
Enter your answer as a decimal in the box.
__ cm
Answer:
61.27
Step-by-step explanation:
Please show the work thank you
A triangle and a rectangle are drawn. The triangle's base is equal to the rectangle's length. The triangle's height is equal to the rectangle's width. Which sentence is true?
A.)exactly 1 of these rectangle's can fit inside this triangle.
B.)2 of these rectangles can fit inside this triangle
C.)exactly 1 of these triangle's can fit inside this rectangle
D.)2 of these triangles can fit inside this rectangle
Exactly 1 of these triangles can fit inside this rectangle.
Explanation: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.
Learn more about Geometry here:https://brainly.com/question/31408211
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Cameron has clear container in the shape of a cube.Each egde 9 centimeters long.He found the volume of the container in cubic centimeters by multiplying the egde length by itself 3 times.What is the volume of the container in the cubic
A 50-foot ladder leans against a wall, as shown in the figure below. If the base of the ladder is 30 feet away from the wall, how tall is the wall?
Select one:
A. 3
B. 4
C. 5
D. 40
If the multiplication expression below were written in exponential form, what would be the exponent be? 24*24*24*24*24
The bottom shape is a square prism with base edges of 3 cm and a height of 10 cm. What is the volume of the composite figure if the top shape is a right pyramid with a height of 2 cm?
90 cm3
60 cm3
6 cm3
96 cm3
please i really need help on this
In a study, researchers found that for every 3 people who preferred brand A toothpaste 1 person preferred brand B toothpaste. Which ratio describes the results of the study?
A. 1:3
B. 1:4
C. 3:1
D. 4:1
What’s the surface area of this tent? Show all work and write your answer below.
The perimeter of a rectangular banner is 72 inches. The width of the banner is 1/3 its length. What is the area of the banner? The first one with a good answer will be count as the brainlist. Please help
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.
If you know it please tell me it would help a lot
5g of margarine contains 3.6g of fat.
How many grams of fat are there in 92g of Margarine?
What is the solution set?
1/2x−6.5>12
Enter your answer in the box.
Answer:
Step-by-step explanation:
your answer is x>37
Visiting team: 20% of supporting visiting team
Home team: 80% of supporting home team
If the total number of people attending the game was 64,000, how many people were supporters of the home team?
A.)12,800
B.)38,400
C.)48,000
D.)51,200
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.
if an office is 120 sq ft what is the measurement in square meters
Answer:
We have to convert the measurement in square meters. Therefore 120 sq. feet = 120×0.093 = 11.148 sq. meters.
Steve needs to take at least 24 milligrams of calcium, 15 milligrams of iron, and 16 milligrams of vitamins. Which ordered pairs of values are solutions for the given system inequalities, where x represents the number of spoonfuls of brand A that Steve takes and y represents the number of spoonfuls of brand B that Steve takes? Select all the correct answers.
Addison brought 5 pounds of oranges and 7 pounds of cherries to make a fruit salad for a fund raiser. She wants to package an equal amount of fruit salad into each of 10 containers.
How much fruit salad should Addison put in each counter?
Addison should put
(________)
pounds of fruit salad into each container.
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.
Use the parabola tool to graph the quadratic function f(x)=x2−12x+27.
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
The vertex of a parabola is the minimum or the maximum point of the parabola
The equation of the parabola is given as:
[tex]f(x) = x^2 + 12x + 27[/tex]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:
https://brainly.com/question/4148030
The state capitol building in Baton Rouge, Louisiana, is 450 feet tall. Ella’s scale model of the building uses the scale 25 feet = 10 inches. How tall is Ella’s model? 18 inches 180 inches 1,125 inches 425 inches
This semicircle has a diameter of 5 meters.
What is the area of this figure?
Use 3.14 to for pi.
Enter your answer as a decimal in the box. Round your answer to the nearest hundredth.
Work out the area of a triangle of base 7.5m and height 6cm
A rectangular prism has a length of 3 1/2 inches, a width of 3 1/2 inches, and a height of 7 inches. Danny has a storage container for the prism that has a volume of 90 cubic inches.
What is the difference in volume between the prism and the storage container?
PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!
Work the following pricing problems for services rendered. (For all calculations use hundredths.) Labor time = 6 1/2 hours Overhead rate = 55% Retail price of parts = $114.70 Total cost of job = $231.08 What is hourly rate for labor? 11.55 27.75 32.55 137.64
Answer:
11.55
Step-by-step explanation: