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how long would it take a ball dropped from a 100 ft building to hit the ground
Final answer:
To find the time it takes for a ball to fall from a 100 ft building, convert the height to meters and use the free fall motion formula. Solving s = (1/2)gt² for time, it takes approximately 2.5 seconds for the ball to hit the ground.
Explanation:
To determine how long it would take for a ball dropped from a 100 ft building to hit the ground, we can use the formula for the free fall motion under the influence of gravity, assuming air resistance is negligible. The formula is s = (1/2)gt², where s is the distance fallen, g is the acceleration due to gravity (approximately 9.8 m/s², but we will need to convert it to feet per second squared for this problem), and t is the time in seconds.
First, convert 100 feet to meters because the standard unit of gravity is in meters per second squared. There are approximately 3.281 feet in a meter, so 100 feet is roughly 30.48 meters.
Now apply the formula and solve for t:
Convert acceleration due to gravity to feet: 9.8 m/s² is approximately 32.2 ft/s².
Use the formula: 100 = (1/2)(32.2)t².
Solve for t: t² = 100 / 16.1.
Find t: t = √(100 / 16.1).
Calculate t: t ≈ 2.49 seconds.
Therefore, it would take approximately 2.5 seconds for the ball to hit the ground.
A punch bowl that holds 150 cups of jungle ounch is to he used at a birthday party. Each plastic cup hols 1 1/2 cups of punch. How many plastic cups can be filled?
What is the value of x?
3x−8=(8x+4
-----
2
3x-8 = 8x+4
subtract 3x from each side
-8 = 5x+4
subtract 4 from each side
-12 = 5x
divide -12 by 5 to get x
x = -12/5 = -2.4
(a) find the slope m of the tangent to the curve y = 5/ x at the point where x = a > 0.(b) find equations of the tangent lines at the points (1, 5) and 4, 5 2 .
Which of the following is equivalent to the expression (9x^2y^3)(12x^-3y^5)( 2xy)? 23x^-5y^8 216^9 -x^-6y^8
Final answer:
The expression (9x^2y^3)(12x^-3y^5)(2xy) simplifies to 216y^9 by multiplying the coefficients and adding the exponents of like bases.
Explanation:
The student's question involves simplifying an algebraic expression by using the properties of exponents. When we multiply expressions with the same base, we add the exponents. The given expression (9x2y3)(12x-3y5)(2xy) can be simplified by multiplying the coefficients (numerical values) and adding the exponents of like bases separately.
Multiply the coefficients: 9 * 12 * 2 = 216
Add the exponents for x: 2 + (-3) + 1 = 0 (x's cancel out because x0 = 1)
Add the exponents for y: 3 + 5 + 1 = 9
Thus, the simplified expression is 216y9.
What is 763 thousandths in scientific notation?
Answer: [tex]7.63\times10^{-1}[/tex]
Step-by-step explanation:
The scientific notation is a technique to express a very large or a very small number in the product of a decimal form of number [commonly between 1 and 10] and powers of ten.We know that one thousandth is written as :
[tex]\text{One thousandth}=\frac{1}{1000}[/tex]
Therefore, 763 thousandths can be written as :
[tex]\text{ 763 thousandths}=\frac{763}{1000}=\frac{7.63}{10}[/tex]
In Scientific notation:
[tex]\frac{7.63}{100}=763\times10^{-1}......[\text{ By law of exponents }](\frac{1}{a^n}=a^{-n})[/tex]
The number [tex]763\text{ thousandths}[/tex] in scientific notation is [tex]\boxed{\bf 7.63\times 10^{-1}}[/tex].
Further Explanation:
The scientific notation is a technique which is used to express a very large or a very small number in the product of a decimal form of number [commonly between 1 and 10] and a power of ten.
It can easily simplify an arithmetic operation and in a scientific calculator it is known as SCI display mode.
In scientific notation, all the numbers can be written as follows:
[tex]\boxed{x\times 10^{y}}[/tex]
Here, [tex]y[/tex] is an exponent integer and [tex]x[/tex] is the real number. The integer [tex]y[/tex] is the order of the magnitude and [tex]x[/tex] is called the mantissa (fractional part of the number).
As we know that one thousandths in mathematical form can be written as follows:
[tex]\boxed{1\text{ thousandths}=\dfrac{1}{1000}}[/tex]
Therefore, the number [tex]763\text{ thousandths}[/tex] in mathematical form is written as follows:
[tex]\boxed{\begin{aligned}763\text{ thousandths}&=\dfrac{763}{1000}\\&=\dfrac{7.63}{10}\end{aligned}}[/tex]
So, in scientific notation the number [tex]763\text{ thousandths}[/tex] is written as follows:
[tex]\boxed{\dfrac{7.63}{10}=7.63\times 10^{-1}}[/tex]
Therefore, the number [tex]763\text{ thousandths}[/tex] in scientific notation is expressed as [tex]\boxed{\bf 7.63\times 10^{-1}}[/tex].
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Number system
Keywords: scientific notation, 763 thousandths, multiplication, division, exponent power, real number, integers, power of ten, scientific calculator, decimal form.
solve the system by elimination -2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5
The solution of the given system of linear equation would be x = 1, y = 1, and z = 0.
What is a linear equation?A linear equation is one in which the greatest power of the variable is always one.
The given system of linear equation as:
-2x+2y+3z=0 ...(i)
-2x-y+z=-3 ...(ii)
2x+3y+3z=5 ...(iii)
Adding the third equation to the (i) and (ii), we get
5y+6z=5
2y+4z=2
Multiplying the equation(ii) by -6/4 and after adding to get
⇒2y=2
Dividing both sides by 2.
⇒y=1
Substitute the value of y=1 into 2y+4z=2, and we get
⇒2+4z=2
Subtracting 2 from both sides, we get
⇒ z = 0
Substitute the values of y=1 and z=0 into -2x-y+z=-3, we get -2x-1+0=-3
By adding 1 to both sides, we get -2x=-2
By dividing both sides by -2, we get x=1
Therefore, the solution of the given system of linear equation would be x = 1, y = 1, and z = 0.
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Identify the percent of change as an increase or a decrease. 68 miles to 42.5 miles
Final answer:
The distance changing from 68 miles to 42.5 miles represents a 37.5% decrease, calculated using the percent change formula.
Explanation:
The question involves calculating the percent of change when the distance changes from 68 miles to 42.5 miles. To find the percent of change, we use the formula: Percent Change = ((New Value - Original Value) / Original Value) x 100%. Here, the original value is 68 miles and the new value is 42.5 miles.
Plugging in the values, we get: Percent Change = ((42.5 - 68) / 68) x 100% = (-25.5 / 68) x 100% ≈ -37.5%. Because the result is negative, this indicates a decrease in the distance traveled.
Therefore, the distance changing from 68 miles to 42.5 miles represents a 37.5% decrease.
Tasha believes that she can rewrite the difference 120 - 36 as a product of the greatest common factor of the two numbers and other difference is she correct explain your answer
three numbers are in the ratio 2:3:4 if the sum of the largest and the smallest equals the sum of the third and 33 find the numbers
Given that (-2,-5) is on the graph of f(x), find the corresponding point for the function f(-2/3x).
The corresponding point for the function f(-2/3x) given the point (-2,-5) on the graph of f(x) is (3,-5), where the x-coordinate is transformed by multiplying -2 by -3/2 and the y-coordinate remains unchanged.
The question asks about finding a corresponding point for the function f(-2/3x) given that the point (-2,-5) is on the graph of the original function f(x). To find the corresponding point, we need to apply the transformation to the x-coordinate of the given point. Since the function is f(-2/3x), this represents a horizontal stretch by the reciprocal of -2/3, which is -3/2. Therefore, we multiply the x-coordinate of the given point by -3/2.
Let's calculate this step by step:
Start with the original point (-2,-5).Apply the transformation to the x-coordinate: -2 multiplied by -3/2 equals 3.The y-coordinate remains unchanged because the transformation applies only to the x-coordinate.Consider the following incomplete deposit slip: Description Amount ($) Cash, including coins 150 75 Check 1 564 81 Check 2 2192 43 Check 3 4864 01 Subtotal ???? ?? Less cash received ???? ?? Total 7050 50 How much cash did the person who filled out this deposit slip receive? a. $849.25 b. $715.56 c. $7,621.53 d. $721.50
The amount of cash did the person who filled out this deposit slip receive [tex]\boxed{\$ 721.50}.[/tex] Option (d) is correct.
Further explanation:
Given:
The options are as follows,
(a). [tex]\$ 849.25[/tex]
(b). [tex]\$ 715.56[/tex]
(c). [tex]\$ 7621.53[/tex]
(d). [tex]\$ 721.50[/tex]
Explanation:
The deposit slip can be expressed as follows,
Cash in the form of coins is [tex]\$ 150.75.[/tex]
The amount of check 1 is [tex]\$ 564.81[/tex], the amount of check 2 is [tex]\$ 2192.43[/tex] and the amount of check 3 is [tex]\$ 4864.01.[/tex]
The less cash received is [tex]\$ 7050.50.[/tex]
The total amount is [tex]\$ 7772.00.[/tex]
The amount of cash did the person who filled out this deposit slip receive can be calculated as follows,
[tex]\begin{aligned}{\text{Amount}} &= 7772.00 - 7050.50\\&= \$ 721.50\\\end{aligned}[/tex]
The amount of cash did the person who filled out this deposit slip receive [tex]\boxed{\$ 721.50}[/tex]. Option (d) is correct.
Option (a) is not correct.
Option (b) is not correct.
Option (c) is not correct.
Option (d) is correct.
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Interest rate
Keywords: Incomplete deposit slip, description amount, cash, including coins, check, person, less cash receives.
C. what is the probability that the flight will be more than 10 minutes late (to 2 decimals)?
If x denotes the length of a side of an equilateral triangle, express the area of the triangle as a function of x.
Using the concept of an equilateral triangle, it is found that it's area is given by:
[tex]A = \frac{\sqrt{3}}{4}x^2[/tex]
In an equilateral triangle, all sides have the same length.The area of a triangle is one half of the base multiplied by the height.For the equilateral triangle in this problem, the base is x, that is, [tex]b = x[/tex]The height is one side of a right triangle, in which the other side is half the base and the other is the base, thus, applying the Pythagorean Theorem:
[tex]h^2 + (\frac{x}{2})^2 = x^2[/tex]
[tex]h^2 + \frac{x^2}{4} = x^2[/tex]
[tex]h^2 = \frac{3x^2}{4}[/tex]
[tex]h = \sqrt{\frac{3x^2}{4}}[/tex]
[tex]h = \frac{\sqrt{3}}{2}x[/tex]
Then, the area is:
[tex]A = \frac{bh}{2} = \frac{1}{2} \times x \times \frac{\sqrt{3}}{2}x = \frac{\sqrt{3}}{4}x^2[/tex]
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How many cups of whole wheat flour does it take to make 30 biscuits if it takes 2 cups of whole wheat flour to make 8 biscuits
Thirty-eight fifth graders at Vernon Elementary are going on the field trip to the art museum. They are riding in vans that each hold 9 students. How many vans will they need for everyone to get to the art museum?
The division is a process of splitting a specific amount into equal parts.
The number of vans they will need for everyone to get to the art museum is 5.
What is division?The division is a process of splitting a specific amount into equal parts.
We have,
Number of five grader students = 38
One van can hold = 9 students.
The number of vans needed to hold 38 students:
= 38 / 9
= 4.2 vans
This means we need 5 vans to accommodate all 38 students because in 4 vans only 36 students will be accommodated and 2 students remaining will need a van.
Thus the number of vans they will need for everyone to get to the art museum is 5.
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Find the derivative of f (x)=(x^2+1)^3 (x^2+2)^6 using chain rule.
When does the proportion form of newton's second law take the form of an equation?
Find all 6 trigonometric ratios of the angle θ =7∏/ 6
1)Solve for x.
5+x+(−2)=−8
2)Solve for h.
6.51−9.32+h=1.02
3)Solve for y.
2/3+y−1/9=7/9 ( the ones with slashes are fractions (: )
4 )Solve for x.
−2/3(3x−4)+3x=5/6
5)
What is the value of s?
0.7(3s+4)−1.1s=7.9
see attached picture for answers:
replaced picture with correct answer for #1
At a recent boat show, Boater's Paradis sold five more boats than Pelican Marine sold. If together they sold 33 boats, how many were sold by each company?
In this mathematics problem about boat sales, Pelican Marine sold 14 boats and Boater's Paradis sold 19 boats. This conclusion was achieved by forming and solving a simple algebraic equation based on the provided problem information.
Explanation:To solve this problem, let's visualize it first. Pelican Marine sold a certain number of boats, and Boater's Paradis sold 5 more than that. If we call the number of boats sold by Pelican Marine as x, and adding Boater's Paradis' sales (x + 5), together they sold 33 boats. So we form the equation as x + (x+5) = 33.
Solving that equation, we will get 2x + 5 = 33, then simplify it to 2x = 28 after subtracting 5 from both sides. Finally, we divide both sides by 2 we get x = 14.
So, Pelican Marine sold 14 boats and Boater's Paradis sold 19 boats (14 boats Pelican Marine sold plus an additional 5 Boater's Paradis sold).
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Terrance is 3.5 years older than Stephanie. Stephanie is 22.5 years old. If the equation t – 3.5 = 22.5 models the situation, find the value for t, Terrance’s age.
Answer:
T= 3.5+22.5
T=26
Hope I helped!!
Step-by-step explanation:
The Age of Terrance is 26 years.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Model Equation : t – 3.5 = 22.5
where t is Terrance’s age.
Now, solving the equation for t we get
t - 3.5 = 22.5
Add 3.5 on both side
t -3.5+ 3.5 = 22.5 + 3.5
t = 26
Hence, Terrance age is 26 years.
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Question
There are 30 students in an art class. Fourteen of the students are girls.
What is the ratio of boys to girls?
due by now
30 total students
14 are girls
so 30-14 = 16 are boys
16 boys to 14 girls = 16/14 reduced to 8/7
The sum of the square of a positive number and the square of 5 more than the number is 37. What is the number?
Student to faculty is 17:3 The total is 740 how many students and faculty are at the college
17+3 =20
so for every 20 people there are 17 students and 3 faculty
740/20 = 37
37*3 = 111 faculty
37 *17 = 629 students
Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is C(x) = 2750 + 8x + 0.1x2 (0 ≤ x ≤ 500). Gymnast Clothing sells the cleats at $100 per pair. Find the revenue and profit functions. How many should Gymnast Clothing manufacture to make a profit?
Answer:
Revenue function: [tex]R(x)=100x[/tex]
Profit function: [tex]P(x)=-0.1 x^2 + 92 x - 2750[/tex]
31 to 500 Gymnast Clothing are manufactured to make a profit.
Step-by-step explanation:
The cost (in dollars) for a run of x pairs of cleats.
[tex]C(x)=2750 + 8x + 0.1x^2[/tex]
Gymnast Clothing sells the cleats at $100 per pair.
The Revenue (in dollars) for a run of x pairs of cleats.
[tex]R(x)=100x[/tex]
Profit = Revenue - Cost
[tex]P(x)=R(x)-C(x)[/tex]
[tex]P(x)=100x-(2750 + 8x + 0.1x^2)[/tex]
[tex]P(x)=-0.1 x^2 + 92 x - 2750[/tex]
We need to find how many should Gymnast Clothing manufacture to make a profit.
[tex]P(x)\geq 0[/tex]
[tex]-0.1 x^2 + 92 x - 2750\geq 0[/tex]
From the given figure it is clear that P(x) is greater than or equal to 0 for 30.931 ≤ x ≤ 889.069.
The value of x can not be more than 500.
31 ≤ x ≤ 500
31 to 500 Gymnast Clothing are manufactured to make a profit.
Please need help to solve this
7times blank equals 56
A 3x3x4 cuboid is painted blue and cut into 1x1 cubes. what is the expected value for the painted sides of a randomly selected cube?
A 3 x 3 x 4 cuboid can be cut into 3(3) (4) = 36 pieces of 1 x 1 cubes.
Out of the 36 pieces of 1 x 1 cubes, there are no 1 x 1 cube with the four
sides painted, there are eight 1 x 1 cubes with simply 3 sides painted, there
are twenty 1 x 1 cubes with only 2 sides tinted, there are 6 cubes with only 1
side painted and there are 2 cubes with no side painted.
The chance that the four sides of a randomly selected cube is painted is 0.
The likelihood that only 3 sides of a randomly selected cube is painted is 8 / 36 = 2 / 9.
The chance that only 2 sides of a randomly selected cube is painted is 20 / 36 = 5 / 9.
The likelihood that only 1 side of a randomly selected cube is painted is 6 / 36 = 1 / 6.
The probability that no side of a randomly selected cube is
painted is 2 / 36 = 1 / 18.
Thus, the expected value for the painted sides of a randomly selected cube is
given by 4(0) + 3(2 / 9) + 2(5 / 9) + 1(1 / 6) + 0( 1 / 18) = 2 / 3 + 10 / 9 +
1 / 6 = 35 / 18 = 1.94