Answer: This type of sample is called a stratified random sample. The population (city) is divided into various zones, and then a random sample of households (5 from each zone) is taken from each stratum (zone). This helps ensure that the sample is representative of the population as a whole and includes a proportional number of households from each zone.
Step-by-step explanation:
stratified random sampling is a powerful tool for researchers to ensure that their sample accurately reflects the population of interest, and can help increase the validity and reliability of research findings.
How to study sample?
This sampling method is an example of stratified random sampling, where the population is divided into different subgroups or strata, and a random sample is drawn from each stratum. In this case, the strata are the various zones of the city, and the researcher randomly selects five households from each zone.
Stratified random sampling is a commonly used sampling method in research because it can increase the representativeness of the sample and reduce sampling error. By dividing the population into different strata based on relevant characteristics, such as geographic location, age, gender, or income level, the researcher can ensure that each stratum is adequately represented in the sample.
In this example, the researcher is interested in studying public transportation usage in different zones of the city. By stratifying the population by zone and selecting a random sample of households from each zone, the researcher can obtain a representative sample of the population and draw conclusions about public transportation usage in each zone.
Overall, stratified random sampling is a powerful tool for researchers to ensure that their sample accurately reflects the population of interest, and can help increase the validity and reliability of research findings.
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Your complete question is :-A city collects data about public transportation. The researcher divides the city into various zones, and randomly chooses 5 households from each zone to survey. Which type of sample does this represent?
Millard Corporation is a wholesale distributor of office products. It purchases office products from manufacturers and distributes them in the West, Central, and East regions. Each of these regions is about the same size and each has its own manager and sales staff.
The company has been experiencing losses for many months. In an effort to improve performance, management has requested that the monthly income statement be segmented by sales region. The company's first effort at preparing a segmented income statement for May is given below.
By analyzing the segmented income statement, Millard Corporation can identify which sales regions are contributing to the overall losses and focus on improving their performance.
We analyze the segmented income statement for Millard Corporation.
Based on the given information, the company distributes office products to three sales regions:
West, Central, and East. Each region has its own manager and sales staff.
To prepare a segmented income statement for May, the company should follow these steps:
Identify the revenue generated by each sales region.
This can be found by tracking the sales from each region and recording them separately.
Allocate direct costs to each sales region.
Direct costs are those that can be directly traced to each region, such as the salaries of the regional manager and sales staff.
Allocate indirect costs to each sales region.
Calculate the contribution margin for each sales region by subtracting the direct costs from the revenue.
This will show the profitability of each region before accounting for the indirect costs.
Subtract the allocated indirect costs from the contribution margin to determine the operating income (or loss) for each sales region.
This information will also help management make informed decisions on resource allocation, budgeting, and strategic planning for the future.
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The quantity of a drug Q mg, present in the body is given by
Q = f(t) = 140te−0.5t
(a) Find f
′
(1), f′
(4)
Step-by-step explanation:
The quantity of a drug, Q mg, present in the body t hours after an injection of the drug is given is Q =f 140te 0.6t Find f (1) , f' (1) , f (6) ,and f' (6) .
how to find area and perimeter of Rhombus
Answer:
To find the area and perimeter of a rhombus, you can follow these steps:
1. Find the length of one side of the rhombus.
2. Use the length of one side to find the length of the diagonals. The diagonals of a rhombus are perpendicular bisectors of each other, which means that they intersect at a 90-degree angle, and each diagonal cuts the rhombus into two congruent right triangles. The length of each diagonal can be found using the Pythagorean theorem: diagonal^2 = (side/2)^2 + (side/2)^2.
3. Once you have found the length of the diagonals, you can use them to calculate the area of the rhombus. The area of a rhombus is equal to half the product of the length of the diagonals: area = (diagonal1 x diagonal2) / 2.
4. To find the perimeter of the rhombus, you simply add up the lengths of all four sides: perimeter = 4 x side.
In summary, the steps to find the area and perimeter of a rhombus are:
1. Find the length of one side of the rhombus.
2. Use the length of one side to find the length of the diagonals.
3. Use the diagonals to calculate the area of the rhombus: area = (diagonal1 x diagonal2) / 2.
4. Add up the lengths of all four sides to find the perimeter: perimeter = 4 x side.
To find the area and perimeter of a rhombus, you can use the following formulas:
Area = (diagonal 1 × diagonal 2) / 2
Perimeter = 4 × side length
What is a rhombus?A rhombus is a quadrilateral that has four equal sides.
Some of the properties we need to know are:
- The opposite sides are parallel to each other.
- The opposite angles are equal.
- The adjacent angles add upto 180 degrees.
We have,
To find the area and perimeter of a rhombus, you can use the following formulas:
Area of a Rhombus:
The area of a rhombus can be found by multiplying the length of the two diagonals and dividing by 2. That is,
Area = (diagonal 1 × diagonal 2) / 2
The perimeter of a Rhombus:
The perimeter of a rhombus can be found by multiplying the length of one side by 4. That is,
Perimeter = 4 × side length
Thus,
To find the area and perimeter of a rhombus, you can use the following formulas:
Area = (diagonal 1 × diagonal 2) / 2
Perimeter = 4 × side length
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Pete surveyed his friends as to the amount of their weekly allowance. the responses were $5, $0, $8, $10, $8, $10, $0, $0, and $1. Pete analyzed the results and stated that more than half of his friends earned $8 or more per week. Find his mistake and correct it. Statical queston
Answer:
Step-by-step explanation:
Bold = $8 or more per week, Underlined = less than 8 per week
$5 = 1 person
$0 = 3 people
$10 = 2 people
$1 = 1 person
$8 = 2 people
The total amount of people = 1+3+2+1+2 = 9
The total amount of people who earn less than $8/week = 1+3+1 = 5 people
The total amount of people who earn $8 or more/week = 2+2 = 4 people
Conclusion, 5/9 total people earned less than $8/week
4/9 people earn $8 or more/week
Mistake there were less than half people who earned $8 or more per week unlike Pete stated
Correction; more than half of Pete's friends earn less than 8 dollars per week
A club had 600 members. 60% of them were males. When 200 new members joined the club, the percentage of male members was reduced to 50%. How many of the new members were males?
Answer: 40
Step-by-step explanation: out of 600 members, 360 (600*0.6) of them were males. When 200 new members joined the club, the total number of members would be 800. If 50% of 800 members were males, then 400 are males. 40 new male members joined.
If the variance of the data values in a population is 441, what is the standard deviation of the data values?
O A. 17
• B. 21
O C. 23
O D. 19
In the given situation if the variance of the data values in a population is 441, the standard deviation of the data values is (B) 21.
What is the standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean.
A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
The variance's square root is the standard deviation of the data values:
S = √V = √441 = 21
Therefore, in the given situation if the variance of the data values in a population is 441, the standard deviation of the data values is (B) 21.
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Fill in the blanks using the available answer choices. The vertices of a quadrilateral are A(–3, 1) , B(4, 2) , C(9, –3) and D(2, –4) . Complete the statement to best classify what type of quadrilateral ABCD is. In quadrilateral ABCD , have equal length and there are right angles, so ABCD is best classified as a .
Answer:
Step-by-step explanation:
Fill in the blanks using the available answer choices. The vertices of a quadrilateral are A(–3, 1) , B(4, 2) , C(9, –3) and D(2, –4) . Complete the statement to best classify what type of quadrilateral ABCD is. In quadrilateral ABCD , have equal length and there are right angles, so ABCD is best classified as a .
Look at ZVSW and ZTSW in the image below.
W
Which of the following is the best description for this pair of angles?
O acute
O complementary
Osupplementary
O straight
VSW and TSW are supplementary angles.
What is supplementary angle?
Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if you have two angles that are supplementary, and you add them together, the result will be a straight line.
What is complementary angle?
Complementary angles are two angles whose sum is equal to 90 degrees (a right angle). In other words, when two angles are complementary, they "complete" a right angle when added together.
According to given information:In geometry, an angle is formed when two lines or rays intersect. Angles are measured in degrees and are classified based on their measures.
The pair of angles VSW and TSW in the image can be classified as supplementary angles.
Two angles are supplementary if their measures add up to 180 degrees.
In this case, angle VSW and angle TSW are adjacent angles that together form a straight angle, which measures 180 degrees. Therefore, VSW and TSW are supplementary angles.
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Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression. tan x(cot x - cos x)
Answer: Starting with the expression:
tan(x)(cot(x) - cos(x))
Recall that cot(x) is the reciprocal of tan(x), so we can substitute cot(x) = 1/tan(x):
tan(x)(1/tan(x) - cos(x))
Simplifying:
1 - cos(x)tan(x)
Next, we can use the identity cos(x) = 1/sec(x) to eliminate the cotangent term:
1 - (1/sec(x))tan(x)
Now, we can use the identity tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x) to express the expression in terms of sine and cosine:
1 - (1/cos(x))(sin(x)/cos(x))
Simplifying:
cos(x)/cos(x) - sin(x)/cos(x)
= (cos(x) - sin(x))/cos(x)
Therefore, the simplified expression in terms of sine and cosine is:
(cos(x) - sin(x))/cos(x)
Step-by-step explanation:
Airplanes are sometimes used to fight fires. A certain airplane can deliver ×4104 liters of water in one trip. How much water can this airplane deliver in 38 trips?
Write your answer in scientific notation.
Find the y-intercept for the equation:
y=2x+6
Y=2x+6
x=2y+6
2y=6-x/÷2
y=[tex]\frac{6-x}{2}[/tex]
A survey of 240 families showed that
91 had a dog;
70 had a cat;
31 had a dog and a cat;
91 had neither a cat nor a dog, and in addition did not have a parakeet;
7 had a cat, a dog, and a parakeet.
How many had a parakeet only?
Ok
so the math that we need to do for this problem will be:
Total number of families = 240
minus the ones that don't have any pets = 91
minus the families that do have dogs = 91
minus the families that do have cats = 70
add back the overlap of dogs and cats = 31
add back the overlap of dogs cats parakeets = 7
240 - 91 - 91 - 70 + 31 + 7
^ this math will give us the families that ONLY have parakeets
so I stand by what I said before that this is the math you would to do get the answer to your problem
therefore its 26 buddy
Step-by-step explanation:
[tex]n(p) only= \: n(p) - n(c n d np) \\ = 91 - 7 \\ = 84[/tex]
Solution check for this math problem
1. The solutions of the equation 6/(x+1)= x/(x-1) are x = 2 and x = 3.
2. The solutions of the equation x+ 4/x= -5 are x = -1 and x = -4.
What are the solutions ?
1. 6/(x+1) = x/(x-1)
To solve this equation, we first need to get rid of the fractions by multiplying both sides of the equation by the least common multiple of the denominators, which is (x+1)(x-1):
6(x-1) = x(x+1)
Expanding the left side, we get:
6x - 6 = x² + x
Moving all the terms to one side, we get:
x² - 5x + 6 = 0
This is a quadratic equation that can be factored as:
(x - 2)(x - 3) = 0
So, the solutions are x = 2 and x = 3. However, we need to check if these solutions are valid, because we cannot divide by zero.
Checking x = 2:
6/(2+1) = 2/(2-1)
2 = 2, which is true
Checking x = 3:
6/(3+1) = 3/(3-1)
3/2 = 3/2, which is true
Therefore, the solutions are x = 2 and x = 3.
2. x + 4/x = -5
To solve this equation, we first need to get rid of the fraction by multiplying both sides of the equation by x:
x² + 4 = -5x
Moving all the terms to one side, we get:
x² + 5x + 4 = 0
This is a quadratic equation that can be factored as:
(x + 1)(x + 4) = 0
So, the solutions are x = -1 and x = -4. However, we need to check if these solutions are valid, because we cannot divide by zero.
Checking x = -1:
-1 + 4/(-1) = -5
-1 - 4 = -5, which is true
Checking x = -4:
-4 + 4/(-4) = -5
-4 - 1 = -5, which is true
Therefore, the solutions are x = -1 and x = -4.
What is common multiple?
A common multiple is a number that is a multiple of two or more given numbers. For example, the common multiples of 2 and 3 are 6, 12, 18, 24, etc. These are all numbers that can be divided by both 2 and 3 without a remainder. A common multiple is "common" to the given numbers because it is a multiple of all of them.
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Complete question is:
1. The solutions of the equation 6/(x+1)= x/(x-1) are x = 2 and x = 3.
2. The solutions of the equation x+ 4/x= -5 are x = -1 and x = -4.
please answer the question and add the label in your answer please I'm putting 30 points please
For the first graph the two lines are parallel, that is they do not intersect. Thus, the system has no solution. For the second graph the y-intercept is 3 units.
What is solution of system of equation?The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all feasible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations. There is only ever one solution to a linear equation with one variable. The one and only position at which LHS and RHS are equivalent upon substitution is the unique solution of a linear equation. When there are two simultaneous linear equations, the answer must be an ordered pair (x, y). The ordered pair will in this instance satisfy the set of equations.
For the first graph the two lines are parallel, that is they do not intersect. Thus, the system has no solution.
For the second graph the y-intercept is 3 units.
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At a basketball game, a vender sold a combined total of 102 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
Mona had 32 math problems for homework. She completed 3/4 of them before dinner and the remaining 1/4 after dinner. How many problems did she complete before dinner?
Answer: 24 problems done before dinner
Step-by-step explanation:
Take the 32 total math problems and divide it by 3/4 (the amount of problems done before dinner) getting you 24 problems done before dinner
please help me to get this right i really need help
Answer:
The top on the left.
Step-by-step explanation:
The function is a square root function. The negative is a reflection across the x axis. The 2 is a vertical stretch by 2. The subtraction of 1 from the x is a horizontal shift right 1 and the addition of 5 to the function is a vertical shift upwards 5. If you would like more detail let met know.
HELP ASAP 20 POINTS
Answer: $ 16,740
Here's a trick:
Mark down, you subtract
Mark up, you add
**Please mark brainliest**Step-by-step explanation:
Hi, so I see you've been asking for help on these questions.
The concept is quite simple so I am going to walk you through it.
First, your going to multiply 55,800 x .7
Once you've done that you will receive 39,060 you will then subtract 39,060 from 55,800
55,800
-
39,060
= 16,740 is your answer
Sheila is climbing on a ladder that is attached against the side of a jungle gym wall. She is 7 feet off the ground and is 3 feet from the base of the ladder, which is 18 feet from the wall. How high up the wall is the top of the ladder?
The top of the ladder is about 24.81 feet up the wall.
EquationsWe can use the Pythagorean theorem to solve the problem and assume the height up the wall that the top of the ladder reaches "x". Then, we have a right triangle with legs of 3 feet and x feet and a hypotenuse of 18 + 7 = 25 feet (the length of the ladder). So, we can write:
[tex]3^{2}[/tex] + [tex]x^{2}[/tex] = [tex]25^{2}[/tex]
9 + [tex]x^{2}[/tex] = 625
[tex]x^{2}[/tex] = 616
x = [tex]\sqrt{616}[/tex]
x ≈ 24.81 feet
What are the components of Pythagoras Theorem?According to Pythagoras's Theorem, the square of the length of a right-angled triangle's hypotenuse (the side that faces the right angle) is equal to the sum of the squares of the lengths of the other two sides (the adjacent and opposite sides) and this can be expressed mathematically as follows [tex]c^{2}[/tex]= [tex]a^{2}[/tex] + [tex]b^{2}[/tex] where c is the hypotenuse's length and a and b are the lengths of the other two sides.
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3(2 +6j what’s the answer
Answer: 6 + 18j
Step-by-step explanation: you distribute the 3
31. Given that f(x) = 55+x and g(x) = 5, it must be true
that (x) = ?
A. 11+
B. 11 + x
C. 11+5x
D. 55+
E. 55+5x
55 + 5x, because we substitute g(x) = 5 in f(x) and get the final function as f(g(x)) = 55 + 5x. option E
How determine if f(x) = 55+x and g(x) = 5 is trueWe are given two functions:
f(x) = 55 + x
g(x) = 5
We need to find the value of f(g(x)), which means we need to substitute g(x) in place of x in f(x).
f(g(x)) = f(5)
Therefore, we need to find f(5).
f(x) = 55 + x
f(5) = 55 + 5 = 60
So, the answer is E. 55 + 5x, because we substitute g(x) = 5 in f(x) and get the final function as f(g(x)) = 55 + 5x.
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help asap will give brainliest hurry
Based on the given information, the value of y is 5.
What is a cyclic polygon?
A cyclic polygon is a polygon that can be inscribed inside a circle in such a way that all of its vertices lie on the circumference of the circle. In other words, a cyclic polygon is a polygon that can be circumscribed by a circle.
In a polygon with n sides, the sum of its interior angles is given by the formula: (n - 2) * 180 degrees. Since this polygon is inside a circle, it must be a cyclic polygon, which means that its opposite angles add up to 180 degrees.
We are given that the opposite angles are 23y and 13y, so we can write:
23y + 13y = 180
36y = 180
y = 5
Therefore, the value of y is 5.
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A painter uses 12 quarts of paint to paint a room and 6 gallons of paint to paint a fence. How many total gallons of paint does the painter use?
Responses
Answer:
9 gallons
Step-by-step explanation:
4 quarts = 1 gallon
12/4=3
3 + 6= 9
9 gallons
Chuck's Chops, an up-scale steak house, received an invoice for 800 pounds of baking potatoes with a cost of $.85 per pound. The terms were, n/30. Chuck was unable to pay the bill in full within the discount period but was able to remit a partial payment of $425.00 within the discount period. How much credit did Chuck receive for his payment?
Chuck received a credit of $369.15 for his partial payment.
What is simple interest?
The interest on a loan or principal sum can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.
The total cost of the baking potatoes is calculated by multiplying the weight of potatoes by the cost per pound:
800 pounds x $0.85/pound = $680
Since the terms are n/30, Chuck has 30 days to pay the invoice in full to receive the discount. He made a partial payment of $425 within the discount period, which means he has a remaining balance of:
$680 - $425 = $255
To determine how much credit Chuck received for his partial payment, we need to calculate the discount he would have received if he had paid the full amount within the discount period. The discount is calculated by multiplying the total cost by the discount rate, which is calculated by dividing the discount period by the number of days in the year:
Discount rate = discount period / number of days in the year
Discount rate = 30 / 365
Discount rate = 0.0822
Discount = total cost x discount rate
Discount = $680 x 0.0822
Discount = $55.85
Since Chuck only paid $425 within the discount period, he is entitled to a credit for the remaining discount amount:
Credit = Discount - Partial payment
Credit = $55.85 - $425
Credit = -$369.15
Therefore, Chuck received a credit of $369.15 for his partial payment.
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I need this in standard form and it’s not showing up??
An expression that equals 24 + 3B in standard form is: 36 + 9m
What is standard form ?
To find an expression that equals 24 + 3B in standard form, we first need to find the value of B and then substitute it into the expression.
Given that B = 3m + 4, we can substitute it into 24 + 3B to get:
24 + 3B = 24 + 3(3m + 4)
Simplifying the expression inside the parentheses, we get:
24 + 9m + 12
Combining like terms, we get:
36 + 9m
Therefore, an expression that equals 24 + 3B in standard form is:
36 + 9m
What is an expression?
In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, ×, ÷, etc.) that represents a value or a relationship between values. Expressions can be simple, such as a single number or variable, or complex, such as a combination of several terms with different operators.
For example, 2x + 3y - 5 is an expression that consists of three terms (2x, 3y, and -5) with two operators (+ and -). This expression can be evaluated for different values of x and y to obtain different numerical results.
Expressions can be used to represent mathematical formulas, describe geometric shapes and patterns, and solve real-world problems in a wide range of fields, including science, engineering, finance, and statistics.
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Complete question is: An expression that equals 24 + 3B in standard form is: 36 + 9m,
12. Pure fruit concentrate must be diluted with water in the ratio 1:7.
How many millilitre of concentrate are needed to make 5litres cool drink?
After answering the presented question, we can conclude that As a equation result, 625 millilitres of pure fruit concentrate are required to generate 5 litres of cold drink.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
If we need to dilute the pure fruit concentrate with water in a 1:7 ratio, this means that we need 7 parts water for every 1 part concentrate.
As a result, in order to prepare 5 litres of cool drink, we will need:
0.625 litres of pure concentration = 1/8 x 5 litres
We multiply litres by 1000 to get millilitres:
625 millilitres of pure concentrate (0.625 x 1000).
As a result, 625 millilitres of pure fruit concentrate are required to generate 5 litres of cold drink.
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A 14- ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 3feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 5 feet from the wall?
The company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.
What is inequalities
In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
To find the point at which the company starts to turn a profit, we need to find the value of x for which the revenue is greater than the cost of production.
The revenue function is R(x) = 7x, and the cost of production is C(x) = 13x + 132.
So, we need to solve the inequality:
R(x) > C(x)
7x > 13x + 132
Subtracting 13x from both sides, we get:
-6x > 132
Dividing both sides by -6 (and flipping the inequality because we're dividing by a negative number), we get:
x < -22
Therefore, the company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.
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Solve the inequality, if possible. 3(5w+4)<12w+15
A. W<1
B. W<3/2
C. W>15
D. Not possible
Answer:
[tex]3(5w + 4) < 12w + 15[/tex]
[tex]15w + 12 < 12w + 15[/tex]
[tex]3w < 3[/tex]
[tex]w < 1[/tex]
A is the correct answer.
Two students, Sean and Felisha, are doing a science project to create protective barrier for an egg. At the conclusion of the project they must drop an egg from a window that is off the ground and NOT break the egg. The trick is to create a barrier that can also slow down the velocity of the falling egg. The equation describes the drop that Sean's egg took The equation describes the drop that Felisha's egg took By how many did Felisha's egg land first? (round answer to decimal places)
The equations for Sean's and Felisha's eggs when dropped from a height of 120 feet are given. By solving for t in each equation, it is found that Felisha's egg landed first by approximately 0.53 seconds.
To find the time it takes for each egg to hit the ground, we need to solve for t in each equation:
For Sean's egg:
f(t) = -16t² + 75t + 120
We want to find t when f(t) = 0 (i.e., when the egg hits the ground)
-16t² + 75t + 120 = 0
Divide both sides by -1 to simplify the equation:
16t² - 75t - 120 = 0
Using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
where a = 16, b = -75, and c = -120.
t = (-(-75) ± √((-75)² - 4(16)(-120))) / 2(16)
t = (75 ± √(75² + 4(16)(120))) / 32
t = (75 ± √(7955)) / 32
We know that the egg cannot hit the ground in negative time, so we can discard the negative solution:
t = (75 + √(7955)) / 32
t ≈ 3.742 seconds
For Felisha's egg:
f(t) = -16t² + 55t + 120
We want to find t when f(t) = 0 (i.e., when the egg hits the ground)
-16t² + 55t + 120 = 0
Divide both sides by -1 to simplify the equation:
16t² - 55t - 120 = 0
Using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
where a = 16, b = -55, and c = -120.
t = (-(-55) ± √((-55)² - 4(16)(-120))) / 2(16)
t = (55 ± √(55² + 4(16)(120))) / 32
t = (55 ± √(7649)) / 32
We know that the egg cannot hit the ground in negative time, so we can discard the negative solution:
t = (55 + √(7649)) / 32
t ≈ 3.212 seconds
Therefore, Felisha's egg landed first by:
3.742 - 3.212 ≈ 0.53 seconds (rounded to 3 decimal places).
Answer: Felisha's egg landed first by approximately 0.53 seconds.
Learn more about solving equations here: brainly.com/question/30066982
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Complete question is in the image attached below
type the correct answer in the box. use numerals instead of words. use / for the fraction bar. there are 57 houses on julian's street. of those houses, 12 have a skylight, 28 have a fireplace, and 5 have both a skylight and a fireplace. the probability, expressed as a fraction in the lowest terms, that julian lives in a house with a skylight or a fireplace is (what fraction in the lowest terms).
The probability that Julian lives in a house with a skylight or a fireplace is 35/57, which can be simplified to 5/8 in the lowest terms. So the answer is: 5/8.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
To calculate the probability that Julian lives in a house with a skylight or a fireplace, we need to add the number of houses that have a skylight and the number of houses that have a fireplace, and then subtract the number of houses that have both a skylight and a fireplace, because we don't want to count those houses twice:
Number of houses with a skylight = 12
Number of houses with a fireplace = 28
Number of houses with both a skylight and a fireplace = 5
Number of houses with a skylight or a fireplace = (12 + 28) - 5 = 35
Therefore, the probability that Julian lives in a house with a skylight or a fireplace is 35/57, which can be simplified to 5/8 in the lowest terms.
So the answer is: 5/8.
To learn more about probability from the given link:
https://brainly.com/question/30034780
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