The required answers are
i) -65.6
ii) -64.8
iii) -64
iv) -64
VelocityThe pace at which an object's position changes in relation to a frame of reference and time is known as its velocity.
Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.
Its SI equivalent is the metre per second (ms-1). A body is considered to be accelerating if its velocity changes, either in magnitude or direction.
Now in the given question,
1. Average velocity
When t=2
i. [2, 2.1]
= y(2.1) - y(2) / 2.1 - 2
= 205 - 16(2.1)^2 - 205 + 16(2)^2 / 0.1
= 205 - 16*4.41 - 205 +16(4) / 0.1
= -70.56 +64 / 0.1
= -6.56 /0.1
= -65.6
ii. [2, 2.05]
= y(2.05) - y(4) / 4.05 - 4
= 205 - 16(2.05)^2 - 205 +16(2)^2 / 0.05
= 205 - 16*4.2025 - 205 + 16(4) / 0.05
= -3.24 / 0.05
= -64.8
iii. [2, 2.01]
= y(2.01) - y(2) / 2.01 - 2
= 205 - 16(2.01)^2 - 205 + 16(2)^2 / 0.01
= 205 - 16*4.0401 - 205 + 16(4) / 0.01
= -64.64 + 64 / 0.01
= -0.64 / 0.01
= -64
iv. Instantaneous velocity
y = 205 - 16t^2
dy/dx = -32t
Considering t = 2
Instantaneous velocity after 2 seconds = -32(2)
Instantaneous velocity after 2 seconds = -64
To know more about velocity, visit:
https://brainly.com/question/18084516
#SPJ4
the sum of a number and 3 is 6 less than twice that number
Answer:
x = 9
Step-by-step explanation:
x + 3 = 2x - 6
3 + 6 = 2x - x
9 = x
x = 9
Hope this helped have a great day!
there are 21 sedans and 12 sports utility rehicles on the lot of a used car dealership. If he ratio of sedans to SUV's stays the same, now man sedans will be in the lot of 99 vehicles?
Answer: 63 sedans
Step-by-step explanation:
21 * 3
angelique builds a fence. After working for 2 5/6 hours, she has built 5/8 of the fence.
Angelique needs 3 8/15 hours to completely build the fence.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Angelique builds a fence and she can build 5/8 of the fence in 2 5/6 = 17/6 hours.
We know a number multiplied to its reciprocal is 1.
Therefore, The amount of time Angelique needs to complete the fence is,
(5/8)×(8/5) the complete fence in (17/6)×(8/5) hours.
= 136/30 hours.
= 3 16/30 hours.
= 3 8/15 hours.
Q. Angelique builds a fence. After working for 2 5/6 hours, she has built 5/8 of the fence, how much time she needs to complete the fence?
learn more about the unitary method here :
https://brainly.com/question/28276953
#SPJ1
The sum of the angles of a triangle is 180". One angle of a triangle 100% and the magnitude of the other two is in the ratio 2:3. Determine the magnitudes of the other two angles.
Answer:
The two angles are 32 degrees and 48 degrees.
Step-by-step explanation:
If one angle of a triangle is 100 degrees, then the sum of the other two angles is 80 degrees (180 - 100). If the magnitude of the other two angles is in the ratio 2:3, then we can call the first angle 2x and the second angle 3x. The sum of these two angles is 5x, so 5x = 80, and x = 16. So, the two angles are 2x = 32 degrees and 3x = 48 degrees.
Complete the process of solving the equation.
Fill in the missing term and select the missing description. Simplify any
fractions.
11(u-4)=-11
U-4 =-1
U=
Add 4 to both sides
POPULATION A city's population is 358,000 and is decreasing at an annual rate of 0.25%.
Which function represents the estimated population after "t" years?
Answer:
pop'n = 358000*(1-0.25%)^t
Step-by-step explanation:
pop'n = 358000
decreasing rate = 0.25%
after t years
pop'n = 358000*(1-0.25%)^t
What is the sum of this expression?
Answer:
B. 9[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Rewriting the two fractions in the expression:
=[tex]\frac{[(8)(2)]+1}{8} + \frac{[(8)(7)]+3}{8}[/tex]
=[tex]\frac{17}{8} + \frac{59}{8}[/tex]
Since the denominators of both the fractions is the same, then the denominator of the resulting simplified fraction will also be the same. In addition, everything written in the numerator level will be copied down as it is:
=[tex]\frac{17 + 59}{8}[/tex]
=[tex]\frac{76}{8}[/tex]
Divide the numerator and denominator by the Highest Common Factor '4':
= [tex]\frac{19}{2}[/tex]
Apply Long Division since:
The numerator is greater than the denominator and The numerator and the denominator cannot be further reduced or simplifiedChoose the highest quotient to be multiplied by 2 to give a number closest to 19 but still less than 19. The quotient turns out to be 9. The remainder is 1
∴ Sum of the expression = 9[tex]\frac{1}{2}[/tex]
Presidential Poll. A research group suspects that less than 48% of Americans support the Republican presidential candidate. To test this claim, they randomly call Americans until they get 1000 responses. Of the 1000 people who responded, 477 of them say they support the Republican presidential candidate. Test the research group's suspicion at a 5% level of significance.
(b) Find the p-value (round to four decimal places).
The p-value for the two-tailed test is 2 mincdf(x), 1 - cdf (x) because a study team believes that less than 48% of Americans are affected.
what is null hypothesis ?A type of data hypothesis known as both a null hypothesis claims that a certain collection of data has no statistically significant results. The viability of hypotheses be evaluated using sample. Sometimes refers to as "zero," and symbolized as H0. The premise made by the researchers is that there is a correlation between the variables. The h0, on the other hand, says that such an association doesn't quite exist. Despite its inability to seem significant, the null hypothesis is a crucial component of a study.
given
Calculating the p-value requires knowledge of the distribution of your test statistic under the assumption that the null hypothesis is true.
Cdf as the p-value for the left-tailed test (x).
Right-tail test: p-value = 1 - cdf (x).
The two-tailed test's p-value is 2 mincdf(x), 1 - cdf (x).
The p-value for the two-tailed test is 2 mincdf(x), 1 - cdf (x) because a study team believes that less than 48% of Americans are affected.
To know more about null hypothesis visit
https://brainly.com/question/28920252
#SPJ1
Elizabeth has 10 mangoes
eats 5 and gives
2 to Mary and throws 1 away how many mangoes are left
Answer:
2
Step-by-step explanation:
10-5=5.....the ones she ate
5-2=3 .... the 2 she gave to Mary
3-1 =2.....the one she threw away
2 mangoes!
10 - 5 = 5
5 - 2 = 3
3 - 1 = 2
Find the value of X and Y.
The value of the side lengths x and y are 29.4 units and 17 units
How to determine the values of the sidesFrom the information given, we have that;
The hypotenuse side = 34The opposite side = yThe adjacent side = xUsing the cosine identity'
sin 30 = y/34
find the value
0. 5000 (34) = y
Multiply
y = 17 units
Using the cosine identity
cos 30 = x/34
multiply
x = 34(0.8660)
x = 29. 4 units
Hence, the values are 17 units and 29. 4 units
Learn about trigonometric identities on:
https://brainly.com/question/7331447
#SPJ1
NEED HELP!!
You are going on a long trip and want to calculate your Miles per gallon. When you start your trip your odometer read 69247 miles. At the end of your trip your odometer reads 69765 miles. You started with a full tank and to return to a full tank you put in 14 gallons of gas total. What is your miles per gallon?
Mpg: ?
Taking the quotient between the total distance and the gallons consumed we can see that:
Mpg = 37 miles per gallon.
How to get the miles per gallon?It is just given by the quotient between the number of miles traveled and the number of gallons used.
We know that at the start the odometer reads 69247 miles and at the end the odometer reads 69765 miles, taking the difference we can see that the total distance traveled is:
69765 mi - 69247 mi = 518 mi
And you consumed 14 gallons of gas, then the miles per gallon is:
Mpg = 518mi/14 gal = 37 miles per gallon.
Learn more about quotients at:
https://brainly.com/question/629998
#SPJ1
1/2
0
|X| + |Y| < 1
otherwise
The function designates an area in the X-Y plane where its value is 1/2 and an area where it is 0. By applying the formula |X| + |Y| = 1, the line separating these two regions is defined as equation.
An equation and an example: what are they?When two expressions are joined by an equal sign, a mathematical statement is called an equation. An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable.
What are equations, and what different varieties are there?Equations can be classified as either conditional equations or identities. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth.
To know more about Equation, visit
brainly.com/question/29657988
#SPJ1
The complete question is: Let f(x)={1/2} = 0 and |X| + |Y| < 1, find the value of x.
Alvin's age is two times Elga's age. The sum of their ages is 27. What is Elga's age?
Answer:
52
Step-by-step explanation:
my boy its 52 she said times it means multiply
Find the value of x. Give reasons to justify your solution.
How the ffffffffffffffffffffffffffffffffffffffffff
Given (11,6)
and (x,−9)
, find all x
such that the distance between these two points is 17
. Separate multiple answers with a comma.
Therefore, the values of x that make the equation distance between (11,6) and (x,-9) equal to 17 are x = 19 and x = 3.
What exactly is a linear equation?The formula y=mx+b is used to draw a simple regression graph. The inclination is B, and the y-intercept is m. It is frequently referred to simply as a "simple method combining many variables," despite the fact that the section before it is divided into distinct sections. Bivariate linear equations have two variables. For problems involving linear equations in applications, there are no proven solutions. Y=mx+b, also known as mx+b, provides a number of straightforward formulae.
Here,
Using the distance formula:
sqrt((x - 11)^2 + (-9 - 6)^2) = 17
Simplifying:
sqrt((x - 11)^2 + 225) = 17
Squaring both sides:
(x - 11)^2 + 225 = 289
(x - 11)^2 = 64
Taking the square root:
x - 11 = ±8
x = 11 + 8 or x = 11 - 8
x = 19 or x = 3
Therefore, the values of x that make the equation distance between (11,6) and (x,-9) equal to 17 are x = 19 and x = 3.
To know more about linear equation visit:
https://brainly.com/question/11897796
#SPJ1
Use StatKey or other technology to find the regression line to predict Y from X using the following data.
X 10 20 30 40 50 60
Y 111 109 110 94 92 93
Click here to access StatKey.
Round your answer for the intercept to one decimal place and the answer for the slope to two decimal places.
The regression equation is Enter your answer; The regression equation, intercept
+ Enter your answer; The regression equation, slope
X.
The regression equation is Y = 95.0 + 0.84X.The regression line is a mathematical model that is used to predict the value of a dependent variable (Y) based on the value of an independent variable (X).
In this case, the regression line is used to predict Y from X using the following data: X = 10, 20, 30, 40, 50, 60 and Y = 111, 109, 110, 94, 92, 93. By using a regression analysis tool such as StatKey, we can calculate the regression equation that best fits this data. The regression equation is Y = 95.0 + 0.84X, where 95.0 is the intercept and 0.84 is the slope. This equation can be used to make predictions about the value of Y for a given value of X. The rounded answer for the intercept is 95.0 and the rounded answer for the slope is 0.84.
Find out more about regression equation
brainly.com/question/22077082
#SPJ4
A $9860 investment earns interest at
2.7% per year
compounded monthly
over 6 years. Use the compound
interest formula to calculate the value
of this investment to the nearest cent.
Answer: Final Balance is $11,591.87 and the total compound interest is $1,731.87.
Step-by-step explanation:
What is the simplified form of 4 log3x + 6 log3y - 7 log3z?
The simplified form of 6 log₃x - 7 log₃y + 4 log₃z is log₃{(x⁶z⁴)/y⁷}.
What are exponents?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.
The simplification of the provided logarithmic expression can be done as follows:-
6 log₃x - 7 log₃y + 4 log₃z,
= log₃x⁶ - log₃y⁷ + log₃z⁴ {Using the Power law}
= log₃x⁶ + log₃z⁴ - log₃y⁷
= log₃x⁶z⁴ - log₃y⁷ {Using the Product law}
= log₃{(x⁶z⁴)/y⁷} {Using the Quotient law}.
Hence, the simplified form of 6 log₃x - 7 log₃y + 4 log₃z is log₃{(x⁶z⁴)/y⁷}.
Learn more about exponents here:
https://brainly.com/question/5497425
#SPJ1
Express the gross salary g of a person who earns per hour as a function of the number x of hours worked.
Answer:
Gross salary =G
Number of worked hours =x
Dollar per hour =$12
substitute the given data into the gross salary formula and simplify.
Gross salary = (number of worked hours)
G =(x) (12)
G =12x
Therefore, G(x) =12x
Hence the function is G(x) = 12x
If you want to estimate the mean height of all the .students at a university, which one of the following sampling strategies would be best? Why? Note that none of the methods are true simple random samplesi. Measure the heights of 50 students found in the gym during basketball intramurals ii. Measure the heights of all engineering majors. iii. Measure the heights of the students selected by choosing the first name on each page of the cam pus phone book.
The optimum sampling strategy is (iii), which is listed below.
By selecting a student's initial name from each page of the cam pus phone book, you may measure the heights of the chosen pupils.
What is Sampling?Sampling is a technique for selecting a small group of people or a subset of the population in order to make generalizations and estimate the features of the population. In order to acquire relevant information without studying the entire society, researchers commonly use a variety of sampling approaches in market research.
To ascertain the average height of all students at a certain institution and guarantee that the result is statistically reliable, the sampling process must be applied.
a. Measure the heights of 50 students found in the gym during basketball intramurals.
This approach is not ideal since you would only sample basketball players while leaving all other university students out; hence, your sample would not be representative of all students, simply those who play basketball.
b. Measure the heights of all engineering majors.
This approach is flawed since the sample exclusively includes engineering majors, leaving out students studying other courses.
c. Measure the heights of the students selected by choosing the first name on each page of the campus phone book.
This strategy, which is the finest of the three, allows you to select students independent of the sport or subject they are pursuing. It is more representative of the university student population.
To know more about sampling, visit:
https://brainly.com/question/14814065
#SPJ4
Which expression represents the correct form for the quotient and remainder, written as partial fractions, of
8x3-2x2-67x-24
The quotient and remainder, when written as partial fractions, of 8x²³-21²-67x-24 is represented by 2x²-x-21.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
given that,
Which expression represents the correct form for the quotient and remainder?
(8x³-21²-67x-24) = (2x²-x-21) + (6x¹-42)
This is done by dividing 8x²³-21²-67x-24 by 2x² and using long division to find the remainder.
The result of the division is a quotient of 4x²-33x+12 and a remainder of 2x²-x-21.
The remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.
To illustrate this further, we can break down the long division process into steps. First, divide 2x² into 8x²³.
The result is 4x².
Then, subtract 4x² from 8x²³ to get the remainder of 4x³.
Next, divide 4x² into 21².
The result is 33x.
Then, subtract 33x from 4x³ to get the remainder of 4x²-33x.
Finally, divide 4x²-33x into 67x.
The result is 12. Subtract 12 from 4x²-33x to get the remainder of 2x²-x-21.
This remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.
To learn more about partial fractions refer to:
brainly.com/question/24594390
#SPJ1
is the following statement true or false? all other things being equal, outliers tend to have a greater effect on the value of the mean, as compared to the value of the median.
All other things being equal, outliers tend to have a greater effect on the value of the mean, as compared to the value of the median. The given statement is true.
What is the mean and median?
Outliers are values that are significantly different from the other values in a data set, and their presence can greatly affect the value of measures of central tendency, such as the mean and the median.
The mean is a measure of central tendency that is calculated as the sum of all the values in a data set divided by the number of values. The presence of outliers can greatly affect the mean because outliers can have a large impact on the sum of the values in the data set. For example, if a data set has a few very large outliers, the mean will be pulled up to be much higher than the median, which represents the midpoint of the data set.
On the other hand, the median is a measure of central tendency that is calculated as the middle value of a data set when the values are arranged in order. The median is not as sensitive to outliers as the mean because outliers do not affect the median unless the number of outliers is so large that it changes the value of the middle value.
Hence, all other things being equal, outliers tend to have a greater effect on the value of the mean than on the value of the median.
To learn more about Mean, Median, Visit
https://brainly.com/question/542771
#SPJ4
QUICK!!! 100 POINTS PLUS BRAINLIEST
Which statements about events in World War II are true?
Choose all answers that are correct.
Responses
German and Japanese scientists succeeded in breaking the Allies' most secret codes.
Nazi terror weapons, called V-1s and V-2s, killed thousands of people in Great Britain.
Germany's industries and cities were devastated by Allied bombing raids.
American forces used new types of ships to attack Japanese-held islands in the Pacific.
Which type of star is the sun?
A.
Supernova
B.
Hypernova
C.
Red giant
D.
Red Supergiant
Answer:
Supernova
Step-by-step explanation:
A supernova is a powerful and luminous explosion of a star, which is what the sun is.
The common denominator for the problem 3/4 + 5/6
Answer:
Step-by-step explanation:
9/12 + 10/12
Simplify
4x^3 - 12x^2
4x^2 + 7x - 2
2x^2 -6x
5x^2 + 11x + 2
2x(5x + 1) / (4x - 1) is the final expression.
Option D is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(4x³ - 12x²) / (4x² + 7x - 2) / (2x² - 6x) / (5x² + 11x + 2)
= (4x³ - 12x²) x (5x² + 11x + 2) / (4x² + 7x - 2) x (2x² - 6x)
Now,
(4x³ - 12x²) = 4x² (x - 3) _____(1)
And,
(5x² + 11x + 2)
Middle term factorizing
= 5x² + (10 + 1)x + 2
= 5x² + 10x + x + 2
= 5x (x + 2) + 1(x + 2)
= (x + 2) (5x + 1) ______(2)
And,
(4x² + 7x - 2)
Middle term factorizing
= 4x² + (8 - 1)x - 2
= 4x² + 8x - x - 2
= 4x(x + 2) - 1(x + 2)
= (4x - 1) (x + 2) ______(3)
And,
(2x² - 6x) = 2x (x - 3) ______(4)
From (1), (2), (3), and (4) we get,
(4x³ - 12x²) x (5x² + 11x + 2) / (4x² + 7x - 2) x (2x² - 6x)
= [ 4x² (x - 3) x (x + 2) (5x + 1) ] / [ (4x - 1) (x + 2) x 2x(x - 3) ]
(x + 2) and (x - 3) gets canceled.
= [4x² (5x + 1)] / [(4x - 1) 2x]
= 2x(5x + 1) / (4x - 1)
Thus,
2x(5x + 1) / (4x - 1)
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
June 1
June 12
• June 23
Jun 30
Inventory 150 unit cost 6$ total cost900$
purchase450 unit cost7$ total 3150$
Purchase400 unit cost 8$ total 3200$
Inventory 80
Assume a Sale of 500 units occured on June 15
for a Selling price of $9 and a sale of 420 units on
June 27 for $9
? The cost of goods available for Sale?
?calculate Moving-Average unit cost of for
June 1.
June12.
June 15.
June23.
June27.
?Calculate the cost of ending inventoryfor each cost flow assumption, using a
perpetual inventory System. Round average cost per Unit
3 decimal places.
on Round answer to 3 decimal
Answer:
Step-by-step explanation:
Cost of goods available for sale:
Starting inventory: 150 units * $6/unit = $900
Purchase on June 1: 450 units * $7/unit = $3150
Purchase on June 23: 400 units * $8/unit = $3200
Total cost: $900 + $3150 + $3200 = $7450
Moving Average Unit Cost:
June 1: $7450 / (150 + 450) = $7/unit (rounded to 3 decimal places)
June 12: $7450 / (150 + 450 + 400) = $7.36/unit (rounded to 3 decimal places)
June 15: $7450 / (150 + 450 + 400 + 500) = $7.51/unit (rounded to 3 decimal places)
June 23: $7450 / (150 + 450 + 400 + 500) = $7.51/unit (rounded to 3 decimal places)
June 27: $7450 / (150 + 450 + 400 + 500 + 420) = $7.43/unit (rounded to 3 decimal places)
Cost of ending inventory using perpetual inventory system:
FIFO: $7.51/unit * 80 units = $604 (rounded to 3 decimal places)
LIFO: $7/unit * 80 units = $560 (rounded to 3 decimal places)
Average Cost: $7.43/unit * 80 units = $594.4 (rounded to 3 decimal places)
In the New York Lotto, there are 51 balls numbered 1 to 51 in a barrel. To enter the lottery, you select six numbers. Then six balls are randomly drawn from the barrel without replacement to determine the six winning numbers. Select the appropriate distribution in the tool below to help answer some of the following questions. The probability that you match exactly two of the winning numbers is ______.
The appropriate distribution to answer questions about the New York Lotto is the hypergeometric distribution, which is used to calculate the probability of a certain number of successes in a sample of items drawn without replacement from a population.
The New York Lotto is a lottery game where participants select six numbers from a set of 51 numbers, 1 to 51. Then, six balls are randomly drawn from a barrel without replacement to determine the six winning numbers. To answer questions about the probability of various outcomes in this game, the appropriate probability distribution is the hypergeometric distribution. This distribution is used to calculate the probability of a certain number of successes in a sample of items drawn without replacement from a population. In the case of the New York Lotto, the population is the set of 51 numbers from 1 to 51, and the sample is the six numbers selected by the participant. The hypergeometric distribution can be used to calculate the probability of matching exactly two of the winning numbers.
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
Find the point-slope equation of the plane passing through the point (2, -12, 4) and having x-slope 15 and y-slope -19.Z = ___
The Point-Slope equation is Z = 15X - 19Y + 204.
What is the slope-point form?
The slope-point form of a line in 3-dimensional space is a equation of the form:
Z = m_x (X - X_0) + m_y (Y - Y_0) + Z_0
where (X_0, Y_0, Z_0) is a point on the line, m_x is the x-slope, and m_y is the y-slope.
Given:
point (2, -12, 4) and x-slope 15 and y-slope -19, we can use the point-slope form to find the equation of the plane:
Z = 15 (X - 2) - 19 (Y + 12) + 4
Hence, the point-slope equation of the plane passing through the point (2, -12, 4) and having x-slope 15 and y-slope -19 is:
Z = 15X - 30 - 19Y + 228 + 4
Z = 15X - 19Y + 204
To learn more about slope-point form, Visit
https://brainly.com/question/24907633
#SPJ4
A runner wants to be able to run 600 meters in 60 seconds. What miles per hour speed must the runner attain to accomplish this goal? The runner knows that there are 1690 meters in a mile. Round to the nearest whole number
Answer:
21 miles per hour
Step-by-step explanation: