The f(x) = -ax²+18 function equation for his parabolic path. x=√8 is he reached, to the nearest tenth of a foot.
What does "function equation" actually mean?A function is an equation that has just one answer for y for every possible value of x. When utilizing a function, each input of a certain type receives exactly one output.
Briefing:f(x) = -ax² + 18
f(2)= -a(2)²+18 = 12
-4a = 12-18
-4a = -6
a = -6/-4
a = 3/2
f(x) = (-3/2) x² + 12
f(0) = (-3/2) x² + 12
(3/2) x² = 12
x² = 8
x = √8
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Seven more than the quotient of a number and 2 equals 9 .
Answer:
4
Step-by-step explanation:
n/2 + 7 = 9
n/2 + 7 - 7 = 9 - 7
n/2 = 2
n = 4
Simplify the expression by using a double-angle formula.
sinπ/7·cosπ/7
After using the trigonometry method the answer is sin 2 (pi/7)/2
What principle underlies trigonometry?
The study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the branch of mathematics known as "trigonometry." Therefore, using trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle.
What distinguishes geometry from trigonometry?
The study of triangle properties, particularly those of right triangles, is known as trigonometry. But the study of geometry focuses on the characteristics of all geometrical figures.
Given that:
sinπ/7·cosπ/7
if we can divide and multiply 2 so it can be converted to sin 2 theta
sin 2 (pi/7)/2
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Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.(The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.
(a) x=3 hours
(b) x=4.5 hours
(c) x=13 hours
(d) x=1.5 hours
ŷ= 6.45x + 31.5 is the equation of the regression line for the given data
How to find the equation of the regression line for a given data?Construct the table of the data as follows:
x >>>> y >>>> x² >>>> y² >>>> xy
1 39 1 1521 39
2 45 4 2025 90
3 52 9 2704 156
4 49 16 2401 196
5 61 25 4096 305
5 72 25 5184 360
................................................................................................
20 318 80 17931 1146
.................................................................................................
∑x = 20, ∑y = 318, ∑x²= 80, ∑xy = 1146, n = 6 (number data points)
The linear regression equation is of the form:
ŷ = ax + b
where a and b are the slope and y-intercept respectively
a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )
a = (6×1146 - 20×318) / ( 6×80-20² )
a = 6876-6360 / 480-400
a = 516 / 80
a = 6.45
x' = ∑x/n
x' = 20/6 = 10/3
y' = ∑y/n
y' = 318/6 = 53
b = y' - ax'
b = 53 - 6.45×(10/3)
b = 53 - 21.5
b = 31.5
ŷ = ax + b
ŷ= 6.45x + 31.5
Thus, the equation of the regression line for the given data is ŷ= 6.45x + 31.5. (The scatter plot of the data is shown in the attached image)
(a) x=3 hours
ŷ= 6.45(3) + 31.5 = 50.85
(b) x=4.5 hours
ŷ= 6.45(4.5) + 31.5 = 60.525
(c) x=13 hours
ŷ= 6.45(13) + 31.5 = 115.35
(d) x=1.5 hours
ŷ= 6.45(1.5) + 31.5 = 41.175
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Jo leaves some money in a bank account that pays
interest. Each year, the balance of her account is
15% more than it was the year before.
If she starts with £400 in her account, work out
her balance for the next three years. Give your
answers in order and rounded to the nearest
pound.
If she starts with £400 in her account, her balance for the next three years IS; $608.35
How to solve exponential equation?
The general formula for exponential equation is;
y = a(b)ˣ
where;
a represents an initial value or amount
b is the constant multiplier, is a growth factor or factor of decay.
We are given;
Initial value; a = £400
constant multiplier; b = an increase of 15% yearly = 1.15
Thus, her balance for the next three years is;
y(3) = 400(1.15)³
y(3) = $608.35
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Please help me I really need it
Answer:
a) 4(8019) +3s ≥ 70000
b) yes
Step-by-step explanation:
Diego has walked an average of 8019 steps per day for 4 days and wants to walk 70000 steps in a week. You want an inequality for the average number of steps per day that Diego must walk for the last 3 days of the week, and you want to know if 12642 is a solution.
a) InequalityThe inequality will express the relationship between the steps walked and the goal. Let s represent the average number of steps walked each day for the last 3 days of the week.
The total number of steps walked in the first 4 days is the average per day times the number of days: 4(8019). The total number of steps walked in the last 3 days is the average per day times the number of days: 3s.
The total for the week is the sum of these. We want that to exceed 70000:
4(8019) +3s ≥ 70000 . . . . . . . the desired inequality
b) SolutionSolving for s, we find ...
3s ≥ 7000 -4(8019)
3s ≥ 37924 . . . . . . . . . subtract 32076
s ≥ 12641 1/3 . . . . . . . . divide by 3
The offered number, 12642, is greater than 12641 1/3, so is a solution.
Diego will meet his goal if he averages 12642 steps per day for the last 3 days of the week.
__
Additional comment
If Diego's 3-day average is 12462, he will have walked 70002 steps for the week, a number that is more than 70000.
The cost of buying gas varies directly with the number of gallons
Suppose that Lena bought 12.2 gallons of gas for $35.99. Write an equation that could be
used to find the unit cost per gallon of gas. Then find out how much 9.5 gallons of gas
would cost. Round to the nearest cent.
Answer:
1 gallon of gas is $2.95
9.5 gallons of gas is $28.025
Step-by-step explanation:
[tex]\frac{12.2}{35.99} =\frac{1}{y}[/tex]
Cross Multiply.
12.2 · y = 1 · 35.99
12.2y = 35.99
12.2y ÷ 12.2 = 35.99 ÷ 12.2
y = 2.95
1 gallon of gas is $2.95.
[tex]\frac{1}{2.95} =\frac{9.5}{y}[/tex]
1 · y = 2.95 · 9.5
y = 28.025
9.5 gallons of gas is $28.025.
It takes Stacy 0.75 hours to drive to school. Her route is 40km long. What is Stacy’s average speed on her
drive to school?
Answer:
Step-by-step explanation:
160/3
The sum of a number and seven is one more than twice the number. What is the number
Answer: x+7=1+2x
Step-by-step explanation:
If x represents the number,The sum of a number and 7 is x + 7One more than twice the number is 1 + 2xThe IS in the middle of the sentence means =So, x + 7 = 1 + 2x Solve this equation,If you need further assistance message me.
Express the confidence interval 71.6% ± 8.2% in the form of a trilinear inequality.
The confidence interval, expressed as a trilinear inequality, is 71.6%
What does a confidence interval mean?
The range of values we see in our sample and expect to find the value that most accurately represents the population are referred to as a confidence interval.
The lower bound is 71.6% - 8.2% = 63.4% and the upper bound is 71.6% + 8.2% = 79.8%.
Thus the confidence interval, expressed as a trilinear inequality, is 63.4% < p < 79.8%, where p= 71.6%.
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solve for the length of the diagonal of the rectangular prism
The diagonal can be written as -
d = √{(L)² + (B)² + (H)²}
What is a right rectangular prism? What is a mathematical equation? What is constant of proportionality?The right rectangular prism has two parallel end faces and four lateral faces, each one of which is a rectangle; the faces are perpendicular to each of its bases. The faces of a non-right rectangular prism (oblique prism) are parallelograms. A right rectangular prism is also called a cuboid.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a graph as shown in the figure.
Since the dimensions of a right rectangular prism are not given, assume the length, width and height to be [L], [W] and [H]. Then the diagonal can be written as -
d = √{(L)² + (B)² + (H)²}
Therefore, the diagonal can be written as -
d = √{(L)² + (B)² + (H)²}
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A truck enters a highway driving 60 mph. A car enters the highway at the same place 6 minutes later and drives 73 mph in the same direction. From the time the car enters the highway, how long will
it take the car to pass the truck?
Answer:
27.7 min
Step-by-step explanation:
In 6 minutes the truck will be 6 miles ahead of the car....
the car is going 13 mph faster and will cover this 6 miles in
6 mi / 13 mi/hr = .4615 hr =27.7 min
Ride and simplify two division expressions they have a negative quotient used to fractions -2/3 5/6 and negative one show your work
The simplification of complex fraction -⅔/⅚ is - 4/5
What are complex fractions?A complex fraction is a rational expression that has a fraction in its numerator, denominator or both. In other words, there is at least one small fraction within the overall fraction.
In fraction when the numerator is bigger than the denominator , then it is called improper fraction, when a fraction consist of whole number and proper fraction is called mixed fraction
-2/3 ÷ 5/6
= -2/3×6/5
= -4/5
Therefore -⅔/⅚ can be simplified to -⅘
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In an assembly of athletes from three sports, six athletes are from the BASKETBALL team labeled 1,2,3,4,5,6, five athletes are from the SWIM team labeled 1,2,3,4,5, and four athletes are from the HOCKEY team labeled 1,2,3,4. If an athlete is randomly chosen, what is the probability that the athlete is SWIM and EVEN?
The probability that the card is between four and eight (inclusive) or is a club is 4/13.
What is Probability?Probability helps us to know the chances of an event occurring.
The number of cards can be written as,
The number of cards between 4 and 8 is 3 {4,5,6,7,8}.
Number of club cards = 13
Number of cards between 4 and 8 from heart, spades, and diamonds = 15
Now, the probability that the card is between four and eight (inclusive) or is a club is,
Probability = desired outcomes / total number of outcomes possible
= (Number of club cards+ Number of cards between 4 and 8)/(Total number of cards)
= (13+15)/(52)
= 28/52
= 4/13
Hence, the probability that the card is between four and eight (inclusive) or is a club is 4/13.
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Complete the square by adding the correct missing term on the left, then factor as indicated:
x²+x+________=(______)²
Answer:
Missing term [tex]\dfrac{1}{4}[/tex]
Factored term on RHS: [tex]$(x+\dfrac{1}{2})^{2}$[/tex]
Step-by-step explanation:
How many boards 6 5/6 in wide will cover floor 205 in wide
By using fraction, it can be calculated that
30 boards are required to cover a floor of width 205 inches wide
What is fraction?
Suppose there is a collection and a part of collection has to be taken.
The part which is taken is called fraction. In other words part of a whole is called fraction.
The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.
This is a word problem on fraction
Width of each board = [tex]6\frac{5}{6}[/tex] inches = [tex]\frac{41}{6}[/tex] inches.
Total width of floor = 205 inches.
Number of boards required = [tex]205 \div \frac{41}{6}[/tex] = [tex]205 \times \frac{6}{41}[/tex] = 30
30 boards are required
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Debbie has 4,000 in an account the interest rate is 15% compounded annually to the nearest and how much interest will she earn in 2 years
need answers fast please and thank you
Answer:
Step-by-step explanation:
The formula you want is: fv=p(1+int/c)^(nc)
future value
principal
int
compound
years
fv=4000(1.04/4)^(16)=$4690.31
2. Table 1 shows the number of pupils attending a motivation camp.
Two pupils from the group are required to take part in a show.
a) If a pupil is chosen at random from school A and another one from school B, calculate the probability that both are girls.
b) If two pupils are chosen at random from the group of boys, calculate the probability that both are from the same school.
a) The probability that both are girls is of: 21/150.
b) The probability that both are from the same school is of: 0.7333 = 73.33%.
How to obtain the probabilities?The probabilities are obtained as the division of the number of desired outcomes by the number of total outcomes.
For item a, the outcomes are given as follows:
One girl from school A -> 7/15 probability.One girl from school B -> 3/10 probability.Hence the probability that both are girls is of:
p = 7/15 x 3/10 = 21/150.
The probability that the two boys are from the same school can be given by these two cases:
School A: 8/15 x 7/14.School B: 7/10 x 6/9.Then the probability is of:
p = 8/15 x 7/14 + 7/10 x 6/9 = 0.7333 = 73.33%.
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Write an equation in solve-intercept form of the line that passes through the point (2, -2) and is parallel to the line y= -x-2.
The equation of the line that is parallel to the line x + y + 2 = 0 and passing through (2, -2) will be x + y = 0.
What is the equation of a parallel line?Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as,
ax + by + d = 0
The equation of the line is given below.
y = - x - 2
x + y + 2 = 0
Then the equation of the line that is parallel to x + y + 2 = 0 is given as,
x + y + d = 0
The line is passing through (2, -2), then we have
2 + (-2) + d = 0
d = 0
The equation of the line that is parallel to the line x + y + 2 = 0 and passing through (2, -2) will be x + y = 0.
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In a survey of 1000 eligible voters selected at random, it was found that 100 had a college degree. Additionally, it was found that 80% of those who had a college degree voted in the last presidential election, whereas 45% of the people who did not have a college degree voted in the last presidential election. Assuming that the poll is representative of all eligible voters, find the probability that an eligible voter selected at random will have the following characteristics. (Round your answers to three decimal places.) (b) The voter did not have a college degree and did not vote in the last presidential election.
The probability that an eligible voter selected at random did not have a college degree and did not vote in the last presidential election is 49.5%.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
The no. of people who don't have a college degree is (1000 - 100) = 900.
45% of the people who did not have a college degree voted in the last presidential election hence (100 - 45) = 55% of the people who did not have a college and did not vote in the last presidential election.
∴ (55/100)×900.
= 495 people.
∴ The probability that an eligible voter selected at random did not have a college degree and did not vote in the last presidential election is,
= 495/1000.
= 0.495.
= 49.5%.
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Simplify 6.5m(3m + 1.8) using the distributive property.
19.5m + 11.7m
19.5m + 1.8
19.5m2 + 11.7m
19.5m2 + 1.8
Answer:
C.
19.5m2+11.7m
Step-by-step explanation:
hope this helps
Answer:
C.
19.5m2+11.7m
Step-by-step explanation:
what i got on the test
Line t passes through points (9, 9) and (2, 5). Line u is perpendicular to t. What is the slope of line u?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
PLEASE HELP!
Research two different movie production companies. For each company, collect data on a categorial variable and a quantitative variable for comparison purposes. For example, you could determine the genre of the last 20 movies produced, the length of the most
recent 30 movies, the amount of money earned by the 50 highest grossing movies of all time, etc.
Display the categorical data that you collected from each of the two individuals in a side-by-side bar graph, segmented bar graph, or mosaic plot.
Nominal and ordinal categorical variables are the two different types.
What are the 2 types of categorical variables explain and give examples each?Nominal and ordinal categorical variables are the two different types.A nominal variable's categories do not naturally have an inherent order.For instance, gender is a categorical variable that has two categories (male and female), neither of which have any inherent ordering.The ordering of an ordinal variable is obvious.Any variable where the data indicate amounts is referred to be a quantitative variable.Any variable where the data represent groupings is referred to as a categorical variable.This comprises categories (like where people placed in a race), rankings (like cereal brands), and binary results.To learn more about categorical variables refer
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If M is the centroid of triangle ABC, AM = 44, CE =54, and DM
= 23, find each missing measure.
The missing sides of triangle ABC, If M is the centroid of triangle ABC, AM = 44, CE =54, and DM = 23, are FM = 22, AM = 44.
What is the centroid of the triangle?Three medians of a triangle intersect to produce the centroid of the triangle. It is one of a triangle's four points of concurrency. When the midpoints of the triangle's opposite sides are linked, the triangle's vertices become the triangle's medians.
Given:
The [tex]M[/tex] is centroid of triangle ABC, AM = 44, CE = 54, and DM = 23,
The centroid of a triangle divides the median in the ratio [tex]2 : 1[/tex]
Therefore, [tex]AM : FM = 2 : 1[/tex]
Let AM = 2x and FM = x
Since, AM = 44
Hence, 2x = 44
x = 44 / 2
x = 22
FM = 22
Therefore, the missing sides are FM = 22 and AM = 44.
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The missing figure is attached below.
ASAP!!!
Find the perimeter of the square
Answer:
156
Step-by-step explanation:
4x + 3 = 3(2x - 5)
4x + 3 = 6x - 15
3 = 2x - 15
2x = 18
x = 9
4(9) + 3
= 36 + 3
= 39
39 * 4 = 156
Hope it helps!
Answer: 156 inches
Step-by-step explanation:
So we know that all of the sides are equal to each other.
Now we need to know what x equals.
4x + 3 = 3(2x -5)
4x + 3 = 6x - 15
3 = 2x -15
18 = 2x
9 = x
Plug 9 into one of the equations.
4(9) + 3
36 + 3 = 39
39 * 4 = 156
Perimeter = 156 inches
Hope this helps!!! :)
hi!! can someone do 14 and 16 or just one if you’d rather do that?? thank you sm i’m just trying to get some of my assignments done by tomorrow and i don’t understand how to do these things
PLS answer this i need it asap
Answer:
b
step by step explanation
PLEASE HELP
ALGEBRA
The explicit formula for the geometric sequence would be [tex]a_n =10000.87\times (0.95)^{n-1}[/tex].
What is a geometric sequence?
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Given:
[tex]a_4=8573.75\\\\a_6=7731.81[/tex]
Now by using the formula for the nth term of a GP, we get
[tex]a_n = ar^{n-1}\\\\a_4=ar{4-1}\\\\8573.75=ar^3[/tex]
Now for n = 6, we get
[tex]a_n = ar^{n-1}\\\\a_6=ar{6-1}\\\\7737.81=ar^5[/tex]
Now divide we get
[tex]\frac{ar^5}{ar^3} =\frac{7737.81}{8573.35} \\\\r^2=0.9025\\\\r=0.95[/tex]
Now we can get the value of a,
[tex]8573.75=ar^3\\\\a = \frac{8573.75}{(0.95)^3}\\\\a = \frac{8573}{0.8573}\\\\a = 10000.87[/tex]
So we can prepare the explicit formula as
[tex]a_n =10000.87\times (0.95)^{n-1}[/tex]
Hence, the explicit formula for the geometric sequence would be [tex]a_n =10000.87\times (0.95)^{n-1}[/tex].
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Factor 132w + 55 using the Distributive Property.
Answer:
11(12w+5)
Step-by-step explanation:
common factors of 132 and 55 is 11
So we can take it out by dividing both terms by 11
11(12w+5)
Hopes this helps
Answer:I hope this is helps
good luck
Step-by-step explanation:
132w+55
Factor out from the expression
11(12w+5) this is the distributive Property
Write the sentences as an equation. 140 is the same as a multiplied by 319
140 is the same as multiplying by 319 as an equation can be written as 140 = a x 319.
What is an equation?An equation is a mathematical expression that contains an equal symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculation.
Hence, the sentence as an equation for 140 is the same as multiplying by 319 is, 140 = a x 319.
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To express the given numbers in equation form it can be written as =
140 is the same as multiplying by 319 as an equation can be written as 140 = a x 319.
What is an equation?
An equation is a mathematical expression that contains an equal symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculation.Hence, the sentence as an equation for 140 is the same as multiplying by 319 is, 140 = a x 319.A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.To know more about equations check out,
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Which of the following groups of numbers are all prime numbers?
O A. 3, 11, 23, 31
OB. 7, 17, 29, 49X
OC. 2, 3, 5, 9%
O D. 2, 5, 15, 196
Answer:
O A. 3, 11, 23, 21
OB. 7, 17, 29
OC. 2, 3, 5
OD. 2, 5
Step-by-step explanation: