The next two numbers on the number pattern are given as follows:
A 12.2, 12.9.
How to obtain the next two points on the number pattern?To obtain the next two points on the number pattern, first we must identify what is the pattern.
The pattern is given as follows:
The double of an amount is calculated.Then 0.7 is increased to double the amount, and we return to step 1, doubling the value.The final term is 6.1, which is obtained after the addition of 0.7 to 5.4. Double 6.1 is obtained multiplying the number by 2, as follows:
2 x 6.1 = 12.2.
Then the number obtained after 0.7 is added to 12.2 is given as follows:
0.7 + 12.2 = 12.9.
Meaning that the correct option to complete the number pattern is given by option A.
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Each survey respondent is asked to rate a specified supermarket based on a variety of factors such
as quality of products, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes the
rating for each respondent with 100 meaning the respondent is completely satisfied in terms of all factors. Sample data
representative of independent samples of Publix and Trader Joe's customers are shown below.
Publix
N₁= 250
X bar 1= 86
Trader Joe's
N₂ = 300
X bar ₂ = 85
p-value= (to 3 decimals)
There is no difference between the population mean customer satisfaction scores for the two retailers, according to p-value: 0.33049.
what is random sample ?chosen at random (purely random, unpredictable). Every person in the demographic being surveyed should have an equal chance of being chosen. She gave an example of a simple representative sample, choosing 25 names at random from a group of 250 employees. The sampling in this case is random since there are 250 of her coworkers in total, and every one has an equal chance of being picked. Researchers select people at random from a population using simple random sampling, which is a type of probability sampling. Every member of the population is given an equal chance at selection.
Given that,
mean(x)=86
standard deviation , σ1 =12
number(n1)=250
y(mean)=85
standard deviation, σ2 =12
number(n2)=300
null, u1 = u2
alternate, H1: μ1 != u2
level of significance, alpha = 0.05
we got |zo | =0.973 & | z alpha | =1.96
(b) test statistic: 0.97
There is no difference between the population mean customer satisfaction scores for the two retailers, according to p-value: 0.33049.
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Julia is allowed to watch no more than 6 hours of television a week. So far this week, she has watched 2.5 hours. Write and solve an inequality to show how many hours of television Julia can still watch this week
Answer: We can write an inequality to show how many hours of television Julia can still watch this week by using the following information:
Julia is allowed to watch no more than 6 hours of television a week.
So far this week, she has watched 2.5 hours.
We can use the inequality x + 2.5 <= 6, where x is the number of hours Julia can still watch this week.
This inequality represents the total number of hours watched (x + 2.5) being less than or equal to the maximum number of hours allowed (6).
To solve this inequality, we can subtract 2.5 from both sides:
x <= 6 - 2.5
x <= 3.5
So, Julia can still watch 3.5 hours of television this week.
Step-by-step explanation:
Answer:
The remaining hours of TV Julia can watch this week can be expressed as
[tex]x \leq 3.5hours[/tex]
Step-by-step explanation:
since Julia is allowed not to watch not more than 6 hours of television a week and she has watched 2.5 hours already
the remaining time (X) would be expressed as
[tex]x \leq (6 - 2.5)[/tex]
[tex]x \leq 3.5[/tex]
Write an equation for a line perpendicular to y= -5x-1 and passing through the point (10,3)
Answer: A line is perpendicular to another line if the slope of the first line is the negative reciprocal of the second line. The equation of the line y = -5x-1 has a slope of -5. The negative reciprocal of -5 is 1/5.
A line passing through a point (x1, y1) has an equation in slope-intercept form of y = m(x-x1) + y1, where m is the slope of the line.
So, we can use the point (10,3) and the slope of the line which is 1/5 to write the equation of the line:
y = 1/5(x-10) + 3
Therefore, the equation of the line perpendicular to y = -5x-1 and passing through the point (10,3) is y = 1/5x + 1/5
Step-by-step explanation:
It's raining, and Vince and his friends are stuck inside. They decide to play a marble game called Revenge. To start, Vince divides a bag of m marbles evenly among the 3 players. Each player gets 10 marbles.
The total number of marbles are 30.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, to start, Vince divides a bag of m marbles evenly among the 3 players. Each player gets 10 marbles.
Here, m/3 =10
m=30
Therefore, the total number of marbles are 30.
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The rectangle below has the dimensions:
5.3 × 5.7
Create another rectangle that is scaled to 4
times the size of the current rectangle.
Answer:
A rectangle of 10.6 x 11.4 dimensions.
Step-by-step explanation:
(5.3*2)*(5.7*2)=5.3*4*5.7=10.6x11.4.
PLEASE HELP ILL GIVE YOU 25 POINTS
The length of side x for the triangle is 5√3.
What is an equilateral triangle?An equilateral triangle is one with equally long sides on both sides. The three angles opposite the three equal sides are equal in size because the three sides are equal. It is also known as an equiangular triangle since each angle is 60 degrees.
Given an equilateral triangle,
length of the side is 10 units,
and a perpendicular is drawn with length x,
so a perpendicular drawn from one of the vertices to the opposite side of an equilateral triangle bisects that side.
we know the angle of the equilateral triangle is 60°,
by the sine function, we can calculate the value of x
sinФ = p/h
p = perpendicular = x
h = hypotenuse = 10
Ф = 60°
sin60 = x/10
x = 10*sin60
x = 10(√3/2)
x = 5√3
Hence the value of x is 5√3.
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One number is fourteen less than the other. If their sum is increased by seven, the result is 83. Find the numbers
Answer:
Let's call the two numbers x and y. We know that:
y = x + 14 (because one number is 14 more than the other)
x + y + 7 = 83 (because the sum of the two numbers plus 7 is 83)
We can substitute the first equation into the second equation:
x + (x + 14) + 7 = 83
Simplifying this equation:
x + x + 14 + 7 = 83
2x + 21 = 83
2x = 62
x = 31
So one number is 31 and the other number is 45 (since one is 14 more than the other).
Thank you everybody in advance for your kind attention and cooperation!
Seats for Sale
State's football program has risen to the ranks of the elite with postseason bowl games in each of the past 10 years, including a national championship game. The Bruins (as the fans are called) fill the stadium each game. Season tickets are increasingly difficult to find. In response to the outstanding fan support, State has decided to use its bowl revenues to expand the stadium to 75,000 seats.
The administration is confident that all 75,000 seats can be sold at the normal price of $40 per game ticket; however, Frank Pinto's job, as athletic director, is to get as much revenue out of the stadium expansion as possible. In addition to stadium boxes for wealthy alums, Frank would like to take this opportunity to repurpose existing seats. A certain number of seats (yet to be determined) would be set aside for premium ticket holders who would pay $200 per ticket for the privilege of 50-yard line seats with chair backs and access to indoor concessions. The question is, how many fans would be willing to pay such a premium? If too many seats are designated in the premium sections, they could remain vacant. Too few premium seats would lose potential revenue for the program.
Frank has decided that if the plan has any chance of success, unsold premium seats should not be sold at reduced rates. It would be better to donate them to local charities instead. Gathering data from his cohorts at peer institutions, Frank has put together the following probability distribution of premium ticket holders. The data begin with 1000 tickets since Frank already has requests for 999 tickets from alumni donors. He is asking for your help in performing the analysis.
No. of Premium Tickets Probability
1,000 0.10
5,000 0.30
10,000 0.24
15,000 0.15
20,000 0.10
25,000 0.06
30,000 0.05
a. Using revenue management, determine how many seats should be reserved for premium ticket holders.
b. Considering your answer to part (a) and the possible outcomes listed above, how much total revenue (i.e., regular and premium) can be expected from ticket sales?
c. The administration is unsure about Frank's plan. The VP of finance thinks an expected value of the number of premium seats would produce better results. How would the number of premium seats change using expected value? Considering the possible outcomes, which approach yields the most potential revenue?
Answer:
b. Considering your answer to part (a) and the possible outcomes listed above, how much total revenue (i.e., regular and premium) can be expected from ticket sales?
A free bus service operates throughout the day around Brelney City Centre. The bus starts from the Railway Station, then stops successively at the Castle, the Shopping Centre, the Park and the Stadium, before returning to the Railway Station. The journey time for each section of the circuit is 5 minutes.
The first departure of the day from the Railway Station is at 09:15. Each time the bus arrives back at the Railway Station it waits for 10 minutes before setting off again.Bart will be the driver for the first 4 circuits tomorrow.At what time will Bart arrive back at the Railway Station for the final time tomorrow?
A 11:25
B 11:35
C 11:45
D 11:55
Answer:
The bus journey takes 25 minutes (5 minutes per stop x 5 stops). The bus leaves the Railway Station every 10 minutes (the wait time between circuits).
The first departure is at 09:15, so the bus will arrive back at the Railway Station at:
09:15 + 25 minutes = 09:40
Bart will drive the bus for 4 circuits, so the bus will arrive back at the Railway Station for the final time at:
09:40 + (4 x 25 minutes + 4 x 10 minutes) = 09:40 + 130 minutes =
11:50.
So the final arrival time will be D 11:55.
Answer:
Step-by-step explanation:
Each circuit takes 25 minutes (5 destinations times 5 minutes) plus the 10 minute wait at the Railway Station. So the entire circuit is 35 minutes with the wait. Bart drives 4 circuits - 4 times 35 minutes is 140 minutes.
140 minutes equals 2 hours and 20 minutes.
Add 2 hrs and 20 minutes to 9:15 and the sum = 11:35
The answer is B - 11:35
In the binomial expression of (1+x)
n
the first three terms are 1+3+4+---. Calculate
the numerical values of n and x, and the values of the fourth term of the expression.
Answer:
x = 1/3n = 9fourth term = 28/9Step-by-step explanation:
Given the first three terms of the expansion of (1 +x)^n are 1 +3 +4, you want the values of x and n, and the next term.
Binomial expansionThe first few terms of the binomial expansion of (1 +x)^n are ...
[tex](1+x)^n=1^n+n\cdot1^{n-1}x+\dfrac{n(n-1)}{2}1^{n-2}x^2+\dfrac{n(n-1)(n-2)}{2\cdot3}1^{n-2}x^3+\dots[/tex]
Comparing termsComparing the terms to those given, we have ...
[tex]nx=3\\\\(nx)((n-1)x)/2=4[/tex]
Expanding the second of these equations, and substituting the first, we get ...
[tex](nx)(nx -x)=8\qquad\text{multiply by 2}\\\\3(3-x)=8\qquad\text{substitute $nx=3$}\\\\9-8=3x\qquad\text{add $3x-8$}\\\\\boxed{x=\dfrac{1}{3}}\qquad\text{divide by 3}\\\\\dfrac{1}{3}n=3\qquad\text{substitute for $x$ in $nx=3$}\\\\\boxed{n=9}\qquad\text{multiply by 3}[/tex]
Fourth termThen the fourth term is ...
[tex]\dfrac{n(n-1)(n-2)}{6}x^3=\dfrac{9\cdot8\cdot7}{6}\cdot\left(\dfrac{1}{3}\right)^3=\boxed{\dfrac{28}{9}}[/tex]
__
Additional comment
Then the expansion is ...
(1 +1/3)^9 = 1 + 3 + 4 + 28/9 + 14/9 + 14/27 + ...
The n-th term is (11-n)/(3(n-1)) times the term before.
how to round 456.173 to the nearest hundredth?
Answer:
456.17
Step-by-step explanation:
Rounding to the nearest hundredths' is asking is the number given 456.173 closer to 146.170 or 146.171. You can see that the number is closer to 146.170 which is the same number as 146.17
Rule
Look at the digit in the thousandths' place. In this case 3. If this number is 5 or greater round up, if this number is 4 or smaller round down. We will round down.
456.17
Answer:456.17
Step-by-step explanation:
If the thousandth place is 5-9, for example 456.178, the answer rounded to hundredth place will be 456.18.
But if the thousandth place is 1-4, the answer rounded to hundredth will be 456.17.
So the answer is 456.17.
Graph the line that has a slope of 1/6 and includes the point (0,2)
Answer:
y=1/6x+2 is the slope formula.
The equation of a line passing through the point (0,2) and having slope 1/6 is: x-6y+12=0
Step-by-step explanation:
Equation of a line passing through a point (x1,y1) and having slope m is: [tex]y-y_{1} =m(x-x_{1} )[/tex]
where m= slope of the line
Given point (x1 , y1)= (0 , 2)
So, the Equation of a line: [tex]=y-y_{1} =m(x-x_{1} )[/tex]
[tex]y-2 =(\frac{1}{6} )(x-0 )[/tex]
[tex]y-2 =(\frac{1}{6} )(x)[/tex]
[tex]6*(y-2) =(x)[/tex]
[tex]6y-12=x[/tex]
[tex]6y-12-x=0[/tex]
[tex]-x+6y-12=0[/tex] OR [tex]x-6y+12=0[/tex]
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6. Using any method(s), solve △KHP when h=16.1, p=24.9 and k=12.8
The angles of the triangle KHP are P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°, respectively.
How to determine the measures of missing angles in a triangle
In this question we have the case of a triangle where the lengths of three sides are known and measures of angles must be determined. The missing angles can be found by means of law of cosine, whose equations related to the triangle are introduced below:
p² = h² + k² - 2 · h · k · cos P
h² = p² + k² - 2 · p · k · cos H
k² = h² + p² - 2 · h · p · cos K
Where:
h, k, p - SidesH, K, P - AnglesIf we know that h = 16.1, p = 24.9 and k = 12.8, then the measures of the angles are:
cos P = (p² - h² - k²) / (- 2 · h · k)
cos P = (24.9² - 16.1² - 12.8²) / (- 2 · 16.1 · 12.8)
cos P = - 0.478
P ≈ 118.555°
cos H = (h² - p² - k²) / (- 2 · p · k)
cos H = (16.1² - 24.9² - 12.8²) / (- 2 · 24.9 · 12.8)
cos H = 0.823
H ≈ 34.614°
cos K = (k² - h² - p²) / (- 2 · h · p)
cos K = (12.8² - 16.1² - 24.9²) / (- 2 · 16.1 · 24.9)
cos K = 0.892
K ≈ 26.844°
Triangle KHP has the following missing angles: P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°.
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Obtain an estimate for the following computation by rounding the numbers so that the resulting arithmetic can easily
be performed by hand or in your head. Then, use a calculator to perform the computation. How reasonable is your
estimate when compared to the actual answer?
348 +598
is O
Round the two numbers to the nearest ten. An estimate of the sum is
More
x 946 is not answer also I need help this homework math please
Answer: it should be 946, maybe you worded Wong
Step-by-step explanation:
o obtain an estimate for the computation 348 + 598, we can round the two numbers to the nearest ten.
348 rounded to the nearest ten is 350
598 rounded to the nearest ten is 600
So, our estimate for the sum of 348 + 598 is 350 + 600 = 950
Using a calculator, the actual computation is 348 + 598 = 946
Our estimate of 950 is 4 more than the actual answer of 946. This means that our estimate is slightly higher than the actual answer. This is not a big difference and it is reasonable as the numbers are rounded to nearest 10.
if the hour hand of a clock is turned anticlockwise from 2 pm to 9 am, through how many degrees will it have turned?
Answer: The hour hand of a clock makes one complete rotation, 360 degrees, in 12 hours or 720 minutes.
The hour hand of a clock turns 30 degrees in one hour or 0.5 degrees in one minute.
In this case, the hour hand is turned anticlockwise from 2 pm to 9 am, which is 21 hours.
So, it will have turned 21 * 30 = 630 degrees.
It is important to note that this answer only accounts for the rotation of the hour hand and does not take into account the rotation of the minute hand.
Step-by-step explanation:
Sum up the series 2/3+5/9+8/27+11/81+..... to n terms
Hope it helps.
If you have any query, feel free to ask.
hey can anuyone please help with this question
answer is 25
use the formula to get the rest of the a's
(Look at picture) thanks! <3
Answer:
Here are the true statements:
Initially, the gas tank has 10 gallons of gasoline. (This is the y-intercept of the equation G(t) = 10 - 2t)It takes 10 hours for the vehicle to run out of gas. (This is the x-intercept of the equation G(t) = 10 - 2t)The rate of gas consumption of the vehicle is 2 gallons per hour. The slope of G(t) represents the rate of fuel consumption of the vehicle.The false statement is:
The G-intercept of G(t) represents the total distance the vehicle traveled. The t-intercept of G(t) represents the time it takes the vehicle to run out of gas. (This is not the case, the y-intercept represents the initial amount of gas and the x-intercept represents the time it takes the vehicle to run out of gas)
the quotient of 18 and a number a as an experision
The expression is 18/a
What is an algebraic expression?An algebraic expression can be described as mathematical expressions consisting of variables, coefficients, terms, factors and constants.
They are also made up of arithmetic operations, such as;
BracketParenthesesDivisionAdditionSubtractionMultiplication, etcWhat is quotient?A quotient can be defined as a quantity determined by the division of two numbers.
From the information given, we have that;
the quotient of 18 and a number a
This is represented as;
18/a
Hence, the representation is 18/a
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When making homemade ice cream in a hand-cranked freezer, the tub containing the ice cream mix is surrounded by a brine (water/salt) solution. To freeze the ice cream mix rapidly so that smooth and creamy ice cream results, the brine solution should combine crushed ice and rock salt in a ratio of 5 to 1. A small ice cream freezer requires cups of crushed ice. How much rock salt should be mixed with the ice to create the necessary brine solution?
If the ratio of crushed ice to rock salt is 5 to 1, for every 5 cups of crushed ice, 1 cup of rock salt is needed.
To find out how much rock salt is needed for the small ice cream freezer, you can use this formula:
Rock Salt = (Crushed Ice / 5) * 1
If the small ice cream freezer requires cups of crushed ice, then:
Rock Salt = (5 cups / 5) * 1 cup
Rock Salt = 1 cup
So, you will need 1 cup of rock salt to mix with the 5 cups of crushed ice to create the necessary brine solution.
An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are β = 6° and θ = 10.5° (see figure). How far apart are the ships? (Round your answer to one decimal place.) ft
Answer:
28.1 ft
Step-by-step explanation:
d = 350 * ( tan 10.5 - tan 6) = 28.1 ft
Casey deposited $1,850 in a bank account that earned simple interest at an interest rate of 4%. How much interest, in dollars, was earned in 8 years?
Answer:
$1850×4÷100×8=$592 as interest
3.
Mrs. Slana pays a babysitter $10.00 an
hour plus an extra $3 for every hour over
five hours. If Santos babysits for eight
hours, how much money will he make?
Answer: $89
Step-by-step explanation: The equation would be P = 10(x) + 3(x-5) assuming P is profit and x is greater than 5. By pluggin in x, the number of hours, we can find that it is 89.
Answer: Santos will make $89
Step-by-step explanation:
Hour 1 - $10
Hour 2 - $10
Hour 3 - $10
Hour 4 - $10
Hour 5 - $10
Hour 6 - $13
Hour 7 - $13
Hour 8 - $13
Please help thank you!
Answer:
i think its done like this
Answer:
12
Step-by-step explanation:
[tex] area = \frac{1}{2} \times \: base \times \: height \\ \frac{1}{2} \times 6 \times height \: = 36 \\ height \: = \frac{36}{3} \\ = 12 \: feet[/tex]
a cylinder container 12 inches tall with a radius of 6 inches is completely filled with vanilla, chocolate, and strawberry ice cream in the ratio 3:2:1. Which statement(s) are correct?
A.) The volume of vanilla ice cream is V = 216π in^3
B.) The total volume of ice cream is V = 1728π in^3
C.) The total volume of ice cream is V = 432π in^3
D.) The volume of strawberry ice cream is V = 288π in^3
E.) The volume of chocolate ice cream is V = 576π in^3
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ h=12 \end{cases}\implies V=\pi (6)^2 (12)\implies \stackrel{\textit{total volume of ice-cream}}{V=432\pi ~in^3}[/tex]
If a driver uses of a tank of gas every day, what fraction of a tank will he use in a) 3 days? b) 1 week?
Answer:
Step-by-step explanation:
a) If a driver uses a full tank of gas every day, the fraction of a tank he will use in 3 days is 3/1, or 3/1 of a tank.
b) If a driver uses a full tank of gas every day, the fraction of a tank he will use in 1 week is 7/1, or 7/1 of a tank.
It's worth noting that tanks of gas come in different sizes, so the amount of gas consumed in a day, week, or any other period of time will depend on the size of the tank, and the consumption of the car, so this answer is based on the assumption that a full tank is used every day.
Consider the scatter plot shown. Which shows the line of best fit? Explain your reasoning.
Therefore , the solution of the given problem of scatter plot comes out to be Line 3 to the right of the graph is best fit line.
What is scatter plot?Line of best fit refers to a line through a scatter plot of data points that best expression the relationship between those points.The graphs that show the association between two variables in a data set are called scatter plots. It displays data points either on a Cartesian system or a two-dimensional plane.
Here,
In the xy plane, a scatter plot is displayed. The x-axis has values from 0 to 9 with 1 increments, while the y-axis has values from 0 to 9 with 1 increments.
On the x-axis, data points range from 0 to 3; on the y-axis, they range from 0 to 8.5. There are three lines marked Line 1, Line 2, and Line 3. Line 1 connects the points in a way that places the majority of the points on the left of the line,
Line 2 connects the points in a way that places the majority of the points on both sides of the line, and Line 3 connects the points in a way that places the majority of the points on the right of the line.
Line 3 to the right of the graph is best fit line
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Find a unit vector in the direction opposite of ⟨−9,−2,−8⟩.
A unit vector u in the direction opposite of ⟨−9,−2,−8⟩ is ⟨-9/√(149) , -2/√(149) , -8/√(149) ⟩
What are vector equations ?
Vector equations allow for the creation of parametric curves. That is, points in space are formed for each value of the parameter by the equation of a vector, where each of its elements has a function with an independent variable that we refer to as a parameter.
Let unit vector u be = k⟨−9,−2,−8⟩.
√(81k^2 + 4k^2 + 64k^2) = 1
SO k = 1/√(149)
So a unit vector u in the direction opposite of v=⟨−9,−2,−8⟩ = (-9/√(149) , -2/√(149) , -8/√(149))
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Please look at the picture and answer the question thank you
Answer:
[ 5, ∞ )
Step-by-step explanation:
brackets on the ends of the interval indicate x can equal the value inside the bracket
parenthesis on the ends of the interval indicate x cannot equal the value inside the parenthesis.
x ≥ 5
expressed in interval notation as
[ 5, ∞ )
The Empty Number Line
Consider the list of six variable expressions:
1. With your partner, think about where you would place each
expression and sketch your conjecture.
2. Compare your number line with another group's number line.
What is the same? What is different?
An empty number line is a visual tool used to represent numbers and their relative positions. It can be used to compare, order, and perform operations on numbers.
How to learn and understand comparison of numbers?A number with more digits is always greater than a number with fewer digits, according to Rule I.
Rule II states that when two numbers have the same number of digits, we compare the digits starting from the leftmost position until we find an unequal number of digits. Greater numbers are those with more digits.
As far as we are aware, a number with more digits is always greater than one with fewer digits.
The sum of the first two digits is bigger than the sum of the first one.The number with three digits is larger than the number with two or one.A four-digit number has more digits than a three-, two-, or one-digit number.A five-digit number over a four-digit number. Three-digit number, etc.Six digits > Five digits > Four-digit number, etc..To learn more about number line visit:
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