Directions: Perform Hypothesis Testing The STEM students of a particular school are interested to know if the average amount of alkaline water placed in the bottles by a local manufacturer is less than 250 ml. Test using 0.01 level of significance if sample of 100 bottles are randomly selected and found to have an average amount of 241 ml. with a standard deviation of 1.02 ml.
Answers
Based on the given data and conducting a one-sample z-test with a significance level of 0.01, we reject the null hypothesis. There is evidence to suggest that the average amount of alkaline water placed in the bottles is less than 250 ml.
To perform the hypothesis test, we will follow the steps below:
State the hypotheses.
The null hypothesis (H₀): The average amount of alkaline water placed in the bottles is equal to or greater than 250 ml. (μ ≥ 250)
The alternative hypothesis (H₁): The average amount of alkaline water placed in the bottles is less than 250 ml. (μ < 250)
Set the significance level.
The significance level (α) is given as 0.01.
Compute the test statistic.
Since the sample size (n = 100) is large, we can use the z-test statistic. The formula for the z-test statistic is:
z = (\(\bar X\) - μ) / (σ / √n)
where \(\bar X\) is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, \(\bar X\) = 241 ml, μ = 250 ml, σ = 1.02 ml, and n = 100.
z = (241 - 250) / (1.02 / √100)
z = -9 / (1.02 / 10)
z = -88.24
Determine the critical value.
Since the alternative hypothesis is one-tailed (less than), we need to find the critical value for a one-tailed test at a significance level of 0.01. Looking up the z-table, the critical value for a one-tailed test with α = 0.01 is approximately -2.33.
Make a decision.
Since the calculated test statistic (-88.24) is smaller than the critical value (-2.33), we reject the null hypothesis.
State the conclusion.
Based on the sample data, there is sufficient evidence to conclude that the average amount of alkaline water placed in the bottles by the local manufacturer is less than 250 ml, at a significance level of 0.01.
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Related Questions
For the situation is below, define a random variable X for the situation, and then decide if they follow a binomial distribution model by commenting on the floor requirements.
1. You roll a DnD (20-sided), 20 times and record the number that shows on the dice.
Answers
After answering the presented question, we can conclude that The equation number of trials is predetermined: We're going to roll the dice 20 times.
What is equation?An equation is a statement in mathematics that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). For example, 2 + 3 = 5 is an equation because the expression on the left-hand side (2 + 3) is equal to the expression on the right-hand side (5).
Equations are used in many areas of mathematics, science, and engineering to describe relationships between quantities and to solve problems. For example, equations are used to model physical phenomena, such as the motion of objects, the behavior of fluids, and the propagation of waves. They are also used in finance, statistics, and many other fields to analyze data and make predictions.
In this case, the random variable X reflects the number of times a specific number appears after rolling a 20-sided die 20 times.
To see if this situation fits the binomial distribution model, we must look at the four conditions listed below:
The trials are impartial: Each throw of the dice is distinct from the others.
There are just two possibilities: Each roll can produce one of the 20 numbers or none at all.
The likelihood of success is constant: The probability of rolling a given number on a 20-sided dice is the same for each roll.
The number of trials is predetermined: We're going to roll the dice 20 times.
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factor the expression using the gcf 25+50
Answers
Answer:
25(1+2)
Step-by-step explanation:
25 goes into 25 once and 50 twice.
a company had 80 employees whose salaries are summarized in the frequency distribution below. find the standard deviation.
Answers
The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.
The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).
By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.
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linear error of closure (leoc) residual for latitude = -0.0241 residual for departure = -0.0168 sum of distances around traverse = 856.67' what is the linear error of closure (leoc) = ?
Answers
If this sum is small, it indicates that the traverse is accurate, while a large sum indicates that the traverse may have significant errors.
The linear error of closure (LEOC) is the algebraic sum of the residuals in the latitude and departure directions.
Given that the residual for latitude is -0.0241 and the residual for departure is -0.0168, we can calculate the LEOC as follows:
LEOC = (residual for latitude) + (residual for departure)
= (-0.0241) + (-0.0168)
= -0.0409
Therefore, the linear error of closure is -0.0409.
Additionally, the sum of distances around traverse is 856.67', which is a measure of the accuracy of the traverse. If this sum is small, it indicates that the traverse is accurate, while a large sum indicates that the traverse may have significant errors.
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a container of hot liquid is placed in a freezer that is kept at a constant temperature of 15f. the initial temperature' of the liquid is 160f. after 6 minutes, the liquid's temperature is 64f. how much additional (not total) time will it take for its temperature to decrease to 32f? round your answer to two decimal places.
Answers
The additional time it will take for the liquid's temperature to decrease from 64°F to 32°F is 2 minutes, considering a rate of temperature decrease of 16°F per minute.
To find the additional time it will take for the liquid's temperature to decrease from 64°F to 32°F, we can consider the rate at which the temperature is decreasing.
From the given information, we know that the liquid's temperature decreases from 160°F to 64°F in 6 minutes. This means that the temperature decreases by 160°F - 64°F = 96°F in 6 minutes.
Therefore, the rate of temperature decrease is 96°F / 6 minutes = 16°F per minute.
To find the additional time it will take for the temperature to decrease from 64°F to 32°F, we can calculate the difference in temperature and divide it by the rate of temperature decrease
Temperature difference = 64°F - 32°F = 32°F
Additional time = Temperature difference / Rate of temperature decrease
Additional time = 32°F / 16°F per minute = 2 minutes
Therefore, it will take an additional 2 minutes for the temperature to decrease from 64°F to 32°F.
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Which equation represents this statement?
5 times the sum of 7 and a number is 40.
5(n+7)=40
5 + 7n = 40
5⋅7+n=40
5n + 7 = 40
Answers
Answer:
5(n+7)=40
Step-by-step explanation:
It's 5(n+7)=40 because 5 + 7n = 40 and 5n + 7 = 40 is addition not multiplication, and 5⋅7+n=40 is saying 5 times seven plus a number is 40, therefore 5(n+7)=40 is the correct answer because the parenthesis in (n+7) seperates it from 5 so that you have to get the sum of (n+7) before you can multiply it by 5.
The required equation for the given case is 5(n + 7) = 40.
What is a Linear equation?A linear equation is a equation that has degree as one.
To find the solution of n unknown quantities n number of equations with n number of variables are required.
The given word problem can be solved as follows,
Suppose the unknown number be n.
Then, 5 times the sum of the number and 7 can be written as an expression as,
5(n + 7)
Now, as per the question the following equation can be written,
5(n + 7) = 40
Hence, the equation for the given word problem is 5(n + 7) = 40.
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Sheila is making accessories for the soccer team. She uses 853.58 inches of fabric on headbands for 46 players and 3 coaches. She also uses 433.78 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player
Answers
Approximately 17.4 inches of fabric were used on a headband for each player, and 9.43 inches of fabric were used on a wristband for each player.
How much fabric was used on a headband and wristband for each player?Here we want to find how much fabric was used on a headband and wristband for each player, we need to calculate the total fabric used for headbands and wristbands and divide it by the total number of players.
Total fabric used for headbands = 853.58 inchesTotal fabric used for wristbands = 433.78 inchesNumber of players = 46So the formula we need to use is:
Fabric used on a headband = Total fabric used for headbands / (Number of players + Number of coaches)
Fabric used on a headband = 853.58 inches / (46 + 3)
Fabric used on a headband = 853.58 inches / 49 = 17.4 inches
And we also need to use:
Fabric used on a wristband = Total fabric used for wristbands / Number of players
Fabric used on a wristband = 433.78 inches / 46 = 9.43 inches
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The amount of fabric that was used on a headband and wristband for each player is: 28 inches
How to solve Algebra Word Problems?The parameters given in the question are:
853.58 inches of fabric used for headbands
433.78 inches of fabric on wristbands
She makes 46 headbands for the players and 3 for the coaches: 46 + 3 = 49 headbands
She only makes wristbands for the players: 46 wristbands
Thus:
Fabric used for each headband = 853.58/49 = 17.42 ≈ 18 inches per headband
Fabric used for wristband = 433.78/46 = 9.43 ≈ 10 inches per wrist band.
Total fabric used = 18 + 10 = 28 inches
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how many cards must be selected from a standard deck of 52 cards to guarantee that at least three cards of the same (matching) suit are chosen
Answers
Answer:
Step-by-step explanation:
17
write a positive or negative integer that represents the situation. the temperature is 31 degrees above zero.
Answers
The integer that represents the given situation is a positive 31.
The temperature being 31 degrees above zero means that it is warmer than the freezing point of water. In this context, "above zero" refers to the Celsius or Fahrenheit scale, where zero represents the freezing point of water. Therefore, a temperature of 31 degrees above zero is a positive value indicating a warm temperature.
In this case, it can be assumed that the temperature is being measured in Celsius since 31 degrees above zero on the Fahrenheit scale would correspond to a very high temperature of approximately 87 degrees Fahrenheit. Overall, the integer that represents this situation is positive 31, which signifies a warm temperature above the freezing point.
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Let there be two goods, L=2. Consider a finite number of Leontief consumers i with utility function u i
(x i
1
,x i
2
)=min{x i
1
,x i
2
} and initial endowments ω i
≫ 0 . Recall that for any price system p=(p 1
,p 2
)≫0, the demand of such a consumer satisfies x i
1
(p)=x i
2
(p)= p 1
+p 2
m i
= p 1
+p 2
pω i
. Use this information to show the following: Suppose the aggregate endowment ω=(ω 1
,ω 2
) of this economy satisfies ω 1
>ω 2
and that p=(p 1
,p 2
) is an equilibrium (market clearing) price system. Then p 1
=0 and p 2
>0.
Answers
We are given an economy with two goods and Leontief consumers who have utility functions that depend on the minimum of the two goods. The initial endowments of the consumers are positive, and we are assuming that the aggregate endowment of the economy has more of the first good than the second. If a price system p=(p1,p2) is an equilibrium with market clearing, we need to show that p1=0 and p2>0.
We start by considering the demand function for a Leontief consumer, which is given by xi1(p) = xi2(p) = (p1 + p2)mi/pi, where mi represents the initial endowment of consumer i and pi represents the price of good i.
Since the aggregate endowment ω=(ω1,ω2) of the economy satisfies ω1 > ω2, we know that the total supply of the first good is greater than the total supply of the second good.
Now, if p1 > 0, then for any positive value of p2, the demand for the second good xi2(p) will be positive for all consumers. This implies that the total demand for the second good will be greater than the total supply, leading to a market imbalance.
To achieve market clearing, where total demand equals total supply, we must have p1 = 0. This is because if p1 = 0, the demand for the first good xi1(p) will be zero for all consumers, and the total supply of the first good will match the total supply. Additionally, p2 must be positive to ensure positive demand for the second good.
Therefore, we have shown that in an equilibrium price system with market clearing, p1 = 0 and p2 > 0, given the initial endowment condition ω1 > ω2.
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Which is the best reason why 3 18 + 368 is not equal to 6?
Answers
Answer:
Basic equality denotes a normative property, that is, the same level of some value, good or reason for action.
Step-by-step explanation:
One single concept of ‘basic equality’, therefore, is cast as the common touchstone of all contemporary political thought.
Omar has a goal of walking 9,000 steps in one day. He has already walked 4,250 steps. You want to know how many more steps he needs to take. If you use the equation n+4,250=9,000 to solve this problem, what does n represent?
Answers
Answer:
n=4750
n+ 4250=9000
-4250= 4250
n= 4750
Answer:
Step-by-step explanation:
idea
Han wants to build a dog house. He makes a list of the materials needed:
At least 60 square feet of plywood for the surfaces
At least 36 feet of wood planks for the frame of the dog house
Between 1 and 2 quarts of paint
Han's budget is $65. Plywood costs $0.70 per square foot, planks of wood cost $0.10 per foot, and paint costs $8 per quart.
write inequalities to represent the material constraints and cost constraints in this situation.
Answers
Answer:
a) \(p \geq 60\,ft^{2}\), b) \(w \geq 36\,ft\), c) \(1\,qt \leq q \leq 2\,qt\), d) \(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\)
Step-by-step explanation:
In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:
a) At least 60 square feet of plywood for the surface
Let \(p\) the surface area of plywood, measured in square feet, and the inequation is:
\(p \geq 60\,ft^{2}\) (Eq. 1)
b) At least 36 feet of wood planks for the frame of the dog house
Let \(w\) the total length of wood planks, measured in feet, and the inequation is:
\(w \geq 36\,ft\) (Eq. 2)
c) Between 1 and 2 quarts of paint
Let \(q\) the total capacity of paint, measured in quarts, and the inequation is:
\(1\,qt \leq q \leq 2\,qt\) (Eq. 3)
d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.
Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let \(p\), \(w\) and \(q\) the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:
\(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\) (Eq. 4)
Write an inequality to represent each constraint(material and cost)
Inequality to represent cost constraints is 0.70p + 0.10pw + 8pa ≤ 65Plywood:
plywood ≥ 60 square feet
Planks:
planks ≥ 36 feet
Paints
1 quarts ≤ paints ≤ 2 quarts
Inequality to represent cost constraint
Plywood = $0.70
planks of wood = $0.10
paint costs $8
Total cost = $65
0.70 × p + 0.10 × pw + 8 × Pa ≤ 65
0.70p + 0.10pw + 8pa ≤ 65
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Find X
Please don't answer in decimal form
Answers
Answer:
14 / (cos 45)
Step-by-step explanation:
cos 45 = 14/x
x = 14/( cos 45)
Which equation can be used to find the measure of angle BAC? tan−1(StartFraction 5 Over 12 EndFraction) = x tan−1(StartFraction 12 Over 5 EndFraction) = x cos−1(StartFraction 12 Over 13 EndFraction) = x cos−1(StartFraction 13 Over 12 EndFraction) = x
Answers
Answer:
tan−1(StartFraction 12 Over 5 EndFraction) = x
Step-by-step explanation:
The measure of the angle x in the right triangle ABC is equal to
Scenario A) Using cos
Cos x=adjacent/hypotenuse
=AC/AB
=5/13
x=cos x^-1=5/13
Scenario B) using sin
Sin x=opposite/hypotenuse
=BC/AB
=12/13
x=sin x^-1=12/13
Scenario C). Using tan
tan x=opposite/adjacent
=BC/AC
=12/5
x=tan x^-1=12/5
tan−1(StartFraction 12 Over 5 EndFraction) = x
The correct answer is option B which is \(tan^-1(\dfrac{12}{5})=x\)
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
The measure of the angle x in the right triangle ABC is equal to
Scenario A)
Using cos
Cos x =adjacent/hypotenuse
Cos x = AC/AB
Cos x = 5/13
x = cos x^-1 = 5/13
Scenario B)
using sin
Sin x = opposite/hypotenuse
Sin x = BC/AB
Sin x = 12/13
x=sin x^-1=12/13
Scenario C).
Using tan
tan x =opposite/adjacent
tan x =BC/AC
tan x =12/5
x = tan x^-1=12/5
From the figure attached, we can see that the angle BAC will be\(tan^-1(\dfrac{12}{5})=x\).
Therefore the correct answer is option B which is \(tan^-1(\dfrac{12}{5})=x\)
The complete image of the triangle is attached with the answer below.
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(a) on the axes given below, sketch and label graphs of the velocity as a function of time for rock a and rock b. label the time tb . times ta and 12ta are given on the graph.
Answers
Equal, due to both being released with zero vertical velocity and having the same downward acceleration.
What is the velocity?
The directional speed of an item in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity.
Here, we have
Given: the velocity as a function of time for rock a and rock b.
Space is the direction of a moving object's speed as a representation of the rate at which its position may change, as measured by a certain body of time and reference points.
The displacement that a thing or particle goes through with respect to time can be expressed vectorially as speed. The meter per 2d m/s is the standard unit of velocity important, usually referred to as speed.
While speed is the charge and direction of an item's movement, speed is the time price at which an object is moving along a direction. In other words, pace is a vector, but speed is a scalar cost.
Hence, due to both being released with zero vertical velocity and having the same downward acceleration.
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Jonna ran a mile in a physical education class
Answers
PLEASE HELP ME OUT
I WILL GIVE BRAINLIEST
PERFORM THE FOLLOWING CONVERSIONS USING UNIT FACTORING
400mg = _____kg
30 cm = _____ mm
Answers
30 cm = 300 mm
30cm=300mm
solve.x-6=-18
12345678
Answers
The solution of the linear equation x - 6 = - 18 will be negative 12.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The linear equation is given below
x - 6 = - 18
If the degree of the equation is 1, then the equation will be a linear equation.
Simplify the equation, then we have
x - 6 = - 18
x = - 18 + 6
x = - 12
The solution of the linear equation x - 6 = - 18 will be negative 12.
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Classify the triangle with sides 1, 4, and 7. select one.
Answers
The triangle with sides 1, 4, and 7 is classified as an impossible triangle.
A triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. In this case, the sides are 1, 4, and 7. Adding the lengths of any two sides, we have:
1 + 4 = 5, which is less than 7
1 + 7 = 8, which is greater than 4
4 + 7 = 11, which is greater than 1
Since 1 + 4 is not greater than 7, the triangle inequality theorem is not satisfied, and therefore, a triangle with sides 1, 4, and 7 cannot exist.
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What's the inverse of f x )= 1 4x 7?
Answers
The inverse of f is a function which takes any value x and divides it by 4, then adds 7 to the result.
The inverse of a function is the opposite of the original function, meaning that it takes the output of the original function and turns it back into the input. In this case, the original function is f(x)=1/4x+7. To find the inverse, we need to solve for x in the equation, which can be done by subtracting 7 from both sides and then multiplying both sides by 4. This gives us x=(x+7)/4, which is the inverse of the original function. To put it simply, the inverse of f takes any output of the original function, adds 7 to it, and then divides it by 4 to get the original input.
example;
If f(x)=1/4x+7 and x=3, then
f(3) = (1/4)3 + 7
7.75
The inverse of f is f^-1(x) = (x + 7) / 4.
If f^-1(7.75) = (7.75 + 7) / 4, then
f^-1(7.75) = 14.75 / 4
3.6875
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Order the numbers from least to greatest. Drag one number into each box
90.089
89.89
90.9
90.98
90
Answers
Answer:
Least to greatest:
89.89
90
90.089
90.9
90.98
Step-by-step explanation:
determine the slope given the two points. (-19,4) (17,11) PLEASE SHOW WORK
Answers
Answer:
m=7/36
Step-by-step explanation:
we need two points in order to find the ratio of the change in y and change in x, which is the slope
m=(y-y1)/(x-x1) (you can choose any point as y1 but be careful that you use the corresponding x1 value in the denominator)
m=(11-4)/(17-(-19))
m=7/36
whats the quotient of 36 and 6
Answers
Answer:6
Step-by-step explanation: 36/6 is 6
Please help need this ASAP!!!
Answers
Answer:
I'm sorry I don't know this
Step-by-step explanation:
0.58 kilogram of flour each day for 4 weeks. How many grams did Destiny use in those 4 weeks?
1 kg = 1,000 g
Answers
Answer: 28.58
Step-by-step explanation: you find 7x4 which is 28 and then 28 + 0.58 and that gives you 28.58
A man walks due west for 4km. He then changes direction and walks on a bearing of 197°. Until he is south west of his starting point. How far is he then from his starting point
Answers
The distance between the man and the starting point will be 13.08 km.
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angles of right-angle triangles.
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.
Given that a man walks due west for 4km. He then changes direction and walks on a bearing of 197°.
The distance will be calculated as,
tanΘ = P/B
tan(73) = y / 4
y = 4tan73
y = 13.08 km
Therefore, the distance between the man and the starting point will be 13.08 km.
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Derek advises a patient to have a scale every 4 months and a polish every 6 months. If they have a scale and polish today, how long will they wait before they can have both during the same appointment?
Answers
Answer:
12 months time
Step-by-step explanation:
To find this, we simply find the lowest common multiple of the two months
Mathematically, we have the lowest common multiple of 4 and 6 as 12
Thus, the time they would have the appointment together is the simply 12 months
Answer:
12 months
Step-by-step explanation:
LCM= 2 I4,6
2,3
LCM=12
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the title pattern shown was used in pompeii for paving. if the diagonals of each rhombus are 2 and 3 inches, what area makes up each cube in the pattrn
Answers
Each cube in the pattern has an area of 3 square inches.
To determine the area of each cube in the pattern, we need to find the area of each rhombus formed by the pattern.
The pattern consists of rhombuses, and we know that the diagonals of each rhombus are 2 inches and 3 inches.
The formula to find the area of a rhombus is given by:
Area = (d1 * d2) / 2,
where d1 and d2 are the lengths of the diagonals.
In this case, d1 = 2 inches and d2 = 3 inches.
Plugging the values into the formula, we get:
Area = (2 * 3) / 2
= 6 / 2
= 3 square inches.
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(x+4)(x+4)/2 pls help
Answers
Answer:
x^2/2+4x+8 hope this helps