The equivalent expression of the given expression 4(x - 2 + y) is 4x-8+4y.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is 4(x - 2 + y). The equivalent expression will be solved as,
E = 4(x - 2 + y)
E = 4x - 8 + 4y
Therefore, the equivalent expression of the given expression 4(x - 2 + y) is 4x-8+4y.
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an engineer designed a valve that will regulate water pressure on an automobile engine. the engineer designed the valve such that it would produce a mean pressure of 5.7 pounds/square inch. it is believed that the valve performs above the specifications. the valve was tested on 12 engines and the mean pressure was 5.9 pounds/square inch with a variance of 0.81. a level of significance of 0.1 will be used. assume the population distribution is approximately normal. determine the decision rule for rejecting the null hypothesis. round your answer to three decimal places.
the decision rule for rejecting the null hypothesis is, to reject H₀ if t > 1.363.
Right-tailed test: H0µ = k H1:>k P-value = P(z>z x) This indicates the probability of obtaining a test statistic as high as or higher than z x. If the P-value is less than α, we reject H0(null hypothesis) and conclude that the data are statistically significant at the level α. We do not reject H0 if the P-value is greater than α.
H0: µ = 5.3 , H1: µ> 5.3
it is a right-tailed test
n = 12
α = 0.10
therefore the decision rule for rejecting the null hypothesis is, Reject H0 if t> 1.363.
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using traditional methods, it takes 11.8 hours to receive a basic driving license. a new license training method using computer aided instruction (cai) has been proposed. a researcher used the technique with 13 students and observed that they had a mean of 12.0 hours with a standard deviation of 1.9. a level of significance of 0.1 will be used to determine if the technique performs differently than the traditional method. assume the population distribution is approximately normal. find the value of the test statistic. round your answer to three decimal places.
The test statistics value is 0.380
What is the standard deviation?
A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
Standard deviation It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
For example: To find the standard deviation, you have to add up all the numbers in the data set, then divide by how many numbers there are, and that will get you your answer.
Formula:
t=(mean-time)/(standard deviation/√(number of students) )
=( 12 - 11.8) / (1.9 / √13 )
= 0.380
This is test statistics value.
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1. Jorge used 2 7/8 packs of pencils in the first 1/3
of the year. At what rate is Jorge using
pencils
Answer:
Jorge is using pencils at a rate of 6 packs a year or a rate of 2 packs every four months.
Step-by-step explanation:
1/3 of a year is four months so that would be 2 packs every four months and if you multiply that by three you’d get 12 month, or one year, and 6 packs of pencils.
HELP MEEEEEE PLEASEEEEE
Answer:
1000-400=600km
good luck i hope it helped, its all about reading the graph!
What is the slope, m, of the following linear equation? y=x-6
Answer:
1
Step-by-step explanation:
because the 1 is actually invisible
its called invisible math
y=mx+b
10 PIONTS ANSWER PLEZ IT IS NOW DUE!!!!!!
15. A triangle pattern is shown below.
Figure Perimeter
1 triangle 24
2 triangles 30
3 triangles 36
Which equation relates the number of triangles in the figure (n) to the perimeter of the figure (P)?
(1 point)
P = 6n + 18
P = 9n + 6
P = 6n + 9
P = 9n + 12
The equation which relates the number of triangles in figure (n) to the perimeter of the figure (P) is P = 6n + 18. Option A is correct.
We are given:
The perimeter of the 1 triangle = 24
The perimeter of the 2 triangle = 30
The perimeter of the 3 triangle = 36
As we can see in the given figures two sides with lengths of 9 are fixed and the side with a length of 6 is varying.
So, we can write this as,
P = 6n + 18, where n = number of triangles.
Now, check the equation formed by substituting the values;
Substitute n = 1, and we get;
P = 6(1) + 18
P = 6 +18
P = 24 True.
Substitute n = 2, and we get;
P = 6(2) + 18
P = 12 +18
P = 30 True.
Substitute n = 3, and we get;
P = 6(3) + 18
P = 18 + 18
P = 36, true.
So, it is true for all the figures.
Thus, the equation which relates the number of triangles in figure (n) to the perimeter of the figure (P) is P = 6n + 18. Option A is correct.
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Quadrilateral ABCD is inscribed in this circle.
What iS the measure of LA?
Enter your answer in the box.
The measure of ∠A is 106°.
Quadrilateral ABCD is inscribed in this circle.
To find out the measure of LA:
We are given that, 'Quadrilateral ABCD is inscribed in the circle'.
So, we get that,
'ABCD is a cyclic quadrilateral' that is The sum of the opposite interior angles is 180°.
Thus, we have,
∠A +∠C = 180°
i.e. ∠A + 74° = 180°
i.e. ∠A = 180° - 74°
i.e. ∠A = 106°
Thus, the measure of ∠A is 106°.
Hence the answer is the measure of ∠A is 106°.
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10 points
Sup,
Use the order of operations to simplify this expression. Express your answer in the simplest form.
1/4 + 1/2 ÷ 3/8
Options
1
1 7/12
2
8/9
Have a great day answer Asap
Answer:
2
Step-by-step explanation:
1/4 + 1/2 ÷ 3/8
0.25 + 0.5 ÷ 3/8
0.25 + 1.33
= 1.58
approximately 2
Juan is 12. His father put $2000 into his bank account. The account
gained interest at a rate of 2.3% per year, compounded bi-monthly.
Assuming no more money was deposited and none was withdrawn, how
much money will be in the account when Juan turns 18? Round to the
nearest cents.
A=P
n
A accumulated amount
P = principal
r = interest rate
n = compounding per period
t = number of periods
Amount of money present in Juan's account when she is 18 years old is $2,284.73
When Juan is 12 years old ;
Given P = principal = $ 2000
r = interest rate = 2.3 %
t = number of periods = 2
To start, multiplying R percent by 100 gives us 2.3%/100, or 0.023 each year.
Simply converting time into years, 2 months divided by 12 months each year equals 0.166667 years.
How to resolve our equation
A = 2000(1 + (0.023 × 0.166667)) = 2007.666682
A = $2,007.67
Simple interest on a principal of $2,000.00 at a rate of 2.3% annually for 0.166667 years (2 months)
Juan when she is 18 years old
time = 18 - 12 = 6 years
rate = 2.3 %
Principal = $2,007.67
Accrued money = A = $2,284.73
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–2.5x – 7.5 = x + 6.5
Answer:
Step-by-step explanation:
x=-4 that should be the answer i don't really know how too explain but i did this 2 years ago
Answer:
Step-by-step explanation:
Marcus is selling t-shirts at the state fair. He brings 200 shirts to sell. He has long sleeved T-shirts and short sleeved t-shirts for sale. Obe the first day of the fair , he sells 1/2 of his long-sleeved t-shirts and 1/3 of his short sleeved t-shirts for a total of 80 t shirts sold. How many of each type of shirt did Marcus bring to the fair?
The number of each type of shirt that Marcus bring to the fair is 80 long-sleeved T-shirts and 120 short-sleeved T-shirts .
Let x =Number of long-sleeved T-shirts
Let y = Number of short-sleeved T-shirts
Hence,
x + y = 200
1/2x + 1/3y = 80
Using linear Combinations Method:
6[1/2x + 1/3y = 80]
x +y =200
3x + 2y =480
So,
-2(x +y = 200)
3x + 2y = 480
-2x -2y=-400
3x + 2y = 480
x = 80 (Long sleeved)
Solve for y
80 + y =200
y = 200 -80
y = 120 (Short sleeved)
Therefore he brought 80 and 120 T-shirts .
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Write an equation of
the line that passes
through (7, 10) and
is perpendicular to the
line y =
x-9.
Equation:
2
Equation of the line that passes through (7, 10) and is perpendicular to the line y =x-9 is y = -x+17.
Given equation, y = x-9
Slope = m = 1
Slope of line perpendicular to given line = -1/m
= -1/1
= -1
Let the equation of line be y = mx + c
Passes through A(7,10)
10 = -1(7) + c
10 = -7 + c
c = 10 + 7
= 17
Hence, equation is y = -x+17
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help me please...........................................................................................................................
The solution is
The Hypotenuse = FD
Side Opposite of ∠F = MD
Side Adjacent of ∠F = MF
Side Opposite of ∠D = MF
Side Adjacent of ∠D = MD
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
The triangle FMD and the ∠M is a right angle
So , ∠M = 90°
From the figure , we can deduce that
The Hypotenuse = FD
Side Opposite of ∠F = MD
Side Adjacent of ∠F = MF
Side Opposite of ∠D = MF
Side Adjacent of ∠D = MD
Hence , the required solution is based on trigonometric relations
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the temperature was -20 degrees in the morning when Rae woke up. At dinner time, the temperature shows 35 degrees. What was the change in temperature from the time Rae woke up un dinner time? Draw a picture and write an equation to solve.
The change in temperature is 15°
How to find Change in temperature ?
If temperature rise then Change in temperature ,t₂ = t₁ + final temperature
If temperature dropped then Change in temperature ,t₂ = t₁ - final temperatureWe have given,
In morning, when Rae woke up the temperature is (t₁) = -20°
At dinner time, the temperature is = 35°
t₂ = t₁ + 35
t₂ = (-20) + 35
t₂ = 15°
Hence, the change in temperature is 15°
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how will coefficient of restitution change with angle of impact?
Kinematic parameters is the way by which coefficient of restitution change with angle of impact.
The ratio of a boulder's velocities or energy prior to and following its impact with the slope is represented by the coefficient of restitution, which is a dimensionless number. Different definitions of the coefficient of restitution have been put forth in earlier studies, but it has not been determined which definition is better suitable for predicting rockfall.
The determination of suitable values for the coefficients of restitution, which often change with the kinematic parameters and terrain conditions, is essential for the accuracy of a computer program modelling a rockfall trajectory. Using small-scale laboratory testing, the effects of the impact angle with regard to the slope on the coefficients of restitution have been identified and analyzed. to determine the validity of the current conclusion based on limited laboratory testing.
This study conducted a medium-scale laboratory test employing spherical limestone polyhedrons impacting concrete slabs to determine how the impact angle affects the coefficients of restitution when the test scale is changed. A 3D motion capture system measures the velocities before and after the collision during free fall tests. Several general laws apply when taking into account the impact angle's effect, regardless of the test scales and conditions, according to the results comparison between our test and the existing small-scale tests. The normal coefficient of restitution (Rn), the kinematic coefficient of restitution Rv, and the kinetic energy coefficient of restitution Re will all decrease as the impact angle increases.
In contrast, it will cause Rt's tangential coefficient of restitution to increase. The impact of the impact angle is significantly influenced by the rotation. The normal coefficient of restitution Rn and tangential coefficient of restitution Rt are always higher when more kinetic energy is converted to rotational energy.
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Write the equation using function notation
x - y = -4
A) f(x) = x - 4
B) f(x) = x + 4
C) f(x) = -x + 4
D) f(x) = -x - 4
Answer:
C
Step-by-step explanation:
Rewrite the following equation in slope-intercept form.
y + 6 = 9(x − 8)
Write your answer using integers, proper fractions, and improper fractions in simplest form.
At an elevation of 1221. 4 feet, lake mead will hold 28,945,000 acre-feet of water. Which number is the best estimate of this amount of water?.
The best estimate of this amount of water is [tex]3*10^{7}[/tex].
Given:
At an elevation of 1221. 4 feet, lake mead will hold 28,945,000 acre-feet of water.
So, the amount of water that is in the lake will be 28,945,000 acre-feet which is estimated to be 30000000 acre-feet of water.
Because the nearest estimate to 28945000 is 30000000.
= 30000000
= 300000*[tex]10^{2}[/tex]
= 30000*[tex]10^{3}[/tex]
= 3000*[tex]10^{4}[/tex]
= 3*[tex]10^{3} *10^{4}[/tex]
= 3*[tex]10^{7}[/tex]
Therefore The best estimate of this amount of water is [tex]3*10^{7}[/tex].
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If Bruce can eat 2 1/2 bananas per day, how many bananas can Bruce can eat in 4 weeks?
The number of bananas Bruce can eat in 4 weeks is 70 bananas
Calculating numberFrom the question, we are to calculate the number of bananas Bruce can eat in 4 weeks.
From the given information,
Bruce can eat 2 1/2 bananas per day
First, we will determine the number of days there are in 4 weeks
NOTE: There are 7 days in 1 week
If there are 7 days in 1 week
Then,
There are 4 × 7 days in 4 weeks
4 × 7 = 28 days
That is, 4 weeks = 28 days
Now, we will determine the number of bananas Bruce can eat in 28 days
If Bruce can eat 2 1/2 bananas per day
Then,
Bruce can eat 28 × 2 1/2 bananas in 28 days
28 × 2 1/2 = 28 × 5/2
= 14 × 5
= 70
Hence, Bruce can eat 70 bananas in 4 weeks
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Answer:
70
Step-by-step explanation:
Bruse can eat 2 1/2 bananas in one day so:
1day=2 1/2bananas.
if 1wk=7days
4wks=x =28days
1day=2 1/2 bananas
28da
28×2 1/2
=28×5/2=70
answer=70bananas
what is the anser for Latanya has a points card for a movie theater.
She receives 60 rewards points just for signing up.
She earns 9.5 points for each visit to the movie theater.
She needs 117 points for a free movie ticket.
How many visits must Latanya make to earn a free movie ticket?
If Latanya receives 60 rewards points just for signing up. She earns 9.5 points for each visit to the movie theater. She needs 117 points for a free movie ticket. Then 6 visits Latanya has to make to earn a free ticket.
What is slope intercept form of line?
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Given that,
Latanya has 60 rewards points just for signing up.
For each visit to theatre she earns 9.5 points.
To get free ticket she needs 117 points.
We need to find how many visits she has to do to get free ticket.
We use Linear equation to solve this
Let y = total number of rewards points
x = number of visits to the movie theater
m=Points for each visit
y=mx+b
117=9.5x+60
Subtract 60 on both sides
117-60=9.5x
57=9.5x
x=6
Hence she has to make 6 visits to earn a free ticket.
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Answer:
6 x=6
Step-by-step explanation:
solve the equation by elimination method 4x-2y=8,5x+3y=6
Solving the set of equation by elimination method gives
x = 1.64
y = -0.727
How to solve the equation by elimination methodThe given data
4x - 2y = 8 (1)
5x + 3y = 6 (2)
multiplying (1) by 3/2 and adding the result to (2)
6x - 3y = 12
5x + 3y = 6
6x + 5x - 3y + 3y = 12 + 6
11x = 18
x = 18/11
x = 1.64
substitute x = 18/11 into (1)
4 * 18/11 - 2y = 8
72/11 - 2y = 8
2y = 72/11 - 8
2y = -16/11
y = -8/11
y = -0.727
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18 feet:5 yards
Please helpppppppppppppp
Answer:
Foot: 18.416666666666668
Yard: 6.1388888888888892836
I could get these right but, Its being rude to
me so Im trying one more time to clarify.
Answer: The correct answer is the one that has 4 + 5 + 2 + 3.
(I didn't say which side it is in case you got confused but it's the one right above the speaker sign.)
Step-by-step explanation:
Newton and Descartes have a $50.00 gift card to a pet store.
Newton's total is $18.95 and Descartes's total is $24.38. How much
money do they have left on their gift card?
Given that the point (-90, -56) is on the
terminal side of an angle, 0, find the exact
value of the following:
sin(0)=
cos(0)=
tan (0) =
csc(0)=
sec(0)=
cot (0)=
The value of sinθ = - 28/53, cosθ = - 45/53, tanθ = 28/45, cosecθ = -53/28, secθ = -53/45, cotθ = 45/28.
Given that:
The point (-90, -56) is on the terminal side of an angle, θ
Using Pythagoras' theorem,
Hypotenuse^2 = Perpendicular^2 + Base^2
Hypotenuse^2 = (-56)^2 + (-90)^2
Hypotenuse^2 = 3136 + 8100
Hypotenuse^2 = 11236
Hypotenuse = 106
The value of hypotenuse = 106
The exact value of the following is:
sinθ = Perpendicular/Hypotenuse = -56/106 = - 28/53
cosθ = Base/Hypotenuse = -90/106 = - 45/53
tanθ = Perpendicular/ Base = - 56/-90 = 28/45
cosecθ = 1/sinθ = -53/28
secθ = 1/cosθ = -53/45
cotθ = 1/tanθ = 45/28
Hence, we got all the values of θ.
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6.The percents of three types of tickets collected at the gate for a high school football game are shown.
a.Write the percents as decimals and as fractions.
b.There is one other type of ticket that is not shown. It is a ticket for a child under 5. What percent of the tickets were of this type?
The percentage of three types of tickets collected at the gate:
ai) student's ticket as a percent: 48%, as a fraction: 48/100, and as a decimal: 0.48.
aii)Adult's ticket as a percent:28%, as fraction:28/100, and as decimal: 0.28.
aiii) Senior's( 65 and older) ticket: 14%, as fraction:14/100 and as decimal: 0.14.
b)Tickets for children under 5years is: 10%, as fraction:10/100, and as decimal: 0.10.
what is percentage?
This is a number written as a ratio of a hundred or as a fraction of a hundred. it is represented with "%".
How to calculate the percentages:
.As a fraction: Write it as a ratio of a hundred.
ticket type for
i) students48% =48/100
ii)Adult 28%=28/100
iii)Senior's( 65 and older)14% =14/100
.As a decimal: Write it as a ratio of hundred then divide by hundred.
ticket type for:
i) students48% =48/100=0.48
ii)Adult 28%=28/100=0.28
iii)Senior's( 65 and older)14% =14/100=0.14
b)To calculate the percentage of tickets of children under 5 years:
Percent(% )means 100
Therefore,
100 - student ticket %- Adult's ticket % - Senior's( 65 and older) ticket%
100- 48 - 28 - 14 = 10%
Thus for children under 5 years,
i)As percent is:10%,
ii)as fraction:10/100
iii)decimal: 0.10.
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the number of hours spent watching television by students in the week before final exams has a normal distribution with a standard deviation of 4.5 hours. a random sample of 30 students is taken. is the probability that the sample standard deviation exceeds 3.5 hours more than 0.95?
The probability that the sample standard deviations exceeds 3.5 hours more than 0.95 is 0.23 < 0.95 ..
The numbers of hours spent on watching television by a student in a weak before is normally distributed.
We have provide the following details, standard
deviations of sample ( Number of hours in weak) (σ) = 4.5 hours
sample size (n) = 30
we shall compute the mean and variance of sample .
The E of s squared is equal to 4.5 squared. The variance of S squared is equal to twice the square of sigma divided by 1, which is 30 minus 1, which is 28.6, 28.2817. The chi-square distribution here has 29 degrees of freedom, which equals 29 squared to 4.5 squared. We want to find probabilities greater than 90 because the standard deviation of our sample is greater than 3.5 hours. The probability that S squared is greater than 3.5 is The probability that chi-square with 29 degrees of freedom is greater than
17. 54321 is very high. This is the same as zero.
This is equal to 1 minus the probability that 29 degrees of freedom chi-square is greater than 51 points 5556, which is what we want for part B. we are given one Probability will be zero.
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#Complete question
The number of hours spent watching television by students in the week before final exams has a normal distribution with a standard deviation of 4.5 hours. A random sample of 30 students was taken.a. Is the probability more than 0.95 that the sample standard deviation exceeds 3.5 hours?b. Is the probability more than 0.95 that the sample standard deviation is less than 6 hours?
Questions 1-4: The number of classes (X) a student takes in a given semester follows the following probability distribution: X 0 1 2 3 4 5 PIX) 0.4 0.25 0.15 0.08 0.02 ??? 1. What is the probability they take 5 classes? 2. What is the probability they take at least one class? 3. What is the probability a student will take 2 or 3 classes in a semester? 4. What is the expected number of classes a student will take in a given semester? (show your work on this one, and a screenshot of how you worked it out on the calculator or excel).
The probability to take 5 classes is 0.1, while the probability to take at least one class is 0.6, the probability to take 2 or 3 classes is 0.23 and the expectation of the distribution is 1.37.
The distribution given is
X PIX)
0 0.4
1 0.25
2 0.15
3 0.08
4 0.02
5 ???
1.
We know that the sum of all the probabilities in a probability distribution is always equal to 1.
Let the probability of X = 5 be p
Hence,
0.4 + 0.25 + 0.15 + 0.08 + 0.02 + p = 1
or, 0.9 + p = 1
or, p = 1 - 0.9
or, p = 0.1
Hence the probability to take 5 classes is 0.1.
2.
We need to find P(X ≥ 1)
= 1 - P(X = 0)
From the distribution we know that P(X = 0) is 0.4
Therefore, P(X ≥ 1)
= 1 - 0.4
= 0.6
Hence, the probability to take at least one class is 0.6
3.
The probability to take 2 or 3 classes in a semester
= P( X = 2) + P(X = 3)
= 0.15 + 0.08
= 0.23
4.
The expectation of any distribution
= ∑xp(x)
where,
x is the random variable
p(x) is the probability of the random variable
Therefore,
E(X) = 0 X 0.4 + 1 X 0.25 + 2 X 0.15 + 3 X 0.08 + 4 X 0.02 + 5 X 0.1
= 0 + 0.25 + 0.30+ 0.24 + 0.08 + 0.50
= 1.37
Therefore the expectation is 1.37
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f/4 + 6 ≤ 7 what is the answer
Answer:
f ≤ 4
Step-by-step explanation:
f/4 + 6 ≤ 7
f/4 ≤ 7 - 6
f/4 ≤ 1
f ≤ 4
Answer:
F<4
________
________
Solve this equation please :)
The ratio of BE/BC is 1:3.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
In triangle ABC, the ratio of FA and CF is 1:2.
Since, the point G is the midpoint of BF,
Implies that G divides BF in ratio 1:1.
By using mass point geometry,
The ratio of BE/BC=1:3
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