to complete the square , use , [ half X coefficient of x ]^2
\(\begin{gathered} \frac{1}{2}\times-6=-3 \\ \\ (x-3)^2=x^2-6x+9 \\ (x-3)^2-9=x^2-6x \end{gathered}\)replece x^2-6x with (x-3)^2 - 9
\(\begin{gathered} (x-3)^2-9=119 \\ (x-3)^2=119+9 \\ (x-3)^2=128 \end{gathered}\)simplify the expression and explain each step.
1. 4(3x + 2) -2
2. factor the expression completely 20b -16
please explain how to solve! will mark brainliest
Answer:
is the 3x a expression ill comment the awnser if is
Step-by-step explanation:
Trig Ratios assignment
The trignometric ratios are given by1. B = 180 - (90 + 58) (sum of triangles)
B = 32°
Let's find a and b using trigonometric ratios:
Reference angle = 58°
Opposite = a = ?
Hypotenuse = c = 27
Adjacent = b = ?
✔️To find a, apply SOH:
Sin 58 = Opp/Hyp
Sin 58 = a/27
a = 27*Sin 58
a = 22.8972986 ≈ 22.9 (nearest tenth)
✔️To find b, apply CAH:
Cos 58 = Adj/Hyp
Cos 58 = b/27
b = 27*Cos58
b = 14.3 (nearest tenth)
2. B = 180 - (90 + 63) (sum of triangles)
B = 27°
Let's find a and b using trigonometric ratios:
Reference angle = 63°
Opposite = a = 11
Hypotenuse = c = ?
Adjacent = b = ?
✔️To find b, apply TOA:
Tan 63 = Opp/Adj
Tan 63 = 11/b
b = 11/Tan 63
b = 5.6 (nearest tenth)
✔️To find c, apply SOH:
Sin 63 = Opp/Hyp
Sin 63 = 11/c
c = 11/Sin 63
c = 12.3 (nearest tenth)
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PLEASE HELP MUST BE AT LEAST 5 SENTENCES PLEASE HELP DUE IN 5 MINS
Answer:
I think that Thomas Clarksons motive for publishing this drawing of a slave ship was to inform people what it was like. He wanted to show how crowded it was. Thomas might have wanted to show how people were treated.
( i dunno what else to put but you could talk about how he felt about the slave trade)
1. Which of the following is equivalent to 6/10? 5/9 9/15 8/12 36/100
Please solve the following problem 194=27-x
Answer:
hello! :)
-167
Answer: 167
Step-by-step explanation:
First get X by itself.
substract 27 to each side
194=27-x
194= 27 -27 -x
194 - 27 = X
X= 167
An Airplane uses the equation y=0.28x+24 to calculate the fare y, in dollars, for a trip of x miles. What is the fare for 500-mile trip?
The fare for a 500-mile trip is 164.
What is the fare for a 500-mile trip?The equation provided in the question is known as a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.
The general form of a linear equation is:
y = mx + b
Where:
m = slope b = interceptIn the equation used to calculate the fare, y=0.28x+24, 0.28 is the variable cost and 24 is the fixed cost.
Cost of a 500-mile trip = y=0.28(500) +24
y = 140 + 24
y = 164
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Helppp pls …………………….
Answer:
B
Step-by-step explanation:
the two angles lies on the same lines and they have the same vertex
In a kilometer race, Meera beats Michille by 50 meters or 10 seconds. What time does A take to complete
the race? *
Answer:
You would need to multiply the needed time with the amount of time already shown hope this helps :)
Step-by-step explanation:
Answer:
In a kilometer race, Meera beats Michille by 50 meters or 10 seconds. What time does A take to complete the race? Time taken by Michille to run 1000 meters = (1000 * 10)/50 = 200 sec. Time taken by Meera = 200 - 10 = 190 sec
Step-by-step explanation:
Hope You Enjoy !
PLEASE HELP ASAP! This composite figure is created by placing a sector of a circle on a triangle. What is the area of this composite figure? Use 3.14 for n. Round to the nearest hundredth. Show your work.
Answer: 24
Step-by-step explanation:
To find the area of the composite figure, we need to find the area of the sector and the area of the triangle and then add them together.
Area of sector = (θ/360) * π * r^2, where θ is the angle of the sector in degrees, r is the radius of the circle.
The angle of the sector can be found by subtracting the angle of the triangle from 360 degrees. The radius of the circle can be found by dividing the length of the arc by the angle of the sector.
Length of the arc = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 4 = 4.19
Radius of the circle = 4.19/60 = 0.07
Angle of sector = 360 - 60 = 300 degrees
Area of sector = (300/360) * 3.14 * 0.07^2 = 0.0041
The area of the triangle can be found using the formula:
Area of triangle = (1/2) * base * height = (1/2) * 8 * 6 = 24
Therefore, the total area of the composite figure is:
0.0041 + 24 = 24.0041
Rounding to the nearest hundredth, the area of the composite figure is approximately 24.00.
Which ordered pairs represent points on the graph of this equation? Select all that apply. y = 2x - 3 a)3-3 b) 0,-3 c) 5,7 d) -2,-7 e) 2,1 or f) 4,5
The ordered pairs that represent points on the graph of y = 2x - 3 are (0,-3), (5,7), (-2,-7), (2,1), and (4,5).
What is equation?An ordered pair is a pair of numbers written in a specific order (x,y) that represents a point in the coordinate plane.
What is graph?A graph is a visual representation of data or a mathematical function that is plotted on a coordinate plane, usually with an x and y-axis. It is used to analyze trends and relationships between variables.
According to the given information:
To determine whether a given ordered pair represents a point on the graph of the equation y = 2x - 3, we need to substitute the values of x and y into the equation and see if the equation is true.
a) (3,-3):
y = 2x - 3
-3 = 2(3) - 3
-3 = 3
This is not true, so (3,-3) is not on the graph.
b) (0,-3):
y = 2x - 3
-3 = 2(0) - 3
-3 = -3
This is true, so (0,-3) is on the graph.
c) (5,7):
y = 2x - 3
7 = 2(5) - 3
7 = 7
This is true, so (5,7) is on the graph.
d) (-2,-7):
y = 2x - 3
-7 = 2(-2) - 3
-7 = -7
This is true, so (-2,-7) is on the graph.
e) (2,1):
y = 2x - 3
1 = 2(2) - 3
1 = 1
This is true, so (2,1) is on the graph.
f) (4,5):
y = 2x - 3
5 = 2(4) - 3
5 = 5
This is true, so (4,5) is on the graph.
Therefore, the ordered pairs that represent points on the graph of the equation y = 2x - 3 are: (0,-3), (5,7), (-2,-7), (2,1), and (4,5). Answer: b), c), d), e) and f).
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The random variable X represents the number of calls per hour to a call center in the last month. The probability distribution for X is below. 1 2 4 5 6 7 P(x) 0.01 0.10 0.26 0.33 0.18 0.06 0.03 a. What is the missing value in the table? b. Find the mean. c. Find the variance and standard deviation. d. Interpret your results. B. In a quality control analysis, the random variable X represents the number of defective products per each batch of 100 products produced Defects (x) Batches 2 87 3 5 95 113 64 13 a. Use the frequency distribution above to construct a probability distribution? b. Find the mean. c. Find the variance and standard deviation.
a. The missing value in the table 0.03
b. The mean is 4.18
c. The variance is 3.23 and standard deviation is 1.80
d. The larger the standard deviation, the greater the spread of the probability distribution.
A random variable is a variable that can take on different values depending on the outcome of a random event. In this case, the random variable X represents the number of calls per hour to a call center in the last month.
a. The missing value in the table is the number of calls per hour for the probability 0.03. From the table, we see that the number of calls per hour is 7.
b. The mean, also known as the expected value, is a measure of the center of the probability distribution. It is calculated by taking the sum of the product of each possible value of X and its corresponding probability. In mathematical terms, the mean of X is given by:
E(X) = 1 * P(1) + 2 * P(2) + 4 * P(4) + 5 * P(5) + 6 * P(6) + 7 * P(7)
E(X) = 0.01 + 0.2 + 1.04 + 1.65 + 1.08 + 0.21 = 4.18
So, the mean number of calls per hour to the call center in the last month is 4.18.
c. The variance of X is a measure of the spread of the probability distribution. It is calculated by taking the sum of the squared differences between each possible value of X and the mean, multiplied by the corresponding probability. In mathematical terms, the variance of X is given by:
Var(X) = (1 - 4.18)² * P(1) + (2 - 4.18)² * P(2) + (4 - 4.18)² * P(4) + (5 - 4.18)² * P(5) + (6 - 4.18)² * P(6) + (7 - 4.18)² * P(7)
Var(X) = 3.23
The standard deviation is the square root of the variance, and it is also a measure of the spread of the probability distribution. In mathematical terms, the standard deviation of X is given by:
=> SD(X) = √(Var(X)) = √(3.23) = 1.80
d. Interpretation:
The mean of 4.18 calls per hour represents the average number of calls to the call center in the last month.
The standard deviation of 1.80 indicates that the number of calls per hour deviates from the mean by approximately 1.80 calls on average.
This means that about 68% of the time, the number of calls per hour will be between 2.38 (4.18 - 1.80) and 6.08 (4.18 + 1.80).
Complete Question:
The random variable X represents the number of calls per hour to a call center in the last month. The probability distribution for X is below.
x 1 2 4 5 6 7
P(x) 0.01 0.10 0.26 0.33 0.18 0.06 0.03
a. What is the missing value in the table?
b. Find the mean.
c. Find the variance and standard deviation.
d. Interpret your results.
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i need to find out the total volume for this thing
Answer:
81
Step-by-step explanation:
you add all of them together to get your answer
the scientist creates an equation that models her data for each tree so that she can predict the diameter in the future. complete a linear equations that fits the data for tree 1, where x is the year and y is the trunk diameter, in inches. click on the variables and number you want to select and drag them into the boxes.
The linear equation obtained is y = 0.3X + 18.3
What is linear equation?A linear equation is an equation that can be written in the form ax + b = 0, where a and b are real numbers and x represents an unknown variable. The solutions of linear equations are often graphed on a coordinate plane, forming a straight line. Linear equations can be used to model many real-world situations, such as population growth, the rate of change of a physical quantity, or the total cost of an item. Linear equations can also be used to solve systems of equations, where several equations must be solved simultaneously.
Given that data :
x = year ;
y = trunk diameter, in inches
Year ________trunk diameter
1 __ 18.6
3 __ 19.2
5 __ 19.8
7 __ 20.4
9 ___21.0
11 __ 21.6
13 __ 22.2
Using the linear regression calculator :
The linear equation obtained is :
y = 0.3X + 18.3
Where ;
Slope = 0.3 ; intercept, c = 18.3
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What is the favorite food of sixth-grade students? Determine whether it's a stratical question or a non-stratical question.
On a shopping trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets at $10 each and a number of necklaces at $11 each. She wrote a check for $1,270 to pay for the order. How many bracelets and how many necklaces did Rosaria purchase?
Will give brainiest to whoever answers this
9514 1404 393
Answer:
50 bracelets70 necklacesStep-by-step explanation:
Let n represent the number of necklaces Rosaria ordered. Then the total cost of the order is ...
10(120 -n) +11(n) = 1270
n = 70 . . . . . . . . . . . . . simplify, subtract 1200
120 -70 = 50 . . . . . . . the number of bracelets
Rosaria purchased 70 necklaces and 50 bracelets.
Express the following sentence in algebraic language. A store sold a fourth, a fifth, and a sixth of a piece of cloth. There are still 20 meters left.
Algebraic Language
Let:
x = Initial length of a piece of cloth
Then:
x/4 = A fourth of the piece
x/5 = A fifth of the piece
x/6 = A sixth of the piece
After selling the fractions of the pieces, there still remain:
x - x/4 - x/5 - x/6
According to the conditions given in the problem, this is equal to 20 meters, thus:
x - x/4 - x/5 - x/6 = 20
12 4/5 - 4 1 /25 reduce lower terms
Given the following expression:
\(12\frac{4}{5}-4\frac{1}{25}\)You can follow the steps shown below in order to reduce it:
1. Try to reduce the fractions of the Mixed numbers. In this case, you can notice that the fractions cannot be reduced.
2. Since it cannot be reduced, you can find the difference as following:
- You must subtract the Whole numbers part:
\(12-4=8\)- Now you can subtract the fractions:
\(\frac{20-1}{25}=\frac{19}{25}\)- Finallt, you must combine the Whole number obtained above and the Fraction part. So you get:
\(=8\frac{19}{25}\)Help please!! Thanks
Answer:
Q2 2010
Step-by-step explanation:
Let the number of quarters = x
Samsung increases by 6 each quarter.
Apple decreases by 1 each quarter.
Samsung
L = a + (x - 1)*6
a = 1
L = 1 + (x - 1)*6
Apple
L = a - (x - 1)*1
a = 53
L = 53 - (x - 1)*1
Now the problem is how many quarters go by until they meet?
1 + (x - 1)*6 = 53 - (x - 1) Remove the brackets
1 + 6x - 6 = 53 - x + 1 Combine like terms on both sides.
-5 + 6x = 54 - x Add 5 to both sides
6x = 59 - x Add x to both sides
7x = 59
x = 59/7 = 8 3/7
So sometime in the 8th quarter from zero they will be equal. At the end of the quarter, Samsung will be greater than Apple
So the answer should be 4 quarters from Q2 2009 or Q2 2010
Question
A watermelon is assumed to be spherical in shape while it is growing. Its mass, M kg, and radius, rcm, are related by the formula M = kr³, where k is a constant. It is also assumed that the radius is increasing at a constant rate of 0.1 centimetres per day. On a particular day the radius is 10 cm and
the mass is 3.2 kg. Find the value of k and the rate at which the mass is increasing on this day.
Thus, the mass is increasing at a rate of 0.15625 kg per hour, and the mass on this day is 4.5 kg.
Let's consider a general formula for finding the rate of increase:Rate of increase = k x original valueHere, k is a constant that represents the rate of increase per unit of time, and the original value is the initial value of the quantity being measured.
For example, if the original value is 3.2 kg and the rate of increase is 0.5 kg per hour, we can use the formula to calculate the mass at any time t as follows: Mass at
time t = 3.2 + (0.5 x t)
where t is the time elapsed in hours.In order to find k, we need to know the rate of increase and the original value.
Once we have these values, we can rearrange the formula to solve for
k:k = rate of increase / original value
For example, if the mass is increasing at a rate of 0.5 kg per hour and the original value is 3.2 kg, we can calculate k as follows:
k = 0.5 / 3.2k = 0.15625
To find the rate of increase on a specific day, we need to know how much time has elapsed since the original value was measured. Once we have this information, we can plug it into the formula we derived earlier:Mass at time t = 3.2 + (k x t)For example, if 8 hours have elapsed since the original value was measured, we can calculate the mass on that day as follows:
Mass at time t = 3.2 + (0.15625 x 8)
Mass at time t = 4.5 kg
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Can someone help me please
Answer: Least to greatest: 6, 4+2n, 12.5, 4n
Step-by-step explanation:
pi = 3.14
4n = 12.56
4 + 2n = 10.28
Least to greatest: 6, 4+2n, 12.5, 4n
Answer:
4π, 12.5, 4+2π, 6
Step-by-step explanation:
4π=12.56637
12.5=12.5
4+2π= 10.2831853
6=6
a vendor has 130,240and 150 oranges to put into bags so that each bag has the same number and there are no oranges left over.what is the largest number of oranges can the vendor put into each dag?
is this multiple choice?
The average amount of money spent for lunch per person in the college cafeteria is $6.4 and the standard deviation is $2.03. Suppose that 48 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.
The average amount of money spent for lunch per person in the college cafeteria is $6.45 and the standard deviation is $2.55. Suppose that 44 randomly selected lunch patrons are o
population mean is 6.45
population standard deviation is 2.55.
sample size is 44.
z-score is indicated because you are using population standard deviation and sample size is greater than 30.
Compare the sample mean to the population mean.The z-score formula is \((x - m) / s\)
in this case, x is the sample mean, m is the population mean, s is the standard error.
\(standard error = standard deviation / sqrt(sample size0 = 2.55 / sqrt(44) = .3844\) rounded to 4 decimal places.
z-score formula becomes \(z = (x - 6.45) / .3844\)
solve for x to get:
\(x = .3844 * z + 6.45\)
since you don't have a z-score, you can't find x.
the best you can do is find the critical z-scores, and hence, the critical raw scores.
In order to do that you need to to know the confidence level.
if you know that, you can find the critical z-scores and, from that, the critical x-scores.
we'll compare two confidence levels.
the first is at 99% confidence level.
the second is at 90% confidence level.
with a 99% two-tail confidence level, the critical z-scores are plus or minus 2.5758 rounded to 4 decimal places.
the critical raw scores are found by using the z-score formula.
you get \(x = .3844 * 2.5758 + 6.45 = 7.4401\) for the high score.
you get x = \(.3844 * -2.5758 + 6.45 = 5.4599\) for the low score.
the 99% two-tail confidence level tells you that 99% of your samples of size 44 will have the sample mean between 5.4599 and 7.4401.
that's your 99% confidence interval.
with a 95% two-tail confidence level, the critical z-scores are plus or minus 1.9600 rounded to 4 decimal places.
the critical raw scores are found by using the z-score formula.
you get \(x = .3844 * 1.9600 + 6.45 = 7.2034\) for the high score.
you get\(x = .3844 * -1.9600 + 6.45 = 5.6966\) for the low score.
the 95% two-tail confidence level tells you that 95% of your samples of size 44 will have the sample mean between 5.6966 and 7.2034.
that's your 95% confidence interval.
the higher the confidence level, the wider the confidence interval when you are dealing with the same population mean and population standard deviation and same sample size.
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Correct and complete question:
The average amount of money spent for lunch per person in the college cafeteria is $6.45 and the standard deviation is $2.55.
Suppose that 44 randomly selected lunch patrons are observed.
Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.
b. What is the distribution of x?
x-N(6.45,_________________)
Help please Which reason is the justification for the statement that angle A ≅ angle B?
A) Vertical angles are congruent.
B) Linear angles are equal.
C) Intersecting lines form opposing angles.
D) Lines intersect at one point.
L 1.5.3 Quiz: Solving Literal Equations and Formulas
Question 6 of 10
2 Points
The formula to convert Fahrenheit to Celsius is c= 5/9 (F-32). Convert 30°C to
Fahrenheit. Round to the nearest degree.
Answer:
86F
Step-by-step explanation:
C=5/9 (F-32)
30 = 5/9 (F-32)
F = (30*9)/5 + 32
F = 86
5) Using the formula A=652
find the surface area of a
cube with sides measuring 8
inches.
Answer:
81.5
Step-by-step explanation:Cube has all sides of equal dimensions and like that it has 6 faces.
So total surface area of cube is equal to the combined area of all the six faces.
Now each face has equal dimensions so same area
Therefore,
area of a single face =side²
Therefore, area of entire cube = 6 times the area of a single face
= 6 * side²
.
Choose the graph of y=|x|-2 by translating the parent function
The graph of function y = |x| - 2 by translating the parent function is shown in image.
We have to given that;
Function is,
⇒ y = |x| - 2
Now, We can formulate;
Since, Function is,
⇒ y = |x| - 2
It is translation of parent function y = |x| by 2 units down.
Thus, The graph of function y = |x| - 2 by translating the parent function is shown in image.
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Kelsi spent $6.75 every Saturday for breakfast what is the total amount of money keksie spends on breakfast for 14 Saturdays
Multiplication is the outcome of the product of two numbers. The total amount of money Kelsi spends on breakfast for 14 Saturdays is $94.5.
What is multiplication?A product is the outcome of multiplication or an expression that indicates the elements that will be multiplied.
Given that Kelsi spent $6.75 every Saturday for breakfast. Therefore, the total amount that will be spent on 14 Saturdays breakfast will be,
\(\rm Total\ Amount = \$6.75 \times 14 = \$94.5\)
Hence, the total amount of money Kelsi spends on breakfast for 14 Saturdays is $94.5.
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Answer:
$94.50
Step-by-step explanation:
i did the test and aced it
Jack plots points showing equivalent ratios on the coordinate plane above.
which ordered pair if plotted above would represent a ratio that is equivalent to those shown?
Answer:
(4,18)
Step-by-step explanation:
it would fit right into the line. i hope this helps.
If 5/8 of the people in a water aerobics class are over age 65 and 1/4 of the people in the class are under age 40, what fraction of the people in the class are either over 65 or under 40?
Answer:
7/8
Step-by-step explanation:
You just need to add the two fractions together. Since no one can be both, no other revision is needed.
5/8 + 1/4 = 5/8 + 2/8 = 7/8
A coin is tossed and a square spinner labeled A,B,C,D is twirled. Determine the probability of obtaining: a head and consonant
For a coin, there are two possible outcomes
It is either head or tail
For square spinner labeled A, B, C, and D
the outcomes are
Therefore, to find the probability of obtaining head or a consonant
The probability of getting head =1/2
The probability of consonant =3/4
\(P(HnC)=\frac{1}{2}\times\frac{3}{4}=\frac{3}{8}\)Answer = 3/8