Answer:
Subtract
2
from both sides of the equation.
3
x
=
11
−
2
Subtract
2
from
11
.
3
x
=
9
Step-by-step explanation:
what does given mean
Answer:
something that has been passed down to you or a gift that someone has gave you:)
Step-by-step explanation:
solve each equation by factoring x^2 + 8x + 12=0
The solutions to the equation x² + 8x + 12 = 0 are x = -2 and x = -6.
What is factor?A factor refers to a number or expression that divides another number or expression without leaving a remainder. In other words, factors are the numbers or expressions that are multiplied together to obtain a given product.
According to question:To solve the equation x² + 8x + 12 = 0 by factoring, we need to find two numbers that multiply to give us 12 (the constant term) and add to give us 8 (the coefficient of the x term).
Let's factor the equation:
x² + 8x + 12 = 0
The factors of 12 are:
1 * 12
2 * 6
3 * 4
We need to find a pair of factors that add up to 8. In this case, the pair that satisfies this condition is 2 and 6.
So, we can rewrite the equation using these factors:
(x + 2)(x + 6) = 0
Now we can apply the zero-product property, which states that if a product of factors equals zero, then at least one of the factors must be zero. We then solve for x by setting each factor equal to zero:
x + 2 = 0
x + 6 = 0
Solving for x in each equation:
x + 2 = 0
x = -2
x + 6 = 0
x = -6
So the solutions to the equation x² + 8x + 12 = 0 are x = -2 and x = -6.
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a population mean is 13. the sample mean is 12.8, and the sample standard deviation is two. the sample size is 20. what distribution should you use to perform a hypothesis test? assume the underlying population is normal.
To perform a hypothesis test we use students' t distribution.
What is a hypothesis test?
A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters thanks to hypothesis testing.
Here, we have
Given, the population mean is 13. the sample mean is 12.8, and the sample standard deviation is two. the sample size is 20.
We have to find distribution to perform a hypothesis test.
The students t distribution is used when
1- sample size less than 30. Here 20.
2-population standard deviation not given.
3-population is normal.
Hence, we concluded that to perform a hypothesis test we use students' t distribution.
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What are 6 types of angles in parallel lines?
Match the definitions on the left with the terms on the right.
Just want to make sure. Am I right??? Pls help Thxs!
can you help me on part D? dont use advanced math please
Answer:
A. the first quartile represents the median of the lower half of the data set
B. the third quartile represents the median of the upper half of the data set
Step-by-step explanation:
Find the period and the amplitude of the periodic function. I'm awful with graphs :(
A period is the difference in x over which a sine function returns to its equivalent state and the amplitude is A/5.
Amplitude:
The amplitude of a periodic variable is a measure of its change over a period of time, such as a temporal or spatial period. The amplitude of an aperiodic signal is its magnitude compared to a reference value. There are various definitions (see below) of amplitude, which is any function of the magnitude of the difference between the extreme values of a variable. In the previous text, the phase of a periodic function is called the amplitude.
X = A sin (ω[ t - K]) + b
A is the amplitude (or peak amplitude),
x is the oscillating variable,
ω is angular frequency,
t is time,
K and b are arbitrary constants representing time and displacement respectively.
According to the Question:
An equation does not have an amplitude. This "equation" represents the formula of a vibration, and was better written as:
X= A/5* sin(1000.t + 120)
These oscillations have a certain amplitude. X values can vary from minimum to maximum. Normally, the stop position of the oscillation is X=0. In this case, we can see that the maximum occurs when the sine is +1 and the minimum occurs when the sine is -1.
For theses cases X= A/5 respectively -A/5.
Therefore,
The amplitude is A/5.
For formulas of this type, the term in front of the sinus (or cosine) is equal to the amplitude.
Complete question:
Can I find the amplitude of this equation? A/5 *
find all values of c so that v = 1, 6, c and w = 1, −6, c are orthogonal. (enter your answers as a comma-separated list.
The only possible values of c that would make the vectors v and w orthogonal are the square roots of 35 and their negatives.
To find the values of c that make v and w orthogonal, we need to use the dot product formula:
v · w = (1)(1) + (6)(-6) + (c)(c) = 1 - 36 + \(c^2\)
We know that v and w are orthogonal when their dot product is equal to 0. So, we can set the equation we just formed equal to 0 and solve for c:
1 - 36 + \(c^2\) = 0
\(c^2\) = 35
c = ± √35
Therefore, the values of c that make v and w orthogonal are √35 and -√35. We can write the answer as a comma-separated list:
c = ± √35
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solve by using subsitution or elimnation by addition. 4x-3y=3 -8x 6y=-6
If we solve 4x-3y=3, -8x +6y=-6 by substitution or elimination, we will have x=3/4 and y=0
We have the following simultaneous equations:
4x-3y=3.....................(i)
-8x+6y=-6..................(ii)
We solve using substitution:
Make x the subject of formula in equation(i):
4x=3+3y
x=(3+3y)/4
Now, replace the value of x in equation(ii)
-8x+6y=-6, and x=(3+3y)/4
-8((3+3y)/4)+6y=-6
-2(3+3y)+6y=-6
-6-6y+6y=-6
y=0
Now, we replace the value of y=0 in any equations we have to find the corresponding value of x:
4x-3y=3, but y=0
4x-3(0)=3
4x=3
x=3/4
Hence, x=3/4, y=0
The question was incomplete, the complete question is given below:
solve by using substitution or elimination by addition. 4x-3y=3 -8x+6y=-6
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Answer these please!!!
The graph of 3x-2y≤6 is the third graph, for 3x-2y<6 is the first graph, for 3x-2y>6 is the fourth graph and for 3x-2y≥6 is the second graph. The solution has been obtained using concept of linear inequality.
What is linear inequality?
A linear inequality is one that would produce a linear equation if the equals relation were used instead of the inequality. When multiplying or dividing both sides by a negative number in order to solve the inequality, the direction of the inequality is reversed. The entire set of solutions to an inequality is known as the solution set.
We are given for graphs, of which two graphs are dotted and two are simple straight line graphs.
The dotted graphs are drawn for the inequalities having < or >
Whereas the simple straight line graphs are drawn for the inequalities having ≤ or ≥.
Now, to notice the shaded pattern, we will see whether the equations are true for (0,0) or not
1. 3x-2y≤6
⇒ 0≤6
So, the equation is true for the point.
Hence, the third graph represents this equation.
2. 3x-2y<6
⇒ 0<6
So, the equation is true for the point.
Hence, the first graph represents this equation.
3. 3x-2y>6
⇒ 0>6
So, the equation is false for the point.
Hence, the fourth graph represents this equation.
4. 3x-2y≥6
⇒ 0≥6
So, the equation is false for the point.
Hence, the second graph represents this equation.
Hence, the graphs are matched with the inequalities.
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Since, there are multiple questions so, the question answered above is attached below.
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}, C = {1, 3, 5, 7, 9, 11, 13, 15, 17). Use the roster method to write the set C.
The set C, using the roster method, consists of the elements {\(1, 3, 5, 7, 9, 11, 13, 15, 17\)}.
In the roster method, we list all the elements of the set enclosed in curly braces {}. The elements are separated by commas. In this case, the elements of set C are all the odd numbers from the universal set U that are less than or equal to 17.The roster method is a way to write a set by listing all of its elements within curly braces. In this case, we are given the set U and we need to find the set C.Set U: \(\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}\)Set C is defined as the subset of U that contains all the odd numbers. We can list the elements of C using the roster method:Set C: \(\{1, 3, 5, 7, 9, 11, 13, 15, 17\}\)This represents the set C using the roster method, where we have listed all the elements of set C individually within the curly braces. Each number in the list represents an element of set C, specifically the odd numbers from set U.Therefore, the set C can be written using the roster method as \(\{1, 3, 5, 7, 9, 11, 13, 15, 17\}\).Thus, the complete roster representation of set C is {\({1, 3, 5, 7, 9, 11, 13, 15, 17}.\)}
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how to solve 6x+4+5X+2=12X-4 to solve for x
11x+6=12x-4
6-4=12x-11x
therefore x=2
simple
Answer the question using the value of r and the given best-fit line on the scatter diagram.
The scatter diagram and best-fit line show the data for the price of a stock (y) and U.S. employment (x). The correlation coefficient r is 0.8. Predict the stock price for an employment value of 9.
Based on the information, the predicted stock price for an employment value of 9 is 12.2.
How to calculate the valueThe correlation coefficient r is a measure of the linear relationship between two variables. In this case, the correlation coefficient r is 0.8, which indicates a strong positive linear relationship between the price of the stock and U.S. employment. This means that as U.S. employment increases, the price of the stock is likely to increase as well.
The best-fit line equation is y = mx + b, where y is the stock price, x is the employment value, m is the slope of the line, and b is the y-intercept.
The slope of the line is 0.8, and the y-intercept is 5. Therefore, the equation for the best-fit line is y = 0.8x + 5.
In order to predict the stock price for an employment value of 9, we can substitute 9 for x in the equation. This gives us y = 0.8(9) + 5 = 7.2 + 5 = 12.2.
Therefore, the predicted stock price for an employment value of 9 is 12.2.
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A storage tank consist of a hemisphere and a cylinder which share a common base. The tank has a height of 16.5 m and the cylinder has a base diameter of 4.7m. Find the total capacity of the tank.
The total capacity of the tank is 272.675 cubic meters.
Given that,
A storage tank consist of a hemisphere and a cylinder which share a common base.
The base of both hemisphere and cylinder will be the same circle with the same radius.
Also, we have,
Height of the tank = 16.5 m
Base diameter of the cylinder = 4.7 m
Radius of the base of the cylinder = 4.7 / 2 = 2.35 m
Radius of the hemisphere = 2.35 m
Height of the cylinder = Total height of the tank - Height or radius of the hemisphere
Total capacity of the tank = Volume of hemisphere + Volume of cylinder
= 2/3 π r³ + π r² h
= 2/3 π (2.35)³ + π (2.35)² (16.5 - 2.35)
= 8.652π + 78.143π
= 272.675 cubic meters
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You are the accounting manager for Kool Ragz, Inc., a manufacturer of men's and women's clothing. The company needs to borrow $1,300,000 for 90 days in order to purchase a large quantity of material at "closeout" prices. The interest rate for such loans at your bank, Rimrock Bank, is 15% using ordinary interest.
(a) What is the amount (in $) of interest on this loan?
$ ?
(b) After making a few "shopping" calls, you find that Southside National Bank will lend at 15% using exact interest. What is the amount (in $) of interest on this offer? (Round your answer to two decimal places.)
$ ?
(c) So that it can keep your business, Rimrock Bank has offered a loan at 14.5% using ordinary interest. What is the amount (in $) of interest on this offer?
$ ?
(d) (Challenge) If Southside National wants to compete with Rimrock's last offer (part c) by charging $1,125 less interest, what rate (as a %), rounded to the nearest hundredths of a percent, must it quote using exact interest?
% ?
Amount of interest on loan at Rimrock Bank, using ordinary interest at a rate of 15%, is $48,750 and at rate of 14.5%, is $47,125. In Southside National Bank , interest at a rate of 15%, is $49,500.
To compete with Rimrock Bank's offer, Southside National Bank would need to quote a rate of 14.38% using exact interest. (a) To calculate the amount of interest on the loan at Rimrock Bank, we use the formula I = PRT, where I is the interest, P is the principal amount, R is the interest rate, and T is the time in years. Plugging in the values, we have I = $1,300,000 * 0.15 * (90/365) = $48,750.
(b) The amount of interest on the loan at Southside National Bank using exact interest is calculated the same way as in part (a), resulting in I = $1,300,000 * 0.15 * (90/360) = $49,500. (c) Similarly, using the same formula, we find the interest on the loan at Rimrock Bank with a rate of 14.5% to be I = $1,300,000 * 0.145 * (90/365) = $47,125.
(d) To determine the rate at which Southside National Bank should quote to compete with Rimrock Bank's last offer, we subtract the given interest difference of $1,125 from the interest calculated in part (b). Solving for R, we have $48,750 - $1,125 = $1,300,000 * R * (90/360). Solving this equation results in R ≈ 0.1438, which is 14.38% rounded to the nearest hundredth of a percent.
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4:3 is an example of...
Answer:
A ratio
Step-by-step explanation:
A quantitative relation between two amounts showing the number of times one value contains or is contained within the other
Which number line and expression show how to find the distance from -4 to
1?
O A.
B.
C.
O D.
5
4
3
-2
|-4-1|
4
4-(-1)
4-1
-1 0
|-4-(-1)
1
2 3 4
23
The distance from -4 to 1 is 5 units.
The correct number line and expression to find the distance from -4 to 1 are:
Number line: -4 -3 -2 -1 0 1
Expression: |-4 - 1|
To find the distance, we subtract the smaller number (-4) from the larger number (1) and take the absolute value:
|-4 - 1| = |-5| = 5
Therefore, the distance from -4 to 1 is 5 units.
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Please help
I’m need this because it’s already late
Answer:
KL = 12
Step-by-step explanation:
KL/GH = NK/JG
KL/37 = 17/52.5
52.5·KL = 629
KL = 11.98
50 minus 17 4/6 plzzzzzzzzzz answer rn
Answer:
32 1/3 or 2/6
Step-by-step explanation:
but 1/3 is better
Answer:
decimal form= 32.3
Step-by-step explanation:
fraction form 32 1/3
determine whether the geometric series is convergent or divergent. [infinity] (2)n 6n 1 n = 0
Answer:
To determine whether the geometric series [infinity] (2^n)(6n+1), n=0, is convergent or divergent, we can use the ratio test.
The ratio test states that if the limit of the absolute value of the ratio of the (n+1)th term to the nth term is less than 1, then the series is convergent. If the limit is greater than 1, the series is divergent. If the limit is equal to 1, the test is inconclusive.
Let's apply the ratio test to this series:
|(2^(n+1))(6(n+1)+1)|
--------------------- = |2 * 6n + 13|
|(2^n)(6n+1)|
As n approaches infinity, the absolute value of the ratio simplifies to:
|2 * 6n + 13|
-------------
|2^n|
Dividing both the numerator and denominator by 2^n, we get:
|6n/2^n + 13/2^n|
------------------
1
As n approaches infinity, 6n/2^n approaches 0, and 13/2^n approaches 0. Therefore, the limit of the absolute value of the ratio is 0 + 0 = 0, which is less than 1.
Since the limit of the absolute value of the ratio is less than 1, the series [infinity] (2^n)(6n+1), n=0, is convergent.
help i give you brinly
a website advertises job openings on its website, but job seekers have to pay to access the list of job openings. the website recently completed a survey to estimate the number of days it takes to find a new job using its service. it took the last 32 customers an average of 80 days to find a job. assume the population standard deviation is 10 days. calculate a 90% confidence interval of the population mean number of days it takes to find a job.
The 90% confidence interval for the population mean number of days it takes to find a job using the website's service is approximately 77.09 to 82.91 days.
To calculate a 90% confidence interval for the population mean number of days it takes to find a job using the website's service, follow these steps:
1. Identify the sample mean (X), sample size (n), and population standard deviation (σ). In this case, X = 80 days, n = 32, and σ = 10 days.
2. Determine the desired confidence level. Here, it's 90%.
3. Find the critical value (z) associated with the 90% confidence level. You can look this up in a standard normal distribution table or use a calculator that provides this functionality. For a 90% confidence interval, the critical value is approximately 1.645.
4. Calculate the standard error (SE) by dividing the population standard deviation (σ) by the square root of the sample size (n). In this case, SE = σ/√n = 10/√32 ≈ 1.77.
5. Multiply the critical value (z) by the standard error (SE) to obtain the margin of error (MOE): MOE = z * SE = 1.645 * 1.77 ≈ 2.91.
6. Calculate the lower and upper bounds of the confidence interval by subtracting and adding the margin of error (MOE) from the sample mean (X). In this case, the lower bound = 80 - 2.91 ≈ 77.09, and the upper bound = 80 + 2.91 ≈ 82.91.
Thus, the 90% confidence interval for the population mean number of days it takes to find a job using the website's service is approximately 77.09 to 82.91 days.
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please give a step by step ASAP
The correct option is the fourth one, the slope and y-intercept are different.
Which statement is correct?Here we have the linear equation:
3x - 5y = 4
We know that it is dilated by a scale factor of 5/3, so let's find the dilation.
We can rewrite the linear equation as:
-5y = 4 - 3x
y = (3/5)x - 4/5
Now let's apply the dilation:
y = (5/3)*[ (3/5)x - 4/5]
y = x - 4/3
Then we can see that the slope and the y-intercept are different, the correct option is 4.
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Explain in your own words the meaning of equivalent
ratios.
Answer:Equivalent ratios are ratios that make the same comparison of numbers. Two ratios are equivalent if one can be expressed as a multiple of the other.
Answer:
ratios that make the same comparison of numbers
Step-by-step explanation:
i hope thats good for u
50,56,62,68 what is the 12th term
2 Shape 1 and Shape 2 are congruent pentagons.
Shape 1
Shape 2
Shape 2 is congruent to Shape 1 because -
Shape 2 is a translation of Shape 1.
Shape 2 is a reflection of Shape 1.
Shape 2 is a rotation of Shape 1.
D. Shape 2 and Shape 1 are both pentagons.
A.
B
C.
The shape 1 and shape 2 are congruent pentagons becuase shape 2 is a reflection of shape 1.
Given that shape 1 and shape 2 are congruent pentagons.
We are required to choose the option which is correct according to the given statemment that shape 1 and shape 2 are congruent pentagons.
Pentagons are the shape which have 5 sides and 5 angles.
Two shapes are congruent if they are copy of each other means all the corresponding sides are equal to each other.
The shape 1 and shape 2 are congruent pentagons becuase shape 2 is a reflection of shape 1.
Hence the shape 1 and shape 2 are congruent pentagons becuase shape 2 is a reflection of shape 1.
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The weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 60% chance it will be good tomorrow, a 30% chance it will be indifferent, and a 10% chance it will be bad. If the weather is indifferent today, there is a 50% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 40% chance it will be good tomorrow and a 30% chance it will be indifferent. The stochastic matrix for this situation is shown to the right. In the long run, how likely is it for the weather in Columbus to be indifferent on a given day? 0.6 0.5 04 P-1 0.3 0.2 0.3 0.1 0.3 0.3 In the long run, how likely is it for the weather in Columbus to be indifferent on a given day?
In the long run, the likelihood of indifferent weather in Columbus on a given day is approximately 29.3%.
To find the long-term likelihood of indifferent weather in Columbus, we need to find the steady-state probabilities of the stochastic matrix provided. The matrix is given as:
P = | 0.6 0.5 0.4 |
| 0.3 0.2 0.3 |
| 0.1 0.3 0.3 |
1. First, find the transpose of the matrix P:
P^T = | 0.6 0.3 0.1 |
| 0.5 0.2 0.3 |
| 0.4 0.3 0.3 |
2. Next, subtract the identity matrix I from the transpose of P:
P^T - I = | -0.4 0.3 0.1 |
| 0.5 -0.8 0.3 |
| 0.4 0.3 -0.7 |
3. To find the steady-state probabilities, we need to solve the system of linear equations:
(-0.4)x + 0.3y + 0.1z = 0
0.5x - 0.8y + 0.3z = 0
We also have an additional constraint since the sum of probabilities must equal 1:
x + y + z = 1
4. Solve this system of linear equations using any method (substitution, elimination, or matrix method). The resulting probabilities are:
x = 0.432 (good weather probability)
y = 0.293 (indifferent weather probability)
z = 0.275 (bad weather probability)
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Please help giving 90 points
Answer:
m=9
Step-by-step explanation:
AB = 3.2 cm
BC= 8.4 cm
The area of triangle ABC is 10 cm²
Calculate the perimeter of triangle ABC.
Give your answer correct to three significant figures.
Answer:
Therefore, perimeter of the given triangle is 18.300 cm.
Step-by-step explanation:
Area of the triangle ABC = \(\frac{1}{2}(\text{AB})(\text{BC})(\text{SinB})\)
10 = \(\frac{1}{2}(3.2)(8.4)(\text{SinB})\)
Sin(B) = \(\frac{10}{3.2\times 4.2}\)
B = \(\text{Sin}^{-1}(0.74405)\)
B = 48.08°
By applying Cosine rule in the given triangle,
(AC)² = (AB)² + (BC)²-2(AB)(BC)CosB
(AC)² = (3.2)² + (8.4)² - 2(3.2)(8.4)Cos(48.08)°
(AC)² = 10.24 + 70.56 - 35.9166
(AC)² = 44.88
AC = \(\sqrt{44.8833}\)
AC = 6.6995 cm
Perimeter of the ΔABC = m(AB) + m(BC) + m(AC)
= 3.200 + 8.400 + 6.6995
= 18.2995
≈ 18.300 cm
Therefore, perimeter of the given triangle is 18.300 cm
Evaluate
(-)))
729
4096
243
1024
243
1024
729
4096
Answer:
= 729/4096.
Step-by-step explanation:
Here is the solution