O 2. Draw two more arrangements with dots to form the sequence: 1; 3; 6; 10; 15;... ล th th 3. How many dots will there be in the 9 and 10" arrangements? Explain how you got your answer. (3) 4. What do you observe if you take any two consecutive arrangements and add the number of dots? (2) [19]
Answers
The 9th arrangement will have 36 dots, the 10th arrangement will have 45 dots, and when adding the number of dots in any two consecutive arrangements, the result will be the number of dots in the next arrangement.
To determine the number of dots in the 9th and 10th arrangements, we need to understand the pattern in the given sequence: 1, 3, 6, 10, 15, ...
To find the pattern, we can observe the differences between consecutive terms: 2, 3, 4, 5, ...
We notice that these differences increase by 1 each time. This indicates that the sequence is formed by adding consecutive positive integers to the previous term.
Using this pattern, we can determine the 9th and 10th arrangements as follows:
9th arrangement:
Starting with the 1st arrangement, we add the positive integers consecutively: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36.
Therefore, the 9th arrangement will have 36 dots.
10th arrangement:
Starting with the 1st arrangement, we add the positive integers consecutively: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.
Therefore, the 10th arrangement will have 45 dots.
Now, let's address the observation when we take any two consecutive arrangements and add the number of dots.
If we take the nth arrangement and the (n+1)th arrangement, we can observe that the number of dots in the (n+1)th arrangement will be the sum of the number of dots in the nth arrangement and the number of dots added in the (n+1)th step.
For example, let's consider the 2nd and 3rd arrangements:
2nd arrangement: 3 dots
3rd arrangement: 3 + 3 (adding 2, the next positive integer) = 6 dots
This pattern holds true for any two consecutive arrangements in the sequence.
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Related Questions
Please awnser asap I will brainlist
Answers
The number of $10 tickets sold is 1210 tickets.
The number of $20 tickets sold is 1344 tickets.
The number of $30 tickets sold is 827 tickets.
How to determine the number of each type of tickets sold?In order to write a system of linear equations to describe this situation, we would assign variables to the number of each tickets sold, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent the number of $10 tickets.Let the variable y represent the number of $20 tickets.Let the variable z represent the number of $20 tickets.Since the basketball team sold 3381 tickets overall, 134 more $20 tickets than $10 tickets and the total sales are $63,790, a system of three linear equations to model this situation is given by;
x + y + z = 3381
y - x = 134
10x + 20y + 30z = 63790 ⇒ x + 2y + 3z = 6379
Next, we would solve the system of three linear equations simultaneously as follows;
x + x + 134 + z = 3381
2x + 134 + z = 3381
z = 3247 - 2x
x + 2(x + 134) + 3(3247 - 2x) = 6379
x = 1210 tickets.
For the value of y, we have:
y = x + 134
y = 1210 + 134
y = 1344 tickets.
For the z-value, we have:
z = 3247 - 2x
z = 3247 - 2(1210)
z = 827 tickets.
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Complete Question:
A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3381 tickets overall. It has sold 134 more $20 tickets than $10 tickets. The total sales are $63,790. How many tickets of each kind have been sold?
How many $10 tickets were sold?
How many $20 tickets were sold?
how many $30 tickets sold?
Delaware has a K-12 student enrollment of 120,475 across 19 districts. Alabama has 630,683 students across 137 districts. If Delaware was proportional to Alabama in enrollment to the district, how many districts would Delaware have? Round to the nearest whole number.
Answers
Answer:
If Delaware was proportional to Alabama in enrollment to the district, it would have approximately 37 districts.
Here's how I calculated it:The ratio of students to districts in Alabama is 630,683/137 = 4,603 students per district. If Delaware had the same ratio of students to districts, it would have 120,475/4,603 = 26.16 districts. Rounding to the nearest whole number, Delaware would have approximately 26 districts if it was proportional to Alabama in enrollment to the district.
URGENTTTT!! please help me solve 5x² - 10x = 23
Answers
Answer:
3.36643191324
-1.36643191324
Step-by-step explanation:
subtract 23 from both sides so that everything is on one side
5x²-10x-23=0
you can't factor this, so you need to use the quadratic formula:
(-b±√(b²-4*a*c))/2a
in our case, a= 5 b= -10 and c = -23
(-(-10)±√(10²-4*5*(-23)))/(2*5)
(10±√(100+460))/10
(10±√560)/10
we solve this twice. once where ± is + and again where ± is -
(10+√560)/10 = 3.36643191324
(10-√560)/10= -1.36643191324
100 Points! Geometry question. Photo attached. Only looking for an answer to B. Please show as much work as possible. Thank you!
Answers
Answer: Read the solution
Step-by-step explanation:
A. For diagram A, triangles ANC and BDE are similar. Thus, we can use similarity ratios to find the length of AC. (x+1)/12 = (x+5)/15. 15x+15=12x+60. Thus 3x=45, and x=15. Since we need to find AC, AC = 15+1 = 16.
B. For diagram B, triangles SRT and VUT are similar. Again, using similarity ratios, (4x-1)/14=(x+2)/6 or 14x+28=24x-6. 10x=34, x=3.4.
Related Rates:
Please answer the question pictured.
Answers
The value of dy/dt at x= 1 if y = [tex]3x^2[/tex] - 3 and dx/dt = 3 is 18.
To find dy/dt at x = 1, we need to differentiate the given equation y = [tex]3x^2[/tex] - 3 with respect to t and then substitute x = 1 and dx/dt = 3.
Let's begin by differentiating y = [tex]3x^2[/tex]- 3 with respect to t using the chain rule. Since y is a function of x and x is a function of t, we have:
dy/dt = (dy/dx) * (dx/dt)
Given dx/dt = 3, we can rewrite the equation as:
dy/dt = [tex](dy/dx) * 3[/tex]
Now, let's find the derivative of y = [tex]3x^2 - 3[/tex] with respect to x:
dy/dx = d/dx[tex](3x^2 - 3)[/tex]
= 6x
Substituting this back into the equation for dy/dt, we get:
dy/dt = [tex](6x) * 3[/tex]
= 18x
Finally, we can evaluate dy/dt at x = 1:
dy/dt at x = 1 = 18(1)
= 18
Therefore, the value of dy/dt at x = 1 is 18.
It's important to note that the value of dx/dt = 3 was given, and we used it to find dy/dt using the chain rule and the derivative of the equation with respect to x.
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PLEASE HELP ASAP WOULD APPRECITAE IT
Answers
The values of w, x, y, z are 120°, 60°, 120° , 60° respectively.
What are angles on parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
lines PQ and RS are parallel to each other and AB and CD are also parallel to each other. A pair of parallel line will serve as transversal.
Angles on parallel lines can be ;
Vertically opposite, alternate, corresponding and in each case the angles are equal.
w = 120°( vertically opposite angles)
x = 180-120 = 60( corresponding angles)
x = z = 60° ( corresponding angles)
y = 180-60 = 120°( angles on a straight line)
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Please use the following for the next 7 questions. A random sample of 172 students was asked to rate on a scale to from 1 (not important) to 5 (extremely important) health benefits as a job characteristic (note that the rating scale can also have decimals, i.e. a student can give a rating of 1.32). The sample mean rating was 3.31, and the sample standard deviation was 0.70. For a type I error of 1% (alpha), can you be reasonably certain that the average rating is more than 3 in the population?
1.State the null and alternative hypotheses.
a. H0: µ = 0, Ha: µ > 3.31
b. H0: µ = 0, Ha: µ < 3.31
c. H0: µ = 0, Ha: µ > 3
d. H0: µ = 0, Ha: µ ≠ 3
2. Specify the rejection region for = 0.01. Reject H0 if
a. z > 2.33
b. t > 2.32
c. z < 2.33
d. t < 2.32
3. Calculate the test statistic
a. 2.3
b. -5.8
c. 0.44
d. 5.8
4. What is your conclusion?
a. Reject H0
b. Fail to Reject H0
c. Reject Ha
d. Fail to reject Ha
5. Obtain the lower bound of a 99% confidence interval for the mean rating.
a. 0.31
b. 0.34
c. 3.44
d. 3.17
6. Obtain the upper bound of a 99% confidence interval for the mean rating.
a. 0.31
b. 0.34
c. 3.44
d. 3.17
7. What assumption(s) do you need to make in order to answer the above questions?
a. No assumptions are needed
b. The population distribution is assumed to be normal.
c. The population distribution is assumed to be t-distributed.
d. The sampling distribution of the sample is assumed to be normal.
Answers
State the null and alternative hypotheses.
c. H0: µ = 0, Ha: µ > 3
The null hypothesis (H0) states that the population mean rating is equal to 3, while the alternative hypothesis (Ha) suggests that the population mean rating is greater than 3.
Specify the rejection region for α = 0.01. Reject H0 if
a. z > 2.33
The rejection region for a one-tailed test with a significance level of 0.01 (α) is in the upper tail of the distribution. In this case, we reject the null hypothesis if the test statistic (z-score) is greater than 2.33.
Calculate the test statistic
c. 0.44
To calculate the test statistic, we use the formula:
z = (sample mean - population mean) / (sample standard deviation / √n)
Plugging in the given values, we get:
z = (3.31 - 3) / (0.70 / √172) ≈ 0.44
What is your conclusion?
b. Fail to Reject H0
Since the calculated test statistic (0.44) does not exceed the critical value (2.33) in the rejection region, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the average rating is significantly greater than 3 in the population.
Obtain the lower bound of a 99% confidence interval for the mean rating.
d. 3.17
To obtain the lower bound of a 99% confidence interval, we subtract the margin of error from the sample mean. The margin of error can be calculated by multiplying the critical value (obtained from the z-table for a 99% confidence level) with the standard error (sample standard deviation divided by the square root of the sample size).
The lower bound is given by:
3.31 - (2.33 * (0.70 / √172)) ≈ 3.17
Obtain the upper bound of a 99% confidence interval for the mean rating.
c. 3.44
To obtain the upper bound of a 99% confidence interval, we add the margin of error to the sample mean. Using the same calculation as above, the upper bound is given by:
3.31 + (2.33 * (0.70 / √172)) ≈ 3.44
What assumption(s) do you need to make in order to answer the above questions?
b. The population distribution is assumed to be normal.
To perform hypothesis testing and construct confidence intervals, it is typically assumed that the population distribution is approximately normal. Additionally, assumptions such as random sampling and independence of observations are generally made.
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-1/4 plus 3/5
Answer or else
Answers
The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.
To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.
The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:
-1/4 = -5/20
3/5 = 12/20
Now that the fractions have the same denominator, we can add them:
-5/20 + 12/20 = (-5 + 12)/20 = 7/20
Therefore, -1/4 + 3/5 is equal to 7/20.
To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.
Thus, the final answer is 7/20.
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Nave Corporation manufactures and sells custom home elevators. From the time an order is placed until the time the elevator is installed in the customer's
averages 44 days. This 44 days is spent as follows
12 days
5 days
Help
What is Naven's manufacturing cycle efficiency (MCE) for its elevators?
Answers
Nave Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 27.27%.
To calculate the manufacturing cycle efficiency (MCE) for Nave Corporation's elevators, we need to determine the ratio of value-added time to the total lead time.
Value-added time refers to the time spent on activities that directly contribute to the production or customization of the elevators, while lead time refers to the total time from order placement to installation.
Given the breakdown of time:
12 days for manufacturing and customization
5 days for waiting or non-value-added time
The value-added time is 12 days, and the total lead time is 44 days.
To calculate MCE, we divide the value-added time by the total lead time and multiply by 100 to express it as a percentage:
MCE = (Value-added time / Total lead time) x 100
MCE = (12 / 44) x 100
MCE = 27.27%
Therefore, Nave Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 27.27%.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
Step-by-step explanation:
According to the triangle proportionality theorem (or thales theorem), the lines are parallel if AD/BD = AE/CE
15/12= 1.25
10/8 = 1.25
Because the ratios are equal, the lines are parallel to each other.
help me please i would appreciate it so so much
Answers
a) The triangles in this problem are congruent.
b) The reason is the SAS congruence theorem.
What is the Side-Angle-Side congruence theorem?The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.
The equal sides for this problem are given as follows:
Hypotenuses and PS.
As angle P is bisected, we have <1 = <2, which are the angles between the equal sides, hence the SAS theorem holds true for this problem.
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A translation is shown on the grid below in which triangle A is the pre-image and triangle B is the image.
On a coordinate plane, triangle A is shifted 6 units to the right to form triangle B.
Which rule describes the x-coordinates in the translation?
x + 0
x + 6
x – 6
x + 4
Answers
Answer:
(b) x + 6
Step-by-step explanation:
You want the rule for the x-coordinate when the transformation is a right shift of 6 units.
Right shiftA point that is the image of a pre-image point with x-coordinate x will be 6 units farther right of the y-axis than the pre-image point.
The x-coordinate measures how far right of the y-axis a point is. When that distance increases by 6 units, the x-coordinate increases by 6 units:
x ⇒ x+6 . . . . . . the x-coordinate transformation rule
<95141404393>
Figure 1 has been transformed to produce figure 2.
N
O A.
O B.
c.
O D.
76
8
6-
2-
ON
60
Which notation describes this transformation?
(z,y)= (z+ 9,y - 2)
(z,y)= (-y, z)
(z',y)= (z - 9,y + 2)
(z,y)= (-z, y)
8
X
Answers
The notation of the transformation of the polygons is (x, y) = (x - 9, y + 2)
Describing the notation of the transformationFrom the question, we have the following parameters that can be used in our computation:
The polygons 1 and 2
In the graph, we can see that
Polygon 1 is shifted up by 2 unitsPolygon 2 is shifted left by 9 unitsusing the above as a guide, we have the following:
(x, y) = (x - 9, y + 2)
This means that the transformation of the polygons is (x, y) = (x - 9, y + 2)
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What is Navems manufacturing cycle efficiency (MCE) for its elevators
Answers
Navern Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 11.36%.
How to calculate the valueValue-added time is the time spent on activities that directly add value to the product.
Value-added time: Process time = 5 days (the process of manufacturing the elevators)
Total cycle time: Wait time + Inspection time + Process time + Move time + Queue time
= 12 days + 12 days + 5 days + 6 days + 9 days
= 44 days
MCE = (Value-added time / Total cycle time) * 100
= (5 days / 44 days) * 100
≈ 11.36%
Therefore, Navern Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 11.36%.
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Please awnser asap I will brainlist
Answers
Answer: true
Step-by-step explanation:
100 Points! Geometry question. Determine whether each pair of triangles is similar. If so, write a similarity statement. If not, what would be sufficient to prove the triangles similar? Explain your reasoning. Photo attached. Thank you!
Answers
Answer:
Yes, the triangle are similar.
Step-by-step explanation:
To prove that 2 triangle are similar you only need to prove that 2 corresponding angles are equal.
The sum of the interior angles add to 180.
< m on the left measures 30 degrees.
80 - 90 - 60 = 30
> t on the right measures 60 degrees.
180 - 90 - 30 = 60
If two corresponding angles of two triangles are equal that forces the third pair to be congruent, since the total of the angles must add up to 180.
Although we are not given the corresponding sides, there are proportional because the angles are equal.
Helping in the name of Jesus.
Answer:
Similar triangles are triangles that have the same shape but different sizes. In other words, if two triangles are similar, then their corresponding angles are congruent and their corresponding sides are in equal proportion.
For Question:
In Δ MSK and ΔQRT
∡S=∡R right angle
∡K=∡T=180°-90°-30°=60° Given
∡M=∡Q=180°-90°-60°=30° Given
Therefore,
Δ MSK [tex]\bold{\sim}[/tex] ΔQRT
By AA similarity.
Hence Proved:
Which equations represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2)? Select two
options.
Oy=-3x+1
03x-4y=-4
4x-3y=-3
Oy-2=-(x-4)
Oy+2=2(x+4)
Answers
The equations that represent a line parallel to 3x - 4y = 7 and passes through the point (-4, -2) are:
0 = 3x - 4y - 4
3x - 4y = 4
To determine which equations represent a line that is parallel to the given line and passes through the point (-4, -2), we need to find the equations that have the same slope as the given line.
The equation 3x - 4y = 7 can be rewritten in slope-intercept form as y = (3/4)x - 7/4. From this form, we can see that the slope of the given line is 3/4.
Now let's analyze the options:
Oy = -3x + 1: This equation has a slope of -3, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
0 = 3x - 4y - 4: This equation can be rewritten as 3x - 4y = 4. Comparing this to the given line, we can see that it has the same coefficients of x and y, which means it has the same slope of 3/4. Therefore, this option represents a line parallel to the given line.
4x - 3y = -3: This equation has a slope of 4/3, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
Oy - 2 = -(x - 4): This equation can be rewritten as y = -x + 2. The slope of this line is -1, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
Oy + 2 = 2(x + 4): This equation can be rewritten as y = 2x + 6. The slope of this line is 2, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
In conclusion, the equations that represent a line parallel to 3x - 4y = 7 and passes through the point (-4, -2) are:
0 = 3x - 4y - 4
3x - 4y = 4
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It takes 41 minutes for 9 people to paint 9 walls.
How many minutes does it take 1414 people to paint 14 walls?
Answers
The time taken for 1414 people to paint 14 walls is 6,430.44 minutes.
To find out how many minutes it would take 1414 people to paint 14 walls, we can use the information given to find the ratio.
We know that it takes 9 people 41 minutes to paint 9 walls.
Let's find the ratio:
(9 people) : (1414 people) = (41 minutes) : (x minutes)
Use the mutual multiplication property of the resulting ratio:
9 * x = 1414 * 41
Right simplification:
9x = 57974
To solve this problem, create a ratio using the information provided:
(9 people) : (1414 people) = (41 minutes) : (x minutes)
We can multiply the ratios:
9 * x = 1414 * 41
On the right side of the equation, calculate the product of 1414 and 41, which equals 57974.
4 444 So:
444 9x = 57974 To separate
4 share both sides of the equation with 9:
4 x = 57974/9
share both sides with 9:
4 x = 6430.44
It will take 6,430.44 minutes for 1,414 people to paint 14 walls.
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Kylie suspected that when people exercise longer, their body temperatures change. She randomly assigned people to exercise for
30
3030 or
60
6060 minutes, then measured their temperatures. The
18
1818 people who exercised for
30
3030 minutes had a mean temperature of
�
ˉ
30
=
38.
3
∘
C
x
ˉ
30
=38.3
∘
Cx, with, \bar, on top, start subscript, 30, end subscript, equals, 38, point, 3, degrees, start text, C, end text with a standard deviation
�
30
=
0.2
7
∘
C
s
30
=0.27
∘
Cs, start subscript, 30, end subscript, equals, 0, point, 27, degrees, start text, C, end text. The
24
2424 people who exercised
60
6060 minutes had a mean temperature of
�
ˉ
60
=
38.
9
∘
C
x
ˉ
60
=38.9
∘
Cx, with, \bar, on top, start subscript, 60, end subscript, equals, 38, point, 9, degrees, start text, C, end text with a standard deviation
�
60
=
0.2
9
∘
C
s
60
=0.29
∘
Cs, start subscript, 60, end subscript, equals, 0, point, 29, degrees, start text, C, end text.
Kylie wants to estimate the difference in the mean body temperature after exercising for the two amounts of time
(
30
min.
−
60
min.
)
(30min.−60min.)left parenthesis, 30, start text, m, i, n, point, end text, minus, 60, start text, m, i, n, point, end text, right parenthesis. Assume that the conditions for inference have been met.
Which of the following is an appropriate confidence interval for
�
30
−
�
60
μ
30
−μ
60
mu, start subscript, 30, end subscript, minus, mu, start subscript, 60, end subscript?
Choose 1 answer:
Answers
Therefore, an appropriate confidence interval for μ30−μ60μ30−μ60 (the difference in mean body temperature) would be −0.796−0.796 to −0.404−0.404 (rounded to the appropriate decimal places).
To estimate the difference in the mean body temperature after exercising for 30 minutes versus 60 minutes, we can construct a confidence interval. Since the conditions for inference have been assumed to be met, we can proceed with the following steps:
Calculate the difference in sample means: xˉ30−xˉ60=38.3−38.9=−0.6xˉ30−xˉ60=38.3−38.9=−0.6.
Determine the standard error of the difference, which is given by the formula:
SE=(s302n30)+(s602n60)SE=(n30s302)+(n60s602)
Substituting the values, we have:
SE=(0.27218)+(0.29224)≈0.100SE=(180.272)+(240.292) ≈0.100.
Choose an appropriate confidence level. Let's say we want a 95% confidence interval.
Using the standard error, calculate the margin of error, which is given by multiplying the critical value (corresponding to the chosen confidence level) by the standard error. For a 95% confidence level, the critical value is approximately 1.96.
Margin of Error = 1.96 * 0.100 ≈ 0.196.
Construct the confidence interval by subtracting and adding the margin of error to the difference in sample means:
−0.6−0.196−0.6−0.196 to −0.6+0.196−0.6+0.196.
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Identify the number of solutions of the system of linear equations.
x=y+3z=6
x-2y = 5
2x - 2y + 5z = 9
no solution
exactly one solution
infinitely many solutions
Solve the system. If there are infinitely many solutions, write the ordered triple in terms of z. If there is no solution, lea
The solution is (x, y, z)
-1.2
3
Answers
The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.
Let's solve the system of linear equations correctly.
The given system of linear equations is:
x = y + 3z = 6
x - 2y = 5
2x - 2y + 5z = 9
To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:
From equation 1, we have:
x = y + 3z
Substituting this value of x in equation 2:
(y + 3z) - 2y = 5
y + 3z - 2y = 5
-z + 3z = 5 - y
2z = 5 - y
Now, let's substitute the value of x in equation 3:
2(y + 3z) - 2y + 5z = 9
2y + 6z - 2y + 5z = 9
11z = 9
Simplifying the equation, we find:
z = 9/11
Now, substituting this value of z back into the equation 2z = 5 - y, we get:
2(9/11) = 5 - y
18/11 = 5 - y
18/11 - 5 = -y
18/11 - 55/11 = -y
-37/11 = -y
y = 37/11
Finally, we can substitute the values of y and z into equation 1 to find the value of x:
x = y + 3z
x = 37/11 + 3(9/11)
x = 37/11 + 27/11
x = 64/11
Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).
The system has exactly one solution.
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The graph of F(x), shown below, has the same shape as the graph of
G(x)=x2, but it is shifted to the left 1 unit. What is its equation?
-F(x)=
-
OA. F(x)=x²2 +1
B. F(x)=x²-1
C. F(x) = (x + 1)²
D. F(x)=(x-1)²
Answers
To shift the graph left, we need to subtract 1 from x. This gives us F(x) = (x - 1)², which matches option D. Therefore, the correct answer is D.
The graph of F(x) is a parabolic graph, just like the graph of G(x)=x². F(x) is shifted to the left by 1 unit.
The equation for the graph of F(x) is F(x) = (x - 1)². This is because when a parabolic graph is shifted left or right, it affects the x-value of the vertex of the parabola.
The standard form of the equation for a parabolic graph is y = a(x - h)² + k, where (h, k) is the vertex of the graph and a determines whether the graph is facing up or down. In this case, the vertex of the graph of G(x)=x² is (0, 0).
When we shift this graph left by 1 unit, the vertex becomes (-1, 0). Therefore, the equation for F(x) is F(x) = a(x + 1)².
To determine the value of a, we can look at the y-intercept of the graph, which is (0, 1). Plugging these values into the equation, we get 1 = a(0 + 1)², which simplifies to 1 = a.
Therefore, the equation for F(x) is F(x) = (x + 1)². However, if we expand this equation, we get F(x) = x² + 2x + 1, which is not in the form given in the options.
To shift the graph left, we need to subtract 1 from x. This gives us F(x) = (x - 1)², which matches option D. Therefore, the correct answer is D.
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Help with math problem please
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In 2020 there were 18,700 students at college a with a projected enrollment increase of 500 students per year in the same year there were 26,200 students at college B with a projected enrollment decline of 1000 students per year according to these projections when will the colleges have the same enrollment? What will be the enrollment in each college at that time?
Answers
In 2025, both colleges will have an enrollment of 21,200 students.
To determine when the colleges will have the same enrollment, we need to set up an equation based on the projected enrollment increases and declines.
Let's assume the number of years from 2020 is represented by 'x'.
For College A, the projected enrollment can be represented by: 18,700 + 500x.
For College B, the projected enrollment can be represented by: 26,200 - 1000x.
To find when the colleges will have the same enrollment, we need to solve the equation:
18,700 + 500x = 26,200 - 1000x
Combining like terms, we get:
1500x = 7,500
Dividing both sides by 1500, we find:
x = 5
Therefore, the colleges will have the same enrollment in 5 years, or in the year 2025.
To determine the enrollment at that time, we substitute x = 5 into either equation. Let's use College A's equation:
Enrollment in College A in 2025:
18,700 + 500(5) = 18,700 + 2500 = 21,200 students
Enrollment in College B in 2025:
26,200 - 1000(5) = 26,200 - 5000 = 21,200 students
Both colleges will have an enrollment of 21,200 students in the year 2025 when they have the same enrollment.
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Un cultivo de 32 200 bacterias aumenta un 25% cada 20 minutos. ¿Cuál será la población de bacterias al transcurrir 4 horas?
Answers
Para calcular la población de bacterias al cabo de 4 horas, primero necesitamos determinar cuántos intervalos de 20 minutos hay en 4 horas.
4 horas son equivalentes a 240 minutos. Dividiendo 240 minutos entre 20 minutos por intervalo, obtenemos 12 intervalos.
Dado que la población de bacterias aumenta un 25% cada 20 minutos, podemos aplicar este crecimiento a cada intervalo de 20 minutos.
Para cada intervalo de 20 minutos, la población de bacterias aumentará en un 25%.
Por lo tanto, podemos calcular la población de bacterias al final de los 12 intervalos de la siguiente manera:
Población final = Población inicial * (1 + tasa de crecimiento)^número de intervalos
Población inicial = 32,200 bacterias
Tasa de crecimiento = 25% = 0.25
Número de intervalos = 12
Población final = 32,200 * (1 + 0.25)^12
Realizando los cálculos, obtenemos la población final de bacterias al cabo de 4 horas.
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Let Q be an orthogonal matrix with an eigenvalue λ1=1. Let x be an eighenvector beloinging to λ1. Show that x is also an eigenvector of QT
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If Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).
To show that x is also an eigenvector of QT, we need to demonstrate that QT * x is a scalar multiple of x.
Given that Q is an orthogonal matrix, we know that QT * Q = I, where I is the identity matrix. This implies that Q * QT = I as well.
Let's denote x as the eigenvector corresponding to the eigenvalue λ1 This means that Q * x = λ1 * x.
Now, let's consider QT * x. We can multiply both sides of the equation Q * x = λ1 * x by QT:
QT * (Q * x) = QT * (λ1 * x)
Applying the associative property of matrix multiplication, we have:
(QT * Q) * x = λ1 * (QT * x)
Using the fact that Q * QT = I, we can simplify further:
I * x = λ1 * (QT * x)
Since I * x equals x, we have:
x = λ1 * (QT * x)
Now, notice that λ1 * (QT * x) is a scalar multiple of x, where the scalar is λ1. Therefore, we can rewrite the equation as:
x = λ2 * x
where λ2 = λ1 * (QT * x).
This shows that x is indeed an eigenvector of QT, with the eigenvalue λ2 = λ1 * (QT * x).
In conclusion, if Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).
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The amount of time needed to complete a job, t, varies inversely with the number of workers, w. If 9 workers can complete a job in 56 minutes, how many minutes would it take 14 workers?
Answers
Therefore, it would take approximately 36 minutes for 14 workers to complete the job.
To solve this inverse variation problem, we'll use the formula: t = k/w, where t represents the time needed, w represents the number of workers, and k is the constant of variation.
We can find the value of k by plugging in the given values of 9 workers and 56 minutes into the formula:
56 = k/9
To find the value of k, we multiply both sides of the equation by 9:
k = 504
Now that we know the constant of variation, we can determine the time it would take for 14 workers to complete the job. Plugging in the values into the formula:
t = 504/14
t ≈ 36
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In this triangle what is the value of x
Answers
Answer:
Step-by-step explanation:
error
Answer:
x ≈ 75.2
Step-by-step explanation:
using the tangent ratio in the right triangle
tan62° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{40}[/tex] ( multiply both sides by 40 )
40 × tan62° = x , then
x ≈ 75.2 ( to the nearest tenth )
1. Which one of the following is NOT true about polynomial functions f(x) and g(x) if deg (f) = man * d deg * (g) =n?
A. deg (f + g) = max(m, n)
B. deg (f_{g}) <= m + n
C. If g is a factor of f then deg( f )<= m
D. The deg (f ^ 3) = 3m
Answers
The option that is not true about polynomial functions is:
Option D. The deg (f ^ 3) = 3m
How to Interpret the degree of Polynomial functions?For polynomial functions f(x) and g(x), if deg(f) = m * deg(g) = n, then we have the following:
Option A: deg(f + g) = max(m, n)
This is true because we know that the degree of the sum of two polynomials is the maximum of their individual degrees.
Option B: deg(f * g) <= m + n
This is true because we know that the degree of the product of two polynomials is at most the sum of their individual degrees.
Option C: If g is a factor of f, then deg(f) <= m
This is true because If g is a factor of f, it means that f can be divided by g without leaving a remainder. In this case, the degree of f is less than or equal to the degree of g.
D. The deg(f ^ 3) = 3m
This is not true because the degree of the polynomial f raised to the power of 3 is not necessarily equal to 3 times the degree of f. The degree of f^3 will depend on the individual terms and their exponents.
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Please awnser asap I will brainlist
Answers
The matrix is not a square matrix because it does not have an equal number of rows and columns.
The additive inverse of a matrix is obtained by changing the sign of each element. Therefore, the additive inverse of the given matrix is:
7 -6 4
3 -4 2
Regarding the matrix type, the given matrix is not a column matrix because it has more than one column. It is not a row matrix because it has more than one row. Hence, the correct classification for the given matrix is of no special type (B).
Answer:
1) no special type; B
2) see below
Step-by-step explanation:
Additive inverse of the matrix is the negative of that number:
[ -7 6 -4]-> [7 -6 4]
[-3 4 -2] -> [ 3 -4 2]
Kirsten got paid $432.50 for her work this month. She worked for 35 hours but broke a coffee mug so had to take $5 out of her pay. Write an equation, define your variable and solve. How much does she make an hour?
Answers
Answer:
Kirsten makes $12.50 per hour
Step-by-step explanation:
The total is $432.50
$5 is taken out of her paycheck, so that will be negative.
35 hours is the time she spent working.
The unknown variable we are looking for is the amount she makes in one hour.
Setting up the equation, we get:
$432.50 = $35x - $5
where x is the amount she makes every hour
Solve for x:
$437.50=$35x
$437.50 / $35 = x
Therefore, x = $12.50