The Sample standard deviation would be 3.56 and the confidence interval is between72.74 to 78.60.
What is a confidence interval?
A confidence interval is a range of values that is estimated to contain the true value of a population parameter with a certain level of confidence. It is a measure of the uncertainty associated with an estimate of a population parameter, such as the mean, the proportion, or the variance.
a)
sample mean = 75.67
sample std. dev. = 3.56
b)
Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 2.015
[tex]CI = (xbar - tc * s/\sqrt{n} , xbar + tc * s/\sqrt{n})\\\\CI = (75.67 - 2.015 * 3.56/\sqrt{6} , 75.67 + 2.015 * 3.56/\sqrt{6})\\\\\CI = (72.74 , 78.60)[/tex]
Hence the Sample standard deviation would be 3.56 and the confidence interval is between72.74 to 78.60.
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Which expressions are equivalent to
5^2/5^8
Please help will mark Brainly
One glass of milk and one snacks bar have a total of 23 carbs.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Two glass of milk and Three snacks bar have a total of 56 carbs.
And, Four glass of milk and two snacks bar have a total of 72 carbs.
Now,
Let the amount of milk = x
And, The amount of snacks bar = y
So, We can formulate;
Two glass of milk and Three snacks bar have a total of 56 carbs.
⇒ 2x + 3y = 56 ..(i)
And, Four glass of milk and two snacks bar have a total of 72 carbs.
⇒ 4x + 2y = 72
⇒ 2x + y = 36
⇒ y = 36 - 2x ..(ii)
Substitute above value in equation (i),
⇒ 2x + 3y = 56
⇒ 2x + 3 (36 - 2x) = 56
⇒ 2x + 108 - 6x = 56
⇒ 108 - 56 = 4x
⇒ 4x = 52
⇒ x = 13
And, from (ii);
⇒ y = 36 - 2x
⇒ y = 36 - 2 × 13
⇒ y = 36 - 26
⇒ y = 10
Thus, One glass of milk and one snacks bar have a total of carbs
= 13 + 10
= 23
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mayco, a mail-order department store, has five telephone lines available for customers who wish to contact customer service. if the probability is 1 6 that any one of the five telephone lines is engaged during business hours, find the probability that all five lines will be in use when a customer calls customer service. (round your answer to four decimal places.)
Answer:
The probability that all five lines will be in use when a customer calls customer service is 1/7776.
What is probability?
The proportion of favorable cases to all possible situations that can occur indicates how likely an event is to occur.
Step-by-step explanation:
Given that there are 5 lines and the probability for each line to be engaged in working hours is 1/6.
So, for all 5 lines to be engaged is
= 1/6 * 1/6 * 1/6 * 1/6 * 1/6
= [tex]\frac{1}{6} ^{5}[/tex]
= [tex]\frac{1}{7776}[/tex]
Therefore, the probability that all five lines are engaged is 1/7776.
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Mario's current credit card balance is $2,673.19 with a minimum payment of $102.00. Over the next month, he plans to spend $626.00. If the APR is 26.99%, what will Mario's new balance be, including
interest? (2 points)
$3,201.98
$3,269.10
$3,197.19
$3,394.68
If the APR on Mario's credit card is 26.99%, Mario's new balance, including interest will be B. $3,269.10.
What is the APR?Annual percentage rate (APR) is the annual finance charge applied to a credit balance.
The APR includes interest and other fees for borrowing credit.
Current credit card balance = $2,673.19
Minimum payment within the month = (102.00)
Purchase payments 626.00
Finance Charge $71.91 ($3,197.19 x 26.99% x 1/12)
Ending credit card balance = $3,269.10 ($3,197.19 + $71.91)
Annual percentage rate = 26.99%
Monthly percentage rate = 2.25% (26.99% ÷ 12)
Thus, Mario will end up with a credit card balance of $3,269.10 after one month with APR of 26.99%.
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the position of a particle moving along a coordinate line is s=√(3+6t), with s in meters and t in seconds. Find the particle's velocity at t=1 sec.
The particle's velocity at time t = 1 seconds is equal to 3 meters per seconds.
What is a position vs time graph?In Mathematics, a position vs time graph can be defined as a type of graph that is used to graphically represent the distance traveled (covered) by an object from its starting position with respect to the time when it is started moving.
Generally speaking, the position of a physical object (body) in a position vs time graph is always plotted on the y-coordinate (y-axis) while time is always plotted on the x-coordinate (x-axis).
From the information provided about this particle on a position vs time graph, we have;
s =√(3 + 6t)
Where:
s in meters.t in seconds.Substituting the given parameters into the formula, we have;
s =√(3 + 6(1))
s =√(3 + 6)
s =√9
Distance, s = 3 meters.
Now, we can determine the velocity as follows;
Velocity = distance/time
Velocity = 3/1
Velocity = 3 meters per seconds.
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PLEASE HELP WITH THE QUESTION IN THE PICTURE
Answer:
(9.22 x 10⁻⁵) + (1.078 x 10⁻⁵)
You can take 10⁻⁵ as common from both terms and add the remaining ones.
(9.22 + 1.078) x 10⁻⁵
10.298 x 10⁻⁵
Kelly has the following income and expenses:
$200 per month paychecks
$50 cell phone
$40 gasoline
$40 Miscellaneous expenses
How much are Kelly's total planned expenses?
•
Which linear function has the greatest initial value? Which has the greatest rate of change? Use the drop-down menus to show your answer.
The linear function that has greatest initial value is function C
The linear function that has greatest rate of change is function B
Consider the function A
The y intercept = 0
Consider two points (2, 5) and (4, 10)
The slope of the line = (10-5) / 4-2
= 5 /2
The equation will be
y = 5/2x + 0
Consider the function B
y = 3x - 1
Which is in the form of slope intercept form
The slope of the line = 3
The y intercept = -1
Consider the function C
y intercept = 2
Consider the points (0, 2) and (3, 3)
The slope of the function = 3-2 / 3 -0
= 1/3
The equation is
y = 1/3x + 2
Therefore, function C has greatest initial value and function B has greatest rate of change
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A line passes through point (5, –3) and is perpendicular to the equation y = x. What's the equation of the line?
Question 26 options:
y = –x + 2
y = x
y = x + 3
y = –x – 7
y= - x + 2.
Step-by-step explanation:1. Find the slope of the given line.The slope of any linear equation will always be the coefficient of the "x" variable when the equation is solved for "y". Since there isn't any number written to the left of "x", the slope of the line is 1.
2. Find the slope of the new line.When looking for the slope of a line perpendicular do another, take the value of the slope and find its multiplicative inverse and change the sign of this value as well. This is how you do it:
Original slope value: 1.
Multiplicative inverse: 1/1= 1
Changing the sign: -1
3. Form the new equation.Using the calculated value of the slope "m", which is -1, use the formula for calculating linear equations with both the slope and the values of the ordered pair:
[tex]y-y_{1} =m(x-x_{1} )[/tex]
Substitute the values and simplify.
[tex]y-(-3) =(-1)(x-(5) )\\ \\y+3=(-1)(x)-(-1)(5)\\ \\y+3=(-1x)-(-5)\\ \\y+3=-1x+5\\ \\y=-1x+2\\ \\y=-x+2[/tex]
4. Conclude.A line that passes through point (5, –3) and is perpendicular to the equation y = x is y= - x + 2.
-------------------------------------------------------------------------------------------------------
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After spending many hours studying for your math class (I am being hopeful here!) you decide to reward yourself with a case of soda. Unfortunately the store only had a warm case left (the Kent students got there first and got all of the cold ones). You buy several bags of ice and decide to chill it at home. When you get home the temperature of the soda is 76 degrees F and you proceed to pack it in ice. After ten minutes the temperature has cooled to 70 degrees F. If the soda is best served at 60 degrees F or cooler, how much longer must you wait to enjoy your soda? Note that you have not been given the temperature of the surroundings, but you should be able to figure out what that should be (you are packing it in ice that is at the freezing point of water so...).
the difference between the two temperatures as 16 degrees F. You must wait for another 6 minutes for the soda to cool down to 60 degrees F.
Since the initial temperature of the soda is 76 degrees F and the desired temperature is 60 degrees F, we can calculate the difference between the two temperatures as 16 degrees F. We also know that the temperature of the ice is at the freezing point of water which is 32 degrees F. This means that the temperature difference between the soda and the ice is 44 degrees F. Since the temperature difference between the soda and the ice is greater than the temperature difference between the desired temperature and the initial temperature, we can divide the desired temperature difference (16 degrees F) by the temperature difference between the soda and the ice (44 degrees F) and multiply it by the time elapsed (10 minutes) to calculate the remaining time needed for the soda to cool down to the desired temperature. 16/44 * 10 = 6. Therefore, we must wait for another 6 minutes for the soda to cool down to 60 degrees F.
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Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
9x2 + xy + 9y2 = 19, (1, 1) (ellipse)
y = ________________?
The equation of the tangent line to the ellipse 9x^2 + xy + 9y^2 = 19 at the point (1, 1) is y = -18x + 19, which can be found using implicit differentiation.
We can find the equation of the tangent line to the ellipse 9x^2 + xy + 9y^2 = 19 at the point (1, 1) using implicit differentiation. Firstly, we take the partial derivatives of both sides of the equation with respect to x and y, which gives us y' = (9x + y)/(9y +x). Then, we plug in the given point (1,1) into the equation for y' and solve for y'. This gives us y' = (9 + 1)/(9 + 1) = 10/10 = 1. This means that the slope of the tangent line at this point is 1. We can then use the point-slope form of a line equation, y - 1 = 1(x - 1), to find the equation for the tangent line at this point, which is y = -18x + 19.
y' = (9x + y)/(9y +x)
At the given point (1,1):
y' = (9 + 1)/(9 + 1) = 10/10 = 1
Equation of the tangent line:
y - 1 = 1(x - 1)
y = -18x + 19
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What would:
2x + -2y = ?
Make?
Answer:
[tex]y=x[/tex]
Step-by-step explanation:
[tex]2(-y+x)=0\\\\-y+x=0\\\\-y=-x\\\\y=x[/tex]
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Question 7
The cone will fit in 4 times and the volume of the cone is 535.89 in³
Volume of a ConeA cone is a pyramid with a circular cross-section. A right cone is a cone with its vertex above the center of the base. It is also called right circular cone.
The formula of volume of a cone is given as;
V = 1/3πr²h
v = volume of the coner = radius of the coneh = height of the coneHowever, we have to calculate the volume of the sphere which is given as
V = 4/3 πr³
The volume of the ball = 4/3 * 3.14 * 8³ = 2143.57in³
The volume of the cone = 1/3 * 3.14 * 8² * 8 = 535.89 in³
The number of times it will fit into will be 2143.57 / 535.89 = 4
It will fit in 4 times
b)
The volume of the cone is 535.89in³
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Consider this conditional statement.
If a person is a professional athlete, then the person is a professional hockey player.
(a) Give the contrapositive of the statement.
If (Choose one)
then (Choose one)
(b) Give the converse of the statement.
If (Choose one)
then (Choose one)
(c) Give the inverse of the statement.
If (Choose one)
then (Choose one)
If a person is a professional athlete, then the person is a professional hockey player.
Given :
( a ) Give the contrapositive of the statement.
If not the person is a professional hockey player .
then not a person is a professional athlete .
( b ) Give the converse of the statement.
If the person is a professional hockey player .
then a person is a professional athlete .
( c ) Give the inverse of the statement .
If not the person is a professional hockey player.
then not a person is a professional athlete .
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2. *
In a table of values for a pattern, P=3 when n=1; which of the following equations might represent the pattern?
a) P=3 n
b) P=n+3
c) P=2 n+1
d) P=3-n
A
B
C
Both A andC
In a table of values for a pattern, P=3 when n=1; the equations P=3n and 2n+1 might represent the pattern. So the option d "Both A and C" is correct option.
In the given question, In a table of values for a pattern, P=3 when n=1; which of the following equations might represent the pattern.
a) P=3n
b) P = n+3
c) P = 2n+1
d) P = 3-n
We find the pattern we firstly observe the given diagram closely.
We firstly check which option can given P=3 when n=1.
Firstly taking the option a.
P = 3n
Now put n=1, so
P = 3
Hence, the option one is following the condition.
Now taking the option b.
P = n+3
Now put n=1, so
P = 1+3
P = 4
Hence, the option b is not following the condition.
Now taking the option c.
P = 2n+1
Now put n=1, so
P = 2(1)+1
P = 2+1
P = 3
Hence, the option c is following the condition.
Now taking the option d.
P = 3-n
Now put n=1, so
P = 3-1
P = 2
Hence, the option d is not following the condition.
Hence, the option a and c is following the condition. So the option d "Both A and C" is correct option.
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X’(t) = [-4 0 0 0 8 -3 4 0 1 0 -5 0 2 1 4 -1 ] X(t)X0 = [ 1234]1. (67 points) Use Theorem 1 on page 350 to solve the above system of differential equations (see section 5.6 video).2. (33points) Use your solution to show that your solution solves the original system of differential equations
To solve the system of differential equations using Theorem 1, we first need to find the eigen values and eigen vectors of the matrix X'.
The characteristic equation is given by |X' - λI| = 0, where I is the identity matrix. Solving this equation, we find the eigenvalues to be λ = -2, 0, 3, 5.
Next, we need to find the corresponding eigenvectors. For each eigenvalue, we solve the equation (X' - λI)v = 0 to find the eigenvector.
For λ = -2, the eigenvector is v = [-2 -2 -2 -2 -2 1 -2 -2 -2 -2 -2 1 -2 -2 -2 1]
For λ = 0, the eigenvector is v = [-4 1 -2 -2 4 -3 2 -2 1 -2 -5 0 1 0 4 -1]
For λ = 3, the eigenvector is v = [4 -2 -2 -2 -4 3 -2 -2 -1 -2 5 0 -1 0 -4 1]
For λ = 5, the eigenvector is v = [0 2 2 2 0 -1 2 2 2 2 0 -1 2 2 0 -1]
Using these eigen values and eigen vectors, we can use Theorem 1 to find the general solution to the system of differential equations:
X(t) = c1e^(-2t)v1 + c2e^(0t)v2 + c3e^(3t)v3 + c4e^(5t)v4
where c1, c2, c3, and c4 are constants.
To show that this solution solves the original system of differential equations, we substitute it into the given differential equation:
X'(t) = -2c1e^(-2t)v1 + 0c2e^(0t)v2 + 3c3e^(3t)v3 + 5c4e^(5t)v4
This simplifies to:
X'(t) = [-4 0 0 0 8 -3 4 0 1 0 -5 0 2 1 4 -1 ]
which is equal to the given matrix X'(t). Therefore, the solution we have found does indeed solve the original system of differential equations.
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Determine the number and type of solutions for the equation
5x^2−x−3=0
-Two different irrational-number solutions
-Two imaginary-number solutions
-One repeated rational-number solution
-One repeated irrational-number solution
-Two different rational-number solutions
The equation has one repeated rational number solution. thus Option C is correct.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
The given equation is the quadratic equation:
[tex]5x^2-x-3=0[/tex]
It is required to determine the number and type of solutions.
Noted that If the discriminant equals zero, the equation has one repeated rational number solution.
If the discriminant is positive, then the equation has two real solutions.
If the discriminant is negative, then the equation has two imaginary solutions.
If the discriminant is a perfect square, then then the equation has two real rational number solutions, it has two irrational number solutions.
Calculate the discriminant of the equation [tex]5x^2-x-3=0[/tex] by substituting a= 5, b=-1 and c= 3 into the discriminant formula:
Since the discriminant equals zero, it follows that the equation has one repeated rational number solution.
The equation has one repeated rational number solution.
Option C is correct.
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the perimeter of a rectangle is 124ft and the length is 5 more than twice its width, find the length and the width. note: p
Answer:
length = 43 ft ; width = 19 ft
Step-by-step explanation:
perimeter/2 = 124/2 = 62 ft
l = 2w + 5
l + w = 62
2w+5 + w = 62
3w = 62 - 5
3w = 57
w = 57/3
w = 19 ft
l = 2 · 19 + 5
l = 38 + 5
l = 43 ft
The vertex is (-4,-2) and the parabola opens up. What is the domain and range
Answer:
Domain: -∞ < x < ∞
Range: y ≥ -2
Step-by-step explanation:
The domain of a parabola graph is all real numbers, this is written as;
-∞ < x < ∞
The range of this parabola graph is all numbers greater than and equal to -2, since the parabola opens up and the vertex is at (-4, -2). This is written as;
y ≥ -2
Which of the following is NOT one of the three main methods of inventory evaluation as described in your reading material? A. weighted average, B. straight average, C. FIFO, D. LIFO
Answer:
A or B
Step-by-step explanation:
I think it's B.. according to the people I know
the product of 3 and a number is twice 23
What is the range of the set of ordered points defined below?
{(–1 , 3), (2 , 3), (4 , 5)}
Answer:
Rang is the output values or the y values.
3 and 5
Step-by-step explanation:
An ordered pair is in the form (x, y) The x is the input or the domain and the y is the output or the range.
help me with this question please
Answer:
Step-by-step explanation:
You just have to recall those rules in geometry. :/
for 1 RU = QT
the red single marks on the segment mean those are the same length
for 2 ∠T = ∠U
the red arc means they are the same angle
for 3 QT is parallel to RU
because of both red marks, same length, and same angles
for 4 RQT = SRU
because both of these angles come from the same line, and have the same length and angle below
for 5 triangle QRT = RSU
because of both red marks and starting from the same line.
This morning, Kenneth took a history test. He got 42 out of 56 problems right. What percentage did Kenneth get right?
\
the following data represent the running times of films produced by two motion-picture companies. company time (minutes) i 103 94 110 87 98 ii 97 82 123 92 175 88 118 compute a 90% confidence interval for the difference between the average running times of films produced by the two companies. assume that the running-time differences are approximately normally distributed with unequal variances
The 90% confidence interval for the difference between the average running times of films produced by the two companies ≅ (- 35.5 , 10.8)
Given that:
Company (i) :
[tex]n_{1}[/tex] = 5 , [tex]x_{1}[/tex]bar = 98.4
[tex]S_{1} ^{2}[/tex] = [tex]\frac{1 }{n_{1} - 1}[/tex] ∑ [tex](x_{i} - x_{1} bar)^{2}[/tex]
= [tex]\frac{1}{5 - 1}[/tex] [ [tex](103 - 98.4)^{2}[/tex] + [tex](94 -98.4)^{2}[/tex]+........+ [tex](98 - 98.4)^{2}[/tex] ]
= [tex]\frac{1}{4}[/tex] [ [tex](4.6)^{2}[/tex] + [tex](-4.4)^{2}[/tex]+..........+[tex](0.4)^{2}[/tex] ]
= [tex]\frac{1}{4}[/tex] [ 305.2]
= 76.3
Company (ii) :
[tex]n_{2}[/tex] = 7 , [tex]x_{2}[/tex] bar = 110.7143
[tex]S_{2} ^{2}[/tex] = [tex]\frac{1 }{n_{2} - 1}[/tex] ∑ [tex](xi - x_{2} bar)^{2}[/tex]
= [tex]\frac{1}{7-1}[/tex] [ [tex](97 - 110.7143)^{2}[/tex]+ [tex](82-110.7143)^{2}[/tex]+.........+[tex](118 - 110.7143)^{2}[/tex] ]
= [tex]\frac{1}{6}[/tex] [ [tex](-13.7143)^{2}[/tex]+ [tex](-28.7143)^{2}[/tex]+.........+[tex](7.2857)^{2}[/tex] ]
= [tex]\frac{1}{6}[/tex] [ 6125.4274]
≅ 1035.9045
For 90% confidence interval
difference between = 5+7-2 = 10, critical value is [tex]t_{c}[/tex] = 1.812.
90% confidence interval for the difference between the average running times is
[ ([tex]x_{1}[/tex] bar - [tex]x_{2}[/tex] bar) ± [tex]t_{c}[/tex] . [tex]\sqrt{\frac{S_{1}^2 }{n_{1} } } + \sqrt{\frac{S_{2}^2 }{n_{2} }}[/tex] ]
= [(98.4 - 110.7143) ± 1.812 [tex]\sqrt{\frac{76.3}{5} } + \sqrt{\frac{1035.90457}{7} }[/tex] ]
= [-12.3143 ± 23.1515]
= (- 35.4658 , 10.8372)
≅ (-35.5 , 10.8)
Therefore, 90% confidence interval for the difference between the average running times of films produced by the two companies is
≅ (- 35.5 , 10.8)
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two machines fill 32-oz cartons with cereal. the quality control manager believes the two machines are not filling the cartons with the same amount of cereal. samples from each line were taken and the following results were obtained. assume that the assumptions and conditions for inference with a two- sample t-test are met. at the 0.01 level of significance, test the claim that the population mean for machine 1 is different from the population mean for machine 2.
The conclusion hypothesis is to reject the null hypothesis and accept the alternative hypothesis. The z score of 0.14 is in the rejection area
What is hypothesis?
In statistics, hypothesis refers a testable statement about the relationship between two or more variables or a proposed variable.
Here we have given that two machines fill 32-oz cartons with cereal. the quality control manager believes the two machines are not filling the cartons with the same amount of cereal. samples from each line were taken and the following results were obtained. assume that the assumptions and conditions for inference with a two- sample t-test are met. at the 0.01 level of significance, test the claim that the population mean for machine 1 is different from the population mean for machine 2.
And we need to find the conclusion hypothesis.
While we looking into the given question, we have identified the following values,
Sample mean: Machine 1 25 31.8 oz 2.2 oz
Sample SD: Machine 2 36 30.9 OZ 1.98 oz
So, the hypothesis is calculated as, the claim is the population mean of cereal cartons from machine 1 is larger than that from the machine 2
Null hypothesis: H0 : The population mean of cereal cartons for machine 1 and machine 2 is same
Alternative hypothesis H1: The population defines the statistical inference experiment.
So, the conclusion of hypothesis is, the critical value (cutoff point) is 2.353. In left-tail hypothesis testing, any z score less than the critical value will be rejected. Since 0.14 is less than 2.353, we reject the null hypothesis. We accept the alternative hypothesis.
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It would he quite risky for you to insure the life of a 21 -year-old friend under the terms of Exercise 14. There is a high probability that your friend would live and you would gain $\$ 1250 dollars in premiums. But if he were to die, you would lose almost \$ 100,000$. Explain carefully why selling insurance is not risky for an insurance company that insures many thousands of 21 -year-old men. (b) The risk of an investment is often measured by the standard deviation of the return on the investment. The more variable the return is, the riskier the investment. We can measure the great risk of insuring $\mathrm{u}$ single person's life in Exercise 14 by computing the standard deviation of the income $Y$ that the insurer will receive. Find or using the distribution and mean found in Exercise 14.
The standard deviation of Y can be determined which is 9708.
Given in the question that the high probability would gain in premiums. If die, would lose almost . Selling insurance is not risky for an insurance company that insures many thousands of -year-old men.
According to the information, the gain around is 1250
Amount would lost in case of death is 100000.The expected value with its probability is:
E(X) = ∑x ×P(x)
=(-99750) × 0.00183 + ...+ (1250) × 0.99058
= 303.35
The standard deviation of the investment return is used to determine the risk of an investment. The riskier the investment is, the more varied the return is
The standard deviation of Y can be determined as
α = under root {∑x2 × P(x) - (∑x × P(x) }
[tex]\sqrt{(-99750 - 303.3525)sq. X 0.00183 + .... + (1250 - 303.3525)sq. X 0.99058 }[/tex]
= 9708
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can someone help me figure out how to solve this problem
Answer:
To find the fourth term in the given sequence, we can use the formula for the nth term, which is a^n = 2 (a^n-1) + 4. We can then plug in the value of a^1, which is 3, and the value of n, which is 4, to find the fourth term:
a^4 = 2 (a^3) + 4
= 2 [2 (a^2) + 4] + 4
= 2 [2 [2 (a^1) + 4] + 4] + 4
= 2 [2 [2 (3) + 4] + 4] + 4
= 2 [2 [10] + 4] + 4
= 2 [24] + 4
= 52
Therefore, the fourth term in the sequence is 52.
Answer:
[tex]a_4 = 52\\[/tex]
Step-by-step explanation:
There is no way around this one. You just had to calculate each term until you got the fourth term.
[tex]a_2 = 2(a_1) + 4 = 2(3) + 4 = 10[/tex]
[tex]a_3 = 2(a_2) + 4 = 2(10) + 4 = 24[/tex]
[tex]a_4 = 2(a_3) + 4 = 2(24) + 4 = 52[/tex]
For linear function f, f(2)=0 and f(4)=-6.
Write function f in slope-intercept form.
Hint
Examples:
f(5)=0 means (5,0) is a point on the line.
f(3)=-2 means (3,-2) is a point on the line.
How do you find the slope of the line when you have 2 points?
Answer:
f(x) = -3x + 6
Step-by-step explanation:
f(2)=0 point (2, 0)
f(4)=-6 point (4, -6)
m = slope = (y_2 - y_1)/(x_2 - x_1)
m = (-6 - 0)/(4 - 2) = -6/2 = -3
y = mx + b
y = -3 x + b
0 = -3 × 2 + b
0 = -6 + b
b = 6
y = -3x + 6
f(x) = -3x + 6
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ABC has vertices A(1, 3), B(2, 5), and C(5, 3). What are the coordinates of B′ after the transformation (x, y) ⟶ (–y, x), then translation 1 unit right and 4 units up?
Answer: we first need to apply the transformation to the x- and y-coordinates of the point individually
Step-by-step explanation:
To transform the coordinates of a point (x, y) using the transformation (x, y) ⟶ (–y, x), we first need to apply the transformation to the x- and y-coordinates of the point individually. This means that the x-coordinate becomes –y and the y-coordinate becomes x.
In the case of point B, the original coordinates are (2, 5), so the transformed coordinates are (–5, 2). This means that the x-coordinate becomes –5 and the y-coordinate becomes 2.
Next, we need to apply the translation that moves the point 1 unit right and 4 units up. To do this, we simply add 1 to the x-coordinate and add 4 to the y-coordinate. After this translation, the coordinates of B′ become (–4, 6). Therefore, the final coordinates of B′ are (–4, 6).