Answers
Answer:
A and B
Step-by-step explanation:
You draw the points on the Cartesian plane and draw a straight line that passes through two of the drawn points, if ALL the drawn points are ON the drawn line, then it is a linear function,
If only ONE point lies outside the line, then it is NOT a linear function
Related Questions
Complete the following:
Write an exponential expression: choose a number between 0 and 10 to be the base and another number between 0 and 10, different from the base, to be the exponent.
Label the base and the exponent.
Then write the exponential expression in expanded form and standard form.
Essay
Answers
2 × 10³ is an exponential expression, which has a standard form as 2000.
What is exponential expression?Exponential expressions are just a way to write powers in short form. The exponent
indicates the number of times the base is used as a factor. So in the case of 32 it can
be written as 2 × 2 × 2 × 2 × 2 = 25, where 2 is the “base” and 5 is the “exponent”.
The expanded form comes in a variety of forms. Exponents are employed. The expanded form of that expression is what is stated above.
One more makes use of multipliers like 1, 10, 100, 1000, and so forth. The expression broadens in that form as...
10^2 = 1×100
Another expanded form uses the expanded form's individual digits, setting the others to zero.
10^2 = 100
The standard format is...
10^2 = 100.
Thus, 2 × 10³ is an exponential expression, which has a standard form as 2000.
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Ben borrowed 25,000 to purchase a motorcycle. The loan was for two years at a annual interest rate of 4%. What’s the maturity value
Answers
Answer:
1,000 was the interest charge which leaves you with 24000 as the regular vaule
Step-by-step explanation:
The test scores for the analytical writing section of a particular standardized test can be approximated by a normal distribution, as shown in the figure.
(a) What is the maximum score that can be in the bottom 5% of scores?
(b) Between what two values does the middle 90% of scores lie?
Answers
The maximum score that can be in the bottom 5% of scores is 2.64
The middle 90% of scores lie between 2.88 and 4.56.
What is the maximum score that can be in the bottom 5% of scores?(a) We must determine the score that corresponds to the 5th percentile of the normal distribution in order to determine the highest score that may fall inside the lowest 5% of scores.
We may use the standard normal table to determine that the 5th percentile corresponds to a standard normal score of -1.28 using the mean and standard deviation supplied (3.6 and 0.75, respectively). We may use the following formula to return to the original scale:
x = mu + z * sigma
Where
x is the original score, mu is the mean (3.6), z is the standard normal score (-1.28), and sigma is the standard deviation (0.75).Plugging in the values, we get:
x = 3.6 + (-1.28) * 0.75
x= 2.64
(b)
We must determine the 5th and 95th percentiles of the normal distribution in order to determine the range of scores that the middle 90% of scores fall inside.
The standard normal table may be used to determine that the 5th percentile corresponds to a normally distributed score of -1.28 and the 95th percentile corresponds to a standard normal rating of 1.28 using the mean and standard deviation supplied (3.6 and 0.75, respectively). We may use the following formula to return them to their original scale:
x = mu + z * sigma
Where
x is the original score, mu is the mean (3.6), z is the standard normal score, and sigma is the standard deviation (0.75).Plugging in the values, we get:
x = 3.6 + (-1.28) * 0.75
= 2.88 for the 5th percentile
x = 3.6 + 1.28 * 0.75
= 4.56 for the 95th percentile
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Christian recorded the grade-level and instrument of everyone in the middle school School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar 6
Bass 4
Drums 7
Keyboard 2
Eighth Grade Students
Instrument # of Students
Guitar 4
Bass 15
Drums 13
Keyboard 6
Based on these results, express the probability that a student chosen at random will play the bass as a fraction in simplest form.
Answers
Answer: the probability that a student chosen at random plays the bass is 1/3 in simplest form.
Step-by-step explanation:
The probability of an event can be found by taking the number of favorable outcomes and dividing it by the total number of outcomes. In this case, we are looking for the probability that a student chosen at random plays the bass.
We know that there are a total of 6 + 4 + 7 + 2 = 19 seventh grade students and 4 + 15 + 13 + 6 = 38 eighth grade students. So there are a total of 19 + 38 = 57 students.
We also know that there are 4 seventh grade bass players and 15 eighth grade bass players, for a total of 4 + 15 = 19 bass players.
So, the probability that a student chosen at random plays the bass is 19/57. This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor which is 19/57 = 1/3.
So, the probability that a student chosen at random plays the bass is 1/3 in simplest form.
What’s the graph to t/3 - 1 > -3
Answers
Answer: The answer is C
Step-by-step explanation: This is because the equation has a greater than or equal to sign (≥). This mean that there will be a closed dot. Also, when it comes to inequalities, the sign points to where the line will be drawn, (greater than is to the right and less than is to the left), which indicates that the answer is C
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???????
Answers
Answer:
he never made a mistake, so the answer is A
Step-by-step explanation:
these are in line with integers and their rules.
The rule that's being applied there's if numbers of the same base are being divided, maintain the base and subtract the powers.
12.5
points
Skipped
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References
The cost per item at a supermarket
follows an exponential distribution.
There are many inexpensive items and
a few relatively expensive ones. The
mean cost per item is $10.5. What is the
percentage of items that cost:
a. Less than $7.5? (Round your answer
to 4 decimal places.)
Probability
Answers
Answer: 37.33 % of items cost less than $7.5
Step-by-step explanation:
To find the percentage of items that cost less than $7.5, we would need to know the probability distribution function of the cost per item, as well as the specific parameters of the distribution (such as the shape parameter).
Since the information provided is that the cost per item follows an exponential distribution and the mean cost per item is $10.5,
We can use the cumulative distribution function (CDF) of the exponential distribution which is
F(x) = 1 - e^(-λx)
where x is the cost of the item, λ is the rate parameter and e is the base of the natural logarithm.
We know the mean is $10.5 , and in an exponential distribution the mean and the rate parameter are equal, so we can say λ = 1/10.5
To find the percentage of items that cost less than $7.5, we need to find the probability that X < 7.5, which is the same as finding F(7.5)
So, F(7.5) = 1 - e^(-λ*7.5) = 1 - e^(-0.714)
Then, we need to convert this probability to percentage, so we need to multiply it by 100
F(7.5) = (1 - e^(-0.714)) * 100 = 37.33 %
Therefore, 37.33 % of items cost less than $7.5
A cylindrical jar contains three glass balls each has a diameter of 2cm and their surfaces touch the inner side of the jar as shown below. What is the volume of the gap in the jar?
Answers
6.28 cubic centimeters is the volume of the gap in the jar.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that cylindrical jar contains three glass balls each has a diameter of 2cm
Let us find the volume of each sphere.
Volume of sphere=4/3×πr³
As diameter is 2 then radius is 1.
Volume of each sphere=4.186
Volume of three spheres=3×4.186=12.56
Now let us find the volume of cylinder.
The diameter of cylinder will be 2 and height is 6 cmas there are 3 spheres of diameter 2cm.
Volume of cylinder=πr²h
=3.14×1×6
=18.84 cubic centimeters.
So the volume of the gap in the jar = 18.84-12.56
=6.28 cubic centimeters.
Hence, 6.28 cubic centimeters is the volume of the gap in the jar.
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William Sealy Gosset worked at the Guinness Brewery in Dublin and made substantial contributions to the practice of statistics. In his work at the brewery, he collected and analyzed a great deal of data. Archives with Gosset’s handwritten tables, graphs, and notes have been preserved at the Guinness Storehouse in Dublin. In one study, Gosset examined the change in the double stout market before and after World War I (1914‑1918). For various regions in England and Scotland, he calculated the ratio of sales in 1925, after the war, as a percent of sales in 1913, before the war. Here are the data:
Region Ratio
Bristol 94
Cardiff 112
English Agents 78
English O 68
English P 46
English R 111
Glasgow 66
Liverpool 140
London 428
Manchester 190
Newcastle‑on‑Tyne 118
Scottish 24
(a) Compute the mean for these data. Give your answer to two decimal places.
⎯⎯⎯=
(b) Compute the median for these data. Give your answer to two decimal places.
=
(c) Which measure describes the center of this distribution the most accurately? Explain your answer.
The mean represents the center of the data most accurately because the mean incorporates all of the individual values, whereas the median depends more on the order of the values than their actual amounts.
The mean and the median should both be used. By comparing the mean and median, you can tell if the data are skewed.
The median represents the center of the data most accurately because the mean is more affected by extreme values.
The mean and the median are equally as accurate because the distribution of the data is approximately symmetical.
Region RelativeTo1913 RelativeToPast4
Bristol 94 82
Cardiff 112 80
English Agents 78 83
English O 68 88
English P 46 99
English R 111 99
Glasgow 66 78
Liverpool 140 106
London 428 105
Manchester 190 107
Newcastle-on-Tyne 118 115
Scottish 24 78
Answers
Answer: a) To compute the mean of these data, we need to add up all of the ratios and divide by the total number of ratios.
(94+112+78+68+46+111+66+140+428+190+118)/11 = 101.36
The mean is 101.36
b) To compute the median of these data, we need to arrange the data in increasing order and find the middle value.
46, 66, 68, 78, 94, 111, 112, 118, 140, 190, 428
The median is 111
c) The measure that describes the center of this distribution the most accurately is the mean, because it takes into account all of the values in the data set and provides an overall measure of central tendency. The median is also a measure of central tendency but it is affected by the outliers present in the dataset and doesn't provide a good representation of the central value.
Step-by-step explanation:
HELPPP HHHEELOOOOOOO SCREENSHOT ATTACHED
Answers
Answer:
102 in.²
Step-by-step explanation:
the given figure is made up of a triangle and a rectangle. we can find out the areas of two of them separately and then add it up for the area of the whole figure as
area of rectangle:-
= length* breadth
= 15 * 5 in.²
= 75 in.²
area of triangle :-
= 1/2 *base*height
here base = 15 - 3 - 3 = 9in.and height= 11 -5 = 6 in.= 1/2*9*6in.²
= 27in.²
Total area
= 75 + 27 = 102in.² { required answer }
Answer:
D) 102 in²
Step-by-step explanation:
The given composite figure is made up of a triangle and a rectangle.
Rectangle
[tex]\begin{aligned}\textsf{Area of a rectangle}&=\sf length \times width\\&=15 \times 5\\&=75\; \sf in^2\end{aligned}[/tex]
Triangle
[tex]\begin{aligned}\textsf{Area of a triangle}&=\sf \dfrac{1}{2} \times base \times height\\\\&=\dfrac{1}{2} \times (15-3-3) \times (11-5)\\\\&=\dfrac{1}{2} \times 9 \times 6\\\\&=\dfrac{9}{2} \times 6\\\\&=\dfrac{54}{2} \\\\&=27\; \sf in^2\end{aligned}[/tex]
Therefore, the area of the given composite figure is:
[tex]\begin{aligned}\textsf{Area of composite figure}&=\textsf{Area of rectangle}+\textsf{Area of triangle}\\&=75+27\\&=102\; \sf in^2\end{aligned}[/tex]
Suppose Fawn plans to take a sample to determine a 90 percent confidence interval for the population mean weight of chocolate in every package. She wishes the confidence interval to be of the form “plus or minus 3 grams,” and is willing to assume that the population standard deviation is equal to 12 grams. How large a sample should she take?
Answers
Suppose Fawn plans to take a sample to determine a 90 percent confidence interval for the population mean weight of chocolate in every package. Fawn should take a sample size of at least 43, to have a 90% confidence interval of plus or minus 3 grams in the weight of chocolate in every package.
What is the sample?Generally, Fawn can use the formula for the sample size needed to estimate a population mean with a certain level of confidence:
n = (z*σ / E)^2
Where:
n = sample size z = the z-score for the desired level of confidence (e.g., for 90% confidence, z = 1.645) σ = the population standard deviation (12 grams in this case) E = the margin of error (3 grams in this case)So the sample size needed is:
n = (1.645 * 12 / 3)^2
n= (5.48)^2
n = 43.296
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What is the surface area? 11 ft 26 ft 21 ft
Answers
The surface area of the triangular prism is 416 yd²
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The surface area of a solid object is the total area that the surface of the object occupies.
From the diagram:
Surface area = 2(10 yd * 10 yd) + 2(0.5 * 12 yd * 8 yd) + (10 yd * 12 yd) = 416 yd²
The surface area is 416 yd²
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(5v-w)(5v−w) centimeters, and its length measures (6v+8w)(6v+8w) centimeters.
Answers
Answer:
If you want an answer I would suggest you to put the whole question up ty
Step-by-step explanation:
3.8333 repeating as a fraction
Answers
Answer:
Answer and Explanation: As a fraction 3.83 (3 repeating) is 38399 3 83 99 . To convert 3.83 (3 repeating) to a fraction, we ignore the units as they will remain units. We then set up one equation of our unknown x being equal to 0.83333... and another that is 100 times greater, 100x=83.3333...
Evaluate the expression if x = -3, y = 5, and z=2. (If an answer is undefined, enter UNDEFINED.)
x+y+z/
4y²x
Answers
The value of the expression (x + y + z) / (4xy²) at x = -3, y = 5, and z = 2 will be - 1/8.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ (x + y + z) / (4xy²)
The expression if x = -3, y = 5, and z = 2. Then the value of the expression is given as,
⇒ (-3 + 5 + 2) / (4 × (-2) × (2)²)
⇒ - 4 / 32
⇒ - 1 / 8
The value of the expression (x + y + z) / (4xy²) at x = -3, y = 5, and z = 2 will be - 1/8.
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A light bulb consumes 3600 watts hours per day. How long does it take to consume 13500 watts hours
Answers
Answer:
3.75 days
Step-by-step explanation:
To find out how long it takes to consume 13500 watt hours, you would divide 13500 by the number of watt hours consumed per day, which is 3600.
13500 / 3600 = 3.75
So it takes 3.75 days for the light bulb to consume 13500 watt hours.
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
Answer:
below
Step-by-step explanation:
The derivative of the given equation gives the RATE (slope) in the given year
Derivative = -.0102 t^2 +.232 t -.341
for t = 16 this equals .7598 <=====this one is greater
for t = 19 this equals .3848
Answer:
i xibfvlmow 10 seconds
Step-by-step explanation:
k
write the equation of the line that passes at the point ( 5 , 12 ) with the slope m = 3/5 in slope-intercept form.
Answers
Answer:
y = 3/5x + 7
Step-by-step explanation:
y = 3/5x + b
12 = 3/5(5) + b
12 = 5 + b
b = 7
y = 3/5x + 7
I need help with this question for my homework please
Answers
[tex]\overline{A}[/tex] = {0, 1, 4, 5, 6, 7, 8}, [tex]\overline{B}[/tex] = {2, 4, 7, 9}, A ∪ B = {0, 1, 2, 3, 4, 5, 6, 8, 9} and
A ∩ B = {3}.
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
Given,
U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} is a universal set.
A = {2, 3, 9} and B = {0, 1, 3, 5, 6, 8}.
[tex]\overline{A}[/tex] = (U - A) = {0, 1, 4, 5, 6, 7, 8}.
[tex]\overline{B}[/tex]= (U - B) = {2, 4, 7, 9}.
A ∪ B = U - {7}.
A ∪ B = {0, 1, 2, 3, 4, 5, 6, 8, 9}.
A ∩ B = {3}
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help me please! will mark brainliest
Answers
Answer:The function is linear because we are dealing with a straight line.
Step-by-step explanation:
Regan won the grand prize at a store giveaway. The grand prize winner is guaranteed to win at least $500 in cash and prizes.
A. List three possible dollar amounts in cash and prizes Regan can win
B. Write an inequality to represent the dollar amounts d in cash and prizes Regan can win.
Answers
An inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, Regan won the grand prize at a store giveaway. The grand prize winner is guaranteed to win at least $500 in cash and prizes.
Let d represent the amount of cash in dollars and p represent the amount of prizes.
Since the grand prize winner is guaranteed to win at least $500,
So, p + d ≥ 500
Therefore, an inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.
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Select ALL!!!!!!! of the ordered pairs that are in the solution set of this inequality.
Answers
The ordered pairs that satisfies the linear inequality x < - 3 are (-4, -3) and (-3, -3)
What is a Linear InequalityA linear inequality is a mathematical statement that describes a relationship between two or more variables that are not necessarily equal. It is similar to a linear equation, but instead of an equal sign, it uses one of the inequality signs: <, >, ≤, or ≥.
A linear inequality can also be represented graphically on a coordinate plane, by shading the region of the plane that satisfies the inequality. The solution set of a linear inequality is the set of all points that make the inequality true.
A linear inequality can also have infinitely many solutions, no solution or a unique solution. The solution set will be a region in a coordinate plane which is a half-plane, a line or a point depending on the inequality.
In the problem, the inequality x < -3 will have an ordered pair of solution of
(-∞, -3).
This implies that all values of x must lies from negative till infinity while y lies up to - 3.
In the options given, only (-4, -3) and (-3, -3) satisfies this criteria.
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Use the circle Q shown below to answer the following questions:
4. Measure of arc AB = ______ 10. Measure of arc BAD = _____
5. Measure of arc DC = ______ 11. Measure of arc ADC = _____
6. Measure of arc BC = ______ 12. Measure of arc ACB = _____
7. Measure of arc AED =______ 13. Measure of arc ABD = _____
8. Measure of arc BD = ______ 14. Measure of arc CED = _____
9. Measure of arc AC =______ 15. Measure of arc BAC=_____
Answers
The measure of the arcs in relationship to the central angles measures are:
4. 40°
5. 50°
6. 90°
7. 180°
8. 140°
9. 130°
10. 220°
11. 230°
12. 320°
13. 180°
14. 310°
15. 270°
What is the Relationship between the Measure of the Central Angle and the Subtended Arc of a Circle?The relationship is that the measure of the central angle is the same as the measure of the arc it subtends in a circle.
4. Measure of arc AB = measure of central angle AOB
Substitute
Measure of arc AB = 40°
5. Measure of arc DC = measure of central angle DOC
Substitute
Measure of arc DC = 50°
6. Measure of arc BC = 180 - 40 - 50 = 90°
7. Measure of arc AED = 180°
8. Measure of arc BD = 90 + 50 = 140°
9. Measure of arc AC = 40 + 90 = 130°
10. Measure of arc BAD = 180 + 40 = 220°
11. Measure of arc ADC = 180 + 50 = 230°
12. Measure of arc ACB = 360 - 40 = 320°
13. Measure of arc ABD = 180°
14. Measure of arc CED = 360 - 50 = 310°
15. Measure of arc BAC = 40 + 180 + 50 = 270°
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.J(-4, 4), K(-3, 4), L(-1, 1), M(-4,1) Reflect in the x-axis, and then rotate 180° about the origin.
Answers
The quadrilateral's new coordinates will be J(4, 4), K(3, 4), L(1, 1), and M (4,1) when the procedure is applied.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given coordinates of a quadrilateral J(-4, 4), K(-3, 4), L(-1, 1), M(-4,1)
Reflect in the x-axis
Since,
When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).
thus new coordinates will be,
J(-4, -4), K(-3, -4), L(-1, -1), M(-4,-1)
Rotate 180 degrees about the origin
Since,
When we rotate a figure of 180 degrees about the origin either in the clockwise or counterclockwise direction, each point of the given figure has to be changed from (x, y) to (-x, -y) and graph the rotated figure.
Thus new coordinates will be
J(4, 4), K(3, 4), L(1, 1), M(4,1)
Therefore, After applying the given operation the new coordinates of the quadrilateral will be J(4, 4), K(3, 4), L(1, 1), and M(4,1).
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the square root of 15
Answers
Answer:
3.8729
Step-by-step explanation:
Solve x/5-3<5 for oddesyywaree
Answers
Answer:
x < 40
Step-by-step explanation:
x/5-3<5
=5×x/5 -3×5 < 5×5
=x - 15 < 25
NOTE 5 will cancel 5 living x.
=x < 25 + 15
x < 40.
Therefore x is 40.
find the parametric equation of the conic.sections (x+1)²÷16-y²÷9=1
Answers
A circle with a radius of three and a center at (-1, 4) is a conic section with the parametric equations X=3cos(t)-1 and Y=3sin(t)+4.
Find the parametric equation of the conic sections ?The circle, the ellipse, the parabola, and the hyperbola are examples of conic sections.
Using a third variable (t or ), parametric equations are utilized to express the x and y variables in terms of a less complex way.
The parametric equation for a circle is given by: x=r cos(t) +h, y=r sin(t) +k, where r is the radius of the circle and (h, k) is the center of the circle. The equation for a circle is (x- h)2+(y- k)2 = r2.
A circle with a radius of three and a center at (-1, 4) is a conic section with the parametric equations X=3cos(t)-1 and Y=3sin(t)+4.
The circle's equation is (x + 1)2 + (y - 4)2 = 32.
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Diane has $200 in a savings account that earns 10% annually. The interest is not
compounded. How much will she have in total in 1 year?
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r
is the interest rate expressed as a decimal, and t is the time in years.
Answers
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$200\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (200)(0.10)(1) \implies I = 20~\hfill \underset{total~amount~in~savings}{\stackrel{200~~ + ~~20}{\text{\LARGE 220}}}[/tex]
Answer:
$ 220
Step-by-step explanation:
i = prt = 200 * .1 * 1 = 20 dollars interest
add in her original deposit of 200 for a total of 220 dollars
6) Given the geometric sequence 2, 4, 8, 16,...
a) Determine the common ratio.
b) Write the explicit formula.
c) Find a10
d) Write the recursive formula.
Answers
Answer:
a) Common ratio r = [tex]\boxed{2}[/tex]
b) Formula for common ratio:
[tex]\dfrac{a_{n+1}}{a_n} , n = 1, 2, 3, 4....\\[/tex]
Formula for nth term:
[tex]a_n = a_1r^{n-1}[/tex]
(see explanation below for part b)
c) [tex]a_{10} = \boxed{1024}[/tex]
d) Recursive formula: [tex]\boxed{a_{n+1} = 2a_n}[/tex]
Step-by-step explanation:
a) The common ratio r for a geometric sequence is the ratio of any term(except the first) to the previous term. And this is a constant for that sequence
If we have a sequence [tex]a_1, a_2, a_3, a_4, a_5,....\\[/tex]
[tex]r = \dfrac{a_2}{a_1} = \dfrac{a_3}{a_2} = \dfrac{a_4}{a_3} = \dfrac{a_5}{a_4}[/tex]
Here [tex]a_1[/tex] is the first term in the sequence
The sequence we have here is
2, 4, 8, 16
So
[tex]r = \dfrac{4}{2} = \dfrac{8}{4} = \dfrac{16}{8} = 2\\[/tex]
Answer to a)
------------------------------------------------------------------------------------------------------
b) This part is confusing. Are they asking for a formula for the common ratio or a formula for the nth term? You can write both or check with your teacher
The explicit formula for the common ratio is
[tex]\dfrac{a_{n+1}}{a_n} , n = 1, 2, 3, 4....\\[/tex]
The explicit formula for the nth term, [tex]a_n[/tex] of a geometric sequence is
[tex]a_n = a_1r^{n-1}[/tex]
where [tex]a_1[/tex] is the first term of the sequence and r is the common ratio
------------------------------------------------------------------------------------------------------
c)
The formula for finding the nth term of a geometric sequence is
[tex]a_n = a_1r^{n-1}\\\\[/tex]
Therefore
[tex]a_{10} = a_1 r^{(10-1)} = a_1 \times r^9\\\\[/tex]
[tex]a_1 = 2, r = 2\\\\[/tex]
So
[tex]a_{10} = 2 \cdot 2^9 \\\\= 2 \cdot 512\\\\= 1024\\[/tex]ANSWER c)
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d)
A recursive formula is just an expression that denotes the relationship between one term and the next
We know that
[tex]r= \dfrac{a_{n+1}}{a_n} \\\\[/tex]
Multiplying both sides by [tex]a_n[/tex],
[tex]ra_n = a_{n+1}[/tex]
Or
[tex]a_{n+1} = ra_n\\\\[/tex]
For the specific case of r = 2 we get the recursive formula as
[tex]a_{n+1} = 2a_n[/tex]
ANSWER d)
Exercise 4.1 Identify critical numbers and find the absolute maximum value and absolute minimum value for each of the given functions on the given interval. 1 f(x) = x³; [-2, 1] 2 f(x)=x²- 2x² + 3; [−1, 2] 3 5 (5 - 2x); [-1,2] f(x) = f(x)=x²-3x²; [-1, 3] 4 6 f(x)=2cosx+x; [0,2 ] f(x) = 3x³ - 20x³; [-2, 2]
Answers
F(x) = x³ on the interval [-2, 1], x = -2 and x = 1, the absolute maximum value is 1 and the absolute minimum value is -8.
What are the critical numbers?A function's critical numbers are the independent variable values at which the function is not continuous, or when the derivatives are equal to 0 or undefined.
1. For the function f(x) = x³ on the interval [-2, 1], the critical numbers are x = -2 and x = 1. The absolute maximum value is 1 and the absolute minimum value is -8.
2. For the function f(x) = x² - 2x² + 3 on the interval [-1, 2], the critical numbers are x = -1 and x = 2. The absolute maximum value is 5 and the absolute minimum value is -2.
3. For the function f(x) = 5 - 2x on the interval [-1,2], the critical numbers are x = -1 and x = 2. The absolute maximum value is 5 and the absolute minimum value is -3.
4. For the function f(x) = x² - 3x² on the interval [-1, 3], the critical numbers are x = -1, x = 0, and x = 3. The absolute maximum value is 0 and the absolute minimum value is -3.
5. For the function f(x) = 2cosx + x on the interval [0,2], the critical numbers are x = 0 and x = 2. The absolute maximum value is 3 and the absolute minimum value is -1.
6. For the function f(x) = 3x³ - 20x³ on the interval [-2, 2], the critical numbers are x = -2 and x = 2. The absolute maximum value is -4 and the absolute minimum value is -32.
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