The slope of line a is -5, the slope of line b is 2.
Step-by-step explanation:
Answer:
Line A: -5
Line B: 2
Step-by-step explanation:
Hello!
Slope-Intercept Form: [tex]y = mx + b[/tex]
y = outputx = inputm = slopeb = y-interceptLine A: y=-5x-2The slope of this is the "m" value, so that would mean it would be -5.
Line B: Y=2x+ 3The slope of this would be 2, as it is the "m" value in the equation.
3(2x - 1) =
1
2
(4x - 2) + 2
Answer:
x=1
Step-by-step explanation:
HOPE I HELPEDPLZZ MARK AS BRAINLIEST !!!What is the slope of the line that passes through the points (-9, 10)(−9,10) and (21, 15) ?(21,15)?
Answer:
1/6 or 1.666667
Step-by-step explanation:
(y2-y1)/(x2-x1)
(15-10)/(21- -9) = 1/6
Answer:
1/6
Step-by-step explanation:
Lena‘s observed that in the last 12 issues of rise over run weekly 384o out of950 pages contain an advertisement what is the probability that the next page she turns to will contain an advertisement
Answer:
Probability thay the next page she turns to will have an advert = 0.4042
Step-by-step explanation:
In the last 12 issues of the magazine, 384 out of 950 pages contain an advertisement.
We now need to find the probability that the next page has an advertisement.
Probability of an event
= n(of that event) ÷ n(total sample spaces)
n(of the event of an advert) = number of pages with adverts in those issues = 384
n(total sample spaces) = total number of pages = 950
Probability that the next page or any page at all will have an advert = (384/950) = 0.4042
Hope this Helps!!!
A restaurant is offering a new buffet with six types of sandwiches, four sides, and five desserts. If customers are allowed to select one sandwich, one side, and one dessert, how many meal combinations are possible?
Answer:
240
Step-by-step explanation:
Multiply everything together. 6*4*5 is 240.
Which of the following lines best fits the data shown in the scatter plot
Answer:
Im pretty sure its A
Step-by-step explanation:
Therefore, the option (A) is the correct answer.
What is the scatter plot?
Scatter plots are the graphs that present the relationship between two variables in a data-set. It represents data points on a two-dimensional plane or on a Cartesian system.
As per the given information, the correct graph is in option (A) because in this graph it is moving upward with respect to the line of curve.
Hence, the option (A) is the correct answer.
To know more about the scatter plot
https://brainly.com/question/17222820
#SPJ5
Simplify.
Remove all perfect squares from inside the square root.
Assume x is positive.
\sqrt{20x^8}
Answer:
[tex]2x^4\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{20x^8}[/tex] = [tex]\sqrt{4*5*(x^4)^2}[/tex] = [tex]2x^4\sqrt{5}[/tex]
The solution of the equation after remove all perfect squares from inside the square root is,
⇒ 2x⁴√5
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;
The expression is,
⇒ √20x⁸
Now, We can simplify and remove all perfect squares from inside the square root as;
⇒ √20x⁸
⇒ √2 × 2 × 5 × (x⁴)²
⇒ 2x⁴√5
Thus, The solution of the equation after remove all perfect squares from inside the square root is,
⇒ 2x⁴√5
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ5
the difference of two numbers is 15. five times the smaller number is the same as 9 less than twice the larger number. find the numbers
Answer:
your 2 numbers are going to be 7 and 22
Kareem sent a chain email to 10 of his friends the number of people who got the email increases by a factor of 1.4 every week
Answer: 10×1.4^6
Step-by-step explanation:
This question is about exponential growth in mathematics.
Explanation:This question is about exponential growth in mathematics. The number of people who received the email increases by a factor of 1.4 every week.
Learn more about exponential growth here:https://brainly.com/question/12490064
#SPJ12
A school is trying to schedule Prayers of chemistry and algebra two. They find that a total of 386,000 are taking either one or both of the two courses. 209 students signed up for algebra two and 300 need to have signed up for chemistry , what would be the probability that a student chosen at random from the 386 will be signed up for both of the courses? Ronja answer to the nearest whole number percent
Answer: 32%
Step-by-step explanation:
The total number of students that signed up for chemistry and algebra
two is 386.
Let x represent the number of students that signed up for both chemistry and algebra two
If 209 students signed up for algebra two, then the number of students that signed up for algebra two only is
209 - x
If 300 need to have signed up for chemistry, then the number of students that need to have signed up for chemistry only is 300 - x
Therefore,
x + 209 - x + 300 - x = 386
- x + 509 = 386
x = 509 - 386
x = 123
If 123 students would be signed up for both courses, then the probability that a student chosen at random from the 386 will be signed up for both of the courses is
123/386 × 100 = 32%
The circumference of a circle is 16 ft.
what is the radius?
.
Answer:
The answer is 8. And for the love of God people if you don't know the answer don't waste an answer space just for the points. It makes everyone mad. Stop. Just cut it out.
Step-by-step explanation:
---------- is a measure of amount of work that can be done in a given amount of time or in other way rate or doing work
Answer:
Power
Step-by-step explanation:
Term Definition
power: Measure of the amount of work that can be done in a given amount of time.
Answer:
Power
Step-by-step explanation:
power, measure of the amount of work that can be done in a given amount of time.
I hope this helps :)
Apply the distributive property to the expression to write an equivalent expression. Complete the statements. 4x + 16 Find the GCF of . Now factor out the GCF by dividing each term in the expression by . 4x divided by the GCF is , and 16 divided by the GCF is . The equivalent expression is .
Answer:
[tex]4(x+4)=4x+16[/tex]
Step-by-step explanation:
a) The Greatest Common Factor, of both terms 4x and 16 is 16.
4,16|2
2,8|2
1,4|2
1,2|2
1,1| = 2*2*2*2=16
b) Let's divide each term by 4 their
4x+16
[tex]\frac{4x}{4}=x\\\\\frac{16}{4}=4[/tex]
Placing their common divisor outside the parentheses, and inside the sum of this result:
[tex]4(x+4)=4x+16[/tex]
The equivalent expression after factoring out the GCF is [tex]\(4(x + 4)\)[/tex].
To apply the distributive property to the expression \(4x + 16\), we can factor out the greatest common factor (GCF) of the two terms. In this case, the GCF of 4 and 16 is 4. By dividing each term in the expression by 4, we can factor out the GCF.
\(4x\) divided by the GCF (4) is \(x\), and \(16\) divided by the GCF (4) is \(4\). Therefore, the expression \(4x + 16\) can be factored as \(4(x + 4)\) using the distributive property.
To summarize:
- GCF of 4 and 16 is 4.
- \(4x\) divided by the GCF (4) is \(x\).
- \(16\) divided by the GCF (4) is \(4\).
For more such questions on equivalent expression
https://brainly.com/question/30607584
#SPJ3
what is the solution to the inequality -3x-42>3
Answer:
X<-15
Step-by-step explanation:
-3x-42>3 collect like terms
-3x>3+42
-3x>45 divide both side by -3
X<-15
Hint ; when you divide both side by a negative sign, the sign changes.
Answer:
Just here for the points also it -135
Step-by-step explanation:
Find the quotient of 24 and 0
Answer:
it is either zero or infinity
Step-by-step explanation:
Use The Interactive tool to determine if the two triangles are congruent. Then, select the true statement.
Answer:
it would be the first answer I think. not very sure
A multiple choice test is composed of 10 questions. Each question has four possible answers, only one of the four possible answers is correct. A student randomly selects the answer for each question. Assume that all selections are independent. Let X count the student’s number of correct answers on the test. a) What is the expected number of correct answers? Round your answer to the nearest tenth.
Answer:
Let X the random variable of interest "Number of correct anwers on the tet", on this case we now that:
[tex]X \sim Binom(n=10, p=0.25)[/tex]
And the expected value is given by:
[tex] E(X) = np =10*0.25 = 2.5[/tex]
Step-by-step explanation:
Previous concepts
A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Solution to the problem
Let X the random variable of interest "Number of correct anwers on the tet", on this case we now that:
[tex]X \sim Binom(n=10, p=0.25)[/tex]
And the expected value is given by:
[tex] E(X) = np =10*0.25 = 2.5[/tex]
8) An ultimate frisbee team has to order jerseys, shorts, and hats. They have a budget of $1350 to
spend on $50 jerseys, $20 shorts, and $15 hats. They want to buy 40 items in preparation for the
oncoming season and must order as many jerseys as shorts and hats combined. How many of
each item should they order? Write a system of equations to help you solve this problem.
Answer:
Step-by-step explanation:
By using j, s ,h to represent the number of jerseys,shorts and hats respectively.
System of Equations:
j + s + h = 40
j = s + h
50j + 20s + 15h = 1350
(s + h) + s + h = 40
2s + 2h = 40
s + h = 20
s = 20 – h
50[(20 – h) + h] + 20(20 – h) + 15h = 1350
50(20) + 400 – 20h + 15h = 1350
1400 – 5h = 1350
5h = 50h
h = 10
s = 20 – 10
s = 10
j = 10 + 10
j = 20
20 jerseys, 10 shorts, 10 hats
They order 20 jerseys, 10 shorts, 10 hats
What is system of equation?A system of equations, also known as a set of simultaneous or equation system, is a finite set of equations for which we sought the common solutions.
According to the question
By using j, s ,h to represent the number of jerseys ,shorts and hats respectively.
System of Equations:
j + s + h = 40. . . . . Equation (1)
j = s + h. . . . . . .Equation (2)
50j + 20s + 15h = 1350 . . . . . . Equation (3)
By putting the value of j = s + h in equation (1)
(s + h) + s + h = 40
2s + 2h = 40
s + h = 20
s = 20 – h. . . . . . . .Equation (4)
By putting the value of j = s + h and s = 20 - h in equation (3) we get
50[(20 – h) + h] + 20(20 – h) + 15h = 1350
50(20) + 400 – 20h + 15h = 1350
1400 – 5h = 1350
5h = 50h
h = 10
s = 20 – 10
s = 10
j = 10 + 10
j = 20
Hence , 20 jerseys, 10 shorts, 10 hats
To learn more about system of equation from here
https://brainly.in/question/31127448
#SPJ2
Type the expression that results from the following series of steps: Start with x , add 3 , then times by 6
Answer:
6(x + 3), or expanded: 6x + 18
Step-by-step explanation:
We start with x.
"Add 3" means + 3, so we have: x + 3
"Then times by 6" means multiply by 6, or * 6, so we have 6 * (x + 3)
Thus the expression is 6(x + 3), or expanded: 6x + 18
Hope this helps!
Answer:
6(x + 3)
Step-by-step explanation:
Add 3:
x + 3
Times 6:
6(x + 3)
The 2003 Statistical Abstract of the United States reported the percentage of people 18 years of age and older who smoke. Suppose that a study designed to collect new data on smokers and non smokers uses a preliminary estimate of the proportion who smoke of .30.a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of.02? use 95% confidence.b. Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population?c. What is the 95% confidence interval for the proportion of smokers in the population?
Answer:
Step-by-step explanation:
Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
a) From the information given,
Margin of error = 0.02
p = 0.3
q = 1 - 0.3 = 0.7
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.5 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96
Therefore,
0.02 = 1.96 × √(0.3 × 0.7)/n
0.02/1.96 = √0.21/n
0.0102 = √0.21/n
Taking square of both sides, it becomes
0.00010404 = 0.21/n
n = 0.21/0.00010404
n = 2018
Sample size = 2018
b) if n = 2018
x = 520
Then
p = 520/2018 = 0.26
Point estimate of the proportion of smokers in the population is 0.26
c) q = 1 - 0.26 = 0.74
the 95% confidence interval for the proportion of smokers in the population is
0.26 ± 1.96 × √(0.26)(0.74)/2018
= 0.26 ± 0.019
Answer:
a) n = 2017
b) Point estimate is 0.2578
c) 95% Confidence Interval is Minimum = 0.2387, Maximum 0.2769
Step-by-step explanation:
Here we have
At 95%, we have
[tex]z_{\alpha /2}[/tex] = 1.96
To determine sample size, we have
[tex]n = \frac{(z_{\alpha /2})^2 \hat p \hat q}{E^2}[/tex]
Where:
[tex]\hat p[/tex] = 0.3
[tex]\hat q[/tex] = [tex]1-\hat p[/tex] = 0.7
E = 0.02
Therefore, n = 2016.84 ≈2017
b) The point estimate is given by
[tex]\hat p =\frac{x}{n} = \frac{520}{2017}[/tex] = 0.2578
c) The confidence interval is given by;
[tex]CI=\hat{p}\pm z\times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
Which gives
[tex]CI=0.2578\pm 1.96\times \sqrt{\frac{0.2578(1-0.2578)}{2017}}[/tex]
Hence CI = Min = 0.2387 to Max = 0.2769
11 + (3)(9) Step 1: 11 + (9)(3) Step 2: (11 + 9)(3) Step 3: 20(3) Step 4: 60 Analyze the work to find the error.
Answer:
Step 2 is where this person went wrong
Step-by-step explanation:
Should be
11 + (9)(3)= x
11 + 27= x
x = 38
Answer:
Step 2 is where the error started. You can see the person did the order of operations wrong. The person was supposed to multiple (9)(3) first because of PEMDAS; (9)(3)=27 and then you add the 27 to 11 and get 38
Step-by-step explanation:
What is the equation of the line that passes through the point (6,-5)(6,−5) and has a slope of -\frac{3}{2}−
2
3
The equation of the line that passes through the point (6,-5)and has a slope of [tex]-\dfrac{3}{2}[/tex] is y+5 = -3/2(x+6).
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
WE need to find the equation of the line that passes through the point (6,-5)and has a slope of [tex]-\dfrac{3}{2}[/tex].
Given: m=-3/2 and x_1 = -6 and y_1 =-5
So the required equation of a line in a point-slope form;
y+5 = -3/2(x+6)
Hence, The equation of the line that passes through the point (6,-5)and has a slope of [tex]-\dfrac{3}{2}[/tex] is y+5 = -3/2(x+6).
Learn more about slope here:
https://brainly.com/question/2503591
#SPJ2
The equation of the line that passes through the point (6, -5) and has a slope of -3/2 is y = -3/2x + 4.
Explanation:To find the equation of the line, we can use the point-slope form of a linear equation, which is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. In this case, the point is (6, -5) and the slope is -3/2. Plugging these values into the equation, we get y - (-5) = -3/2(x - 6), which simplifies to y + 5 = -3/2(x - 6).
Expanding the equation further, we get y + 5 = -3/2x + 9. To isolate y, we can subtract 5 from both sides of the equation, resulting in y = -3/2x + 4. Therefore, the equation of the line that passes through the point (6, -5) and has a slope of -3/2 is y = -3/2x + 4.
Home CoworkHelper
A
A cylinder has a volume of 10 m' What might its dimensions be (height, area of base, radius, and
diameter)? Give 4 possible cylinders.
Volume 10 m
Height
Area of Base
Radius
Diameter
Cylinder A
Cylinder B
Cylinder
Cylinder D
How do you know your answers are reasonable?
How many possibilities are there? Why do you think so?
B. A cylinder has a diameter of 10 cm. What might its volume be? Give the radius, area of base and
height for 4 possible volumes
Diameter 10 cm
Radius
Area of Base
Height
Volume
Cylinder A
Cylinder B
Cylinder
Cylinder D
How do you know your answers are reasonable?
Answer:
See below.
Step-by-step explanation:
PROBLEM A
The formula for the volume of a cylinder is
V = πr²h, where πr² is the area of the base.
V = area of base x height
Choose any four numbers that are less than 10 for the height.Then, substitute into the formula and isolate "r". 10 = πr²hDouble "r" to find the diameter.The area of the base is found (bolded) while you solve πr².*I will use the calculator button for pi (π)
Cylinder A: h = 1
10 = πr²h
10 = πr²(1)
10 = πr² Area of the base is 10m².
r = √ (10/π)
r = 1.78 Radius is 1.78m.
d = 2r = 1.78*2 = 3.56 Diameter is 3.56m.
Cylinder B: h = 2
10 = πr²h
10 = πr²(2)
5 = πr² Area of the base is 5m².
r = √ (5/π)
r = 1.26 Radius is 1.26m.
d = 2r = 1.26*2 = 2.52 Diameter is 2.52m.
Cylinder C: h = 4
10 = πr²h
10 = πr²(4)
2.5 = πr² Area of the base is 2.5m².
r = √ (2.5/π)
r = 0.89 Radius is 0.89m.
d = 2r = 0.89*2 = 1.78 Diameter is 1.78m.
Cylinder D: h = 5
10 = πr²h
10 = πr²(5)
2 = πr² Area of the base is 2m².
r = √ (2/π)
r = 0.80 Radius is 0.8m.
d = 2r = 0.80*2 = 1.6 Diameter is 1.6m.
The answers are reasonable if the answer is close to 10 when you substitute the rounded numbers back into the formula and solve.
There are infinite possibilities because any numbers when used in the formula equates to 10 are possible. The height/radius can be any decimal number, which would make the other dimensions change.
PROBLEM B
Follow similar steps if you know the diameter of a cylinder. Use the same formula V = πr²h.
We need the radius, which is half the diameter. r = d/2 = 10/2 = 5
Choose a random number for volume that divides easily by 25.Substitute "V" and "r²" (r² = 25).Isolate "h".The area of the base is 78.54 cm² every time (A = πr²).Cylinder A: V = 100
100 = π25h
4 = πh
h = 1.27 The height is 1.27m.
Cylinder B: V = 200
200 = π25h
8 = πh
h = 2.55 The height is 2.55m.
Cylinder C: V = 75
75 = π25h
3 = πh
h = 0.95 The height is 0.95m.
Cylinder D: V = 125
125 = π25h
5 = πh
h = 1.59 The height is 1.59m.
The answers are reasonable if I can substitute two rounded values into the formula and get a number close to the third. The height is also a decimal number which occurs because of pi.
Pedro is building a playground in the shape of a right triangle he wants to know the area of the playground to help him decide how sand to buy what are the dimensions of the rectangle
Answer:
Amount of sand=Area of triangle(ABC)=1/2*AB*BC
Dimension of rectangle as length=BC and breadth=AB
Step-by-step explanation:
Given:
Pedro building a playground in shape of right angled triangle.
To Find:
How much sand he need to buy
And if playground changed to rectangle what will be the dimensions.
Solution:
Consider a ΔABC be the play ground vertex of playground,
And AB and BC be the sides making right angle.
The sand required to fill ground will be the amount of are covered by the ABC triangle.
So,
Area Of triangle(ABC)=1/2* base* height
Here base will be BC and height =AB
Therefore Area of Triangle(ABC)=1/2*BC*AB
Depending on the lengths of base and height amount of sand will be decided.
Now,
For Rectangle dimensions,
We know that if same sized triangles composes each other forms a rectangle.
It requires two triangle to form one rectangle as follows
(Refer the attachment)
Same sized Triangle ACD is imposed on it to from rectangle ABCD.
So dimension for rectangle will be same as the triangle
Dimension=length and breadth
i.e. length=base of triangle=BC
Breadth=Height of triangle=AB
i.e Breadth =AB.
The number of carbon atoms in a fossil is given by the function y= 5100(0.95)^x where x represents the number of years since being discovered what is the percent change each year? Explain your answer.
The function y = 5100(0.95)^x represents an exponential decay of the number of carbon atoms in a fossil, with a base of 0.95. Therefore, the percent change each year is -5%, reflecting a decrease, consistent with the decay of carbon-14.
Explanation:The function y = 5100(0.95)^x represents an exponential decay, with 0.95 being the base of the exponent. This base number, when subtracted from 1 and multiplied by 100, gives the percent change each year for the number of carbon atoms in the fossil.
Using this method, we find: (1-0.95)*100 = 5. So the percent change is -5% each year, with the negative sign indicating a decrease. This is consistent with the decay of carbon-14 (C-14) in fossils, a process used in carbon dating to estimate the age of the fossil.
Learn more about Exponential Decay here:https://brainly.com/question/12900684
#SPJ11
Euclid’s root beer mug is shaped basically like a cylinder that is eight inches tall with a radius of three inches. Aristotle’s root beer glass is shaped basically like a cone that is 18 inches tall with a diameter of four inches. Which vessel holds the most root beer?
The Euclid's mug holds the most root beer.
Step-by-step explanation:
Euclid's mug :
Height = 8 inches
Radius = 3 inches
Volume = π(r x r) h
= (3.14) (9) 8
= 226.08 cubic inches
Aristotle's mug:
Height = 18 inches
Diameter = 4 inches
Radius = 2 inches
Volume = (1/3) π(r x r) h
= (1/3) (3.14) (4) 18
= 37.68 cubic inches
The Euclid's mug holds the most root beer.
How many flowers, spaced every 4 inches, are needed to surround a circular garden with a 200 inch radius?
Find the distance around the circle ( circumference)
Circumference = 2 x PI x r
Circumference = 2 x 3.14 x 200
Circumference = 1256 inches.
Divide circumference by spacing:
1256 / 4 = 314
You can plant 314 flowers.
The function below describes the number of students who enrolled at a university, where f(t) represents the number of students and t represents the time in years.
Initially,_____ students enroll at the university. Every______ , the number of students who enroll at the university increases by a factor of______ .
Answer:
18,500 , 1 , 1.03
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
f(t) =18,500(1.03)^t
1st blank:
19,055
1.03
3
18,500
2nd blank:
t years
2 years
3 years
1 year
3rd blank:
19,055
3
18,500
1.03
My answer:
Given that: f(t) =18,500*[tex]1.03^{t}[/tex]
1st blank:
Initial value when t = 0, so we have:
f(0) =18,500*[tex]1.03^{0}[/tex]
[tex]f(0) =18,500(1)\\ f(0) =18,500[/tex]
So we choose D for 1st blank
2nd and 3rd blank:
Because it's an exponential function f(t) =18,500*[tex]1.03^{t}[/tex] , with every value of t increment f(t) increase by a factor of 1.03 . So Every 1 year the number of students who enroll at the university increases by a factor of 1.03
=> 2nd blank: 1
=> 3rd blank: 1.03
Hope it will find you well.
Answer:
The first blank this is 18,500. Second blank is 1. The third blank is 1.03. hope this helps
Step-by-step explanation:
What is the distance, to the nearest hundredth, from (6, 5) to (−3, −8)?
Answer:
15.81
Step-by-step explanation:
Use the distance formula:
So the distance formula for two given points is
Distance= sqrt((x2-x1)^2 +(y2-y1)^2 ) =sqrt((-3-6)^2 +(-8-5)^2 )
=sqrt((-9)^2 +(-13)^2 )
=sqrt(81+169)
=sqrt(250)
=15.81
Hope this helped
:)
What is 0.21 written as a percentage
Answer:
21 percent
Step-by-step explanation:
Because 0.21 times 100 gives 21 percent
Answer:
21%
Step-by-step explanation:
to change a decimal to a percentage you multiply it by 100 which 0.21 x 100 which will give 21%
The seventh term of an arithmetic sequence is 10.2 and the twelfth term is 17.7. What is the common difference of the arithmetic sequence?
The common difference is ______
Use the explicit formula to find a1.
a1 = _______
What is the explicit formula for the arithmetic sequence?
A: an = 1.2 + (n - 1)1.5
B: an = 1.5 + (n – 1)1.2
C: an = 1.5 + (n – 1)3.9
D: an = 3.9 + (n – 1)1.5
ANSWERS: 1.5, 1.2, A: an = 1.2 + (n – 1)1.5
Answer:
The common difference is 1.5
Use the explicit formula to find a1.
a1 = 1.2
What is the explicit formula for the arithmetic sequence?
= 1.2 + (n - 1)1.5
Step-by-step explanation:
Final answer:
The common difference of the arithmetic sequence is 1.5, and the first term is 1.2. The explicit formula for the arithmetic sequence is A: an = 1.2 + (n - 1)1.5.
Explanation:
To find the common difference of an arithmetic sequence, we can use the information that the seventh term (a7) is 10.2 and the twelfth term (a12) is 17.7. The formula for the nth term of an arithmetic sequence is an = a1 + (n - 1)d, where a1 is the first term and d is the common difference. By creating a system of equations using the given terms, we can solve for d.
For the seventh term: 10.2 = a1 + 6d
For the twelfth term: 17.7 = a1 + 11d
Subtracting the first equation from the second gives: 17.7 - 10.2 = 5d, which simplifies to 7.5 = 5d or d = 1.5.
We can then plug the value of d back into one of the equations to find a1:
10.2 = a1 + 6(1.5)
10.2 = a1 + 9
a1 = 1.2
Therefore, the explicit formula for this arithmetic sequence is A: an = 1.2 + (n - 1)1.5.