The common ratio of the geometric sequence 4, 10, 25, 62.5, . . . is 2.5. The answer is B.
A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a common ratio.
a(n) = a r^(n-1)
Where:
a(n) = nth term
a = first term
r = common ratio
The common ratio must be the same for all pairs of succeeding term to be called a geometric sequence.
To find the common ratio, use the formula
a(n) = a r^(n-1)
let n = 2, a = 4, a(2) = 10
10 = 4(r^(2 - 1)
10 = 4(r)
r = 2.5
Or just simply divide each succeeding pairs of the sequence.
r = 10/4 = 2.5
r = 25/10 = 2.5
r = 62.5/25 = 2.5
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pleasee helppp meee .
Answer:
Ratio of homework papers to exit tickets
Mr. Rowley: 8/7
Ms. Rivera: 16/15
These ratios are not equal
8/7 > 16/15
Step-by-step explanation:
Ratio of homework papers to exit tickets
Mr. Rowley: 16:14
Expressed as a fraction this is
[tex]\dfrac{16}{14}[/tex]
Let's simplify the fraction by dividing numerator and denominator by 2. This is essentially dividing by 1 since 2/2 =1 so the fractional value itself is unchanged.
[tex]\dfrac{16 \div 2}{14 \div 2} = \dfrac{8}{7}[/tex]
Ms. Rivera: 64:60
Expressed as fraction this is
[tex]\dfrac{64}{60}[/tex]
Let's simplify the fraction by dividing numerator and denominator by 2
[tex]\dfrac{64 \div 2}{60 \div 2} = \dfrac{32}{30}[/tex]
This can be simplified further by dividing again by 2:
[tex]\dfrac{32 \div 2}{30 \div 2} = \dfrac{16}{15}[/tex]
(We could have divided by 4 the first time also)
[tex]\dfrac{8}{7}[/tex] [tex]\mathrm {\;is\;\bold{not\; equal\;} to\; }[/tex] [tex]\dfrac{16}{15}[/tex]
We can see that if we multiply both fractions by 105 which is the product of the denominators
[tex]\dfrac{8}{7} \times 105 = 8 \times 15 = 120 \rm \;\;\;\;{ (since 105 \div 7 = 15)}\\\\\dfrac{16}{15} \times 105 = 16 \times 7 = 112 \rm \;\;\;\;{ (since 105 \div 15 = 7)}\\\\\\[/tex]
Since we are multiplying both fractions by the same amount to get rid of the denominator it is easy to see which one is bigger
Obviously 8/7 is bigger than 16/15
We could have converted to decimal also and checked
8/7 = 1.14 rounded to 2 decimal places
16/15 = 1.07 rounded to 2 decimal places
1.14 > 1.07 so 8/7 > 16/15
(You can choose which of the above methods you like)
What is the equation of the line that passes through the point (-1,-1) and has a slope of -4? Explain how you got your answer and HELP PLEASE!!! DUE TONIGHT!!!!
Step-by-step explanation:
slope=m=-4
equation-y=mx+c
equation-y=-4x+c
input y and x to find c
x=-1
y=-1
-1=-4(-1)+c
-5=c
therefore equation is
y=-4x-5
Suppose x has a poisson distribution with a mean of 6. determine the following probabilities. round your answers to four decimal places (e.g. 98.7654).
P(x) = =0.1033 , X has a Poisson distribution with a mean of 6.
Describe the Poisson distribution using an example?
A discrete probability distribution is a Poisson distribution. It provides the likelihood that an event will occur a specific number of times (k) over a predetermined period of time or area. The mean number of occurrences, denoted by the letter "lambda," is the single parameter of the Poisson distribution.Given mean =6
λ=6
To find the probability us ethe below formula
P(X=0)=60 e-6/0!=0.0025
P(X=1)=61e-6 /1!=6e-6 =0.0149
P(X=2)=62e-6 /2!=0.0446
P(X<=2)=P(X=0)+P(X=1)+P(X=2)
=0.0025+0.0149+0.0446
P(X<=2) =0.062
P(X=4)=64e-6/4!
=64e-6 /4.3.2.1
=64e-6 /24
P(X=4) =0.1339
P(X=8)=68 e-6/8!
=4163.351816/40320
=0.1033
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The complete question is -
Suppose X has a Poisson distribution with a mean of 6. Determine the following probabilities: P(x = 0) = P(x le 2) = P(x = 4) = P(X = 8) = Round your answers to four decimal places (e.g. 98.7654).
absolute value of -15
Answer: 15
Step-by-step explanation:
-15 is 15 units to zero (answer should always be positive)
rational form of 0.412
The rational form of 0.412 is 103/250.
According to the question, to write the rational expression for the given link by removing the decimal. When the decimal is removed from the numerator then that many zeros will come in the denominator.
Therefore, the rational expression can be written as:
Required expression = 0.412 = 412/1000 = 103/250
Hence, the correct answer for this expression is 103/250.
What is rational expression?
The rational expression can be represented in the form of ratios which has two polynomials in the numerator as well as in the denominator. The value of the denominator term should never be zero.
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If someone could answer this and give me a detailed explanation with examples about the SSS, SAS, ASA, and AAS, theorems I'd be forever grateful. I just cant seem to get the hang of it and I have fives skills about Proof of Triangle Congruence due tomorrow.
Based on the side-angle-side congruence theorem (SAS),
Missing statement is: ΔHIK ≅ ΔHJK
Missing reason is: SAS
What is the Side-Angle-Side Congruence Theorem (SAS)?If there are two pairs of congruent sides and a pair of included corresponding congruent angles in two triangles, then based on the side-angle-side congruence theorem (SAS), the two triangles are congruent to each other.
The two triangles have the following:
Two pairs of congruent sides which are: HI ≅ HJ, and HK ≅ HK
One pair of included corresponding congruent angles which is: <IHK ≅ <JHK.
This means that both triangles are congruent triangles based on SAS.
Therefore,
Missing statement is: ΔHIK ≅ ΔHJK
Missing reason is: SAS
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HELP ASAP PLSSSSSSS
The equation 8x − 12 = 4x represents two cars traveling in opposite directions, where x represents the distance in miles between the cars. What is the distance, in miles, between the cars?
x = 48
x = 30
x = 3
x = 1
Answer:
x=3
Step-by-step explanation:
8*3 = 24
4*3=12
24-12=12
Answer:
x = 3
Step-by-step explanation:
8x - 12 = 4x ( subtract 4x from both sides )
4x - 12 = 0 ( add 12 to both sides )
4x = 12 ( divide both sides by 4 )
x = 3
the distance between the cars is 3 miles
Write an equation of a parabola with vertex at the origin and the given focus.
focus at (0,-4)
The equation that defines the parabola with vertex at the origin and focus at (0, -4) is
y = -x²/16
We define what a parabola is
What is a parabola?The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.
The canonical equation of a parabola is given by
(x - h)² = 4p(y - k)
The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.
Since the vertex and the focal axis are on the same axis, we analyze that:
v = (0, 0)
f = (0, -4) This means that the focus is on the negative part of the y-axis, the form of the equation of this parabola is y = x²
(x - 0)² = 4p(y - 0)
Focus:
f = (0, 0 + p)
0 + p = -4p = 0 - 4p= -4(x - 0)² = 4*-4(y - 0)
(x)² = 16(y)
y = -x²/16
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Find m∠G.
In the following image shown below
Applying the exterior angle of a triangle theorem, m∠G = 40°.
How to Apply the Exterior Angle Theorem of a Triangle?According to the exterior angle theorem of a triangle, we have the following equation that is derived:
11x - 4 + 55 = 23x + 3
11x + 51 = 23x + 3
11x - 23x = -51 + 3
-12x = -48
-12x/-12 = -48/-12
x = 4
m∠G = 11x - 4 = 11(4) - 4
m∠G = 40°
Thus, applying the exterior angle of a triangle theorem, m∠G = 40°.
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Given f(x)= 2x2+4, find the value of f(−1)
Answer:
f(- 1) = 6
Step-by-step explanation:
substitute x = - 1 into f(x)
f(- 1) = 2(- 1)² + 4 = 2(1) + 4 = 2 + 4 = 6
Find the x - and y -intercepts of each line.
-4 x+y=10
The equation of the line -4x + y = 10 has -5/2 and 10 as its x- and y-intercept, respectively.
The equation of a line is an equation containing variable(s) and constant(s) and can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The x-intercept of a line is the value of x when y = 0 while the y-intercept of a line is the value of y when x = 0.
For an equation written in standard form ax + by = c, the x- and y-intercept is as follows:
x-intercept = c/a
y-intercept = c/b
If the equation of the line is -4x + y = 10, then its x- and y-intercept is as follows:
x-intercept = c/a = 10/-4 = -5/2
y-intercept = c/b = 10/1 = 10
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1.4.5 Working With Box And Whisker Plots
Question:
What do the outliers tell you about the behavior of a few of the senators?
j=g+a solve for a be sure to take into account whether a letter is capitalized or not.
Answer:
a = j - g
Step-by-step explanation:
"solve for a" means to get a all by itself on one side of the equation. You can see the beginning of the answer that is provided on your screen says "a = "
We are starting with:
j = g + a
First, subtract g from both sides of the equation.
j - g = a
Now just trade the left and right sides of the equation.
a = j - g
Fill in your answer in the box: j - g
Rhea had a score of 70 on her first quiz and a score of 77 on her second quiz. What is the percent increase from her first quiz score to her second quiz score?
i already know the answer i just want to test you guys because if you answer this question correctly you at least get 10 pints
Answer:
10%
The increase of her score would be 7 so 7 over 70 which would = to .10 and .10 as a percent is 10%.
Norberto received the following scores on his last five spelling tests: 88, 81, 93, 85, and 98. Which of the following statements
is true?
The median of the numbers which Norberto received in the test is 88.
The median is a measure of central tendency that is used to signify the relative middle point of a data-set.
The median in a data distribution separates the bottom half from the top half of the data.The mean of a data set is the exact average or center point of all data in the distribution. The basic difference between the mean and median is that median is not affected by rogue extreme data such as outliers.The scores of the last five spelling test are : 88, 81, 93, 85, and 98
Here n = 5 and we have to arrange the data in an ordered form.
81 , 85 , 88 , 93, 95
So the formula to calculate the median is given by
median = (n+1)/2 th term of the data set.
hence median = 3rd data = 88
Again the mean of the data is :
(81+85+88+ 93+ 95) ÷ 5 = 440 ÷ 5 = 88
Hence the median of the data is 88 and the mean is also 88.
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Find the first five terms of each sequence. a n = 1/2 aⁿ⁻¹ , where a₁=20
The first five terms of each sequence is 20 , 22, 24, 26 ,28.
What is a term:
In algebra, an algebraic expression is formed by a term or a group of terms together. Term in math is defined as the values on which mathematical operations occur in an algebraic expression.
Now , the mathematical expression.
a1 =20 an =an−1 +2,n>1
putting n=2 a2 =a2−1+2 =a1+2 =20+2=22
h=3 a3 =a3−1 +2 =a2+2 =22+2=24
x=4 a4 =a4−1+2 =a3 +2 =24+2=26
n=5 a5 =a5−1 +2 =a4+2 26+2=28
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Solve each equation. Check your answer.
3(x+1)=9+2 x
The solution of the given linear equation in one variable 3(x+1)=9+2 x is at x = 6.
According to the given question.
We have a linear equation in one variable.
3(x + 1) = 9 + 2x
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Therefore, the solution of the given linear equation in one variable is given by
3(x + 1) = 9 + 2x
⇒ 3x + 3 = 9 + 2x
⇒ 3x - 2x = 9 - 3
⇒ x = 6
Hence, the solution of the given linear equation in one variable 3(x+1)=9+2 x is at x = 6.
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a measuring tool captures rain falling at a constant.The table shows the height of rainwater in the measuring tool and the number of minutes it rains.what is the constant of proportionality for the realationship of millimeters of rainwater to time in hours
The constant of proportionality for the relationship of millimeters of rainwater to time in hours is 48 millimeter/hour.
Given that the measuring tool captures rain falling at a constant.The table shows the height of rainwater in the measuring tool and the number of minutes it rains as shown in attached image.
A ratio is a mathematical comparison between two numbers. In proportion, if two given sets of numbers increase or decrease by the same ratio then the given ratios are said to be proportional.
Now we will calculate the proportion by using the formula
Ratio=(r₂-r₁)/(t₂-t₁)
Here, r₁=4, r₂=8, t₁=5, t₂=10
So, r₂-r₁=8-4=4 and
t₂-t₁=10-5=5
Now, we will convert the time from min to hour by dividing it with 60, we get
t₂-t₁=5/60
Substitute this value in above equation, we get
Ratio=4/(5/60)
Ratio=(4×60)/5
Ratio=4×12
Ratio=48 mm/hr
Hence, the constant of proportionality for the relationship of millimeters of rainwater to time in hours by using the given table is 48 mm/hr.
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The diagram shows a triangle. What is the value of y?
Answer:
y=61°
Step-by-step explanation:
(y-8°)+(y+15°)+(y-10°)=180°
y-8°+y+15°+y-10°=180°
3y-3°=180°
3y=180°+3°
3y=183°
3y÷3=183°÷3
y=61°
The value of y from the given triangle can be calculated using the angle sum property as 61.
Given that:
A triangle has three angles given.
The measures of the angles are y - 8°, y - 10°, and y + 15°.
The angle sum property of triangles is defined as the property which states that the sum of the angles of the triangle is 180°.
Equating the angle measures:
y - 8 + y - 10 + y + 15 = 180
Add the like terms together.
3y - 3 = 180
Take 3 as common.
3(y - 1) = 180
Divide both sides of the equation by 3.
y - 1 = 60
Add 1 on both sides.
y = 61
Hence, the value of y is 61.
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what is 20 times 40 plus 67 minus 3
Answer:
864Step-by-step explanation:
what is 20 times 40 plus 67 minus 3
20 × 40 + 67 - 3 = (remember PEMDAS)
800 + 64 =
864
Answer:864
Step-by-step explanation:
20 x 40 = 800 then you add 800 and 67 then you will get 867 then you subtract 3 that when you get 864
what is the step by step solution: if 3
Answer:
write your full question.
Write a two-column proof of the Alternate Exterior Angles Theorem. (Theorem 3.3)
According to the Alternate Exterior Angles Theorem, when two parallel lines are severed by a transversal, the resultant alternate exterior angles are congruent if and only if the transversal is itself parallel to the two parallel lines.
So, in the figure below, if k ∥ l then
∠1 ≅ ∠7 and ∠4 ≅ ∠6.
Proof.
Since k ∥ l by the Corresponding Angles Postulate,
∠1 ≅ ∠5.
Also, by the Vertical Angles Theorem,
∠5 ≅ ∠7
Then, by the Transitive Property of Congruence,
∠1 ≅ ∠7
You may use the same strategy to demonstrate that ∠4 and ∠6 are equivalent to establish that they are congruent.
It should also be noted that the opposite of this theorem is true; more specifically, if two lines, k, and l, are sliced by a transversal in such a way that the alternative exterior angles are congruent, then k∥l.
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Work out the overall mean for both classes.
Calculator is allowed.
Answer:
68%
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
calculate the sum for both classes
class 1
[tex]\frac{sum}{20}[/tex] = 64 ( multiply both sides by 20 )
sum = 1280
class 2
[tex]\frac{sum}{10}[/tex] = 76 ( multiply both sides by 10 )
sum = 760
combine the 2 sums and divide by count of both classes for overall mean
overall mean = [tex]\frac{1280+760}{30}[/tex] = [tex]\frac{2040}{30}[/tex] = 68%
If your tire says P235/65R17, what is the diameter of your wheel? (Note: this should include the tire and the rim).
If the tire says P235/65R17, the diameter of your wheel will be 17 inches.
How to illustrate the information?The primary purposes of a car's tires are to carry the weight of the car, transmit traction and braking forces to the road surface, insulate against shocks from the road, and change and maintain the direction of motion.
It offers traction for braking and acceleration and reduces the number of road vibrations that reach the car's body.
It should be noted that the numbers that are written on the tire are vital in knowing the diameter that's illustrated.
In this case, when the tire says P235/65R17, the diameter of your wheel will be 17 inches.
In conclusion, it is 17 inches.
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Can y’all please help me
Answer:
B
Step-by-step explanation:
Finding the initial amount and rate of change given a table for a linear function
The initial amount and rate of change given a table for a linear function are $65 and $86, respectively
How to find the initial amount and rate of change given a table for a linear function?The table of linear function represents the given parameter
On the table, we have the following points
(x, y) = (6, 476) and (10, 736)
The rate of change is calculated as
Rate = (y2 - y1)/(x2 - x1)
So, we have
Rate = (736 - 476)/(10 - 6)
Evaluate
Rate = 65
This means that the rate of change is $65
The initial amount is calculated as
y = m(x - x1) + y1
Where
m = 65
So, we have
y = 65(x - x1) + y1
Using one of the points, we have
y = 65(x - 6) + 476
Set x = 0
So, we have
y = 65(0 - 6) + 476
Evaluate
y = 86
Hence, the initial amount and rate of change given a table for a linear function are $65 and $86, respectively
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you rent a bicycle for 4 days. The bike store charges $20 for the first day and $15 for each additional day. Write and graph a step function that represents the relationship between the number x of days and the total cost y (in dollars) of renting the bicycle.
The relationship between the number x of days and the total cost represent as piecewise function.
f(x) = -x < 0
= x if x ≥ 0
The bike store charges $20 for the first day and $15 for each additional day. The relationship between the number x of days and the total cost represent as:
f(x) = 20 , if 0 < x ≤ 1
= 35, if 1 < x ≤ 2
= 50, if 2 < x ≤ 3
= 65, if 3 < x ≤ 4
The absolute value function f(x) = |x| can be written as a piecewise function.
f(x) = -x < 0
= x if x ≥ 0
Piecewise functions: A piecewise function is made up of two or more functions, each defined on a specific domain. Piecewise functions follow the following format:
f(x) ⇒ -x, x < 0
⇒ 0, x = 0
⇒ x, x > 0
The piecewise function above is the absolute value function. As you can see, piecewise functions include:
A curly bracket to indicate that the function is comprised of more than one subfunction
The subfunctions that make up the piecewise function
The subdomains corresponding to each subfunction
The domains of the subfunctions cannot overlap, but one function can end where another starts. If different functions were part of the same domain, the piecewise function would not be a function anymore!
To graph a piecewise function, graph each subfunction at the indicated domain. Be wary of the inequality symbols (< , ≤ , > , ≥) and whether they include or exclude the end of the subdomain. If they include the domain, draw a point and fill it in. If they exclude the domain, draw a point but do not fill it in.
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You know from geometry that the sum of three angles in a triangle is equal to 180. you are given a triangle in which angle b measures 5 more than twice angle a in the triangle. angle c measures 11 less than 3 times the measure of angle a. what is the measure of the small angle, middle angle and the largest angle of this triangle?
The measure of the smallest angle is 31°, the middle angle is 67°, and the measure of the largest angle is 82°.
A triangle is a plane shape with three edges and three vertices. All triangles have three internal angles, and the addition or sum of these angles gives 180°. In the question above, the three angles of the triangle are not given, though, we are given some clues as to how we can find them:
First angle:Not much is said about the first angle, so we'll call it angle a.
Second angle:We are told that the second angle (angle b) is 5 more than twice
angle a. The '5 more' means '5+' twice the value of angle a. Thus;
angle b = 5 + 2a
Third angle:The third angle, angle c is 11 less than 3 times the measure of angle
a, meaning that angle c is 3 times angle a minus 11, thus;
angle c = 3a - 11
The addition of angle a, angle b and angle c gives 180°, hence:
a + 5 + 2a + 3a - 11 = 180°
a + 2a + 3a + 5 - 11 = 180°
6a -6 = 180
6a = 180 + 6
6a = 186
Dividing both sides by 6,
a = 31°
Now that we know the value of angle a, angle b will be
5 + 2(31) = 67°
and angle c is
3(31) - 11 = 82°
Hence, the measure of the smallest angle, angle a is 31°, the middle angle, angle b is 67°, and the largest angle, angle c is 82°.
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Solve the inequality.
8 + 8(x + 9) ≥ 72
find the volume of cylinder
Answer: 678.584in^3
Step-by-step explanation:
Volume= π*(6^2)*6 = 678.584in^3
