Answer:
A geometric sequence is a sequence of numbers such that the ratio of any two consecutive terms is always the same. This ratio is called the common ratio of the sequence.
In this case, the common ratio is 3/2 and the first term is 6. The nth term of a geometric sequence can be found using the formula:
a_n = a_1 * r^(n-1)
where a_n is the nth term, a_1 is the first term, and r is the common ratio.
Substituting the given values, we have:
a_8 = 6 * (3/2)^(8-1) = 6 * (3/2)^7
Calculating, we find that the 8th term is:
a_8 = 6 * (3/2)^7 = 6 * (9/2) = 27
Therefore, the 8th term is 27.
Step-by-step explanation:
Bridgette has drawn a representation of a sphere with a
radius of 3 units, using the graphs of a circle and an ellipse,
as shown in the picture below on the left.
She needs to determine the equations of the graphs that
will generate the representation of the 3D sphere, as
shown in the picture below on the right.
What are possible equations of the circle and ellipse that
Bridgette can use to create her 3D drawing?
Answer:
C
Step-by-step explanation:
You want the equations of the circle and ellipse in the given figure.
EquationsThe standard form equation for an ellipse is ...
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
where 'a' and 'b' are the semi-axes in the x-direction and y-direction, respectively.
You will notice that when a=b=r, the ellipse becomes a circle and the equation can be rewritten as ...
[tex]\dfrac{x^2}{r^2}+\dfrac{y^2}{r^2}=1\ \Longleftrightarrow\ x^2+y^2=r^2[/tex]
ApplicationHere, the radius is 3, the same as the semi-major axis in the x-direction (a=3). The ellipse axis in the y-direction appears to be about 1/3 that value, so b=1, and the equations of the circle and ellipse are ...
[tex]x^2+y^2=9\qquad\text{circle}\\\\\dfrac{x^2}{9}+\dfrac{y^2}{1}=1\qquad\text{ellipse}[/tex]
In a survey, 13 out of 20 teachers respond yesto a proposal for a new after-school club. In the same survey, 37 out of 50 students respond yes. a.Which group is more in favor of the new after-school club, teachersor students? Show your work
Answer: To compare the level of support for the new after-school club between teachers and students, we can calculate the percentage of individuals in each group that responded "yes" to the proposal.
For teachers: 13 out of 20 is equivalent to 13/20 = 0.65 or 65%
For students: 37 out of 50 is equivalent to 37/50 = 0.74 or 74%
Based on the percentage of individuals in each group that responded "yes," we can see that students are more in favor of the new after-school club than teachers. 74% of students responded "yes" to the proposal, while only 65% of teachers responded "yes."
It's worth mentioning that it's important to keep in mind that this comparison is based on the sample size of teachers and students that responded to the survey and not the whole population, also if the sample size isn't representative of the population and not randomly selected it can't be generalized.
Step-by-step explanation:
(1,0) m=-5
Formula
Y-Y1 = m(x-x1)
Slope form
Slope form -
y - y1 = m(x - x1)
y - 0 = -5(x - 1)
y = -5x + 5
3) Mr. Johnson uses 2.34 yards of yarn to knit a scarf. If Mr. Johnson has a total of 30.42 yards of yarn, how many scarfs will he be able to knit?
she will be able to knit 13 scarfs
Given ,
Mr. Johnson uses 2.34 yards of yarn to knit a scarfMr. Johnson has a total of 30.42 yards of yarnTo Find : Scarfs Mr John will be able to make if he has 30.42 yards of yarn
2.34 yards of yarn = 1 scarf
30.42 yards of yarn = [tex]\frac{30.42}{2.34}[/tex]
= 13 scarfs
Hence , the number of scarfs Mr John will make with 30.42 yards of yarn is 13
What does (AM) represent to segment [BC]? Justify.
AM is a perpendicular bisector of BC.
What is a bisector example?A ray that divides an angle into two equal parts is known as an angle bisector or the bisector of an angle. For instance, each measurement will be equal to 30 degrees if ray AX divides an angle of 60 degrees into two equal parts. There is an angle bisector for each angle.
A line's bisector is defined.To divide a segment or an angle into two congruent parts is to bisect it. The midpoint of a line segment will be traversed by its bisector. A line segment's perpendicular bisector is parallel to the line segment and passes through its midpoint.
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4 out 18 students will ride in a car instead of a van
9x9 = ? whattttttttttttttttt
Answer:
81
Step-by-step explanation:
9x9 = 81
What is the inverse of the function [tex]y=x^{2} +4x+4[/tex]
Answer:
y = 2 ± √x is the inverse but it's not a function. (See note below for additional info)
Step-by-step explanation:
Given the quadratic function:
[tex] \displaystyle{y = {x}^{2} + 4x + 4}[/tex]
We can rewrite the function above using perfect square form:
[tex] \displaystyle{y = {(x + 2)}^{2} }[/tex]
Finding an inverse, we swap the terms of x and y:
[tex] \displaystyle{x = {(y + 2)}^{2} }[/tex]
Square root both sides, solving for y:
[tex] \displaystyle{ \sqrt{x }= \sqrt{ {(y + 2)}^{2}} } \\ \\ \displaystyle{ \sqrt{x }= \left| y+ 2\right| } \\ \\ \displaystyle{ \pm \sqrt{x }= y + 2}[/tex]
Subtract both sides by 2:
[tex] \displaystyle{ \pm \sqrt{x } - 2= y+ 2 - 2} \\ \\ \displaystyle{ \pm \sqrt{x } - 2= y} \\ \\ \displaystyle{y = 2 \pm \sqrt{x} }[/tex]
Therefore the inverse of y = x² + 4x + 4 is y = 2 ± √x.
Note: While it's possible to find the inverse of quadratic function, but the inverse version itself is not really a function. So if you want to go by definition or theorem, you can say there's no inverse function. Otherwise, the answer above is the solution.
How many triangles can be formed with the angle measures: 20, 100, and 60 degrees?
There are infinite many triangles that can be formed with the angle measures 20, 100, and 60 degrees
How to determine the number of trianglesFrom the question, we have the following parameters that can be used in our computation:
Angles = 20, 100, and 60 degrees
The above parameters are angles
When only angles are given, the triangle can have as many side lengths as possible
This means that there are infinite many triangles
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Dana's survey showed that 3 out of 8 students preferred pepperoni pizza and
1 out of 8 preferred cheese pizza. How many more of the 72 students surveyed by
Dana preferred pepperoni pizza than preferred cheese pizza?
Answer:
18 more students preferred pepperoni pizza over cheese pizza in the survey.
Step-by-step explanation:
[tex]\frac{3}{8}[/tex] x [tex]\frac{72}{1}[/tex] Can be rewritten
[tex]\frac{3}{1}[/tex] x [tex]\frac{9}{1}[/tex] = [tex]\frac{27}{1}[/tex] = 27 I cross canceled the 8 and 72. They have a common factor of 8. 8 goes into 8 once and 8 goes into 72 9 times.
27 students preferred pepperoni pizza.
[tex]\frac{1}{8}[/tex] x [tex]\frac{72}{1}[/tex] = [tex]\frac{1}{1}[/tex] x [tex]\frac{9}{1}[/tex] = 9
9 students preferred cheese pizza.
27 - 9 = 18
Mr. Smith has saved $1,800 each year for 20 years. A year after the saving period ended, Mr. Smith withdrew $7,500 each year for a period of 5 years. In the sixth and seventh years, he only withdrew $5,000 per year. In the eighth year, he decided to withdraw the remaining money in his account. If the interest rate was 6% per year throughout the whole period, what was the amount he withdrew at the end of the eighth year?
At the end of the eighth year, the amount Mr. Smith withdrew was $41,757.68.
How the ending withdrawal is determined?The amount that Mr. Smith withdrew at the end of the eighth year is a product of a series of computations, involving future value determination.
In this situation, we have used an online finance calculator to determine the future value of the investment at each leg.
First Leg:N (# of periods) = 20 years
I/Y (Interest per year) = 6%
PV (Present Value) = $0
PMT (Periodic Deposits) = $1,800
Results:
FV = $66,214.06
Sum of all periodic payments = $36,000 ($1,800 x 20)
Total Interest = $30,214.06
Second Leg:N (# of periods) = 5 years
I/Y (Interest per year) = 6%
PV (Present Value) = $,
PMT (Periodic Withdrawal) = $-7500
Results:
FV = $46,331.15
Sum of all periodic payments = $-37,500 ($7,500 x 5)
Total Interest $17,617.09
Third Leg:N (# of periods) = 2 years
I/Y (Interest per year) = 6%
PV (Present Value) = $46,331.15
PMT (Periodic Withdrawal) = $-5000
Results:
FV (Final Withdrawal) = $41,757.68
Sum of all periodic payments = $-10,000 ($5,000 x 2)
Total Interest = $5,426.53
Thus, the amount of $41,757.68 was withdrawn by Mr. Smith at the end.
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Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. What is the probability that the area of triangle XYD is at most 20?
The probability that the area of the triangle is at most 20 is 5/9
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here: Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. Thus area of triangle XYZ is
1/2×12×6=36
Now if the area of the triangle is at most 20 then the required probability is = 20/36
=5/9
Hence, The probability that the area of the triangle is at most 20 is 5/9
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Which expression is equivalent to 10 ?
0 x²(√²)
Ox2.2
O
**(√)
5
Mark this and retur
Save and Exit
Next
Submit
The expression 10+(-8) is equivalent to 10 - 8.
What is expression?Different branches of mathematics exist. The branch of knowledge that deals with numbers and operations is arithmetic. We learned how to add, subtract, multiply, and divide two or more numbers through arithmetic.
Shapes and how they are created with various tools, such as a compass, ruler, and pencil, are the focus of geometry. Another fascinating area of study is algebra, which helps us communicate the numerical and alphabetic aspects of daily life (variables).
Any mathematical statement made up of numbers, variables, and an operation between them is called an expression or an algebraic expression. As an illustration, the expression 4m + 5 consists of the terms 4m and 5, as well as the variable m, all of which are separated from one another by the arithmetic sign +.
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Full question
What expression is equivalent to 10-8?
2. A gallon of gas cost $3.50 at the
beginning of the month. At the e
of the month it cost $3.75. What
was the percent change in the
price of a gallon of gas?
Answer: 0.071%
Step-by-step explanation:
To get from $3.50 - $3.75, there was an increase of $0.25.
(Sorry if I'm getting the currency bit wrong, I'm British.)
Divide 0.25 by the original cost of 3.50, and you get:
0.07142857142857142857142857142857
Round this and you get a 0.071% increase
Answer:
The percent change in the price of a gallon of gas is 0.0714%.
Step-by-step explanation:
Given;A gallon of gas costs $3.50 at the beginning of the month.At the end of the month it costs $3.75.Here, The price increased from $3.50 to $3.75, a change of $0.25.
To find What is the percent change.Formula[tex] \frac{changed \: \: price}{original \: \: price} \times 100\% \\ [/tex]So,
$0.25 ÷ $3.50 × 100% = 0.0714%
Thus, The percent change in the price of a gallon of gas is 0.0714%.
someone please help
Which expression is equivalent to 4(x + 2)?
12x
6x
4x + 2
4x + 8
Answer:
4x +2
Step-by-step explanation:
4( x + 2)
= 4*x +4*2
= 4x +2
Someone please solve this pageee!!
On solving the provided question we can say that - the value of the equation x = y^2 -5 from the graph will be 59.
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
here, the equation from the graphs is
[tex]y^2 = x^8 -7.8x-9,=.43y[/tex]
and y = 8
x = 59
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4x+5y=-7
-5x-3y=-1
I need help with this question since im not smart
Answer:
To solve this system of equations, you can use the method of elimination. To do this, you can add the two equations together:
4x + 5y - 5x - 3y = -7 - 1
-x + 2y = -8
Then, you can divide both sides of the equation by -1 to solve for y:
x - 2y = 8
y = (x - 8) / 2
Now that you have solved for y, you can substitute this expression back into either of the original equations to solve for x. For example, you can substitute y = (x - 8) / 2 into the first equation to get:
4x + 5((x - 8) / 2) = -7
4x + 5x - 40 = -7
9x = 33
x = 3.67
Now that you have solved for both x and y, you can find the solution to the system of equations:
x = 3.67
y = (3.67 - 8) / 2 = -2.17
So, the solution to the system of equations is x = 3.67 and y = -2.17.
salve for y √(7-x)²+(9-y)²
The solution for y in the equation √(7 - x)² + (9 - y)² is infinite many solutions
How to determine the solution for yFrom the question, we have the following parameters that can be used in our computation:
√(7-x)²+(9-y)²
Express tthe equation properly
So, we have the following representation
√(7 - x)² + (9 - y)²
The above is an expression, not an equation
This means that the value of the variable y can take any value and the equation will be true
In other words, it means that the variable y has infinite many solutions because it is not an equation but it is an expression
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What Is the slope for these two points (3,-2) and (5,6)?
Answer:
4
Step-by-step explanation:
m = Δy/Δx = (6-(-2))/(5-3) =8/2 = 4
Change this radical to an algebraic expression with fractional exponents.
3√a
The fractional form of the expression [tex]\sqrt[3]a[/tex] is [tex]a^{\frac{1}{3}[/tex]
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Given, A radical expression [tex]\sqrt[3]a[/tex].
We know this describes the cube root of a or one-third root of a.
This can be written as a fractional exponent as [tex]a^{\frac{1}{3}[/tex].
Some common rules of exponents are
xᵃ×xᵇ = xᵃ⁺ᵇ.
xᵃ/xᵇ = xᵃ⁻ᵇ.
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At a cell phone assembly plant, 82% of the cell phone keypads pass inspection. A random sample of 101 keypads is analyzed. Find the probability that the proportion of the sample keypads that pass inspection is between 0.75 and 0.87.
The z-score for the 0.75 proportion is -1.95.
What is z-score?The Z-score calculates the deviation of the measure from the mean in standard deviations. We seek for the p-value linked with this Z-score after locating the Z-score in the z-score database.
The likelihood that the value of the measure will be less than X, or the percentile of X, is represented by this p-value. The likelihood that the value of the measure is greater than X is obtained by deducting 1 from the p-value.
In a set with mean X and standard deviation μ, the z score of a measure X is given by:
Z=(X-μ)/σ
In this problem, we have that:
n=100,p=0.82
So,μ=E(X)=np=100×0.82=82
Therefore, √V(X)=√np×(1-p)=√100×0.82×0.18=3.841
For Finding the probability that less than 75 in the sample keypads pass inspection.
Using continuity correction, this is (P(75-0.5)<=P(74.5)), which is the p-value of Z when X = 74.5.
=>z= (74.5-82)/3.841
=>z= - 7.5/3.841
=>z= - 1.95 has a p-value to 0.
Hence, if a random sample of 100 keypads is analyzed and 75 pass inspection, then the z-score for 0.75 proportion is -1.95
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Compare 8.002 to 8.20. Which is greater?
Answer:
8.20
Step-by-step explanation:
8.20 is greater than 8.002 due to 0.20 being greater than 0.002
Please help answer question
Answer: x = 9
Step-by-step explanation: To find the value of x, we must understand a few things:
- whatever is in lines like | 2x + 4 | means it's the absolute value or positive value of the number.
Now, with that out of the way, I have one more thing to explain.
- whenever trying to find the value of a variable, you need to do inverse operations, so the opposite of adding is subtracting, and the opposite of multiplication is division. Now, let's solve:
22 - 4 = ?
? = 18
18 / 2 = ?
?(x) = 9
Therefore, x = 9
We can check our answer by doing:
| 2(9) + 4 | = 22
2 x 9 = 18
18 + 4 = 22
22 = 22
So, both answers add up, so x = 9
I hope this helps!
While analyzing a data set, a scientist notices one data value that is 2 IQRs below the first quartile. She decides to remove this value from further analysis.
What might happen to the mean, median, and mode of the data set after the value's removal?
(select all right answers)
The mode will increase.
The median may stay the same.
The mean will increase.
The mode will stay the same.
The median may decrease.
The mean will decrease.
The required correct options of data set after the value's removal.
1. The mean will increase. 3. The median may stay the same. 5. The mode will stay the same.
What is the value's removal?The Index Sponsor computes the Removal Value in the same way that Fund Interests in the linked Fund are valued.
Here,
While analyzing a data set, a scientist notices one data value that is 2 IQRs below the first quartile.
As for the properties of statistics, Change in the IQR does affect the median and mode, So options 3 and 5 are correct.
And also mean will increase.
Thus, the correct options are shown above.
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) If x, x+10 makes a right angle, find them.
Answer:
x+x+10=90 being Right angle triangle.
2x=90-10
2x=80
x =40
then x+10= 40 + 10
= 50
what is the closest estimate of x where f(x) = g(x)?
helppppppppo please
Step-by-step explanation:
the area of a trapezoid is
(a + b)/2 × x
a and b being the 2 bases. and x, as requested, is the height.
A
it does not matter which base is which, as long as we keep using them consistently.
so, let's assume a is the first base :
a = x + 5
and then for the second base
b = 2x - 1
now we use that in the main formula :
(x + 5 + 2x - 1)/2 × x = (3x + 4)/2 × x = (3x² + 4x)/2
A = (3/2)x² + (4/2)x = (3/2)x² + 2x ft²
B
now the height is increased by 4 ft.
that means we need to replace x by x + 4.
(3/2)(x+4)² + 2(x+4) = (3/2)(x² + 8x + 16) + 2x + 8 =
= (3/2)x² + (24/2)x + (48/2) + 2x + 8 =
= (3/2)x² + 12x + 24 + 2x + 8 =
= (3/2)x² + 14x + 32 ft²
with x being the original height, of course.
What is a remainder
A remainder is the remaining amount of a number than comes out of a division. I'm not sure how to explain it better, so I'll give you an example:
Let's say you want to divide 5 by 2. We know that 5 can't be divided by 2 evenly, it won't give you a whole number. Instead it will give you a decimal 2.5.
In this case, 1 is the remainder and I will explain why! Do the long division for 5/2. 2 fits into 5 two times, so you multiply 2 * 2, which gives you 4. If you subtract that number from 5, you get 1. We know that 2 can't fit into one, therefore, 1 is the remainder. once you start getting into decimals, you can fit numbers into other numbers, which is why technically you can fit 2 into 5, but you can't fit it in evenly, if that makes sense!
I hope this example helps see what a remainder is. It's just the number in a long division that the divisor (in my example, 2 is the divisor) can't fit in!
A model of a railroad car has a Scale Ratio of 1:87.1. If the model railroad car is 1.4 in high, how
tall is the actual railroad car?
Please answer this for me quick it’s due on Monday for me!!!
Answer:
The scale ratio of 1:87.1 means that for every 1 unit of measurement on the model (in this case, inches), there are 87.1 units of measurement on the actual railroad car. This means that the actual railroad car is 87.1 times larger than the model in every dimension. If the model is 1.4 inches tall, the actual railroad car would be 1.4 x 87.1 = <<1.4*87.1=122.54>>122.54 inches tall.