determine 7th term in the geometric sequence whose first term is 5 and whose common ratio is 2.
The 7th term of the geometric sequence with the first term being 5 and a common ratio of 2 is calculated using the formula Tn = [tex]a * r^{n-1}[/tex]. The 7th term is found to be 320.
The question asks us to determine the 7th term in a geometric sequence where the first term is 5 and the common ratio is 2. The formula for the nth term of a geometric sequence is given by
Tn = [tex]a * r^{n-1}[/tex], where Tn is the nth term, a is the first term, r is the common ratio, and n is the term number. Substituting the given values into the formula, we can find the 7th term as follows:
T7 = [tex]5 * 2^{(7-1)}[/tex] = 5 * 2⁶ = 5 * 64 = 320. Hence, the 7th term of the geometric sequence is 320.
Find the measure of the central angle that you would draw to represent 67% in a circle graft round your answer to the nearest degree
A cat and a dog have a race. The cat’s strides are 30% shorter than the dog’s but it makes 30% more strides than the dog. Which of them will win the race?
using a table of value determine the solution to the equation below to the nearest fourth of a unit
2^(-x) + 1 = 5^x + 2
x= -1.50
x= 2.50
x= -0.50
x= 0.75
what is the slope of the line
Danny bought 5 candies. Lucy bought 2 fewer than danny. Jimmy bought 4 more than lucy. how many candies did jimmy buy
To prepare for the party, the host made a large batch of punch. The recipe makes 8 gallons of punch. How many cups of punch can be served from this batch?
A. 24
B. 128
C. 64
Find the coordinates of the image after a translation of the figure below using (x, y) (x + 3, y + 2).
A'(
a1,
a2)
B'(
a3,
a4)
C'(
a5,
a6)
D'(
a7,
a8)
The coordinates are
A(-4,-3) →A'(-1, -1)
B(-1, 1) → B'(2, 3)
C(3, 5) → C'(6, 7)
D(2,-5) → D'(5,-3)
Step-by-step explanation:
Given the graph of figure whose coordinates are
A(-4, -3), B(-1, 1), C(3, 5), D(2, -5)
We have to find the coordinates of the image after a translation using T(x, y) → (x + 3, y + 2).
Coordinates after translation are
A(-4,-3) → A'(-4+3, -3+2)=A'(-1, -1)
B(-1, 1) → B'(-1+3, 1+2)=B'(2, 3)
C(3, 5) → C'(3+3, 5+2)=C'(6, 7)
D(2,-5) → D'(2+3, -5+2)=D'(5,-3)
which are required coordinates of the image after a translation of the figure below using (x, y) → (x + 3, y + 2).
hope this helps :)
cylinder A has a volume of 360 cm3. Cylinder B has a base and height identical to that of cylinder B, but leans to the right in such a way that its slant is greater than 4 cm. what is the volume of cylinder B
The scale factor of the dilation of figure ABCD is?
2 is the scale factor of the dilation of figure ABCD
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.
The scale factor of a dilation is a number that represents how much a figure's size alters following a dilation. It is the ratio of similar sides' lengths in the original and dilated figures.
A figure is stretched or extended if the scale factor is larger than 1, and lowered or shrunk if it is less than 1. If the scale factor is 1, the dilation has no effect on the figure; if it is less than 1, the figure is reflected beyond the line of dilation.
The scale factor is represented by the symbol k, and its value may be determined using the formula below:
k = Length of the corresponding side in the dilated figure / Length of the corresponding side in the original figure.
On the given figure,
Before dilation the measurement of the side AD = 1 unit.
After dilation the measurement of the same side = 2 units
Thus, from the formula
k = 2/1
k=2
Therefore, The scale factor of the dilation of Figure ABCD is 2.
Learn more about coordinates here:
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The lengths of infants at birth in a certain hospital are normally distributed with a mean of 18 inches and a standard deviation of 2.2 inches. find the probability that an infant selected at random from this hospital measures between 16 and 21 inches.
(a) [5 points] using only the definition, find the laplace transform y (s) of y(t) = e a t where a is a constant. for what values of s does the laplace transform y (s) exist? (b) [10 points] solve, using laplace transforms, the initial value problem: y 00 − 4y 0 + 4y = 3, y(0) = 0, y0 (0) = 1.
A plane left Chicago at 8 A.M. At 12 P.M., the plane landed in Los Angeles, which is 1,700 miles away.
If the plane travels at a constant rate, how many miles did it travel per hour?
Which table represents a linear function? (Will give brainliest)
Answer:
x y
1 0.5
2 1
3 1.5
4 2
Table (1) represents a linear functions.
Step-by-step explanation:
Given : Tables with x and y values.
We have to choose the table that represents a linear function.
Since, A linear function is of the form y = mx + c , where m is slope and c is y- intercept
Consider the table (1),
x y
1 0.5
2 1
3 1.5
4 2
Consider two points , (1,0.5) and (2,1)
0.5 = m(1) + c
and 1 = m(2) + c
Subtract both , we have,
m = 0.5
and Put m = 0.5 back, we have,
c = 0
Thus, y = 0.5x
Thus, Table (1) represents a linear functions.
3x^2-2x+7 divided by x+1 what is the quotient?
Conrad and jill have a taxable income of 63,670. they discovered that they are able to receive $1,500 tax credit for purchasing an energy efficient furnace. How will this tax credit affect their taxes?
A) the tax credit will increase their taxable income by $1,500
B) the tax credit will reduce their taxable income by $1,500
C) the tax credit is added to the tax owed, not the taxable income
D) the tax credit is subtracted from the tax owed, not taxable income
Use the distributive property to factor the expression below.
54x2y - 12x2y2
Suppose that $2000 is invested at a rate of 2.1% compounded annually. Assuming that no withdrawals are made find the total amount after 5 years. Do not round any intermediate computations, and round your answer to nearest cent.
hey can you please help me posted picture of question
at the end of his shift, Bruno had $340 worth of tips all in $10 and $20 bills .if he had two more $20 bills than $10 bill .how many of each bill did Bruno have
PLEASE HELP!!!!!! WHICH OF THE FOLLOWING IS A CORRECT EQUATION FOR THE LINE PASSING THROUGH THE POINT (-2 1) AND HAVING SLOPE M = 1/2
Q #11 Solve the equation
A basketball is thrown with an initial upward velocity of 30 feet per second from a height of 6 feet above the ground. The equation h=-16t^(2)+30t+6 models the height in feet t seconds after the basketball is thrown. After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground. About how long after it was thrown does it go into the hoop?
To finance her community college education, Sarah takes out a loan for $3700. After a year Sarah decides to pay off the interest, which is 5% of $3700. How much will she pay?
One state leads the country in tart cherry production, producing 80 out of every 100 tart cherries each year. a. What percent of tart cherries are produced in this state?
express 0.41 as a fraction in simplest form
Express 0.41 as a fraction in the simplest form will be 41/100.
What is a fraction number?A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.
The number is 0.41.
Then express 0.41 as a fraction in the simplest form will be
⇒ 0.41
Multiply and divide by 100. Then we have
⇒ 0.41 x 100 / 100
⇒ 41 / 100
More about the fraction number link is given below.
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David’s starting pay for his summer job is $10.00 per hour. Halfway through the summer he receives a 50 cent per hour raise. David is hired the next summer and receives a 10% raise. Halfway through the second summer he receives a 50 cent per hour raise. David is hired for a third summer and is given a 5% raise. How much money does David earn per hour during the third summer? Show or explain your work.
Nancy wove a pot holder with a area of 80 square inches. The lengths and widths of the sides are whole numbers. Which dimensions make the most sense for a potholder? Explain
Final answer:
The dimensions of 8 inches by 10 inches make the most sense for a pot holder with an area of 80 square inches, as they are practical in size. This is similar to the concept of a square whose area scales by the square of the side length when dimensions are increased by a scale factor.
Explanation:
The student asked which dimensions make the most sense for a potholder with an area of 80 square inches where the lengths and widths are whole numbers. It's crucial to consider practical sizes that would be convenient for handling hot items without being too large or too small.
Common dimensions for a pot holder could be 8 inches by 10 inches since 8 x 10 equals 80 square inches, and these measurements are suitable for a pot holder. These measurements make sense as they provide enough space to protect hands from heat but are not excessively large, making them impractical. They are comparable to the measurements of a placemat, which is typically used in dining settings and is also manageable in size.
Comparing this to the information about squares and areas, if Marta has a square with side length 4 inches, its area would be 16 square inches. A similar square with side lengths that are twice as long (8 inches) would have an area of 64 square inches because the area is proportional to the square of the side length. Consequently, the area of the larger square is four times that of the smaller square (since 2 squared is 4).
This example of scaling dimensions and areas can assist in understanding how dimensions that are whole numbers relate to the area and the practical use of an object. The mentioned scale factor is integral in determining how the area increases with increased side lengths.
what is the diameter of a circle with a circumference of 30 pi inches
Given the equation f(x) = (x + 3)2 – 8, fill in the blanks:
Axis of symmetry: x =
Vertex:( , )
Number of real solutions:
Final answer:
This detailed answer explains the axis of symmetry, vertex, and number of real solutions for the given quadratic equation.
Explanation:
Given the equation f(x) = (x + 3)² – 8
Axis of symmetry: x = -3
Vertex: (-3, -8)
Number of real solutions: 1