Answers
In general, the explicit formula of a geometric series is
\(a_n=a_{}r^{n-1}\)Where a and r are constants, and a_n is the n-th term.
In our case,
\(\begin{gathered} a_3=20 \\ \text{and} \\ a_3=ar^{3-1}=ar^2 \\ \Rightarrow ar^2=20 \end{gathered}\)On the other hand,
\(\begin{gathered} a_5=80 \\ \text{and} \\ a_5=ar^{5-1}=ar^4 \\ \Rightarrow ar^4=80 \end{gathered}\)Use the two equations to find a and r, as shown below
\(\begin{gathered} ar^2=20 \\ \Rightarrow r^2=\frac{20}{a} \\ \Rightarrow a(r^2)^2=80 \\ \Rightarrow a(\frac{20}{a})^2=80 \\ \Rightarrow\frac{400}{a}=80 \\ \Rightarrow a=5 \end{gathered}\)Finding r,
\(\begin{gathered} a=5 \\ \Rightarrow5r^2=20 \\ \Rightarrow r^2=4 \\ \Rightarrow r=\sqrt[]{4}=\pm2 \end{gathered}\)Thus, the explicit formula is
\(a_n=5(\pm2)^{n-1}\)Set n=1 and find a_1 as shown below,
\(\begin{gathered} n=1 \\ \Rightarrow a_1=5(\pm2)^{1-1}=5 \\ \Rightarrow a_1=5 \end{gathered}\)The answer is a_1=5
Related Questions
HELP ASAP. I can’t miss anymore please help
Answers
\(4\pi\)
Step-by-step explanation:
\(C = 2\pi r,\:\:\:\:r = 4\)
The circumference of the circle of radius 4 is \(8\pi\). Since we are dealing with only half of the circle, the arc length is then half the circumference or \(4\pi\).
please help me I will def give brainliest <3
Answers
Answer:
1) 10:1:3
2)a. Soup-20 oz. Cheese-2 cups, Pasta-6 cups
2)b. Soup-5 oz. Cheese-1/2 cup, Pasta-1 1/2 cups
2)c. Soup-50 oz. Cheese-5 cups, Pasta-15 cups
2)d. Soup-2 oz. Cheese- 1/5 cup, Pasta-3/5 cup
3) 3:6 = 1:2
4)a. 3 batches
4)b. 6 batches
4)c. 1/2 batch
Elaboration
1) Yes, because it simplifies down to 5:3.
2) Yes, because it also simplifies down to 5:3.
3) 25:15 and 35:21
4) If they share a zoom factor then they are equivalent.
5) Equivalent ratios are ratios that make the same comparison of numbers.
Evaluation
1) 2:3
2) They are equivalent because they share a zoom factor of 2.
Last Page
4)a. 28 oz of cream cheese. (35*0.8)
4)b. 4.8 weeks (1.6*3)
4)c. $4,000 (4*1,000)
Evaluation
1) 2 lbs-$6, 0.33 lbs-$1, 1 lbs-$3
2) 0.33 is the amount in pounds that you can get at the price of $1, and 1 pound of grapes will cost $3
7(5+2c)+3c I need help
Answers
Answer:
35 + 17c I hope this helps!! Plz give brainliest!!!
Step-by-step explanation:
7(5+2c)+3c
35+14c+3c
35+17c
Determine A ÷ B, where A = 62x – 100 and B = 2x – 3.
Answers
Answer:
60x-97
Step-by-step explanation:
The question is not properly written. Here is the correct question.
Determine A - B, where A = 62x – 100 and B = 2x – 3.
Given
A = 62x – 100 and
B = 2x – 3.
Required
A-B
A-B = 62x-100-(2x-3)
Open the parenthesis
A-B = 62x-100-2x+3
Collect like terms
A-B = 62x-2x-100+3
A-B = (62x-2x)-(100-3)
A-B = 60x-97
Therefore the expression for A-B is 60x-97
Type an equation for the following pattern.
Answers
y = -3x + 8
To find the slope, we can use two pairs of points and follow the process of y-y/x-x.
Doing so, let’s use the two points (1,5) and (2,2) and carry this out:
2 - 5 = -3
2 - 1 = 1
-3/1 = -3
Our slope is -3.
As the pattern goes further, the y values subtract by 3 each time.
Since that’s the case, we can use the point (1,5) and add 3 to 5 to get our initial value of y:
5 + 3 = 8
Upon addition, 8 is our y-intercept.
The final equation is: y = -3x + 8
Prompt
Why is it advantageous to take market trends into consideration when planning a career path?
Answers
It is advantageous to take market trends into consideration when planning a career path because the necessary skill sets needed in the current market are highlighted.
What is a Career?This is usually in the form of a profession which undergoes special training and knowledge and acts as a life work for the individual and examples include Doctor etc. This helps to provide the main source of income in which a person is dependent on in ensuring his/her family are well taken care of.
The market trends into consideration when planning a career path because of the knowledge of the necessary skills in the market which therefore ensures it is lucrative and more money is earned as a result. This helps to reduce the various vices which are associated with unemployment.
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The lower edge of a 5 foot tall painting is 5 feet above your eye level. At what distance should you stand from the wall so your viewing angle of the painting is maximized?
Answers
Answer:
x = sqrt(50) = 5sqrt(2) = 7.071 ft (to 3 decimals)
Step-by-step explanation:
referring to the diagram
theta (x) = atan(10/x) - atan(5/x)
differentiate with respect to x
theta'(x) = 5/(x^2+25) - 10/(x^2+100)
For x to have an extremum (max. or min)
theta'(x) = 0 ="
5/(x^2+25) - 10/(x^2+100) = 0
transpose and cross multiply
10(x^2+25) -5(x^2+100) = 0
expand and simplify
10x^2+250 - 5x^2-500 = 0
5x^2 = 250
x^2=50
x = sqrt(50) = 5sqrt(2) = 7.071 ft (to 3 decimals)
Since we know that if x becomes large, theta will decrease, so
x = 5sqrt(2) is a maximum.
Experıment wıth systems of equatıons 2x+4y =8....(1)
2x+2y=2....(2) answer?
Answers
Answer:
Solve by substitution;
2x +4y =8 ...(1)
\(2x + 4y = 8 \\ \\ 4y = 8 - 2x \\ \\ y = \frac{8 - 2x}{4} \\ \\ y = 2 - \frac{x}{2} \)
We substitute y into the second equation.
2x + 2y=2 ... (2)
\(2x + 2y = 2 \\ \\ 2x + 2(2 - \frac{x}{2} ) = 2 \\ \\ 2x + 4 - x = 2 \\ \\ x + 4 = 2 \\ x = 2 - 4 \\ x = - 2\)
And we substitute x into the equation y .
\(y = 2 - \frac{x}{2} \\ \\ y = 2 - \frac{( - 2)}{2} \\ \\ y = 2 + 1 \\ y = 3\)
(x,y) —> (–2 , 3 )
I hope I helped you^_^
what is the property of 3x(5x7)=(3x5)7
Answers
The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.
In the equation you provided: 3x(5x7) = (3x5)7
The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.
Find the midpoint of the segment between the points (17,−11) and (−14,−16)
Answers
Answer:
(1.5, -13.5)
Step-by-step explanation:
Midpoint Formula: \((\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\)
Simply plug in our coordinates into the formula:
x = (17 - 14)/2
x = 3/2
y = (-11 - 16)/2
y = -27/2
Answer:
(-1.5, -13.5)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates and divide by 2
( 17+-14)/2 = 3/2 =1.5
To find the y coordinate of the midpoint, add the x coordinates and divide by 2
( -11+-16)/2 = -27/2= - 13.5
Consider the following system of two linear equations:
4y + 3x = 0
4y - x = 16
What is the point of intersection?
Answers
Answer: The two lines intersect at (-4,3)
Step-by-step explanation:
So our first step would be to turn both of these into standard slope-intercept form.
1.)
4y + 3x = 0
4y = -3x
y = -3/4x
2.)
4y - x = 16
4y = x + 16
y = 1/4x + 4
Now that we have our 2 equations, y = -3/4x and y = 1/4x + 4 we can graph them to get an intersection at (-4,3)
Find the value of given PSRQ is a parallelogram
Answers
Angle S and angle R are supplementary angles and need to add together to equal 180 degrees.
This means angle r = 180-145 = 35 degrees.
36x -1 = 35
Add 1 to both sides:
36x = 36
Divide both sides by 36
X = 1
Answer:
Work attached below :D
Please Help
8x + 1
115⁰
Answers
180-115=65
8x+1=65
(remove the +1 by -1 from both sides)
8x=64
(remove the 8• by dividing by 8 on each side)
64/8
x=8
ANSWER: x=8
Find the perimeter of the figure.
Answers
5+5+7+16+7+11 = 51m
HELP 10 MIN LEFT!!!!
Answers
Answer:
To one decimal place,
y = 16.3 m
Step-by-step explanation:
Using SOHCAHTOA,
In this case we need to use CAH,
WE know the angle = 25 and the hypotenuse H = 18,
so,
y = adjacent
\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)
Answer: 16.3 in.
Step-by-step explanation:
use SOH CAH TOA
cos x = adj/hyp
cos 25 = y/18
18 cos 25 = y
y= 16.3
HELP ASAP PLS ANSWER THE QUESTION IN THE PIC I GIV BRAINLEST AND LOTS OF POINTS TO CORRECT ANSWER
Answers
Answer:
They are congruent
Step-by-step explanation:
Since they are corresponding they're gonna be the same angle measure.
(20 points) A product with 400 die per wafer has an average die yield of 60% and a die area of 0.5 cm^2. The best die yield is observed near the center of a stacked wafer map is 82% and this yield occurs at two die sites. The stack included 750 wafers believed not be involved in any temporal yield excursions. (a) (6 points) Estimate the stationary baseline random yield (i.e., the yield when systematic losses are not present), and estimate the systematic mechanisms limited yield.
Answers
To estimate the stationary baseline random yield, we need to consider the average yield of the die on the wafer, which is 60%. We also need to consider the number of die per wafer, which is 400.
The stationary baseline random yield can be calculated by multiplying the average yield of the die by the number of die per wafer. This gives us a stationary baseline random yield of 400 * 0.6 = 240 die.
The systematic mechanisms limited yield is the maximum yield that can be achieved when all the systematic mechanisms are addressed. In this case, the best yield observed was 82% at two die sites. Since this yield occurs at only two die sites, we can estimate the systematic mechanisms limited yield by multiplying the number of die per wafer by this yield. This gives us a systematic mechanisms limited yield of 400 * 0.82 = 328 die.
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Stella has 215 coins and 89 of them are nickels. Two-thirds of the remaining coins are pennies. How many pennies does Stella have?
A. 38
B. 42
C. 66
D. 84
Answers
Answer: 84
Step-by-step explanation:
215 - 89 = 126
126 divided by 3 = 42
42 x 2 = 84
( this was how my teacher taught me to do these kind of problems)
Hope this helps! <3
Answer:
The answer is 84
Step-by-step explanation:
got it right on edge :D
on a separate sheet of paper, sketch the rectangle for each problem using any method round and estimate to check your answer problem 1 5 x 4,751
Answers
The rounded off answers for the area of the rectangles are as follows: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.
What is rounding of a number?Rounding of a number is a mathematical process of approximating a given number to a specified level of accuracy or precision. Rounding is done to make numbers easier to work with or to communicate, especially when the number has many decimal places or digits.
The process of rounding involves changing a number to a nearby value that is easier to use or communicate, while still retaining its approximate value. The number is rounded to a certain number of decimal places or significant digits, depending on the required level of accuracy.
1. 5 x 4751 ≈ 5 x 4800 = 24,000.
To check the answer, we can estimate 4751 as 4800, and then multiply 5 by 4800 to get the approximate product of 24,000.
2. 7 x 6000 = 42,000.
To check the answer, we can simply multiply 7 by 6000 to get the product of 42,000.
3. 6 x 5214 ≈ 6 x 5200 = 31,200.
To check the answer, we can estimate 5214 as 5200, and then multiply 6 by 5200 to get the approximate product of 31,200.
4. 8 x 3867 ≈ 8 x 3900 = 31,200.
To check the answer, we can estimate 3867 as 3900, and then multiply 8 by 3900 to get the approximate product of 31,200.
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The following are the scaled off results for the rectangles' area:: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.
What is rounding of a number?The mathematical process of approximating a given number to a predetermined degree of accuracy or precision is known as rounding. In particular when a number has numerous decimal points or digits, rounding is done to make numbers simpler to work with or communicate.
In order to make a number simpler to use or communicate, a number is rounded to a more manageable value while retaining its general meaning.
Depending on the necessary level of accuracy, the number is rounded to a particular number of significant digits or decimal places.
1. 5 x 4751 ≈ 5 x 4800 = 24,000.
To verify the result, we can convert 4751 to 4800, then increase 5 by 4800 to obtain a result that is roughly 20,000.
2. 7 x 6000 = 42,000.
We can quickly multiply 7 by 6000 to obtain the result of 42,000 to verify the solution.
3. 6 x 5214 ≈ 6 x 5200 = 31,200.
By converting 5214 to 5200 and multiplying that number by 6, we can approximate the solution to be 31,200.
4. 8 x 3867 ≈ 8 x 3900 = 31,200.
To verify the solution, we can convert 3867 to 3900 and multiply 8 by 3900 to obtain a result that is roughly 31,200.
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What is the value of k in the equation below?
5 k minus 2 k = 12
1 and one-fifth
1 and StartFraction 5 Over 7 EndFraction
3
4
Answers
Answer:
The answer is D: 4
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Help immediately. Must do all for max reward it’s sideways
Answers
Answer:
8.
10x-1=14x-37[corresponding side of congruent triangle are equal]
37-1=14x-10x
36=4x
x=36/4
x=9
9.
6x+13=16x-7[corresponding angle of congruent triangle are equal]
13+7=16x-6x
10x=20
x=20/10
x=2
10.
8x-27=4x+33
8x-4x=33+27
4x=60
x=60/4
x=15
PQ=8×15-27=93
11.3x+5=12x-13
13+5=12x-3x
9x=18
x=18/9=2
now
<BDC=12×2-13=11
12.
5x-8=9x-28
28-8=9x-5x
4x=20
x=20/4
x=5
now
<YWX=5x-8+9x-28=5×5-8+9×5-28=34
13..5x-4=2x+5
5x-2x=5+4
3x=9
x=9/3=3
now
ML=5×3-4=11
ML=11
please help me !!! continuity
for the function
Answers
The function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4 is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4
What is the continuity of a function?A function is said to be continuous if there are no breaks or jumps in the functions
Conditions for continuity of a function
The function exists at x = aThe limit of the function as x approaches a existThe limit of the functions a s x a pproaches a equals the value of the function at x = a.Now, for the given function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4
We need to determine the interval of continuity, We proceed as follows.
Since f(x) = sin⁻¹x, x ≠ π/4 , we know that the minimum value of x is - 1 and its maximum value is 1.
So, x must lie in the interval (-1, 1) for x ≠ π/4,
Now, when x = π/4 f(x) = sinx. We know that x = π/4 lies in the interval (-1, 1).
But we know that f(x) = sinx at x = π/4. So, there is a removable discontinuity at x = π/4.
So, from the left, f(x) is continuous on the interval [-1, π/4) and from the right, f(x) is continuous on the interval (π/4, 1]
So, combining both intervals, we have f(x) is continous on the interval [-1, π/4) ∪ (π/4, 1] and since f(x) = sinx at x = π/4, there is a removable discontinuity at x = π/4
So, the function f(x) is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4
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Solve the equation.
-5r-1=7r+5
Answers
Answer:
r=-1/2
Step-by-step explanation:
(-5*-1/2=2.5)( 2.5-1=1.5) (7x -1/2= -3.5)-3.5+5 =1.5
(ANSWER ASAP!! :) GIVING BRAINLIEST WHEN I CAN)
There are 3 teaspoons in each tablespoon. Which equation best represents y, the total number of teaspoons in x tablespoons?
A: x = 3 + y
B: y = 3x
C: y = 3 + x
D: x= 3y
Answers
The equation that best represents y, the total number of teaspoons in x tablespoons is B: y = 3x.
What is an equation?An equation is a mathematical statement showing the equality or equivalence of two or more mathematical expressions.
While mathematical expressions combine variables, numbers, constants, and values with algebraic operands, equations are two or more expressions combined with the equation symbol (=).
The number of teaspoons in each tablespoon = 3
Let the number of teaspoons = y
Let the number of tablespoons = x
Equation:y = 3x.
Thus, the correct equation is Option B.
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Suppose you are interested in how participants behave in different color conditions. You select 30 participants and assign them to one of three rooms. The rooms differ only with respect to the color of the walls. One room is white, one is pale blue, and a third is bright red. Each participant is served a meal of a hamburger and french fries, and you then measure how long it takes them to finish eating. What would be the independent variable in this study
Answers
The answer is the color of the room
Explanation:
In this study, the color of the room is the factor or variable that is modified by the researcher. Also, it is expected the color of the room affects participants' behavior but not the opposite. This shows the color of the room is an independent variable because this factor is not affected by other variables, and it modifies the dependent variable (behavior). Moreover, in studies, the independent variable is always the one that is changed by the researcher.
Picture of coordinates (5,4) (3,4)
On a Cartesian plan
Answers
Both the coordinate points are plotted on the graph. The cartesian graph is attached with the answer.
What are coordinates?Coordinates are numbers which determine the position of a point or a shape in a particular space (a map or a graph). In the cartesian coordinate system, the coordinates are of the form (x, y).Other coordinate systems are : cylindrical and spherical coordinate systemGiven are the two coordinates to be plotted on a Cartesian plan -
(5, 4) , (3, 4).
The two given coordinate points are (5, 4) , (3, 4).
Refer to the graph attached. It shows both the points plotted.
Therefore, both the coordinate points are plotted on the cartesian graph.
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Express 75 as a product of its prime factors write the prime factors in ascending order and give your answer in index form
Answers
Step-by-step explanation:
75 = 3 x 5 x 5 in prime factorization
Answer:
Step-by-step explanation:
3x5x5
How many centimeters are in 3.2 inches? [1 inch = 2.5 cm] Show your work.
Answers
Answer:
8 cm
Step-by-step explanation:
Just multiply 3.2 by 2.5
3.2 x 2.5 = 8
Answer:
Sure, your answer is 8
Step-by-step explanation:
3.2 * 2.5=8
HELP BRAINLIEST IF RIGHT
Answers
Answer:
x<2.93
Step-by-step explanation:
A cone has a diameter of 16 cm and a height of 35 cm. What is its volume?
Answers
Answer: if with 3.14 v= 37512.5333
if with pi v= 37531.56
Step-by-step explanation:
the formula is 1/3hπr^2
r= 2d so radius is 32
plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)