Answers
ANSWER:
[tex]\begin{gathered} A\left(n\right)=a_{n-1}\times 2 \\ A\left(n\right)=0.05\cdot\left(2\right)^{n-1} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have that the Arnolds family are going to save a nickel on the first day of the month and then double the amount each day.
One nickel is equal to $0.05, therefore, we can make an recursive formula, it is a geometric sequence where the initial value is 0.05 and the ratio is equal to 2, because it doubles every day, therefore:
[tex]A(n)=0.05\cdot(2)^{n-1}[/tex]Now, from the above we can deduce the explicit formula, since the next value will be double the previous value, therefore, the explicit formula would be:
[tex]A(n)=a_{n-1}\times2[/tex]Therefore, the correct answers are the 1st and 4th options.
Related Questions
When you have a figure like this how you find the slope
Answers
Hello there. To find the slope of the line, we have to figure out two points of the line and plug in the formula for the slope.
Given two points (x0, y0) and (x1, y1) from the line, the slope m can be found with the following formula:
[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]In this case, the image gave us two points from the line: (-4, -2) and (3, -4)
Plugging in the values, we have:
[tex]m=\frac{-4-(-2)}{3-(-4)}[/tex]Add the values
[tex]m=\frac{-4+2}{3+4}=\frac{-2}{7}[/tex]This is the slope of this line.
Use a rectangular array to write the product in standard form 3(4b + 12c + 11)
Answers
The given product is:
[tex]3(4b+12c+11)[/tex]It is required to use a rectangular array to write the product in standard form.
Draw the rectangular array as shown:
Partition the sum to give small rectangles as shown:
Calculate the area of each rectangle by multiplying the width and length, then find the sum to write the product in standard form:
Write the areas as a sum:
[tex]12b+36c+33[/tex]Hence, the required product in standard form is 12b+36c+33.
The required product in standard form is 12b+36c+33.
The barrel of a rifle has a length of 0.983m. A bullet leaves the
muzzle of a rifle with a speed of 602m/s. What is the
acceleration of the bullet while in the barrel? A bullet in a rifle
barrel does not have constant acceleration, but constant
acceleration is to be assumed for this problem.
Answer in units of m/s^2
Answers
The acceleration of the bullet while in the barrel is 184335.7 m/s^2.
First, let us understand the acceleration:
Any action where the velocity changes are said to it as acceleration. There are only two ways to accelerate: altering your speed or altering your direction, or altering both. This happens because velocity is both a speed and a direction.
We are given;
The length of the barrel of the rifle is 0.983 m.
The speed of the bullet is 602m/s.
From the third equation of motion, we know that,
v^2 = u^2+ 2aS
Initial velocity, u=0
Final velocity, v = 602m/s.
Distance, S = 0.983 m.
Substitute the given values in the above formula,
v^2 = u^2 + 2aS
(602)^2 = 0 + 2 * a * 0.983
1.966a = 362404
a = 362404/1.966
a = 184335.7 m/s^2.
Thus, the acceleration of the bullet while in the barrel is 184335.7 m/s^2.
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Suppose that $2500 is invested at an interest rate of 7.2%. How much is the investment worth after 5 years if interest is compounded monthly? (Do not use the money sign and round to the hundredths place (2 spots))
Answers
The investment worth after 5 years if interest is compounded monthly is $3,579.47.
Calculation:-
FV = P (1+ r/m)^mt
= $2500 ( 1 + 7.2/12)¹²ˣ⁵
= $3,579.47.
The Future value is $3,579.47.
The total compound interest is $1,079.47.
FV - the future value of the investment, in our calculator it is the final stability
P - the preliminary stability (the fee of the funding)
r - the once-a-year interest charge (in decimal)
m - the variety of instances the interest is compounded in keeping with 12 months (compounding frequency)
t - the wide variety of years the cash is invested for 5 years
Compound interest, may be calculated with the use of the method FV = P*(1+R/N)^(N*T), wherein FV is the destiny price of the mortgage or investment, P is the initial important amount, R is the yearly interest charge, N represents the variety of times hobby is compounded in keeping with year, and T represents time in years.
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Dion makes and sells stained glass suncatchers in different shapes. For one of his designs, he attaches semicircles to each side of a square that has a side length of 4 centimeters. He builds a frame around the outside of each suncatcher to hold it together.What is the approximate length of the frame that Dion used on this suncatcher?
Answers
Designs shape is:
So length is :
Perimeter of half circle is:
[tex]\text{ Perimeter =}\pi r+2r[/tex]Radius of circle is:
[tex]\begin{gathered} r=\frac{D}{2} \\ r=\frac{4}{2} \\ r=2 \end{gathered}[/tex]So the length is:
[tex]\begin{gathered} =4(\pi r+2r) \\ =4(2\pi+2(2)) \\ =4(2\pi+4) \\ =4(6.283+4) \\ =4\times10.283 \\ =41.132 \end{gathered}[/tex]So the approximate length is 41 centimeter.
The food service manager at a large hospital is concerned about maintaining reasonable food costs. The following table lists the cost per serving, in cents, for items on four menu's. On particular day, a dietician orders 68 meals from menu 1, 43 meals from menu 2, 97 meals from menu 3, and 55 meals from menu 4.Part AWrite the information in the table as a 4x5 matrix M. Maintain the ordering of foods and menu's from the table.M=[__]Part BWrite a row matrix N that represents the number of meals ordered from each menu. Maintain the ordering of menu's from the tableN=[___]Part CFind the product NMNM=[___]1st blank options (average or total)2nd blank (each food, food, or each menu)
Answers
Answer and step by step:
a) To write the information in the table as a 4x5 matrix:
b) Write a row matrix N that represents the number of meals ordered from each menu.
c) Find the product NM:
To find the product of two matrices, the matrices have to be the same number of columns and rows. Then it cannot be solved.
-3 (2x + 4) - (2x + 4) < -4(2x +3)
Answers
-3 (2x + 4) - (2x + 4) < -4(2x +3)
expand
-6x - 12 - 2x - 4 < -8x - 12
Collect like terms
-6x + 8x - 2x < 12 + 4 -12
The is no solution
y = 2x - 9 y = -1/2x + 1Graph both equations to find the solutionfor this system.
Answers
To answer this question, we can graph both lines equations using the intercepts of both lines. The intercepts are the x- and the y-intercepts for both lines.
The x-intercept is the point where the line passes through the x-axis. At this point, y = 0. Likewise, the y-intercept is the point where the line passes through the y-axis. At this point, x = 0.
Therefore, we can proceed as follows:
1. Graphing the line y = 2x - 9First, we can find the x-intercept. For this, y = 0.
[tex]\begin{gathered} y=2x-9\Rightarrow y=0 \\ 0=2x-9 \\ 9=2x \\ \frac{9}{2}=\frac{2}{2}x \\ \frac{9}{2}=x\Rightarrow x=\frac{9}{2}=4.5 \end{gathered}[/tex]Therefore, the x-intercept is (4.5, 0).
The y-intercept is:
[tex]y=2(0)-9\Rightarrow y=-9[/tex]Therefore, the y-intercept is (0, -9).
With these two points (4.5, 0) and (0, -9) we can graph the line y = 2x - 9.
2. Graphing the line y = -(1/2)x +1We can proceed similarly here.
Finding the x-intercept:
[tex]\begin{gathered} 0=-\frac{1}{2}x+1 \\ \frac{1}{2}x=1 \\ 2\cdot\frac{1}{2}x=2\cdot1 \\ \frac{2}{2}x=2\Rightarrow x=2 \end{gathered}[/tex]Therefore, the x-intercept is (2, 0).
Finding the y-intercept:
[tex]\begin{gathered} y=-\frac{1}{2}(0)+1 \\ y=1 \end{gathered}[/tex]Then the y-intercept is (0, 1).
Now we can graph this line by using the points (2, 0) and (0, 1).
Graphing both linesTo graph the line y = 2x - 9, we have the following coordinates (4.5, 0) and (0, -9) ---> Red line.
To graph the line y = -(1/2)x + 1, we have the coordinates (2, 0) and (0, 1) ---> Blue line.
We graph both lines, and the point where the two lines intersect will be the solution of the system:
We can see that the point where the two lines intersect is the point (4, -1). Therefore, the solution for this system is (4, -1).
We can check this if we substitute the solution into the original equations as follows:
[tex]\begin{gathered} y=2x-9 \\ -2x+y=-9\Rightarrow x=4,y=-1 \\ -2(4)+(-1)=-9 \\ -8-1=-9 \\ -9=-9\Rightarrow This\text{ is True.} \end{gathered}[/tex]And
[tex]\begin{gathered} y=-\frac{1}{2}x+1 \\ \frac{1}{2}x+y=1\Rightarrow x=4,y=-1 \\ \frac{1}{2}(4)+(-1)=1 \\ 2-1=1 \\ 1=1\Rightarrow This\text{ is True.} \end{gathered}[/tex]In summary, we found the solution of the system:
[tex]\begin{gathered} \begin{cases}y=2x-9 \\ y=-\frac{1}{2}x+1\end{cases} \\ \end{gathered}[/tex]Using the intercepts of the lines, graphing the lines, and the point where the two lines intersect is the solution for the system. In this case, the solution is (4, -1) or x = 4, and y = -1.
Find the product of (x+3)^2
Answers
Find the product of (x+3)^2
Remember that
(x+a)^2=x^2+2xa+a^2
therefore
(x+3)^2=x^2+6x+9
answer is
x^2+6x+9Marcus has his car insurance payment directly withdrawn from his savings account. One month after starting the payment, he had $915 in savings. Nine months after starting the payment, he had $235. Assume Marcus made no other deposits or withdrawals from the account. If the relationship between months and the amount of money in Marcus’s account is linear, what is the slope?
Answers
The slope of a line is given that passes through the points (x1,y1) and (x2,y2) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case we know that:
After one month the account has $915, this can be represented by the point (1,915)
After nine months the account has $235, this can be represented by the point (9,235).
Plugging these two points in the expression for the slope we have:
[tex]\begin{gathered} m=\frac{235-915}{9-1} \\ m=\frac{-680}{8} \\ m=-85 \end{gathered}[/tex]Therefore, the slope is -85.
Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 15 miles. If the two airplanes are 39 miles apart, the eastbound airplane has traveled __ miles.
Answers
Answer:
36 miles
Explanation:
Let's go ahead sketch the given problem as shown below;
From the above diagram, we can go ahead and determine x, which is the distance the eastbound plane has traveled, using the Pythagorean theorem;
[tex]\begin{gathered} 39^2=x^2+15^2 \\ 1521=x^2+225 \\ x^2=1521-225 \\ x=\sqrt[]{1296} \\ x=36\text{miles} \end{gathered}[/tex]The base of the pyramid is a square.158Perimeter of the base =Area of the base =Slant height =Lateral area =square unitsSurface area =square unitsBlank 1:Blank 2:Blank 3:Blank 4:Blank 5:
Answers
The pyramid has a square base.
i) Perimeter of the base implies the perimeter of the square.
Perimeter of a square is given as:
[tex]\begin{gathered} P=4L \\ L=8 \\ P=4\times8 \\ =32 \end{gathered}[/tex]ii) Area of the base implies the area of the square.
Area of a square is given as:
[tex]\begin{gathered} A=L^2 \\ L=8 \\ A=8^2 \\ A=64 \end{gathered}[/tex]iii) The slant height can be obtained by using the pythagoras theorem.
From the diagram, the hypotenuse side is the unknown slant height, the other two(2) sides are of length 15 and 8.
Thus, we have:
[tex]\begin{gathered} H^2=O^2+A^2\text{ (Pythagoras theorem)} \\ H^2=15^2+8^2 \\ H^2=225+64 \\ H^2=289 \\ H=\sqrt[]{289} \\ H=17 \end{gathered}[/tex]Hence, the slant height is 17
iv) The lateral area of a square pyramid is the sum of the areas of all its 4 triangular side faces.
The area of a triangle is given as:
[tex]\begin{gathered} A=\frac{1}{2}\times Base\times Height \\ \text{Base}=8;\text{ Height=15} \\ A=\frac{1}{2}\times8\times15 \\ A=\frac{120}{2} \\ A=60 \\ \text{Hence, the lateral area is 4}\times60\text{ ( since there are 4 triangular faces)} \\ \text{Lateral area= 240} \end{gathered}[/tex]v) The surface area is the sum of the lateral area and the base area.
The lateral area has been obtained to be 240.
The base area has been obtained to be 64.
Thus, the surface area = 240 + 64
Hence, the surface area is 304
Find the product of (x+4) (x+1)
Answers
Expanding:
[tex]\begin{gathered} x(x\text{ + 1) + 4 (x + 1)} \\ x^2\text{ + x + 4x + 4} \end{gathered}[/tex]collect like terms:
[tex]\begin{gathered} x\text{ + 4x = 5x} \\ x^2\text{ }+\text{ 5x + 4} \end{gathered}[/tex]What is the slope? y= x+2
Answers
The given equation is
[tex]y=x+2[/tex]It is important to know that the slope is the coefficient of x when it's expressed in slope-intercept form like this case.
Hence, the slope is 1.here is an expression 2x + 3y Does the ordered pair 6,0 make the value of the expression less than, greater than, or equal to 12
Answers
2x + 3y
ordered pair = (x,y) = (6,0)
Replace in the expression:
2(6)+3(0)
12 +0
12
The ordered pair makes the expression equal to 12.
find the cost of building the new road
Answers
Question:
Solution:
Step 1: Applying the Pythagorean theorem, we find the length of the new path:
[tex]\text{new road = }\sqrt[]{(8000)^2+(15000)^2}\text{ = }17000[/tex]Step 2: Convert the above value to kilometers:
[tex]17000\text{ m (}\frac{1\operatorname{km}}{1000m})\text{ = 17 km}[/tex]Step 3: Multiply the price per kilometer by the above value:
[tex]17\text{ x }160000=\text{ 2720000}[/tex]so that, we can conclude that the correct answer is:
[tex]\text{2720000}[/tex]What is the zero of function f?f(x)=3 square root of x+3 -6
Answers
Solution:
Given:
[tex]f(x)=3\sqrt{x+3}-6[/tex]The zeros of a function are the values of x when f(x) is equal to 0.
Hence,
[tex]\begin{gathered} 0=3\sqrt{x+3}-6 \\ \\ Collecting\text{ the like terms,} \\ 0+6=3\sqrt{x+3} \\ 6=3\sqrt{x+3} \\ \\ Divide\text{ both sides by 3;} \\ \frac{6}{3}=\sqrt{x+3} \\ 2=\sqrt{x+3} \\ \\ Taking\text{ the square of both sides;} \\ 2^2=x+3 \\ 4=x+3 \\ \\ Collecting\text{ the like terms;} \\ 4-3=x \\ 1=x \\ x=1 \end{gathered}[/tex]Therefore, x = 1
The correct answer is OPTION A.
8340 x 58036 + x\y = 2
Answers
The variable y as the subject of the equation is y = x/-484020238
How to make the variable y the subject of the equation?The missing information from the complete question is added at the end of this solution
From the complete question, we have the following equation representing the given parameter
8340 x 58036 + x\y = 2
Evaluate the products in the above equation
So, we have the following representation
484020240 + x\y = 2
Solving further, we subtract 484020240 from both sides of the equation
So, we have the following representation
484020240 - 484020240 + x\y = 2 - 484020240
Solving further, we evaluate the difference
So, we have the following representation
x\y = -484020238
Cross multiply
-484020238y = x
Divide both sides by -484020238
y = x/-484020238
Hence, the solution is x/-484020238
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Complete question
Make y the subject in 8340 x 58036 + x\y = 2
Rewrite the function for the following transformation: the graph is shifted to the left 5 units.
Answers
Name Danielle Klein Datealillar S4: Linear Equations, Functions, and Inequalities T6: Finding Solution Sets to Systems of Equations Using Substitution and Graphing Independent Practice 1. Last Monday, two law students met up at Café Literatura after school to read the pages they were assigned in the Legal Methods class. Alejandro can read 1 page per minute, and he has read 28 pages so far. Carly, who has a reading speed of 2 pages per minute, has read 12 pages so far. Part A: Define the variables and write two equations to represent the number of pages that each student read. DE 4 Variables: X-Minutes they real they head Alejandro:X-XF28 x= Number of payes Carly:apGraph both equations , find when Alejandro has read more pages than Carly, and when they have read the same amount of pages.
Answers
Let t be the time and P be the number of pages that each students has read. In both cases, the equation that relates P and t is a linear equation. The slope-intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where m represents the rate of change of y with respect to x and b represents the initial value when x=0.
In this case, where P represents the number of pages and t represents the time, the relation can be written as:
[tex]P=mt+b[/tex]Adjust the paramenters m and b for each student.
Since Alejandro can read 1 page per minute, then the rate of change of the number of pages with respect to time is 1. Since he has read 28 pages so far, then the initial value is 28. The number of pages that Alejandro reads, is:
[tex]P=t+28[/tex]Since Carly can read 2 pages per minute, the rate of change is 2. Since she has read 12 pages so far, the initial value is 12. The equation for Carly, is:
[tex]P=2t+12[/tex]To graph each equation, evaluate it on two different values of t to find the corresponding values of P.
For Alejandro, let's use t=0 and t=1:
[tex]\begin{gathered} t=0\Rightarrow P=0+28\Rightarrow P=28 \\ t=1\Rightarrow P=1+28\Rightarrow P=29 \end{gathered}[/tex]Plot the points (0,28) and (1,29) in a coordinate plane:
Then, draw a line through them:
Do the same for Carly's equation. We can see that two points on the line would be (0,12) and (1,14):
To find when has Alejandro read more pages than Carly, write an inequality. After t minutes, Alejandro has read t+28 pages, and Carly has read 2t+12 pages. We want t+28 to be greater than 2t+12, then:
[tex]t+28>2t+12[/tex]Substract t from both sides:
[tex]\begin{gathered} t+28-t>2t+12-t \\ \Rightarrow28>t+12 \end{gathered}[/tex]Substract 12 from both sides:
[tex]\begin{gathered} 28-12>t+12-12 \\ \Rightarrow16>t \end{gathered}[/tex]Therefore, whenever t is less than 16 minutes, Alejandro has read more pages than Carly.
Notice that if we replace the ">" sign for a "=" sign, we would find that they have read the same amount of pages when t=16 minutes.
you are given the expression y+8=14 solve the equation by placing the steps in order (from top to bottom)
Answers
you are given the expression y+8=14 solve the equation by placing the steps in order (from top to bottom)
we have
y+8=14
step 1
subtract 8 both sides
so
y+8-8=14-8
simplify
y=6
the steps are
y+8=14
y+8-8=14-8
y+0=6
y=6
I am supposed to give the reasons why these triangles are equal.
Answers
Statements Reasons.
1. NL bisects angles KNM and KLM. 1. Given.
2. KNL = MNL 2. Definition of angle bisector
KLN = MLN
3. NKL = NML 3. Parallelogram theorem.
4. Triangles NKL and NML are congruent. 4. AAA postulate.
The parallelogram theorem mentioned states that opposite interior angles are congruent.
The AAA postulate of congruence states that two triangles are congruent if all three interior angles are congruent correspondingly.
Line LM is the midsegment of trapezoid ABCD. AB = x + 8, LM = 4x + 3, and DC = 187. What is the value of x? (image attached)thank you ! :)
Answers
To solve that question we must remember that
Then
[tex]\text{ LM = }\frac{\text{ AB + DC}}{2}[/tex]Using the value the problem gives, we get the following equation
[tex]4x+3=\frac{(x+8)+187}{2}[/tex]Solving that equation for x
[tex]\begin{gathered} 4x+3=\frac{(x+8)+187}{2} \\ \\ 8x+6=(x+8)+187 \\ \\ 7x=2+187 \\ \\ 7x=189 \\ \\ x=\frac{189}{7} \\ \\ x=27 \end{gathered}[/tex]The value of x is 27.
i need help please.Which of the following expressions are equivalent to 7x + 14 − 3x + 12?1. 21x + 8x2. 7x − 3x + 14 + 123. 4x + 14 + 124. 4x − 25. 7x + 26 − 3x
Answers
The expression is given as ;
7x + 14 -3x + 12 -------collect like terms
7x - 3x + 14 + 12 --------equation 2
perform operation {addition and subtraction}
4x + 26
However at equation 2 above you can write it as ;
7x + 14 + 12-3x --------add the numbers
7x + 26 - 3x ----------equation 5
Additionally at equation 2 above you can subtract the terms with x's as;
7 x-3x + 14 +12
4x + 14 + 12 ------------equation 3
Answer :
2, 3, 5
Point Q is shown on the coordinate grid belowWhich statement correctly describes the relationship between the point (-3,2) and point G
Answers
The coordinate of Q is (-3,-2)
The relationship between (-3, -2) and (-3, 2)
(x,y) changes into (x,-y) which is the reflection along x axis
The point (-3, 2) is a reflection of point Q across the x-axis
Answer : The point (-3, 2) is a reflection of point Q across the x-axis
Question 20 3 pts Find the derivative. 9 4 y = 36 4 dy dx O 23 + - 4x
Answers
we have the following:
[tex]y=\frac{9}{x^4}-\frac{4}{x}[/tex]derivate:
[tex]\begin{gathered} y^{\prime}=9\frac{d}{dx}(\frac{1}{x^4})-4\frac{d}{dx}(\frac{1}{x}) \\ y^{\prime}=9\cdot(\frac{-6}{x^5})-4(\frac{-1}{x^2}) \\ y^{\prime}=-\frac{36}{x^5}+\frac{4}{x^2} \end{gathered}[/tex]therefore, the correct answer is first option
Write the translation of point P(2, -9) to point P'(0, -12). [A] (x, y) =(x-3, y – 2) [B] (x, y) = (x+3, y +2) [C] (x, y) = (x+ 2, y + 3) [D] (x, y) = (x-2, y-3)
Answers
Applying the transformation (x, y) → (x - 2, y - 3) to point P, we get:
P(2, -9) → (2 - 2, -9 - 3) → P'(0, -12)
use the trigonometric ratio to find the measure of θ in the triangle. Give your answer to the nearest degree
Answers
θ = 64°
Explanation:
Trigonometric ratio SOHCAHTOA
hypotenuse = 10cm
angle = θ
opposite = side opposite the angle = 9cm
adjacent = not given
Since we know the opposite and the hypotenuse, we would apply sine ratio (SOH)
[tex]\begin{gathered} \sin \text{ }\theta\text{ = }\frac{opposite}{\text{hypotenuse}} \\ \sin \text{ }\theta\text{ = }\frac{9}{10} \end{gathered}[/tex][tex]\begin{gathered} \sin \theta\text{ = 0.9} \\ \theta=sin^{-1}(0.9) \\ \theta=\text{ 64.16}\degree \\ To\text{ the nearest degr}ee,\text{ }\theta=\text{ 64}\degree \end{gathered}[/tex]Find the third side in simplest radical form: 3 789
Answers
Apply the Pythagorean theorem:
c^2 = a^2 + b^2
Where:
c = hypotenuse (longest side )
a & b = the other 2 legs of the triangle
Replacing:
c^2 = 3^2 + (√89)^2
c^2 = 9 + 89
c ^2 = 98
c = √98 = √(49x2) = √49 √2 = 7 √2
Third side = 7 √2
laura deon and ravi sent a total of 101 text messages during the weekend. ravi sent 2 times as many messages as deon laura sent 9 more messages than deon how many messages did they each send
Answers
Step 1: Represent laura, deon and ravi
[tex]\begin{gathered} \text{let l represents laura's sent messages} \\ \text{let d represents deon's sent messages} \\ \text{let r represents Ravi's sent messages} \end{gathered}[/tex]Step 2: Write the relationship between l, d, and r from the first statement
[tex]l+d+r=101[/tex]Step 3: Write the relationship from the second statements
[tex]\begin{gathered} r=2d \\ l=d+9 \end{gathered}[/tex]Step 4: Substitute the r and l in the first relationship
[tex]\begin{gathered} l+d+r=101 \\ d+9+d+2d=101 \\ d+d+2d=101-9_{} \\ 4d=92 \\ d=\frac{92}{4} \\ d=23 \end{gathered}[/tex]Step 5: Solve for r and l
[tex]\begin{gathered} r=2d \\ r=2\times23=46 \end{gathered}[/tex][tex]\begin{gathered} l=d+9 \\ l=23+9 \\ l=32 \end{gathered}[/tex]Hence, Ravi sent 46 messages, Deon sent 23 messages, and Laura sent 32 messages