Answer:
The sum to infinity of the given series is;
[tex]S_{\infty}=21\frac{1}{3}[/tex]Explanation:
From the given series, we can see that the series is a Geometric Progression (GP) because it has a common ratio;
[tex]\begin{gathered} r=\frac{4}{16}=\frac{1}{4} \\ r=0.25 \end{gathered}[/tex]The formula to calculate the sum to infinity of a GP is;
[tex]\begin{gathered} S_{\infty}=\frac{a}{1-r} \\ \text{For;} \\ 0Where;a = first term = 16
r = common ratio = 0.25.
substituting we have;
[tex]\begin{gathered} S_{\infty}=\frac{16}{1-0.25}=\frac{16}{0.75} \\ S_{\infty}=21\frac{1}{3} \\ S_{\infty}=21.33 \end{gathered}[/tex]Therefore, the sum to infinity of the given series is;
[tex]S_{\infty}=21\frac{1}{3}[/tex]Compute the percent of profit or loss on shares of stock purchased at8.625 and sold at 10.75.
ANSWER:
24.63%
STEP-BY-STEP EXPLANATION:
The first thing is to mention that it is a profit because it was bought at a lower amount than it was sold, therefore
We take 100% as the lowest value, and thus we calculate the profit percentage
[tex]10.75\cdot\frac{100}{8.625}=124.63[/tex]Then the difference between both percentages is the profit percentage
[tex]124.63-100=24.63[/tex]Which ratio table shows equlvalent ratios? O First Quantity 63 Second Quantity 8 5 o First Quantity Second Quantity 15 4 22 First Quantity Second Quantity 6 3 First Quantity 2.1 Second Quantity 4 2
we are asked to determine which ratios are equivalent. For ratios to be equivalent the quotient of the ratios must be the same. For the ratios:
[tex]\frac{2}{4},\frac{1}{2}[/tex]If we take 2/4 and divide the numerator and denominator by 2 we get:
[tex]\frac{\frac{2}{2}}{\frac{4}{2}}=\frac{1}{2}[/tex]Since we got the same fraction that means that the ratios are equivalent.
Match the following. Match the items in the left column to the items in the right column.1. divisor2. decimal fraction3. algorithm4. fraction5.quotient6. reminder7. doidonsa. the result of dividing two numbersb. the number being dividedc. a set of rules to be followed tosolve a problemd. the number of equal parts a number is being divided intoe. a fraction in which the denominator is 10 or a power of 10f. the amount left over after Chivisiong. a number that expresses the portiona whole
We can match as follows:
1. divisor ----> d. the number of equal parts a number is being divided into
2. decimal fraction ----> e. a fraction in which the denominator is 10 or a power of 10
3. algorithm ----> c. a set of rules to be followed to solve a problem
4. fraction ----> g. a number that expresses the portion
5. quotient ----> a. the result of dividing two numbers
6. reminder ----> f. the amount left over after Division
eric is giving a presentation about average rainfall in the united states and wants to create a graph that shows how yearly rainfall has changed over the past decade. what type of chart should he use?
To represent the yearly rainfall in a graph, eric should use the Bar Graph
which is commonly used worldwide
Bar Graph:
The graphic representation of data in the form of vertical or horizontal bars or rectangular strips having uniform width is called bar graphs.
A bar graph is used to give the comparison between two or more groups. It comprises of two or more parallel vertical (or horizontal) rectangles.
With bar graphs, we can compare data sets from different groups. The graph depicts groups on one axis and a discrete value on the other. The main purpose is to display the relationship between the two axes.
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Consider the function y = f(x) shown at right, trace each interval where the function behavior is A. Increasing, using a GREEN pencil Identify the interval(s) ___B. Decreasing, using a RED pencil Identify the interval(s) ___ C. Constant, using a YELLOW pencil Identify the interval(s) ___ D. State the Domain of the function ___ E. State the Range of the function ___ F. What thoughts do you have about the intervals stated above? Did you use brackets (closed/included points) or parentheses (open/non-included points)? Why or why not?
You have a function f(x). To identify the increasing interval and decreasing interval of f(x), you consider that an increasing interval is determined by the values of x in which the value of f(x) increases. For the decreasing interval you focus on the values of x in which the values of f(x) decreases.
You can notice in the given graph:
The increasing interval is (-8 , -4) U (3 , 6)
The decreasing interval is (-4 , -2)
The constant interval is (-2 , 3)
The domain of the function is (-8 , 6)
The previous interval is given by the available values of x
The range of the function is (-4 , 8)
The previos interval is given by the values of f(x) for the values of x in the domain.
The following image is a sketch of the graph with the respective intervals.
Three ships, A, B, and C, are anchored in the atlantic ocean. The distance from A to B is 36.318 miles, from B to C is 37.674 miles, and from C to A is 11.164 miles. Find the angle measurements of the triangle formed by the three ships.A. m∠A=88.28267; m∠B=17.22942; m∠C=74.4879B. m∠A=74.4879; m∠B=17.22942; m∠C=88.28267C. m∠A=17.22942; m∠B=74.4879; m∠C=88.28267D. m∠A=88.28267; m∠B=74.4879; m∠C=17.22942
Question: Three ships, A, B, and C, are anchored in the Atlantic ocean. The distance from A to B is 36.318 miles, from B to C is 37.674 miles, and from C to A is 11.164 miles. Find the angle measurements of the triangle formed by the three ships.
Solution:
Note: In finding the angles of a triangle given its three sides, we will use the Cosine Law.
[tex]\begin{gathered} c^2=a^2+b^2\text{ -2abcosC} \\ or\text{ it can be written as:} \\ \text{Cos(C) = }\frac{a^2+b^2-c^2}{2ab} \end{gathered}[/tex]
In finding angle C, we use the formula given above.
[tex]\begin{gathered} \text{Cos(C) = }\frac{37.674^2+11.164^2-36.318^2}{2\cdot37.674\cdot11.164} \\ \text{Angle C = 74.4879 degrees} \end{gathered}[/tex]Note: Side a is the side opposite Angle A, side b is the side opposite Angle B, and side c is the side opposite Angle C.
Let's find the next angle.
[tex]\begin{gathered} \text{Cos(B) = }\frac{a^2+c^2-b^2}{2ac} \\ \text{Cos(B) = }\frac{37.647^2+36.318^2-11.164^2}{2\cdot37.647\cdot36.318} \\ \text{Angle B = 17.2294}2\text{ degrees} \end{gathered}[/tex]Note: We can still use the cosine law in finding Angle A. But another solution is subtracting the Angles A and B from 180 degrees. The measure of the internal angle of a triangle is always 180 degrees no matter what type of triangle it is.
[tex]\begin{gathered} \text{Angle A = 180-74.4849 -17.22942} \\ \text{Angle A = 88.28 degrees} \end{gathered}[/tex]ANSWER:
A. m∠A=88.28267; m∠B=17.22942; m∠C=74.4879
The Editor-in-Chief of the student newspaper was doing a final review of the articles submitted for the upcoming edition. Of the 12 total articles submitted, 5 were editorials. If he liked all the articles equally, and randomly selected 5 articles to go on the front cover, what is the probability that exactly 3 of the chosen articles are editorials? Write your answer as a decimal rounded to four decimal places.
This is a problem of binomial probability. We have two possible outcomes:
• the article selected is an editorial,
,• the article selected is not an editorial.
The probability of success (select an article that is an editorial) is:
[tex]p=\frac{5}{12}[/tex]Because we have 12 total articles submitted, and 5 of them were editorials.
To calculate the probability that selecting 5 random articles, getting as a result that exactly 3 of the chosen articles are editorials, we use the binomial probability formula:
[tex]P(n,x)=C(n,x)\cdot p^x\cdot(1-p)^{n-x}[/tex]Where:
• n = the number of trials = the number of articles selected randomly = 5,
,• x = the number of success = the number of editorials that we expect = 3,
,• p = the probability of getting an editorial = 5/12,
,• C(n,x) = n! / (x! (n-x)!).
Replacing the data in the formula above, we get:
[tex]P(n=5,x=3)=\frac{5!}{3!\cdot(5-3)!}\cdot(\frac{5}{12})^3\cdot(1-\frac{5}{12})^{5-3}\cong0.24615=0.2462[/tex]Answer
Rounded to four decimal places, the probability that exactly 3 of the chosen articles are editorials is 0.2462.
please help me solve this no tutor can ahelp me
Solution:
Since the confidence interval width is inversely proportional to n , the answer is the smallest n.
CORRECT OPTION: 36
A machinist must follow part drawing with scale 1 to 16. Find the dimensions (in inches) of the finished stock shown in the figure. That is find the lengths A, B, C, and D.
Length of the dimensions of the finished stock shown are as follow:
A = 13/4 inches , B = 3/4 inches , C =5/2 inches , D = 3/16 inches.
As given in the question,
Mechanist must follow part drawing with scale 1 to 16.
Dimensions of the finished stock shown in the figure
A represents the length .
B represents the height
C represents the length
D represents the height
Length of A is
= 3 1/4 inches
= 13 /4 inches
Height of B is
=3/4 inches
Length of C is
= 2 1/2 inches
= 5/2 inches
Height of D is
= 3/16 inches
Therefore, length of the dimensions of the finished stock shown are as follow: A = 13/4 inches ,B = 3/4 inches ,C =5/2 inches , D = 3/16 inches.
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how does the common ratio and ratio of the perimeters of FDE to CAB compare
Answer
The common ratio and the ratio of the perimeters of the two triangles are exactly the same (2/3).
Explanation
The common ratio is obtained by expressing corresponding sides as a fraction of each other.
The common ratio for this triangles = (8/12) = (6/9) = (12/18) = (2/3)
Perimeter is expressed as the sum of all the exterior dimensions of a figure.
For the first figure, Perimeter = 8 + 6 + 12 = 26 inches
For the second figure, Perimeter = 12 + 9 + 18 = 39 inches
Ratio of perimeters = (26/39) = (2/3)
Hope this Helps!!!
A If y = x + 2 and y = -2x + 8, what do you know about x + 2 and -2x + 8?
If y = x + 2 and y = -2x + 8, what do you know about x + 2 and -2x + 8?
we have
y=x+2
y=-2x+8
Solve the system of equations
equate both equations
x+2=-2x+8
x+2x=8-2
3x=6
x=2
Find the value of y
y=(2)+2
y=4
the solution is (2,4)
that means
(2,4) is a common point , that satisfy both equations
For each angle, determine the measure of the arc subtended by the angle's ray in units of 1/10th of the circumference of the given circle.Measurement for the diagram below:
Assuming you want the measure of the arc (in red) shown:
The circumference is divided into 10 equal parts. The red color arc is 1 and a half part.
The circumference is 360 degree and each part is 360/10 = 36 degrees
Thus, 1 and a half part will be:
[tex]1.5\times36=54\degree[/tex]Measure of Arc (in red) is:
54 degrees
3.50 divide by 24.50
Answer:
1/7 or 0.143
Step-by-step explanation:
i hope this helps
A cattle train left the station and traveled toward New York at an average speed of 41.4 mph. A passenger train left 5.6 hours later and traveled in the opposite direction with an average speed of 22.5 mph. How long does the passenger train need to travel before the trains are 513 mi. apart?
You have the following information:
- Average speed of cattle train to New York: 41.4 mph
- Average speed of passenger train: 22.5 mph
- The passenger train left in the opposite direction, 5.6 hour after cattle train started its travel.
In order to determine how long does the passenger need to travel before the trains are 513 mi apart, you take into account that you can express the previous situation in an algebraic way. If you consider x as the distance traveled by cattle train in a time t, the you have:
x = vt = (41.4)t = 41.4 t
Now, if you consider x' as the distance traveled by the passenger train in the opposite direction in a 5.3h after the left of cattle train, you have:
x' = v't = (22.5)(t + 5.3) = 22.5 t + 119.25
Next, if you are interested in the time on which passengers and cattle train will be separated by 513 mi, then you can write:
x - (-x') = 513 Here, you specify the distance between both trains are 513
x + x' = 513
The minussign of -x' is due to the fact the passengers trains goes in the opposite direction.
Then, by replaacing the expressions for x and x' you obtain:
(41.4t) + (22.5t + 119.25) = 513
Now, you can simplify the previous expression, and solve it for t:
41.4t + 22.5t + 119.25 = 513
63.9t = 513 - 119.25
63.9t = 393.75
t = 393.75/63.9
t = 6.16
Hence, both trains will be at a distance of 513 mi apart between them, after 6.16 hours
write a ratio that is equivalent to the ratio 25:10
25:10 can be writen as
[tex]\frac{25}{10}[/tex]Since the numerator and the denominator are divisible by 5, then we have
[tex]\frac{25}{10}=\frac{5\times5}{5\times2}=\frac{5}{2}[/tex]Then, an equivalent ratio of 25:10 is 5:2
Choose the correct equation in point slope form for the line through the given points or through the given point with the given slope
Answer:
[tex]y-3=-1(x+2)[/tex]Explanation:
The point-slope form of the equation of a line is generally given as;
[tex]y-y_1=m(x-x_1)[/tex]where m = the slope of the line
y1 = y-coordinate of the one point
x1 = x-coordinate of the one point
Given the slope of the line as m = -1 and the point (-2, 3) where x1 = -2 and y1 = 3, let's go ahead and substitute these given values into the point-slope formula to obtain the required equation as seen below;
[tex]\begin{gathered} y-3=-1\lbrack x-(-2)\rbrack \\ y-3=-1(x+2) \end{gathered}[/tex]I need help with this practice problem solving This is the subject trigonometry
Given the fucntion:
f(x) = tanx
Let's graph the function and input the correct values in the box.
• To find the y-intercept of the function, input 0 for x and solve:
[tex]\begin{gathered} f(0)=\tan 0 \\ \\ f(0)=0 \end{gathered}[/tex]Therefore, the y-intercept is:
(0, 0)
• The period of the function:
The fundamental period of a tangent function is π.
Now, let's find points on the graph:
Therefore, the points are:
[tex]\mleft(-\frac{\pi}{3},-\sqrt{3}\mright),\mleft(-\frac{\pi}{4},-1\mright),\mleft(0,0\mright),\mleft(\frac{\pi}{4},1\mright),\mleft(\frac{\pi}{3},\sqrt{3}\mright)[/tex]ANSWER:
The tangent function's period is π . The y-intercept of the function is (0, 0).
The points are:
[tex](-\frac{\pi}{3},-\sqrt[]{3}),(-\frac{\pi}{4},-1),(0,0),(\frac{\pi}{4},1),(\frac{\pi}{3},\sqrt[]{3})[/tex]Determine if the following statement uses inductive reasoning and explain in complete sentences. Find a counterexample, if possible.Statement: If the Charleston Chiefs score two touchdowns each quarter, then they must have won the game
Answer:
Explanation:
The given statement is
Statement: If the Charleston Chiefs score two touchdowns each quarter, then they must have won the game
It is an inductive statement
The counterexample would be
If the Charleston team won the game, they must have scored two touchdowns each quarter
Write the expression as a product of two factors. 12s + 10 + 6y
to write the expression as a product between two factors you must identify the common factor between all the terms in tis case the common factow will be 2
[tex]12s+10+6y=2\cdot(6s+5+3y)[/tex]relation and functionFunction OperationComposition of functionsymmetryfunction Inversesrate of change scartterplotsMINIMUM STEPS PLEASE!
In order to find f(2) we just have to replace x by 2 in its equation:
f(x) = 3x - 1
↓
f(2) = 3 · 2 - 1
f(2) = 6 - 1
f(2) = 5
Finding g(x) = f(2)Since g(x) = f(2) is
g(x) = 5
using the equation of g, we have that
2x - 3 = 5
In order to find x we just solve the previous equation
2x - 3 = 5
↓ adding 3 both sides of the equation
2x - 3 + 3 = 5 + 3
2x = 8
↓ dividing by 2 both sides of the equation
2x/2 = 8/2
x = 4
Answer- D: x = 4
A chemist needs to mix a 12% acid solution with a 20% acid solution to obtain 160 ounces of a 15% acid solution. How many ounces of each of the acid solutions must be used?
Answer:
100 ounces of 12% solution and 60 ounces of the 20% solution.
Step-by-step explanation:
Let x ounces be the amount of 12% solution, then there will be 160-x ounces of the 20% solution.
So, we have the equation:
0.12x + 0.20(160 - x) = 0.15* 160
0.12x - 0.20x + 32 = 24
-0.08x = -8
x = 100.
So, it is 100 ounces of 12% solution and 60 ounces of the 20% solution.
Your $8800 investment grows to $15600 over the course of 5 years compounded quarterly. What interest rate did you receive on your investment? (Write your answer with at least four decimal points) Your interest rate is r =
Given:
The initial amount is $8800.
The Future value is $15600.
Number of year = 5 years compounded quarterly .
The interest rate is calculated as,
[tex]\begin{gathered} FV=P(1+\frac{r}{4})^{4\times n} \\ 15600=8800(1+\frac{r}{4})^{4\times5} \\ \frac{39}{22}=(1+\frac{r}{4})^{20} \\ \sqrt[20]{\frac{39}{22}}=1+\frac{r}{4} \\ \frac{r}{4}=\sqrt[20]{\frac{39}{22}}^{}-1 \\ r=4(\sqrt[20]{\frac{39}{22}}-1) \\ r=0.1162 \end{gathered}[/tex]Answer: the interest rate is 0.1162.
ABCD is a rectangle. Find the coordinates of P, the midpoint of AC. [B is (18,12) ]
the coordinates of P is (9, 6)
Explanation:Coordinate of B = (18, 12)
In a rectangle, the opposite parallal sides are equal
AB = DC
AD = BC
We need to find the coordinates of A and C inoder to get P:
Since the x coordinate of B is 18, the x coordinate of C will also be 18
C is on the y axis, this means its y coordinate will be zero
Coordinate of C (x, y) becomes: (18, 0)
The y coordinate of B is 12, the y coordinate of A will also be 12
A is on the y axis. This means the x coordinate of A will be zero
Coordinate of A (x, y becomes): (0, 12)
To get P, we will apply the midpoint formula:
[tex]\text{Midpoint = }\frac{1}{2}(x_1+x_2),\text{ }\frac{1}{2}(y_1+y_2)[/tex]Using the points A (0, 12) and C (18, 0) to get coordinates of P:
[tex]\begin{gathered} x_1=0,y_1=12,x_2=18,y_2\text{ = 0} \\ \text{midpoint = }\frac{1}{2}(0+18),\text{ }\frac{1}{2}(12+0) \\ \text{midpoint = }\frac{1}{2}(18),\text{ }\frac{1}{2}(12) \\ \text{midpoint = (9, 6)} \end{gathered}[/tex]Hence, the coordinates of P is (9, 6)
Speeding tickets provide a significant source of revenue for many American cities. For one city in South Florida, the average annual speeding ticket revenue per police officer is $300,000. The standard deviation for these annual speeding ticket revenues is $58,000. If these amounts have a normal distribution, find the cutoff amount of annual speeding ticket revenue that separates the highest five percent of revenue generating officers from the other ninety-five percent.
Explanation
To find the cutoff amount of annual speeding ticket revenue that separates the highest five percent of revenue-generating officers from the other ninety-five percent.
We will need to find
[tex]P\left(x>z\right)=0.05[/tex]Therefore; using a z score calculator, this gives;
[tex]z=1.645[/tex]We can then find the cutoff amount z using the formula below;
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \end{gathered}[/tex]Since
[tex]\begin{gathered} \mu=$ 300,000. $ \\ \sigma=58,000 \end{gathered}[/tex]Therefore, we will have
[tex]\begin{gathered} 1.645=\frac{x-300000}{58000} \\ \mathrm{Switch\:sides} \\ \frac{x-300000}{58000}=1.645 \\ crossmutiply \\ x-300000=58000\times1.645 \\ x=300000+95410 \\ x=395410 \end{gathered}[/tex]Answer: 395410
What is the product?(4y − 3)(2y2 + 3y − 5)8y3 + 3y + 158y3 − 23y + 158y3 − 6y2 − 17y + 158y3 + 6y2 − 29y + 15
We need to find the product of :
[tex]\mleft(4y-3\mright)\mleft(2y2+3y-5\mright)[/tex]So, the result as following:
[tex]\begin{gathered} \mleft(4y-3\mright)\mleft(2y^2+3y-5\mright) \\ =4y\cdot(2y^2+3y-5)-3\cdot(2y^2+3y-5) \\ =8y^3+12y^2-20y-(6y^2+9y-15) \\ =8y^3+12y^2-20y-6y^2-9y+15 \\ \\ =8y^3+6y^2-29y+15 \end{gathered}[/tex]So, the answer is the option 4. 8y3 + 6y2 − 29y + 15
A store is having a " 15 % off sale on perfume . You have a coupon for 50 % off any perfume . What is the final price , in dollars , of a $ 30 bottle of perfume ? If necessary round your answer to the nearest cent .
ANSWER
$12.75
EXPLANATION
The store is selling the perfumes at 15% off the original price, so if a bottle of perfume costs $30, then they are selling it at,
[tex]30\cdot\frac{100-15}{100}=30\cdot\frac{85}{100}=30\cdot0.85=25.50[/tex]But you also have a coupon for 50% off, so you get to buy the perfume at half that price,
[tex]25.50\cdot\frac{50}{100}=25.50\cdot0.5=12.75[/tex]Hence, the final price of the perfume is $12.75.
The vertices of a figure are A(1, -1), B(5, -6), and C(1, - 6). Rotate the figure 90° counterclockwise about the origin. Find the coordinates of the image. Polygon
A'(1,1)
B' (6,5)
C' (6,1)
Explanation
Step 1
Let
A(1,-1)
B(5,-6)
C(1,-6)
Step 2
find the image (A'B'C')
When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
Hence
[tex]\begin{gathered} A\mleft(1,-1\mright)\rightarrow A^{\prime}(1,1) \\ B(5,-6)\rightarrow B^{\prime}(6,5) \\ C(1,-6)\rightarrow C^{\prime}(6,1) \end{gathered}[/tex]so, the coordinates of the image are
A'(1,1)
B' (6,5)
C' (6,1)
I hope this helps you
A gift wrapping store has 8shapes of boxes, 14types of wrapping paper, and 12 different bows. How many different options are available at this store?
If a gift wrapping store has 8shapes of boxes, 14types of wrapping paper, and 12 different bows. The number of different options that are available at this store is 1344.
How to find the different options?Using this formula to determine the number of different options
Number of different options available = Number of shapes of boxes × Number of wrapping paper × Number of different bowl
Let plug in the formula
Number of different options available = 8 × 14 × 12
Number of different options available = 1,344
Therefore we can conclude that 1,344 different options are available.
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Barbara puts $500.00 into an account to use for school expenses. the account earns 14% interest, compounded annually. how much will be in the account after 7 years?use the formula A= P ( 1 + ).where A is the balance (final amount), p is the principal ( starting amount), r is the Internet rate express as a decimal, n is number of time per year that the interest is compounded, and T is the time in years. Round, your answer to the nearest cent
the formula is:
A = P( 1 + r/n )^nt
then solve:
[tex]undefined[/tex]jonathans science class places weights on a scale during an experiment. each weight weighs 0.2 kilograms. if the class puts 16 weights on the scale at the same time, what will the scale read?
Given the scale reading:
Each weight weighs 0.2 kilograms
If the class put 16 weights on the scale
Then the scale reading will be
[tex]\begin{gathered} 1\text{ weight -}\longrightarrow\text{ 0.2 kg} \\ 16\text{ weight -}\longrightarrow\text{ x} \\ x=16\times0.2 \\ x=3.2\operatorname{kg} \end{gathered}[/tex]Hence the scale reading will be 3.2kg