Answers
Answer:
f(x) = 2[tex](\frac{1}{3}) ^{x}[/tex]
Step-by-step explanation:
exponential in the form
f(x) = C[tex]a^{x}[/tex]
to find C and a use points from the graph
using (0, 2 ) , then
2 = C[tex]a^{0}[/tex] ( [tex]a^{0}[/tex] = 1 ) , so
C = 2
f(x) = 2[tex]a^{x}[/tex]
using (2, [tex]\frac{2}{9}[/tex] )
[tex]\frac{2}{9}[/tex] = 2a² ( divide both sides by 2 )
[tex]\frac{1}{9}[/tex] = a² ( take square root of both sides )
[tex]\sqrt{\frac{1}{9} }[/tex] = a ⇒ a = [tex]\frac{1}{3}[/tex]
f(x) = 2 [tex](\frac{1}{3}) ^{x}[/tex] ← exponential function
Related Questions
You must show your work.
Answers
A data set of monthly expediture rounded to the nearest dollar and cure at coffee shop by a sample of 700 household has a minimum value of 4 and a maximum value of 210 suppose we want to group these data into 6 classes of equal with assuming we take the lower limit of the 1st class as one and the upper limit of the sick class as 210 determine the class limit boundaries and midpoint for a group quantitive data table
Answers
EXPLANATION
Number of households = 700
Minimum value = $4
Maximum value = $210
Dividing this by the upper limit by by the needed number of classes: 210/ 6 = 35
The width of each class is 35.
Class width = 35
Class Limits Lower Boundary Upper Boundary Class midpoint
1 to 35 0.5 35.5 36/2 = 18
36 to 70 35.5 70.5 106/2= 53
71 to 105 70.5 105.5 176/2= 88
106 to 140 105.5 140.5 246/2= 123
141 to 175 140.5 175.5 316/2= 158
176 to 210 175.5 210.5 386/2= 193
convert 62°F to degree Celsius if necessary round to the nearest 10th of a degreeC=5/9 (F-32)F=9/5 C + 32
Answers
Given the following question:
Using the formula:
[tex]undefined[/tex]Using Euler’s formula, how many edges does a polyhedron with 9 faces and 14 vertices have? Thank you
Answers
Solve the Euler's formula above to E (Edges)
[tex]\begin{gathered} \text{Substract 2 in both sides of the equation;} \\ \\ F+V-2=E+2-2 \\ F+V-2=E \\ \\ \text{ Rewrite the equation:} \\ \\ E=F+V-2 \end{gathered}[/tex]Use the given data;
Faces; F=9
Vertices: V=14
[tex]\begin{gathered} E=9+14-2 \\ E=21 \end{gathered}[/tex]The polyhedron has 21 edgesMarks wants to paint a mural. He had 1 1/5 gallons of yellow paint, 1 1/6 gallons of green paint and 7/8 gallon of blue paint. Mark plan to use 3/4 gallons of each paint color. How many gallons of paint will he have left painting the mural?
Answers
Yello paint: 1 1/5
Green paint: 1 1/6
Blue paint: 7/8
After using 3/4 of each paint color, we have
- Yellow:
[tex]\begin{gathered} 1+\frac{1}{5}-\frac{3}{4} \\ \frac{5}{5}+\frac{1}{5}-\frac{3}{4} \end{gathered}[/tex]The least common multiple of 5 and 4 is 20, then...
[tex]\begin{gathered} \frac{5\cdot4}{5\cdot4}+\frac{1\cdot4}{5\cdot4}-\frac{3\cdot5}{4\cdot5} \\ \frac{20}{20}+\frac{4}{20}-\frac{15}{20} \\ \frac{20+4-15}{20} \\ \frac{9}{20} \end{gathered}[/tex]So, for yellow paint, we will have 9/20 gallons
- Green:
[tex]\begin{gathered} 1+\frac{1}{6}-\frac{3}{4} \\ \frac{6}{6}+\frac{1}{6}-\frac{3}{4} \end{gathered}[/tex]The LCM of 6 and 4 is 12
[tex]\begin{gathered} \frac{6\cdot2}{6\cdot2}+\frac{1\cdot2}{6\cdot2}-\frac{3\cdot3}{4\cdot3} \\ \frac{12}{12}+\frac{2}{12}-\frac{9}{12} \\ \frac{12+2-9}{12} \\ \frac{5}{12} \end{gathered}[/tex]So, for green paint, we will have 5/12 gallons
- Blue:
[tex]\frac{7}{8}-\frac{3}{4}[/tex]LCM of 4 and 8 is 8
[tex]\begin{gathered} \frac{7}{8}-\frac{3\cdot2}{4\cdot2} \\ \frac{7}{8}-\frac{6}{8} \\ \frac{7-6}{8} \\ \frac{1}{8} \end{gathered}[/tex]So, for blue paint, we will have 1/8 gallons
Now, we add them upp in order to obtain our anwser:
[tex]\frac{9}{20}+\frac{5}{12}+\frac{1}{8}[/tex]The LCM of 8, 12 and 20 is 120
[tex]\begin{gathered} \frac{9\cdot6}{20\cdot6}+\frac{5\cdot10}{12\cdot10}+\frac{1\cdot15}{8\cdot15} \\ \frac{54}{120}+\frac{50}{120}+\frac{15}{120} \\ \frac{54+50+15}{120} \\ \frac{119}{120} \end{gathered}[/tex]In conclusion, he will have left 119/120 gallons of paint
Evaluate the expression when a=-5 and c=27c-a
Answers
Given:
7c - a
a=-5 and c = 2
Substitute the values into the expression
7(2) - (-5)
=14 + 5
= 19
The sale Price of a swing set is $90. What is the original price?Sale:75% Round your answer to the whole dollar
Answers
To solve this problem we can use the expression that defines percents. What price has a 75% of $90?
[tex]\text{Total}\cdot\frac{\text{percent}}{100}=\text{equivalent number to the percent}[/tex]With the information given, we know that the equivalent number to the percent is $90 and the percent is 75%.
Then, substitute and solve for the total variable:
[tex]\begin{gathered} \text{Total}\cdot\frac{75}{100}=90 \\ \text{Total}=\frac{90\cdot100}{75} \\ \text{Total}=120 \end{gathered}[/tex]The original price of the swing set is $120.
1) Find the equation of the line through the points (-2, 5) and (3, 1). Also, graph this line.
Answers
Answer
The equation of the line is
y - 5 = -0.8 (x + 2)
We can then simplify further
y - 5 = -0.8x - 1.6
y = -0.8x - 1.6 + 5
y = -0.8x + 3.4
Explanation
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
So, for this, we just need to solve for the slope and use one of the two points given to find the equation of the line.
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (-2, 5) and (3, 1)
x₁ = -2
y₁ = 5
x₂ = 3
y₂ = 1
[tex]\text{Slope = }\frac{1-5}{3-(-2)}=\frac{-4}{3+2}=\frac{-4}{5}=-0.8[/tex]Recall
y - y₁ = m (x - x₁)
m = slope = -0.8x
(x₁, y₁) = point = (-2, 5)
x₁ = -2
y₁ = 5
y - y₁ = m (x - x₁)
y - 5 = -0.8 (x - (-2))
y - 5 = -0.8 (x + 2)
We can then simplify further
y - 5 = -0.8x - 1.6
y = -0.8x - 1.6 + 5
y = -0.8x + 3.4
Hope this Helps!!!
Select the correct choice and fill in the blank if necessary
Answers
Given
[tex]f(x)=\frac{x+6}{x-7}[/tex]Recall
The horizontal line test can be used to determine if a function is one-to-one given a graph. Simply superimpose a horizontal line onto a graph and see if it intersects the graph at more than one point. If it does, the graph is not one-to-one and if it only intersects at one point, it will be one-to-one.
The graph
It passed the horizontal line test, therefore is one to one function
Part B
[tex]f(x)=\frac{x+6}{x-7}[/tex]Step 1
Replace f(x) with y
[tex]y=\frac{x+6}{x-7}[/tex]Step 2
Inter change y and x
[tex]x=\frac{y+6}{y-7}[/tex]Step 3
Make y the subject
[tex]\begin{gathered} x=\frac{y+6}{y-7} \\ x(y-7)=y+6 \\ xy-7x=y+6 \\ xy-y=6+7x \\ y(x-1)=6+7x \\ divide\text{ both sides by x-1} \\ y=\frac{6+7x}{x-1} \end{gathered}[/tex]Step 4
Replace y with f^-1
[tex]f^{-1}(x)=\frac{6+7x}{x-1}[/tex]The final answer
[tex]f^{-1}(x)=\frac{6+7x}{x-1}[/tex]Scores on a standardized reading test for fourth-gradestudents form a normal distribution with µ = 60 ando = 20. What is the probability of obtaining a sample mean greater than M = 65 for each of the following?a. A sample of n = 16 studentsb. A sample of n = 25 studentsc. A sample of n = 100 students
Answers
If scores on a standardized reading test form a normal distribution with (µ = 60) and (σ = 20), then the probability of obtaining a sample mean greater than (M = 65) for a sample size of (n = 16) will be .
As per the question statement, Scores on a standardized reading test for fourth-grade students form a normal distribution with (µ = 60) and (σ = 20),
And we are required to calculate the probability of obtaining a sample mean greater than (M = 65) for a sample size of (n = 16).
To solve this question, let us assume that, a random variable "X" follows normal distribution with mean (μ = 60), standard deviation (σ = 20) and a sample size of (n = 16).
Then the probability that a sample of size (n = 16) is randomly selected with a mean greater than 65 can be calculated as follows:
P(M > 65) = [1 - P(M < 65)]
= [1 - P{(M - μ)/(σ/√n) < (65 - 60/(20/√16)}]
= [1 - P{(M - μ)/(σ/√n) < (65-60)/(20/4)}]
= [1 - P{Z < (5/5)}]
= [1 - P(Z < 1)]
= (1 - 0.841344746069)...[Using Excel Function "NORMSDIST (1)]
= 0.158655253931
≈ 0.16
Probability: Probability is the branch of mathematics that deals with the numerical descriptions on the extent to which an event is likely to occur, or how likely it is, that a proposition is true, being calculated by the ratio of the favorable cases to the total number of cases possible.To learn more about Samples and Probability, click on the link below.
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Select the correct answer. Describes the zeros of the graphed function.
Answers
Answer
The function has 3 distinct roots (OPTION A)
SOLUTION
Problem Statement
The question gives us a graph and we are required to find the number of zeros the function has.
Method
- The number of zeros a function has corresponds to the number of times the graph crosses the x-axis. If the graph crosses the x-axis once then there is one zero. If it crosses the x-axis twice, then it has 2 zeros.
- The number of zeros a function has also depends on the way the graph touches the x-axis. If the graph touches the x-axis like a quadratic, then there are 2 zeros or zeros that are multiples of 2, that have the same value.
Implementation
The following can be observed from the figure given to us:
- The graph crosses the x-axis twice at x = -2 and x = 2. This means that the graph has at least 2 zeros.
- The graph curves like a quadratic at x = 0. This means that there are at least 2 zeros of the same value or zeros of the same value.
Thus, we can predict that the function must be:
[tex]x^2\mleft(x-2\mright)\mleft(x+2\mright)[/tex]
Final Answer
The answer is:
The function has 3 distinct roots (OPTION A)
If cos A = 35/37 and sin B = 9/41 and angles A and B are in Quadrant I, find the valueof tan(A - B).
Answers
The given expression is tan(A - B)
Since tan (A - B) is equal to
[tex]\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\tan B}\rightarrow(1)[/tex]Since the values of cos A and sin B are
[tex]\begin{gathered} \cos A=\frac{35}{37} \\ \sin B=\frac{9}{41} \end{gathered}[/tex]We will use the rules
[tex]\begin{gathered} \tan ^2A=\sec ^2A-1\rightarrow(2) \\ \cot ^2B=\csc ^2B-1\rightarrow(3) \end{gathered}[/tex]csc B = 1/sin B, cot B = 1/tan B, sec A = 1/cos A
[tex]\begin{gathered} \csc B=\frac{1}{\frac{9}{41}}=\frac{41}{9} \\ \sec A=\frac{1}{\frac{35}{37}}=\frac{37}{35} \end{gathered}[/tex]Substitute the value of csc B in rule (3) to find cot B
[tex]\begin{gathered} \cot ^2B=(\frac{41}{9})^2-1 \\ \cot ^2B=\frac{1600}{81} \\ \sqrt[]{\cot^2B}=\pm\sqrt[]{\frac{1600}{81}} \\ \cot B=\frac{40}{9} \end{gathered}[/tex]Reciprocal it to find tan B
[tex]\tan B=\frac{1}{\cot B}=\frac{9}{40}[/tex]Substitute the value of sec A in rule (2) to find tan A
[tex]\begin{gathered} \tan ^2A=(\frac{37}{35})^2-1 \\ \tan ^2A=\frac{144}{1225} \\ \sqrt[]{\tan^2A}=\pm\sqrt[]{\frac{144}{1225}} \\ \tan A=\frac{12}{35} \end{gathered}[/tex]Substitute the values of tan A and tan B in rule (1) above
[tex]\begin{gathered} \tan (A-B)=\frac{\frac{12}{35}-\frac{9}{40}}{1+(\frac{12}{35})(\frac{9}{40})} \\ \tan (A-B)=\frac{165}{1508} \end{gathered}[/tex]The value of tan(A - B) is 165/1508
Simple probabilityYou draw a card at random from a deck that contains 3 black cards and 7 red cards.If necessary, round your answer to 2 decimal places.
Answers
The question says you draw a card at random from a deck that contains 3 black cards and 7 red cards.
What is the probability of drawing a black card?
Recall,
Probability = Number of possible outcome
Number of favorable outcome
There are 3 favorable outcomes (the 3 black cards)
There are 10 possible outcomes ( the 3 + 7 = 10 cards)
Therefore,
P(draw a black card) = 3/10
P(draw a black card) = 0.30 (to 2 decimal places)
Ryan earns $20 for every lawn that he mows. Which equation can be used to find t, the total amount Ryan will earn after mowing n lawns?
Answers
Ryan earns $20 for every lawn that he mows.
Let t represents the total amount Ryan will earn.
Let n repreents the number of laws Ryan will mow.
So, the equation becomes
[tex]t=20n[/tex]For example:
How much Ryan will earn if he mows 5 lawns?
Let us substitute n = 5 into the equation
[tex]\begin{gathered} t=20n \\ t=20(5) \\ t=\$100 \end{gathered}[/tex]Therefore, Ryan will earn $100 if he mows 5 lawns.
arch
Convert the following equation
into slope-intercept form.
-8x + y = -9
0
y = [? ] x + [
Copyright © 200g-2022 International Academy of Science. All Rights Reserved
Enter
0
Answers
The slope-intercept form of the given equation is y = 8x - 9
What is slope intercept form?
Using a straight line's slope and the location of its y-axis intersection, the slope-intercept equation can be used to determine the general equation of the line. Y = mx + b is the equation in slope-intercept form.
The slope-intercept form is y=mx+b, where
m is the slope and
b is the y-intercept.
Here, we have
Given equation = -8x + y = -9
Rewrite in slope-intercept form.
Add 8x on both sides of the equation and we get
y = -9 + 8x
y = 8x - 9
Hence, the slope-intercept form of the given equation is y = 8x - 9
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I need help with this practice I am having trouble with it The subject is trig
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given range
[tex](-\infty,-9\rbrack\cup\lbrack5,\infty)[/tex]STEP 2: Find the cosecant function
[tex]\begin{gathered} \text{The range of a cosecant function normally excludes the interval }(-1,1)\text{.} \\ The\text{ range in the question excludes the interval }(-9,5)\text{, which has a width 7 times as great.} \\ \text{Thus, we know the vertical factor is 7.} \\ \\ T\text{he midpoint of the excluded interval of the given function is }\frac{(-9+5)}{2}=-\frac{4}{2}=-2 \\ so\text{ that is the vertical translation.} \\ \text{The cosecant function normally has vertical asymptotes at }x=0\text{ and }x=\pi\text{ so the function is } \\ \text{expanded horizontally by a factor of }2. \end{gathered}[/tex]Hence, the cosecant function is
[tex]undefined[/tex]Question 3 1 pts A pair of designer sneakers was purchased for $120. Since they were purchased their price has increased by 15%. What is the new price, in dollars?
Answers
The new price after the increase of 15%
=120(100 + 15)%
=120 * 115%
= 120 * 115/100
= 138
The new price is $138
What was the total length of all the scarves put together?
Answers
ANSWER :
37.8 feet
EXPLANATION :
From the problem, each scarf is 50.4 inches long.
Since there's a total of 9 scarfs.
The total length will be :
[tex]9(50.4)=453.6\text{ }in[/tex]There are 12 inches in 1 foot.
Divide the result by 12 to get the number of feet.
[tex]\frac{453.6}{12}=37.8\text{ }feet[/tex]A group have in their families. The bar graph of adults were asked how many children they below shows the number of adults who indicated each number of children.How many adults were questioned?
Answers
If we add the frequencies of the histogram ( vertical axis), we get that the number of adults questioned is:
[tex]4+7+5+3+1=20.[/tex]Now, out of those 20, only 5 have 2 children, therefore:
[tex]\frac{5}{20}*100=25\%[/tex]have 2 children.
Answer:
20 adults were questioned,
25% have 2 children.
Septima invests $3,000 in an account with an annual interest rate of 5.2% compounded monthly for 3 years.What is the return on investment for Septima's account?16.8%1.3%14.4%5.3%
Answers
Given:
Principal, P=$3000
Interest rate, r=0.052
Years, t=3 years
To find the return amount is compounded monthly:
Using the formula,
[tex]\begin{gathered} A=P(1+\frac{r}{12})^{12t}_{} \\ =3000(1+\frac{0.052}{12})^{12\times3} \\ =3000(1+0.00433)^{36} \\ =3505.30 \end{gathered}[/tex]Hence, the return amount on investment is $3505.30.
In percentage,
The return on investment is,
[tex]\begin{gathered} \frac{3505.3}{3000}\times100=16.84 \\ \approx16.8\text{ \%} \end{gathered}[/tex]Hence, the answer is 16.8%.
Question 3 of 5Select the correct answer from each drop-down menu.The graph of function p represents the profit, in dollars, from concert ticket sales when the tickets are sold for x dollars each.
Answers
In order for the concert to make money, the graph must be above the x-axis, because they y-axis represents the profit. This happens in the interval:
[tex](20,120)[/tex]For the concert to lose money, the graph must be below the x-axis. This happens in two intervals:
[tex](0,20)\cup(120,\infty)[/tex]Line segment EF is shown on the coordinate grid:A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A line segment EF is shown with E as ordered pair 1, negative 4 and F as ordered pair 5, negative 4.The line segment is rotated by 270 degrees counterclockwise about the origin to form E′F′. Which statement describes E′F′? (1 point)E′F′ is equal in length to EF.E′F′ is half the length of EF.E′F′ is parallel to EF.E′F′ is twice the length of EF.
Answers
the initial coordinates of EF are:
[tex](1,-4),(5,-4)[/tex]then the segment is rotate 270 degrees counterclockwise so:
In a rotation the length do not change so the answer is A) E'F' is equal in length to EF
Elisa is driving at a speed of 65 miles per hour. Let h represent the number of hours that Elisa drives at this speed. Write an algebraic expression to represent the number of miles that Elisa travels during this time.(I NEED HELP NOW , I AM IN RISK OF A WHOOPING)
Answers
We have
Elisa travels 65 miles per hour
h is the number of hours
the al
solve the polynomials in standard form1) y=4x^4+7x^3-2x^3+5x^52) y=(x-3)^2-3(x-4)
Answers
The standard form of a polynomial contains no like terms and the exponents are in descending order (largest to smallest).
[tex]\begin{gathered} y=4x^4+7x^3-2x^3+5x^5 \\ \text{Std Form:} \\ y=5x^5+4x^4+7x^3-2x^3 \end{gathered}[/tex]6 cm Find the missing dimension of each figure. Round your answer to the nearest tenth. 5. V=252 ft 4. V=100 in 6 ft 12 in 14 ft rin. eft Find the volume of each composite figure. Round your answer to the nearest tenth. 6. 6 in. 7. A cylindrical-shaped hole is cut from 11 in. the center of a cube. 2.5 cm 15 in.solve #5 please
Answers
The volume of cuboid is V = 252 ft^3.
The width of cuboid is w = 14 ft.
The height of cuboid is h = 6 ft.
The formula for the volume of cuboid is,
[tex]V=l\cdot w\cdot h[/tex]Substitute the values in the formula to determine the length of cuboid.
[tex]\begin{gathered} 252=l\cdot14\cdot6 \\ l=\frac{252}{84} \\ =3 \end{gathered}[/tex]So length (missing dimension) of the cuboid is 3 ft.
The ratio of short to pants is 1:2 if there are eight shorts how many pants are there? 16,4,6,or 8
Answers
There are 16 pants
Explanation:Ratio of short to pants = 1:2
There are 8 shorts
Let x be the number of pants, then
8/x = 1/2
x = 8 * 2
= 16
There are 16 pants
Please help with this . I am really stuck on it.The graph shows how time required to ring up a customer is related to the number of items being purchased.If it takes 80 seconds to ring up a customer, how many items are purchased?
Answers
First, we have to find the slope of the line. Let's use the points (30, 60) and (40, 80). Using the slope formula, we have.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the points.
[tex]m=\frac{80-60}{40-30}=\frac{20}{10}=2[/tex]Then, we use one point, the slope, and the point-slope formula to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-60=2(x-30) \\ y-60=2x-60 \\ y=2x-60+60 \\ y=2x \end{gathered}[/tex]Then, we use this equation to find the items purchased for 80 seconds.
[tex]y=2\cdot80=160[/tex]Therefore, if it takes 80 seconds to ring up a customer, the number of items purchased is 160.The tree diagram below represents the relationships between the sets and subsets of real numbers. Real Numbers Rational Numbers {..., V2, e, , ...) ? Non-integer Rational Numbers {0, 1, 2, 3, ---) Whole Number Opposites Which group of numbers could replace the question mark in the tree diagram
Answers
The diagram starts with Real Numbers which comprehend all numbers except for complex numbers.
The second level is formed by rational numbers and irrational numbers.
The third level is formed by subsets of rational numbers non-integers rational numbers and integers rational numbers.
Therefore, the right answer is C. -7, 8, -4, since these numbers are rational and integers.Gary and his four friends wish to share 45 cards equally. how many cards will each person get
Answers
The number of persons including Gary and four friends is 5.
Determine the number of cards that each person get.
[tex]\begin{gathered} n=\frac{45}{5} \\ =9 \end{gathered}[/tex]So each person get 9 cards.
A 4-pint carton of soy milk costs $0.96. What is the price per cup?
Answers
The cost of per cup milk cartons is $ 0.24
Given price of a 4 pint carton = $ 0.96
thus to calculate the price of 1 carton
we would have to use unitary method
in unitary method ,
the cost of multiple or the cost of an item is given and we are supposed to find the cost of a single or multiple items respectively.
Here since the cost of 4 pint cartons are given
we will find the cost of 1 carton by dividing :
the cost of 4 pint cartons / number of cartons
thus we will get 0.96/4 = $ 0.24
Thus the cost of 1 carton is $ 0.24
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