Note that the graph of the function f(x) = a(b)^x is attached accordingly. Here a = 8 and b = 5
How is this so?f(x) = a(b^x)......1
from the graph we can see that
When x = 0, y = 8
f(0) = 8
8 = a(b^0)
8 = a x 1
a = 8
f(1) = 4
4 = a(b^1)
4 = ab
8b = 4
b = 0.5
Thus a = 8 and b = 5
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Full Question:
Another copy machine also has the ability to reduce image dimensions, but by a different percentage. This graph shows the results found when copying a design x times. Use the graph to write the equation modeling this relationship
Enter the correct answer in the box by replacing the values of a and b.
f(x) = a(b)^x
Need answer ASAP please!
What is the total perimeter
Answer:
12 + 3 + 12 + (1/2)π(3) = 27 + (3/2)π ft
= 31.71 ft
The equation y = 2x2 – 4x – 3 models the cross-section of a sculpture that sits in the water, where x is horizontal distance, and y is height above sea level. At what two x-values is the sculpture at sea-level?
The two x-values where the sculpture at sea-level are x = 2.581 and x = -0.581
At what two x-values is the sculpture at sea-level?From the question, we have the following parameters that can be used in our computation:
y = 2x^2 - 4x - 3
When the sculpture at sea-level, the value of y is 0
So, we have
2x^2 - 4x - 3 = 0
When solved graphically, we have
x = 2.581 and x = -0.581
Hence, the x values are x = 2.581 and x = -0.581
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Graph the system below and write its solution.
x+3y=-6
Note that you can also answer "No solution" or "Infinitely many" solutions.
Solution:
0
solution
The number of solutions of the system of equations in this problem is given as follows:
Infinitely many solutions.
How to obtain the solution of the system of equations?The system of equations for this problem is defined as follows:
x + 3y = -6.y = -x/3 - 2.Writing the second equation in standard format like the second, we have that:
x/3 + y = -2.
Multiplying by 3:
x + 3y = -6.
The two equations are equal, meaning that the system has an infinite number of solutions, and the two equations are the same on the graph.
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In a football tournament, each team plays exactly 19 games. Teams get 3 points for every win and 1 point for every tie. At the end ot the tournament, Team Olympus got a total of 28 points. From the following options, how many times could Team Olympus have tied? 3, 4, 2, 5, 0?
The number of times the Team Olympus could have tied is not given in the below options
Given data ,
Let's use "W" for the number of victories and "T" for the number of ties. The information available indicates that Team Olympus played 19 games and earned a total of 28 points.
Team Olympus receives three points for each victory, so three victories would result in a total of nine points.
Team Olympus receives one point for each tie, making the sum of the tie-related points (T) equal to one times the number of ties.
We may construct the following equation using the information provided:
3W + 1T = 28 be equation (1)
Now , Since Team Olympus played 19 games in total, the total number of games (W + T) should be equal to 19.
W + T = 19 be equation (2)
Subtracting equation (2) from equation (1) , we get
2W = 9
Divide by 2 on both sides , we get
W = 4.5 wins
And , the supplied possibilities (3, 4, 2, 5, 0) do not add up to a total of 28 points, hence none of them are acceptable answers for Team Olympus.
Hence , in this situation, Team Olympus could not have tied many times
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math project : I need an interesting project idea for mathematics that can relate 3 different topics, I should write a full research paper related on the topic this are some examples related to the project
You must state a question that you would like to answer. This must be a specific question within your topic and should be explored thoroughly to create a complete paper.
Examples:
(i) How can we use Mathematical/Calculus-based tools to study the spread of COVID-19?
(ii) Designing a new Mathematical/Calculus-based model to analyze the spread of COVID-19
(iii) How many entrances should there be at Expo to accommodate all visitors?
(iv) How much water does the UAE need in order to sustain its ever changing population? (i.e. comparing water usage vs. water production)
Literature review:
You must show using multiple references and sources of the current literature on your given topic. This does NOT imply that information is simply copied from the internet but rather you must present a comprehensive review and summary of the latest research on your topic. It is suggested that you chose a specific aspect of your topic in order to include all required elements.
Examples:
(i) Review of the existing Mathematical/Calculus-based models used to analyze the spread of COVID-19
(ii) Review of existing Mathematical/Calculus-based models and calculations regarding risk insurance.
A mathematics topic that van be looked into is how linear algebra, graph theory and optimization can be used on the airline industry.
How to explain the informationIn this case, to solve the scheduling issues faced by airlines such as planning flights, assigning planes and crews to routes - mathematical techniques can be employed.
By leveraging Linear Algebra, operators can simulate the flow of aircrafts and passengers while Graph Theory can help model flight schedules and aircraft routes.
Simultaneously using Optimization techniques in the problem-solving process can work to streamline various operations resulting in reduced costs and improved efficiency which can increase profit margins.
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HELP ME PLEASE ITS DUE TODAY!!! The following data shows the number of times a class of 7th graders ate breakfast over a 30-day period.
{4, 18, 22, 25, 15, 12, 22, 14, 19, 30, 24, 20, 21, 24, 29, 16, 20, 27, 24, 25}
Part A: Determine the best graphical representation to display the data. Explain why the type of graph you chose is an appropriate display for the data. (2 points)
Part B: Explain, in words, how to create the graphical display you chose in Part A. Be sure to include a title, axis label(s), scale for axis if needed, and a clear process of how to graph the data. (2 points)
The best graphical representation to display the data would be a Histogram. This is appropriate because it will display the distribution and frequency of the grades, thus making it easy to compare the classes. To create the graph, you will use bars to depict the range of figures. This is on the x-axis while the y-axis will contain the frequency of occurrence.
How to design a histogramDesigning a histogram requires an understanding of the range of values, the frequency of occurrence, and the general picture that the graph is meant to paint in the mind of the reader.
So, for the histogram above, you can have a title like The distribution of 7th graders' breakfast over a 30-day period. Next, you label the x and y axis and plot the figures based on the information provided.
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On January 1, a company issued a $500,000, 10%, 8-year bond payable, and received proceeds of $487,000. Interest is payable each June 30 and December 31. The total interest expense on the bond over its eight-year life is $400,000. True or False?
Show working
True. The total interest expense on the bond over its eight-year life is $400,000.
What is the total interest?The total interest expense on the bond is calculated as follows;
Annual interest payment = face value of bond x annual interest rate
= $500,000 x 10%
= $50,000
Semi-annual interest payment = Annual interest payment / 2
= $50,000 / 2
= $25,000
The total interest expense over the bond's life is then calculated as:
Total interest expense = Semi-annual interest payment x Number of semi-annual periods
= $25,000 x 16
= $400,000
Therefore, the statement is true.
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A fair, 6-sided die is rolled 60 times. Predict how many times it will land on a number greater than 2. 60 40 20 two thirds
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 15(0.94)
The exponential function in this problem represents a decay, with a percentage rate of 6%.
How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function is classified as growth or decay as follows:
Growth: |b| > 1.Decay: |b| < 1.The function in this problem is defined as follows:
y = 15(0.94)^x.
As |b| = 0.94 < 1, the function is a decay function, and the rate is obtained as follows:
1 - r = 0.94
r = 1 - 0.94
r = 0.06
r = 6%.
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The height of an arch x meters to the right of the center is 1/10(x^2-36). What is the height of 3 meters to the left of the center when x=-3
The height of 3 meter to the left of the center of arch is -2.7 meters which is found by the evaluation of the given equation when x = -3.
We can solve it through
The Height at x = -3 meters on the left of the center = [tex](1/10)(-3^2 - 36) [by Substituting x = -3]= (1/10)(9 - 36)= (1/10)(-27)= -2.7 meters[/tex]
At the end height of the arch at 3 meters to the left of the center when x = -3 is -2.7 meters. This negative value means the point is actually below the ground level at that position. So the height is -2.7 meters where - insists negative value.
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can someone help me with number 1 through 4
1. 13 cm
2. 27.2 in
3.24x
4. 7 m
radius is half of the diameter
diameter is twice of the radius so
radius=diameter/2,diameter =2x radius
Dmitry Mendeleyev and his wife obtained a 30-year, $210,000 mortgage loan from
Community Bank. The interest rate is 6.5%. Their monthly payment is $1,362.06. For the first payment, what is the amount of the interest, payment to principal, and new principal?
The amount of the interest, payment to principal, and new principal for the first payment is solved
Given data ,
Let the loan amount = $ 210,000
Let the interest rate r = 6.5 %
Let the monthly payment be = $ 1,362.06
Now , On calculating the monthly interest rate
Monthly interest rate = 0.065 / 12 = 0.00542 or 0.542%
Calculate the interest amount
Interest amount = 0.00542 x $210,000 = $1,138.20
Calculate the payment to principal
Payment to principal = $1,362.06 - $1,138.20 = $223.86
Calculate the new principal balance
New principal balance = $210,000 - $223.86 = $209,776.14
Hence , for the first payment, the amount of interest is $1,138.20, the payment to principal is $223.86, and the new principal balance is $209,776.14
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Need help with these math problems , I know #2 is on the arrow looking on is original is A = 36 units^2 and scale drawing is A = 9 units^2, just don’t know how I got it.
The areas of the figures are 36 square units & 9 square units and the scale factor of dilation is 1/2
Estimating the areas of the figuresFrom the question, we have the following parameters that can be used in our computation:
The composite figures
The areas of the figure is calculated using the sum of the individual areas
So, we have
Figure 1 = Rectangle + Triangle
Using the area formulas, we have
Figure 1 = 5 * 4 + 1/2 * 8 * 4
Evaluate
Figure 1 = 36
The second figure is not clear
However, from the question text we have the area to be
Figure 2 = 9
So, the scale factor from figure 1 to 2 is
Scale factor = √[Figure 2/Figure 1]
This gives
Scale factor = √[9/36]
Evaluate
Scale factor = 1/2
Hence, the scale factor is 1/2
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Y varies inversely as x. If x = 8 then y = 6. FInd y when x = 2.
Y=
Answer: If y varies inversely as x, then:
y = k/x
where k is a constant of proportionality. To find k, we can use the initial condition that y = 6 when x = 8:
6 = k/8
Solving for k, we get:
k = 48
Now we can use this value of k to find y when x = 2:
y = 48/2 = 24
Step-by-step explanation:
Problem
Look at the image below.
Find the area of the parallelogram.
square units
The area of the parallelogram is A = 72 units²
Given data ,
Let the parallelogram be represented as ABCD
Now , the height of the parallelogram is = 12 units
The base of the parallelogram = 6 units
And , area of parallelogram A = base x height
On simplifying , we get
A = 12 x 6
A = 72 units²
Hence , the area is A = units²
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Elijah wrote two numbers that follow the rules in box below. Both numbers are less than 10. Both numbers are whole numbers. The least common multiple of th numbers is 18. The greatest common factor of the number is 3.
Answer:
2,3,6 is answer for this question
Kevin has money in two savings accounts. One rate is 8% and the other is 12%. If he has $450 more in the 12% account and the total interest is $176, how much is invested in each savings account?
Answer:
8%: $61012%: $1060Step-by-step explanation:
You want the amounts in each of two accounts, one earning 8% interest, and the other, with an initial balance that is $450 greater, earning 12% interest. The total interest earned is $176.
SetupLet x represent the initial balance in the 12% account. Then the initial balance in the 8% account is (x -450). The total interest earned is ...
0.08(x -450) +0.12(x) = 176
Solution0.20x - 36 = 176 . . . . . simplify
0.20x = 212 . . . . . . add 36
x = 1060 . . . . . . divide by 0.2
x -450 = 610
The 8% account had $610 invested; the 12% account had $1060 invested.
The data shows the weight of the potting soil brought by each student. Draw a line plot and answer the questions below. 1 1/2 kg 3/4 kg 1 1/2 kg Title: 1 kg 1 1/2 kg 2 kg 3/4 kg 2 kg 3/4 kg Roading and Math for K-5 2 kg 2 kg 2 kg 2 1/2 kg 3/4 kg 1 kg 1. How many students brought 3/4 kg of soil? 2. How many students brought less than 1 1/2 kg? 3. How many students brought 1 kg or more? 4. How many fewer students brought 1 kg than 2 kg? 5. How many students brought more than 1 1/2 kg but less than 2 1/2 kg? 6. How much soil was brought by all the students together?
Answer:
|
| 3/4 kg
| x
|
| x
| x
| x
| x
| x
| x
|_________
1 kg 1 1/2 kg 2 kg 2 1/2 kg
Two students brought 3/4 kg of soil.
Four students brought less than 1 1/2 kg of soil (the ones who brought 3/4 kg and the one who brought 1 kg).
Eight students brought 1 kg or more of soil.
Two fewer students brought 1 kg than 2 kg (two students brought 1 kg and four students brought 2 kg).
Two students brought more than 1 1/2 kg but less than 2 1/2 kg (the ones who brought 2 kg).
The total amount of soil brought by all the students is:
Copy code
1 1/2 kg + 3/4 kg + 1 1/2 kg + 1 kg + 2 kg + 3/4 kg + 2 kg + 2 kg + 2 kg + 2 1/2 kg + 3/4 kg
= 19 3/4 kg
Step-by-step explanation:
Answer:
Step-by-step explanation:
it is timed by 1 1/2kg
A contractor can by two types of wood. she got 45 expensive wood and 60 cheap wood for the same total price. if the 45 expensive wood cost $3.00 more than the 60 cheap wood, then which equation below shows the correct relationship between the 2 types of wood that she purchased. Also (x =price of the 60 cheap wood)
A.45(x+3)=60x
B.45(x-3)=60x
C.60(x-3)=45x
D.60(x+3)=45x
The base of a box is 8 Square centimetres and its height is 10cm. Find its volume
Answer:
80 cm³
Step-by-step explanation:
Volume = w x l x h = width x length x height
You already know the area of the base: w x l = 8 cm², so the volume is:
V = 8 cm² x 10 cm = 80 cm³
A bag of apples weighs 8 7 8 pounds. A crate of bananas is 6 times as heavy as the apples. How much heavier are the bananas than the apples?
The crate of bananas is heavier than the bag of apples by 53 1/4 pounds.
How much heavier are the bananas than the apples?An apple and a banana are both kinds of fruits. They both weigh differently.
Weight of a bag of apple = 8 7/8 pounds
Weight of a crate of bananas = 6 times as heavy as the apples
= 6 × 8 7/8
= 6 × 71 /8
= 426 / 8
= 53 1/4 pounds
Therefore, the weight of a crate of bananas is 53 1/4 pounds
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Identify a fraction that is greater. than five-eighths and less than thirteen-eighths. Write the fraction using three different forms.
One of the fractions is 7/8 and can be written as
decimal notation of 0.875, percent representation at 87.5%, and fraction form = 7/8 How to find the fractionInformation made available in the question includes
a fraction that is greater. than five-eighths and less than thirteen-eighthsMathematically this is written as
assuming the number is x
five-eighth = 5/8thirteen-eighths = 13/85/5 < x < 13/8
For fractions greater than five eighths but lesser than thirteen eighths is seven eighths (7/8) within the two.
This fraction can be expressed in three unique forms which include:
decimal notation of 0.875,
percent representation at 87.5%, and
fraction form = 7/8
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Express each of the following as a function or 15°:
1. sin195°
2. cos75°
3. tan345°
4. sin105°
5. sin225°
You can express sin195° as -sin15° by using the trig identities.
Here is how to simplify trigWe will be applying trig identities to solve this question
sin195°:
Recall that:
sin(x + 180°) = -sin(x)
then:
sin(195°) = sin(15° + 180°) = -sin(15°)
Therefore,
sin(195°) = -sin(15°).
cos75°:
Recall that:
cos(x) = sin(90° - x)
then:
cos(75°) = sin(90° - 75°) = sin(15°)
Therefore,
cos(75°) = sin(15°)
tan345°:
Recall that:
tan(x + 180°) = tan(x)
then:
tan(345°) = tan(15° + 330°) = tan(15°)
Therefore,
tan(345°) = tan(15°)
sin105°:
Recall that:
sin(x + 90°) = cos(x)
then:
sin(105°) = cos(15°)
Therefore,
sin(105°) = cos(15°).
sin225°:
Recall that:
sin(x + 180°) = -sin(x)
then:
sin(225°) = sin(45° + 180°) = -sin(45°)
Therefore,
sin(195°) = -sin(15°).
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Question is below ⬇️.
The missing statement about base angles of the isosceles trapezoid is ∠TPR ≅ ∠ TAR.
What is the missing statement about the trapezoid?
The base angles of isosceles trapezoids are congruent.
In an isosceles trapezoid, the base angles (the angles formed by one of the bases and a leg) are congruent.
Since the opposite angles in an isosceles trapezoid are congruent, the base angles must also be congruent.
In the given diagram, we will identify the base angles as follows;
∠TPR ≅ ∠ TAR
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Lee watches TV for 3 hours per day. During that time, the TV consumes 250 watts per hour. Electricity costs (18 cents)/(1 kilowatt-hour). How much does Lee's TV cost to operate for a month of 30 days?
Lee's TV costs $4.05 to operate for a month of 30 days.
To calculate the cost of operating Lee's TV for a month, we need to find out the total number of kilowatt-hours (kWh) of electricity consumed by the TV during that time.
First, let's find out how many watts Lee's TV consumes in a day:
250 watts/hour x 3 hours/day = 750 watts/day
To convert this to kilowatts, we divide by 1000:
750 watts/day ÷ 1000 = 0.75 kilowatts/day
Now, we can calculate the total number of kilowatt-hours consumed by the TV in a month:
0.75 kilowatts/day x 30 days = 22.5 kilowatt-hours
Finally, we can calculate the cost of operating the TV for a month:
22.5 kilowatt-hours x 18 cents/kilowatt-hour = $4.05
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For each relation, decide whether or not it is a function.
Answer:
relation 1-function
relation 2-not a function
relation 3-function
relation 4-funtion
Trigonometry. Can someone help? (Do as many as you can please)
Answer:
1) Let x be the distance from Alberto to the base of the building. Using trigonometry, we have:
tan(70) = 40 / (x + 6)
x + 6 = 40 / tan(70)
x = 40 / tan(70) - 6
x ≈ 11.1 feet
Therefore, Alberto is about 11.1 feet away from the base of the building.
2) Let h be the height of the building. Using trigonometry, we have:
tan(θ) = h / (100 + 1.55)
h = (100 + 1.55) tan(23)
h ≈ 42.9 feet
Therefore, the height of the building is about 42.9 feet.
3) Let θ be the angle of elevation for each ramp. Using trigonometry, we have:
sin(θ) = 22 / 122
θ = sin⁻¹(22/122)
θ ≈ 10.3 degrees
Therefore, the measure of the angle of elevation for each ramp is about 10.3 degrees.
4) Let d be the distance from the boat to the base of the lighthouse. Using trigonometry, we have:
tan(28) = 40 / d
d = 40 / tan(28)
d ≈ 78.5 feet
Therefore, the distance from the base of the lighthouse to the boat is about 78.5 feet.
5) Let x be the distance from General Han Xin's position to the palace. Using trigonometry, we have:
tan(35) = x / 800
x = 800 tan(35)
x ≈ 595.4 meters
Therefore, the palace is about 595.4 meters away from General Han Xin's position.
6) Let h be the height of the clouds. Using trigonometry, we have:
tan(80) = h / 165
h = 165 tan(80)
h ≈ 702.4 meters
Therefore, the clouds are about 702.4 meters high.
Step-by-step explanation:
please i need
thank you so much
Step-by-step explanation:
Similar triangle ratio:
15 is to 10 as AB is to 6
15/10 = AB / 6
6 * 15/10 = AB = 9 units
Q14 20 students take a maths test. Their tutor records the scores. The list below shows
their scores:
15, 24, 6, 8, 29, 6, 12, 17, 24, 22, 25, 30, 18, 3, 11, 7, 18, 27, 28, 27
Present these scores in three suitable groups
The scores of the maths students recorded by their tutor presented in three suitable groups are 1 - 10, 11 - 20, 21 - 30.
How to present scores in groups?Math test scores: 15, 24, 6, 8, 29, 6, 12, 17, 24, 22, 25, 30, 18, 3, 11, 7, 18, 27, 28, 27
The group of scores when divided into 3;
Group frequency
1 - 10 5
11 - 20 6
21 - 30 9
Therefore, the groups 1 - 10, 11 - 20, 21 - 30 have the frequency 5, 6 and 9 respectively.
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I need help with this please
Answer:
Multiply row 1 by 1/7
The resulting matrix is
[tex]\begin{pmatrix}1&-\frac{4}{7}&\frac{8}{7}\\ -12&7&-13\end{pmatrix}[/tex]
Step-by-step explanation:
Original matrix is
[tex]\begin{pmatrix}7&-4&8\\ -12&7&-13\end{pmatrix}[/tex]
Multiplying any one row by a nonzero scalar is a valid matrix operation. This will not affect the final solution of the matrix
So all we have to do is to multiply row 1 by 1/7 and you get a 1 in row 1, column 1
[tex]R_1 \times \dfrac{1}{7} \longrightarrow \begin{pmatrix}1&-\frac{4}{7}&\frac{8}{7}\\ -12&7&-13\end{pmatrix}[/tex]