Answers
Answer:
? = 13.7
Step-by-step explanation:
Right triangle equation A^2 + B^2 = C^2
7.6^2 + 11.4^2 =
57.76 + 129.96 = 187.72
find the square root of 187.72 by putting it in the calculator
187.72 = 13.70109485^2
Estimate = 13.7^2
Related Questions
abc is dilated by a scale factor of 4 with a center of dilation at the origin to form a’b’c’ then a’b’c’ is dilated by a scale factor of 3 over 4 with a center of dilation at the origin to create a’’b’’c’’ what are the coordinates of a’’b’’c’’
Answers
The coordinates of the vertices of the triangle A''B''C'' after the two successive dilations are (3 times the x-coordinate and 3 times the y-coordinate of the original triangle's vertices).
To find the coordinates of the vertices of the dilated triangle A''B''C'' after two successive dilations, first with a scale factor of 4 and then with a scale factor of 3/4.
Firstly, Apply the first dilation with a scale factor of 4 to the original triangle ABC, with a center of dilation at the origin. This can be done by multiplying each coordinate of the original triangle by 4.
The coordinates of the dilated triangle A'B'C' after the first dilation would be;
A' = (4 × x-coordinate of A, 4 × y-coordinate of A)
B' = (4 × x-coordinate of B, 4 × y-coordinate of B)
C' = (4 × x-coordinate of C, 4 × y-coordinate of C)
Now, we apply the second dilation with a scale factor of 3/4 to the dilated triangle A'B'C', again with a center of dilation at the origin. This can be done by multiplying each coordinate of A'B'C' by 3/4.
The coordinates of the dilated triangle A''B''C'' after the second dilation would be;
A'' = ((3/4) × x-coordinate of A', (3/4) × y-coordinate of A')
B'' = ((3/4) × x-coordinate of B', (3/4) × y-coordinate of B')
C'' = ((3/4) × x-coordinate of C', (3/4) × y-coordinate of C')
Plugging in the values of A', B', C' obtained from the first dilation, we get;
A'' = ((3/4) × 4 × x-coordinate of A, (3/4) × 4 × y-coordinate of A)
B'' = ((3/4) × 4 × x-coordinate of B, (3/4) × 4 × y-coordinate of B)
C'' = ((3/4) × 4 × x-coordinate of C, (3/4) × 4 × y-coordinate of C)
Simplifying further, we get;
A'' = (3 × x-coordinate of A, 3 × y-coordinate of A)
B'' = (3 × x-coordinate of B, 3 × y-coordinate of B)
C'' = (3 × x-coordinate of C, 3 × y-coordinate of C)
Therefore, the coordinates of the vertices of the triangle A''B''C'' after the two successive dilations are (3 times the x-coordinate and 3 times the y-coordinate.
To know more about coordinates here
https://brainly.com/question/16634867
#SPJ1
1. The law of demand predicts that
a. the more consumers purchase a good, the greater the demand for the good
b. consumers are willing to buy more of a good at a lower price than at a higher price
c. as prices go up, the quantity of a particular good that consumers will buy also rises
d. consumers are willing to buy more of a good at a higher price than at a lower price
2. The function of price in a market system
a. is a way of adjusting the balance between the forces of supply and demand
b. acts as an incentive to producers to either increase or decrease the quantity supplied
c. is a means of rationing the available supply among those who demand it
d. all of these
3. A key advantage of the corporate form of business organization is
a. that the business lives on even if the owners of the business die
b. limited liability of stockholders
c.
the ability to raise significant amounts of financial capital
d.
all of these
Answers
1) consumers are willing to buy more of a good at a lower price than at a higher price Option B
2) All of these
3) All of these
What is the law of demand?An economic theory known as the law of demand states that, all other things being equal, if a good or service's price rises, consumers will demand fewer units of it, and vice versa.
Price and quantity demanded are inversely related, to put it another way. This is a fundamental concept in economics and plays a key role in shaping market behavior and pricing strategies.
The price system is a way of adjusting the balance between the forces of supply and demand. A key advantage of the corporate form of business organization is the ability to raise significant amounts of financial capital.
Learn more about demand and supply:https://brainly.com/question/14741584
#SPJ1
The mean absolute deviation of Mr. Zimmerman's class is 0.46. What does this mean?
Answers
Answer:
is a measure of the average absolute distance between each data value and the mean of a data set.
Choose any dataset (from any online resource). Describe any variable on the dataset where you can apply CLT for mean and CLT for proportions.
Answers
Here is a possible dataset with variables for which the central limit theorem could be applied:
A dataset of customer spending at different retail stores.
Variable for which CLT for mean could be applied:
Average monthly spending per customer. As the number of customers at each store increases, the sample mean spending will approach a normal distribution.
Variable for which CLT for proportions could be applied:
Proportion of customers who spend over $200 per month. Even with a small number of customers at each store, the proportion will be approximately normally distributed as the sample size increases due to the CLT for proportions.
The central limit theorem states that the sampling distribution of the sample mean and sample proportion will be normally distributed for large sample sizes, regardless of the original distribution. So these variables from the retail dataset would satisfy that condition. Please let me know if you would like any clarification or have a different dataset in mind. I can provide additional examples.
For CLT for mean:
We can take random samples of age from the dataset and calculate the mean age of each sample. If we repeat this process many times, the distribution of sample means will tend towards a normal distribution, as long as the sample size is large enough. This is because the mean age of the population is likely to be normally distributed, and as we take more samples, the sample means will become more and more representative of the population mean.
For CLT for proportions:
We can look at the proportion of passengers who survived (the "Survived" variable) within different age groups. If we take random samples of passengers from the dataset, we can calculate the proportion of survivors in each sample for each age group. If we repeat this process many times, the distribution of sample proportions will tend towards a normal distribution, as long as the sample size is large enough. This is because the proportion of survivors in the population is likely to be normally distributed, and as we take more samples, the sample proportions will become more and more representative of the population proportion.
When abraham was born his parents put 2000 into an account that yielded 1.2%
Answers
When abraham was born his parents put 2000 into an account that yielded 1.2%, Abram will receive $2,213.10 on his 16th birthday.
To calculate how much Abram will receive on his 16th birthday, we need to use the compound interest formula:
A = [tex]P(1 + r/n)^{(nt)[/tex]
Where:
A = the amount Abram will receive
P = the principal amount (initial investment) = $2,000
r = the annual interest rate = 1.2% = 0.012
n = the number of times the interest is compounded per year = 2 (semi-annually)
t = the number of years = 16/2 = 8 (since interest is compounded twice a year)
Plugging in the values, we get:
A = $2,000(1 + 0.012/2)¹⁶
A = $2,000(1.006)¹⁶
A = $2,000(1.10655)
A = $2,213.10
To learn more about interest click on,
https://brainly.com/question/29381151
#SPJ1
Complete question is:
When Abram was born, his parents put $2,000 into an account that yielded 1.2% interest, compounded semi-annually. When he turns age 16, his parents will give him the money to buy a car. How much will Abram receive on his 16th birthday?
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answers
The answers are A = 46% and B = 20%.
Given that, a table of data, each cell in the table shows the number of cars in that category.
A) The probability that the car's total repair cost is less than $10000 =
86 / (86+35+67) x 100 = 86/188 x 100 = 46%
B) The probability that the car's purchase was more than $40,000 =
40 / (40+86+71) x 100 = 40/197 x 100 = 20%
Hence, the answers are A = 46% and B = 20%.
Learn more about probability, click;
brainly.com/question/30034780
#SPJ1
Solve this system please.
FOR 35 POINTS
I WILL AWARD BRANLIEST
Answers
Answer: x=1 y=2 z=1
Step-by-step explanation:
Add the first 2 equations to eliminate y (easiest to eliminate)
2x + y - 3z = 1
x - y + 2z = 1
3x -z = 2 => 3x - z = 2
Multiply the 2nd equation by 3 to eliminate y again with the 3rd equation
(You want to eliminate same variable but using the 3rd equation)
3(x - y + 2z = 1)
3x - 3y + 6z = 3
Now add that to 3rd equation
3x - 3y + 6z = 3
x + 3y - z = 6
4x + 5z = 9 => 4x + 5z =9
Now you want to eliminate another variable from the 2 equations you just found(equations in bold above
To do that I will multiply the top one by 5
5(3x - z = 2)
15x - 5z = 10
Now add that to the other equation
15x - 5z = 10
4x + 5z = 9
19x =19
19x=19 solve for x
x=1
Now substitute that into one of the added equations to solve for z
3x - z = 2
3(1) - z = 2 simplify
3 - z = 2
-z = -1
z = 1
Now subsitute x and z into one of the original equations
2(1) + y - 3(1) = 1 simplify
2 + y - 3 = 1
-1 + y = 1
y=2
assume you are realtor in bradenton, florida. you have recently obtained a listing of selling prices of the homes that have sold in that area in the last 6 months.you wish to organize those data so you will be able to provide potential buyers with useful information statistic question
Answers
To know more aboutWhat is the average selling price of homes in Bradenton, Florida over the last 6 months?
What is Average Selling Price?The average selling price is a statistical measure that represents the total sum of all selling prices divided by the number of items being sold. It provides a useful indication of the typical or central value of a dataset.
According to the given information:
Fom the given information we can frame a question -
To know more aboutWhat is the average selling price of homes in Bradenton, Florida over the last 6 months?
To calculate the average selling price of homes in Bradenton, Florida over the last 6 months, you would need to:
1) Gather the selling prices of all the homes that have sold in the area over the last 6 months.
2) Add up all of the selling prices to get a total sum.
3) Divide the total sum by the number of homes that have sold to get the average selling price.
For example, if there were 100 homes sold in the last 6 months, and the total sum of their selling prices was $25,000,000, then the average selling price would be:
Average Selling Price = Total Sum / Number of Homes Sold
Average Selling Price = $25,000,000 / 100
Average Selling Price = $250,000
Therefore, the average selling price of homes in Bradenton, Florida over the last 6 months is $250,000.
To know more about Average Selling Price visit:
https://brainly.com/question/31491563
#SPJ1
For the given data we've Number of class = 5, minimal value = 67900, Maximum value = 321550, Class range = 50730. The histogram, frequency polygon, and accretive frequency polygon are as shown.
What's histogram?In a graphic representation of data called a histogram, a set of nonstop numerical data is distributed in a given way. Each cube's area is related to the frequency of data values being within a given interval or caddy. It consists of a sequence of blocks or bars. The y- axis displays the frequency or count of values that fall inside each interval, while thex-axis displays the range of values that are divided up into intervals or lockers. Large data sets can be visually summarised using histograms, which can also be used to spot patterns and trends as well as outliers or unanticipated figures.
For the given data we have
Number of class = 5
minimal value = 67900
Maximum value = 321550
Class range = Range/ Number of class
= 321550- 67900/ 5
= 50730
Learn further about histogram here:
brainly.com/question/30664111
#SPJ1
The complete question is:
Barb is saving money to buy a house in ten years. This is an example of a(n) goal. O A. medium-term OB. short-term OC. unrealistic O D. long-term
Answers
Answer: long term
Step-by-step explanation: I got it right on the test
Use the calculator to find each angle measure round to the nearest DEGREE
Need 15 and 16 answers need asap
Answers
Answer:
15. 53.13 16. 66.592
Step-by-step explanation:
Used a calculator
The equation of the line is
Answers
Answer:
y = -x +3
Step-by-step explanation:
You want the slope-intercept equation of the line with the same intercept as -3y = -9 +3x, and the same slope as -2x -2y = -8.
Slope-intercept formThe slope-intercept form of the equation of a line is ...
y = mx +b . . . . . where m is the slope, and b is the y-intercept
For the given equations, we can put them in this form to find the desired parameters.
-3y = -9 +3x
y = -x +3 . . . . . . . . . . divide both sides by -3
We observe that the y-intercept is +3, which we will need for our answer.
The slope-intercept form of the second equation is ...
-2x -2y = -8
x + y = 4 . . . . . . . . . . divide by -2
y = -x +4 . . . . . . . . . . subtract x
We observe that the slope (coefficient of x) is -1, which we will need for our answer.
Desired equationWe want the equation of the line with slope -1 and y-intercept 3. It is ...
y = -x +3 . . . . . . . . . . same as the equation of the first line
__
Additional comment
The slope-intercept equation (green) is plotted using dots, so that you can see it is coincident with the line described by the first equation (red). Parallel lines have the same slope, so our desired line must be parallel to the blue line. (It is.)
22. An airplane pilot approaches an airport with an angle of depression of 11°. His current elevation is 20,000ft.
Find the ground distance from the airplane to the airport to the nearest 100ft.
20,000 ft
11⁰
X
22.
Please help and show work
Answers
Answer: x=102900 feet.
Step-by-step explanation:
The horizontal line extending from the airplane is parallel to the ground. Therefore, the angle of elevation (the angle opposite to the side measuring 20,000 ft) is also 11°. In addition, the angle opposite to x is 90-11=79°. Then, you can use the law of sines to solve for x.
[tex]\frac{sin11}{20000} =\frac{sin79}{x}[/tex]
Solve for x. x=102891. Rounded, 102900.
Or, you can use the tan function. [tex]tan11=\frac{20000}{x}[/tex]
Solve for x. Rounded, x=102900.
the box plots show the target heart rates of men 20-40 years old and men 50-70 years old. which statement is best supported by the information in the box plots.
Answers
The statement that best supports the information in the box plots is: D. the interquartile range value of the data for men 20 - 40 years old is greater than that of men of 50 - 70 years old.
How to Find the Interquartile Range from a Box Plot?The interquartile range of a data set is the difference between the values that are located on both edges of the rectangular box that is displayed in a box plot.
Interquartile range for the men between 20 - 40 years old = 150 - 110 = 40
Interquartile range for the men between 50 - 70 years old = 125 - 95 = 30
This shows that, D. the interquartile range value of the data for men 20 - 40 years old is greater than that of men of 50 - 70 years old.
Learn more about the interquartile range on:
https://brainly.com/question/17083142
#SPJ1
How do you write 9.6522 as a percentage
Answers
Answer:
965.22%
Step-by-step explanation:
To write 9.6522 as a percentage, we can multiply it by 100 and add the percent symbol (%):
9.6522 * 100% = 965.22%
Therefore, 9.6522 is equal to 965.22% as a percentage.
Hope this helps!
Answer:
Step-by-step explanation:
41.67 is the answer brainlist and verifed answer
Si al 15% del 20% de 5N le agregamos el 30% del 50% de 2N obtenemos 270. Calcula N.
Answers
The value of N in the algebraic equation is 600.
How to calculate N in the algebraic equation?An algebraic equation is when two expressions are set equal to each other, and at least one variable is included.
If to 15% of 20% of 5N we add 30% of 50% of 2N we get 270. We have:
(15/100 * 20/100 * 5N) + (30/100 * 50/100 * 2N) = 270
0.15N + 0.3N = 270
0.45N = 270
N = 270/0.45
N = 600
Learn more about algebraic equation on:
brainly.com/question/4344214
#SPJ1
Question in English
If to 15% of 20% of 5N we add 30% of 50% of 2N we get 270. Calculate N.
Calculate for the percentages. Show your solutions.
100% of 30
40% of 60
20% of 80
40% of 50
80% of 20
50% of 30
60% of 80
60% of 10
90% of 70
90% of 60
help please. thank youu!!
Answers
Percentage = (Part/Whole) x 100
Where "Part" is the value we are trying to find the percentage of and "Whole" is the total value.
Let's use this formula to solve the given problems:
1. 100% of 30
Percentage = (Part/Whole) x 100
Percentage = (30/30) x 100
Percentage = 100%
Therefore, 100% of 30 is 30.
2. 40% of 60
Percentage = (Part/Whole) x 100
Percentage = (40/100) x 60
Percentage = 24
Therefore, 40% of 60 is 24.
3. 20% of 80
Percentage = (Part/Whole) x 100
Percentage = (20/100) x 80
Percentage = 16
Therefore, 20% of 80 is 16.
4. 40% of 50
Percentage = (Part/Whole) x 100
Percentage = (40/100) x 50
Percentage = 20
Therefore, 40% of 50 is 20.
5. 80% of 20
Percentage = (Part/Whole) x 100
Percentage = (80/100) x 20
Percentage = 16
Therefore, 80% of 20 is 16.
6. 50% of 30
Percentage = (Part/Whole) x 100
Percentage = (50/100) x 30
Percentage = 15
Therefore, 50% of 30 is 15.
7. 60% of 80
Percentage = (Part/Whole) x 100
Percentage = (60/100) x 80
Percentage = 48
Therefore, 60% of 80 is 48.
8. 60% of 10
Percentage = (Part/Whole) x 100
Percentage = (60/100) x 10
Percentage = 6
Therefore, 60% of 10 is 6.
9. 90% of 70
Percentage = (Part/Whole) x 100
Percentage = (90/100) x 70
Percentage = 63
Therefore, 90% of 70 is 63.
10. 90% of 60
Percentage = (Part/Whole) x 100
Percentage = (90/100) x 60
Percentage = 54
Therefore, 90% of 60 is 54.
Sure, I'd be happy to help you calculate these percentages! Here are the solutions:
- 100% of 30 = 30
- 40% of 60 = 0.4 x 60 = 24
- 20% of 80 = 0.2 x 80 = 16
- 40% of 50 = 0.4 x 50 = 20
- 80% of 20 = 0.8 x 20 = 16
- 50% of 30 = 0.5 x 30 = 15
- 60% of 80 = 0.6 x 80 = 48
- 60% of 10 = 0.6 x 10 = 6
- 90% of 70 = 0.9 x 70 = 63
I hope that helps! Let me know if you have any other questions.
HELP DOING CORRECTIONS DUE IN A HOUR GIVING BRAINLIEST AND 20 POINTS
Answers
x = 12 times square root 2 (45 45 90 triangle)
y = 6 times square root 2 (30 60 90 triangle)
What is the range of the function y=e^4x?
O Y <0
O Y > O
O y <4
O y>4
Answers
The range of the function y=e⁴ˣ is y>0
The range of the function y=e⁴ˣ is the same as the range of any exponential function:
y > 0
The function can take on any positive value, but will never be 0 or negative.
It has a horizontal asymptote of y=0.
To learn more on Functions click:
https://brainly.com/question/30721594
#SPJ1
Kylie, a youth leader at a summer camp, is making clear slime for an activity with the kids. She is placing the slime in 2-ounce plastic containers with lids. If Kylie can mix up the slime and fill 75 containers in 50 minutes, how long will it take her to make the slime and fill up 450 of the 2-ounce plastic containers?
A. 6 hours
B. 5 hours
C. 4 hours
D. 9 hours
Answers
Therefore, the answer is (B) 5 hours. We can start by finding out how long it takes Kylie to fill one 2-ounce container. we can get by forming equation .
what is equation ?
In mathematics, an equation is a statement that two expressions are equal. An equation can contain variables, constants, and mathematical operations like addition, subtraction, multiplication, division, exponents, and roots.
In the given question,
We can start by finding out how long it takes Kylie to fill one 2-ounce container. To do this, we can set up a proportion:
75 containers / 50 minutes = 1 container / x minutes
Solving for x, we get:
x = (50 minutes) / (75/1) = 0.67 minutes per container
Now we can use this information to find how long it will take Kylie to fill 450 containers:
450 containers × 0.67 minutes per container = 301.5 minutes
So it will take Kylie 301.5 minutes to make the slime and fill up 450 containers. We can convert this to hours by dividing by 60:
301.5 minutes / 60 minutes per hour = 5.025 hours
Rounding to the nearest hour, we get 5 hours.
Therefore, the answer is (B) 5 hours.
To know more about equation , visit:
https://brainly.com/question/29657983
#SPJ1
Which point is collinear to the point (0, 0)? ○ A) (1,0) OB) (3,2) OC) (4,1) OD) (1,3)
Answers
Answer:
A) (1, 0)
Step-by-step explanation:
The point (0, 0) lies on the x-axis and y-axis, so any point that lies on either axis will be collinear to it. Therefore, the answer is A) (1, 0).
Hope this helps!
HELP FAST
What is the volume of the rectangular prism?
A rectangular prism with a length of 7 meters, a width of 4 meters, and a height of 3 meters.
19 m3
25 m3
31 m3
84 m3
Answers
The volume is D) 84[tex]m^3[/tex].
What is volume?
The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.
Here the given rectangular prism length = 7m , Width = 4m and Height = 3m.
Now using Volume of rectangular prism formula then,
V = lwh cubic unit.
=> V = 7×4×3
=> V = 84[tex]m^3[/tex]
Hence the volume is D) 84[tex]m^3[/tex].
To learn more about volume refer the below link
https://brainly.com/question/14197390
#SPJ1
Complete the table for the following function y = 3 Superscript x x -3 -2 -1 0 1 2 3 y One-third 1 3 Graph the function and describe what the graph looks like. a. Increases in Quadrant III b. Increases from left to right c. Decreases from left to right d. Decreases in Quadrant II
Answers
The correct answer is to increase from left to right. The correct option is B.
To complete the table for the function [tex]y = 3^x - 3[/tex],
x y
-3 1/27
-2 1/3
-1 0
0 2
1 6
2 18
3 54
To graph the function, we can plot the points from the completed table on a coordinate plane and connect them with a smooth curve.
The graph of the function [tex]y = 3^x - 3[/tex] looks like an exponential function that increases from left to right, passing through the point (0, 2) on the y-axis. The graph is concave up and approaches the x-axis but never touches it.
Therefore, the correct answer is to increase from left to right. The correct option is B.
To know more about function follow
https://brainly.com/question/29152577
#SPJ1
The tolerance for a ball bearing is 0.01. if the true diameter of the bearing is be 2.0 inches and the measured value of the diameter is x inches, express the tolerance using absolute value notation.
Answers
The value of the absolute difference can be expressed as | x - 2 | ≤ 0.01.
What is the expression of the tolerance?
The tolerance for the ball bearing is given as 0.01 inches.
Let x = measured value of the diameter in inches
The absolute difference between x and the true diameter of 2 inches of the ball bearing must be less than or equal to the tolerance of 0.01 inches.
The value of the absolute difference can be expressed using absolute value notation as follows;
| x - 2 | ≤ 0.01
Thus, the inequality above, express the absolute value of the difference between x and 2, which is less than and equal to 0.01.
Learn more about absolute value here: https://brainly.com/question/24368848
#SPJ1
If one flyer is 3.0 × 10-3 inches thick, how thick is a stack of 1.25 × 103 flyers
Answers
If one flyer is 3.0 × 10⁻³ inches thick, the stack of 1.25 × 10³ flyers has a thickness of 3.75 inches.
To find the thickness of a stack of flyers, we need to multiply the thickness of a single flyer by the number of flyers in the stack. In this case, the thickness of a single flyer is given as 3.0 × 10⁻³ inches, and the number of flyers in the stack is 1.25 × 10³.
So, the thickness of the stack can be calculated as:
Thickness of stack = Thickness of a single flyer x Number of flyers in the stack
Thickness of stack = 3.0 × 10⁻³ inches x 1.25 × 10³
Thickness of stack = (3.0 x 1.25) × (10⁻³ × 10³) inches
Thickness of stack = 3.75 inches
To learn more about thickness click on,
https://brainly.com/question/14003988
#SPJ1
Solve and reduce the result to lowest fr
not a decimal.
4
3
+ +2- +5-
5 10
Answer:
58
II
미ㄷ
VŨ Vũ (D)
(89)
Answers
Answer:
8[tex]\frac{29}{40}[/tex]
Step-by-step explanation:
The least common multiply is 40
[tex]\frac{4}{5}[/tex] x [tex]\frac{8}{8}[/tex] = [tex]\frac{32}{40}[/tex]
2 [tex]\frac{3}{10}[/tex] x [tex]\frac{4}{4}[/tex] = 2 [tex]\frac{12}{40}[/tex]
5 [tex]\frac{5}{8}[/tex] x [tex]\frac{5}{5}[/tex] = 5 [tex]\frac{25}{40}[/tex]
Now that we have a common denominator, add these numbers together
[tex]\frac{32}{40}[/tex] + 2 [tex]\frac{12}{40}[/tex] + 5 [tex]\frac{25}{40}[/tex]
7 [tex]\frac{69}{40}[/tex]
7 + [tex]\frac{40}{40}[/tex] + [tex]\frac{29}{40}[/tex] I broke up [tex]\frac{69}{40}[/tex] because I know that [tex]\frac{40}{40}[/tex] equals 1
8 [tex]\frac{29}{40}[/tex]
Helping in the name of Jesus.
Caleb calculated the simple interest on $500 for 1 year rate of 5,5% per year. What is the interest earned ?
Answers
Caleb earned an interest of $27.50 on $500 for 1 year at a rate of 5.5% per year.
Explanation:
The interest earned by Caleb on $500 for 1 year at a rate of 5.5% per year can be calculated using the simple interest formula:
I = P * r * t
where I is the interest earned, P is the principal (starting amount), r is the annual interest rate as a decimal, and t is the time period in years.
Plugging in the given values, we get:
I = 500 * 0.055 * 1
I = 27.50
Therefore, Caleb earned an interest of $27.50 on $500 for 1 year at a rate of 5.5% per year.
Consider the following functions.
[tex]f(x)=x+3[/tex] and [tex]g(x)=\frac{x+5}{3}[/tex]
Step 2 of 2: Find the formula for (g∘f)(x) and simplify your answer. Then find the domain for (g∘f)(x). Round your answer to two decimal places, if necessary.
Answers
Answer:
To find the formula for (g∘f)(x), we need to first evaluate g(f(x)):
g(f(x)) = g(x+3) = (3(x+3)+5)/3 = (3x+14)/3
So, (g∘f)(x) = (3x+14)/3
To find the domain for (g∘f)(x), we need to consider any restrictions on x that would make the function undefined. The only possible restriction is if the denominator of (3x+14)/3 is zero, which occurs when 3x+14=0. Solving for x, we get x=-14/3. Therefore, the domain of (g∘f)(x) is all real numbers except -14/3, or (-∞, -14/3) U (-14/3, ∞).
The number of bacteria P(h) in a certain population increases according to the following function, where time h is measured in hours.
P(h)=2800e^0.09h
How many hours will it take for the number of bacteria to reach 3500?
Round your answer to the nearest tenth, and do not round any intermediate computations.
Answers
It will take 2.48 hours for the number of bacteria to reach 3500.
How many hours to reach 3500?In order to find number of hours to take for the number of bacteria to reach 3500, we can set the function equal to 3500 and solve for h.
The function given is P(h) = 2800e^(0.09h). So, plugging the values of 3500, we will get:
3500 = 2800e^(0.09h)
Dividing both sides by 2800, we get:
e^(0.09h) = 3500/2800
Taking the natural logarithm of both sides, we get:
0.09h = ln(3500/2800)
h = (ln(3500/2800))/0.09
h = 0.22314355131/0.09
h = 2.47937279233
h = 2.48 hours
Read more about exponential
brainly.com/question/2456547
#SPJ1
For the function f(x)=−1(2/3)^x , what is the y -intercept?
Responses
a -1
b -2/3
c 2/3
d 1
Answers
The y-intercept of the function is -1. (option a).
In mathematics, a function is a rule that assigns each input (or argument) of a set, to a unique output (or value) of another set. In this case, the function f(x) is given by f(x)=−1(2/3)^x.
To find the y-intercept of a function, we need to evaluate the function at x=0. This is because the y-intercept is the point at which the graph of the function intersects the y-axis, and the y-axis is where x=0.
To find the y-intercept of the function f(x)=−1(2/3)ˣ, we need to evaluate the function at x=0. This gives us:
f(0) = -1(2/3)⁰
f(0) = -1(1)
f(0) = -1
This means that the graph of the function intersects the y-axis at the point (0,-1).
Hence the correct option is (a).
To know more about function here
https://brainly.com/question/28193995
#SPJ1
Give a recursive defintition for the following set or ordered pairs of positive integers (a|b means that a is a factor of b): [tex]S =[/tex]{[tex](a,b)|a[/tex]∈[tex]Z^+, b[/tex]∈[tex]Z^+, a + b[/tex] is odd}
Answers
[tex](2,1)[/tex], [tex](1,2)[/tex] is your base step
if [tex](a,b)[/tex] is in the set [tex](a+1,b+1)[/tex] will be in the set
if [tex](a,b)[/tex] is in the set [tex](a+2,b)[/tex] will be in the set
if [tex](a,b)[/tex] is in the set [tex](a,b+2)[/tex] will be in the set.
Think about how to solve this problem in general. How can you assure that the sum [tex]a+b[/tex] is odd?
Think about this, what happens when you sum two even numbers? The result is even or odd?
[tex]2+6 = 8 \ \text{(even)}[/tex]
[tex]10+12 = 22 \ \text{(even)}[/tex]
And what happens when you sum two odd numbers ? The result will be even or odd? Look
[tex]3+7 = 10 \ \text{(even)}[/tex]
[tex]5+11 = 16 \ \text{(even)}[/tex]
Therefore to assure that [tex]a+b[/tex] is odd, one of them has to be odd and one of them has to be even, that is why
[tex](2,1)[/tex], [tex](1,2)[/tex] is your base step
if [tex](a,b)[/tex] is in the set [tex](a+1,b+1)[/tex] will be in the set
if [tex](a,b)[/tex] is in the set [tex](a+2,b)[/tex] will be in the set
if [tex](a,b)[/tex] is in the set [tex](a,b+2)[/tex] will be in the set.