An explicit formula in slope intercept form for the given expression is aₙ = 5n - 8.
What is the slope-intercept form?Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided above, we can logically deduce that an equation in slope-intercept form that models the situation is given by:
aₙ = -3 + 5(n - 1)
aₙ = -3 + 5n - 5
aₙ = 5n - 8
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Solve the system of equations.
x + y = 8
y = x2 – 4
(3,5) and (-4,12)
(-3,11) and (4,4)
(4,4) and (5,3)
(12,-4) and (7,1)
Answer:
A) [tex](3,5)[/tex] and [tex](-4,12)[/tex]
Step-by-step explanation:
[tex]x+y=8\\x+(x^2-4)=8\\x^2+x-4=8\\x^2+x-12=0\\(x-3)(x+4)=0\\x_1=3,\,x_2=-4\\\\x_1+y=8\\3+y=8\\y_1=5\\\\x_2+y=8\\-4+y=8\\y_2=12[/tex]
Holly picks 125 she spends 35 on gas for her car
which model represtant how much money holly spent
The second option is the correct representation of the given context.
What is a number line?A number line is a one-dimensional horizontal line where we can represent any real number.
The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.
Look at the model, it starts at 125 and drops to 90.
If she has $125 and spends $35 on gas, the remaining balance is reduced by that amount.
125 - 35 = 90.
Q. Holly has $125 she spends $35 on gas for her car which model represents how much money holly has left?
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A regular hexagon has six congruent sides. If the length of each side is represented by the expression 7x+4. What expression is equivalent to the perimeter of the figure
Answer:
42x + 24
Step-by-step explanation:
6(7x + 4)
42x + 24
Which unit of measurement is part of the metric system?
O pound
Oliter
O quart
O foot
I need some help please
Answer:
[tex]x = - \frac{2}{9} [/tex]
Answer: [tex]\text{x} = \boldsymbol{-\frac{2}{9}}[/tex]
2 goes in the green box up top
9 goes in the gray box down below.
=========================================
Work Shown:
[tex]-2(4+3\text{x}) = 3(\text{x}-2)\\\\-8-6\text{x} = 3\text{x}-6\\\\-6\text{x}-3\text{x} = -6+8\\\\-9\text{x} = 2\\\\\text{x} = \boldsymbol{-\frac{2}{9}}\\\\[/tex]
What are the outliers of the data set?
13, 24, 25, 25, 25, 26, 27, 27, 27, 28, 36
Select EACH correct answer.
Please help quick I don’t have much time!!!
The missing values in table should be completed as follows;
X(input) Y(output)
10 19
12 23
Rule: y = 2x - 1.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At point (3, 5), a linear equation of this line in slope-intercept form can be calculated by using the point-slope form as follows:
y - 5 = (11 - 5)/(6 - 3)(x - 3)
y - 5 = 6/3(x - 3)
y = 2(x - 3) + 5
y = 2x - 1
When x(input) = 10, the y(output) is given by:
y = 2x - 1
y = 2(10) - 1
y = 20 - 1
y = 19.
When y(output) = 23, the x(input) is given by:
y = 2x - 1
23 = 2x - 1
2x = 24
x = 12.
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My friend Vreel has less than 19 pisquets and more than 8 pisquets
Write an inequality that shows the possible amounts of pisquets. Use
x for pisquets.
The inequality that shows the possible amounts of pisquets is 8 < x < 19
How to determine the inequality that shows the possible amounts of pisquetsFrom the question, we have the following parameters that can be used in our computation:
My friend Vreel has less than 19 pisquets and more than 8 pisquets
Using x for Pisquets, we have:
x < 19 and x > 8
When the inequality is combined, we have
8 < x < 19
Hence, the inequality is 8 < x < 19
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PQRS is parallelogram. If PS = 15, then QR =
Answer:
QR = 15
Step-by-step explanation:
Opposite sides of parallelograms are congruent. This means that their lengths are the same.
Hence,
PS = 15 = QR.
Find the median of the following data:
9, 15, 17, 18, 6, 20, 8, 5, 18, 18, 10, 5, 14, 12, 10,7
A. 18
B. 12
C. 11
D. 15
Answer:
18
Step-by-step explanation:
The median of a set of data is the value that separates the lower and upper halves of the data. To find the median, the data must be arranged in numerical order.
The data, arranged in numerical order, is:
5, 5, 6, 7, 8, 9, 10, 10, 12, 14, 15, 17, 18, 18, 18, 20
Since the number of data points is an odd number (17), the median is simply the middle value, which is:
18
So the correct answer is A) 18.
Answer: C
Step-by-step explanation:
To find the median, arrange the numbers in sequential order.
5, 5, 6, 7, 8, 9, 10, 10, 12, 14, 15, 17, 18, 18, 18, 20
When there are an odd number of data in the set, choose the middle number in the set. For example, see the following data set.
2, 4, 6, 8, 9
The middle number in the data set is 6, so it is the median.
When there is an even number of data in the set, choose the middle two numbers, add them together, and then divide them by 2.
There are 16 numbers in this data set. We need to find the two middle numbers in the set.
5, 5, 6, 7, 8, 9, 10, 10, 12, 14, 15, 17, 18, 18, 18, 20
10 and 12 are the two middle numbers in the set.
10 + 12 = 22
22/2 = 11
Median = 11
Which relation is NOT a function?
{(10, –4), (–10, 14), (14, –10)}
{(–4, –10), (–2, –4), (–10, –1), (–1, –7), (1, 10), (–3, –1)}
{(–4, 10), (14, 3), (15, 14), (10, 3)}
{(11, 16), (12, 14), (14, 14), (11, 13), (21, 12)}
{(11, 16), (12, 14), (14, 14), (11, 13), (21, 12)}
This is because the the number 11, an x-value, is used twice and if an x-value is used more than once then it is not a function. A function is a relation between sets where there is only one output for each input
which equation has a slope of -1 and passes through the point (4,-5)
Answer:
y = -x - 1
Step-by-step explanation:
y = mx +c
y = -x + c [ m = slope]
As the line passes through (4,-5)
-5 = -4 + c [Substituting value of x and y]
c = -1 [Solving the above equation]
Part II. Jacob tells you that there is a 40% probability that at least two people in each classroom of 25 students share a birthday (ignore leap years). You don’t believe Jacob and decide to conduct a simulation to see if you get enough evidence to reject his claim.
• State the null hypothesis and the alternative hypothesis.
Use the random number generator to do a simulation and do this simulation 16 times. Record your results in the table below. In each simulation you will be checking how many couple of students share a birthday.
Find the proportion of “classrooms” with at least a couple of students sharing a birthday.
• Find the t-statistic:
Compare P-value (probability of getting a value at least as extreme as your t-statistic under the null hypothesis) with the a level:
• State your conclusion:
Null hypothesis: The probability of at least two people in each classroom of 25 students sharing a birthday is less than or equal to 40%.
Alternative hypothesis: The probability of at least two people in each classroom of 25 students sharing a birthday is greater than 40%.
What are the results from the simulations?Simulation Results:
Simulation 1: 8 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 2: 9 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 3: 7 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 4: 11 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 5: 7 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 6: 6 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 7: 8 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 8: 6 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 9: 10 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 10: 8 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 11: 7 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 12: 11 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 13: 8 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 14: 7 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 15: 10 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 16: 10 out of 16 classrooms had at least 2 students sharing a birthday.
Proportion of classrooms with at least 2 students sharing a birthday = (8+9+7+11+7+6+8+6+10+8+7+11+8+7+10+10)/16 = 0.7125
The mean number of classrooms with at least 2 students sharing a birthday is 0.7125. We can use this value to calculate the t-statistic.
t-statistic = (0.7125 - 0.4) / (sqrt(0.4 * 0.6 / 16)) = 5.766
Using a one-tailed t-test with 15 degrees of freedom and an alpha level of 0.05, the critical t-value is 1.753. Since the calculated t-statistic is greater than the critical t-value, we can reject the null hypothesis.
The p-value is very small (less than 0.0001), indicating strong evidence against the null hypothesis.
Therefore, we can conclude that there is sufficient evidence to suggest that the probability of at least two people in each classroom of 25 students sharing a birthday is greater than 40%.
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Dominique is selling merchandise for a school fundraiser. she is selling calendars for $8 each and coffee mugs for $10 each. she must sell at least $600 of merchandise, including at least 40 calendars, to meet her goals. if x represents the number of calendars and y represents the number of mugs, which system of inequalities represents this scenario? 8x 10y > 600 and y > 40 8x 10y > 600 and x > 40 8x 10y ≥ 600 and y ≥ 40 8x 10y ≥ 600 and x ≥ 40
By answering the given question, we may state that Hence, the interest appropriate response is X = 40 and 8x + 10y = 600
what is interest ?Divide the principal by the interest rate, the length of time, and other factors to arrive at simple interest. Simple return = principal + interest + hours is the marketing formula. This method makes it easiest to calculate interest. The most typical technique to figure out interest is as a portion of the principal sum. He will only pay his share of the 100% interest, for example, if he borrows $100 from a friend and agrees to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you give it out, you must charge interest. Interest is often determined as an annual percentage of the loan total. The interest on the loan is this percentage.
Selling x calendars will cost 8x, while selling y mugs will cost 10y. The scenario is therefore represented by the following system of inequalities in order for her to reach her objective of selling at least $600 worth of stuff, including at least 40 calendars:
(Total cost of goods sold must be at least $600; 8x + 10y)
x ≥ 40 (must sell at least 40 calendars) (must sell at least 40 calendars)
In the first inequality, you'll see that we used the symbol "" rather than ">" since Dominique needs to sell at least $600 worth of goods, not just more than $600.
Hence, the appropriate response is
X = 40 and 8x + 10y = 600
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You pick a card at random.
4 5
6 7 8 9
What is P(5)
Write your answer as a percentage.
Total cards = 4 (6,7,8,9), If the card is not 9, the required card will be (6,7,8), Number of cards that are not 9 is 3, Probability = expected/total P( 5) = 3/4 and the probability of picking 5 is 16.67%.
What is Probability?
The probability of an occurrence is a number used in science to describe how likely it is that the event will occur. It is stated as a number between 0 and 1, or, when using percentage notation, in the range between 0% and 100%.The higher the probability, the more likely it is that the event will occur. The probability is typically expressed as the proportion of positive outcomes to all outcomes in the sample space.It is written as Probability of an Event P(E) = (Number of Favorable Outcomes) (Sample space).Simple probability calculations can be done by adding the probabilities together.Calculating a result or the likelihood that an event will occur is known as simple probability.Probability statistics are used by insurance firms to estimate the likelihood of having to pay out a claim. A simple probability is computed by dividing a particular event by all potential outcomes.There are a total of 6 numbers in the grid, and only one of them is 5. Therefore, the probability of selecting 5 is:
P(5) = 1/6
To write this as a percentage, we multiply by 100:
P(5) = 1/6 * 100% = 16.67%
Therefore, the probability of picking 5 is 16.67%.
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The superintendent of a large school district wants to estimate the percent of district residents who support the building of a new middle school. To gather data, the superintendent will select a random sample of district residents.
What is the most appropriate method for creating such an estimate?
All three options involve conducting a survey using random sampling, which is the most appropriate method for creating an estimate of the percentage of district residents who support the building of a new middle school. The correct answer would be A, B, or C, depending on the availability of resources.
The most appropriate method for creating an estimate of the percentage of district residents who support the building of a new middle school would likely be a survey using random sampling.
Random sampling is a statistical method in which a representative sample of a larger population is selected, in order to make inferences about the population as a whole. When conducting a survey, random sampling helps to ensure that the sample is representative of the population, reducing the potential for bias.
There are several different types of surveys that could be used to estimate the level of support for a new middle school, including telephone surveys, online surveys, and in-person surveys.
Complete question:
The superintendent of a large school district wants to estimate the percentage of district residents who support the building of a new middle school. To gather data, the superintendent will select a random sample of district residents. What is the most appropriate method for the superintendent to estimate the percentage of district residents who support the building of a new middle school?
A. Telephone survey using random sampling
B. Online survey using random sampling
C. In-person survey using random sampling
D. Observing the behavior of district residents
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A 2-column table titled f (x + 1) = 4 (f (x)) has 5 rows. Column 1 is labeled x with entries 1, 2, 3, 4, 5. Column 2 is labeled f (x) with entries 4, a, b, c, 1,024. What are the missing values in the table representing the recursively defined geometric sequence? a = b = c =.
Answer:
16, 64, 256
Step-by-step explanation:
is (bc^2)/a^3b^2c^-2*(2a^-4b^3c^-4)^4 equal to (16c^20/a^13b^13)
Answer: No.
Step-by-step explanation: Unless I read and calculated wrongly, it should be equal to 2b^4/(a^3b^2c^2-2)a^4c^2 -1/256
Value of T please and thank you !!!!
the value of "t" will be 28 degrees for the given circle.
What are the properties of a circle?The following four properties and their proofs were introduced:
1: The angles at the center and at the circumference of a circle are subtended by the same arc.
2: Angles at the circumference are subtended by a diameter.
3: Angles at the circumference of a circle subtended by the same arc.
Given, a circle with an angle between two secants of 28 degrees.
From the intersecting Secant theorem of a circle:
The angle between secant = bigger arc -smaller arc)/2
In our case,
28 = (3t -t)/2
2t/2 = 28
t = 28
therefore, the value of "t" will be 28 degrees for the given data.
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Name
Period
Practice
Example 1
FINANCE Caldonia deposits $150 into an account that pays 7.3% annual interest compo
quarterly.
1.
GO Practice S
a. Write an equation to represent Caldonia's account balance after t years.
b. Write and use a system of equations to determine how many years it will take for the
account reach $200. Round to the nearest year.
It takes for the account to reach $200 is 4 years.
What is Compound Interest?Compound Interest is the interest calculated on the cumulative amount, rather than being calculated on the principal amount only quantity.
Given that aldonia deposits $150 into an account that pays 7.3% annual interest compounded quarterly.
[tex]A = P(1 +\frac{r}{n})^n^t[/tex]
where:
A = the total account balance after t years
P = the initial deposit $150
r = the annual interest rate =0.073
n = the number of compounding periods per year, which is 4 (quarterly) in this case
t = the number of years the money is in the account
Now let us substitute the values
[tex]A = 150(1 + \frac{0.073}{4} )^4^t[/tex] is the equation to represent Caldonia's account balance after t years.
Now let us determine the number of years it will take for the account to reach $200.
[tex]200 = 150(1 + \frac{0.073}{4} )^4^t[/tex]
200=150(1+0.01825)^4t
[tex]1.333=1.018^4^t[/tex]
Take log on both sides
log1.333=4tlog(1.018)
0.1248=4t 0.0077
0.1248=0.0309t
Divide both sides by 0.0309
t=4.038
Hence, it takes 4 years to reach account balance of $200
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Two sprinters, nick and ryan, want to find out who has the faster time when compared to each of their teams. Nick has a time of 10. 8 seconds, and his team has a mean time of 11. 4 seconds and a standard deviation of 0. 4 seconds. Ryan has a time of 11. 2 seconds, and his team has a mean of 11. 5 seconds and a standard deviation of 0. 1 seconds. Who has the faster time when compared to each of their teams?.
Ryan has the faster time when compared to each of their teams,
"Information available from the question"
The time taken by Nick is 10.8 seconds.
The mean time taken by Nick is 11.4 seconds.
The standard deviation of Nick is 0.4 seconds.
The time taken by Ryan is 11.2 seconds.
The mean time taken by Ryan is 11.5 seconds.
The standard deviation of Ryan is 0.1 seconds.
The z-score of Nick is:
[tex]z_1=\frac{10.8-11.4}{0.4}[/tex]
[tex]z_1=-1.5[/tex]
The z-score of Ryan is:
[tex]z_2=\frac{11.2-11.5}{0.1}[/tex]
[tex]z_2=-3[/tex]
Thus, Ryan z-score is lower, so Ryan has the faster time when compared to each of their teams.
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What is 1 meter cm in feet?
100 centimetres make up one metre. 100 centimetres must be multiplied by 0.0328084 to equal one metre in feet. There are 3.28084 feet as a result.
100 cm in one metre
1 cm = 0.0328084 ft
100 cm in 1 metre equals 0.0328084 feet, or 3.28084 feet.
100 centimetres make up one metre. 100 centimetres must be multiplied by 0.0328084 in order to convert 1 metre in cm to feet. This math will show us how many feet are in one metre, centimetre. To proceed step-by-step, we must first multiply one metre by one hundred centimetres. We will get 100 centimetres as a result.Following that, we must multiply 100 centimetres by 0.0328084. This figure represents the number of feet in one centimetre. We can convert 1 metre cm to feet by multiplying these two values, which gives us 3.28084 ft. The length of things can be measured using this conversion in both metric and imperial systems. When attempting to measure objects precisely, it can be helpful to know how to convert between the two systems.
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The table of values represents a linear function.
X Y
-2. 1
0. -9
2. -19
4. -29
6. -39
Complete the equation below to represent the function defined by the table in the form
y = mx + b.
Answer:
5 mx plus b which you have to do 5 plus m to get 5m which is ur answer
how many possibilities are there for a four digit pin where no digit is repeated?
The total number of possibilities for four digit pin with the condition of no digit is repeated is equal to 5040.
Total number of digit used to form pin = 4
Condition is : No digit is repeated.
Number of digits are :
( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 )
Total digits are = 10
Number of possibilities to form four digit pin with no digit repeated
= ¹⁰P₄
= ( 10! ) / ( 10 - 4 )!
= ( 10 × 9 × 8 × 7 × 6! ) / 6!
= 10 × 9 × 8 × 7
= 5040
Therefore, the total number of possibilities to form four digit pin with the given condition is equal to 5040.
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Can you please find the exact value of X?
Answer:
10[tex]\sqrt{50}[/tex]
Step-by-step explanation:
Since it's a isosceles right triangle, so
x^2+x^2=100^2
2x^2=10000
x^2=5000
x=[tex]\sqrt{5000}[/tex]=10[tex]\sqrt{50}[/tex]
Your company manufactures hot water heaters. The life spans of the products are known to be normally distributed with a mean of 13 years and a standard deviation of 1.5 years.
a) You are buying a new hot water heater, based on the information in the problem, between how many years would you expect your hot water heater to last. (Give a range of numbers). Explain your answer.
b) You want to set the warranty on your product so that you have to replace at most 5% of the hot water heaters that you sell. How many years should you claim on your warranty? (Round answer to nearest whole number of years.) Explain your answer.
we should claim a warranty of 11 years (rounded to the nearest whole number) to ensure that we replace at most 5% of the hot water heaters that we sell.
What is mean ?
Mean can be defined as the ratio of sum of the given observations and total number of observations.
a) Since the life spans of the hot water heaters are normally distributed with a mean of 13 years and a standard deviation of 1.5 years, we can use the empirical rule to estimate the range of years we would expect the hot water heater to last. The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.
Using this information, we can estimate that the range of years we would expect the hot water heater to last is approximately 10.5 to 15.5 years. This is because one standard deviation below the mean is 13 - 1.5 = 11.5 years, and one standard deviation above the mean is 13 + 1.5 = 14.5 years. Therefore, we can reasonably expect the hot water heater to last between 10.5 and 15.5 years with about 95% confidence.
b) To set the warranty on the product so that we have to replace at most 5% of the hot water heaters that we sell, we need to find the number of years that corresponds to the 5th percentile of the distribution. This is the value below which 5% of the data falls.
We can use a standard normal distribution table or a calculator to find the z-score corresponding to the 5th percentile, which is -1.645. We can then use the formula z = (x - mu) / sigma to find the number of years, x, that corresponds to this z-score.
-1.645 = (x - 13) / 1.5
Solving for x, we get x = 10.83 years.
Therefore, we should claim a warranty of 11 years (rounded to the nearest whole number) to ensure that we replace at most 5% of the hot water heaters that we sell
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A
rectangular prism has a volume of 9 in. The area of the base
is 4 in? What is the height of the prism?
The height of the rectangular prism whose volume is 9 cubic inches and the base area is 4 square inches will be 2.25 inches.
What is the volume?Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.
The volume of the prism is given as,
Volume = (Base area) x (Height)
The rectangular prism has a volume of 9 cubic inches. The area of the base is 4 square inches.
Then the height of the rectangular prism is given as,
9 = 4 h
h = 9 / 4
h = 2.25 inches
The height of the rectangular prism whose volume is 9 cubic inches and the base area is 4 square inches will be 2.25 inches.
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rawan deposits 13000 into an account that pays 2.6% annual interest compounded every 6 months
The function that represent the balance A in the account after t years is f(t) = 13000( 1.013 )^( 2t ).
This question is incomplete, the complete question is:
Rawan deposits $13,000 into an account that pays 2.6% annual interest compounded every 6 months.
Write a function to represent the balance A in the account after t years.
What is the function that represent the balance A in the account after t years?The formula accrued amount in a compounded interest is expressed as;
A = P( 1 + r/n )^( n × t )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that;
Principal P = $13,000Compounded every 6 months n = 2Interest rate R = 2.6%First, convert R as a percent to r as a decimal
r = R/100
r = 2.6/100
r = 0.026
Given that time = t.
A = P( 1 + r/n )^( n × t )
f(t) = 13000( 1 + 0.026/2 )^( 2 × t )
f(t) = 13000( 1 + 0.026/2 )^( 2t )
f(t) = 13000( 1 + 0.013 )^( 2t )
f(t) = 13000( 1.013 )^( 2t )
Therefore, the accrued amount after t years is f(t) = 13000( 1.013 )^( 2t ).
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Classify the following triangle check all that apply 36,8.68,7,54,5.1
We can see that the triangle is given as one of the angles is 90 degrees . The triangle is a right-angle triangle, and scalene also.
What is a right-angled triangle?A right-angled triangle is a triangle having one of its angles with measure of 90°
The slanted side of that triangle is called Hypotenuse and it is the longest side in that triangle.
We can see that the triangle is given as one of the angles is 90 degrees and the other two angles are 36 and 54 degrees.
If one of the angles is 90° then the triangle is a right-angled triangle.
Also, the length of the two sides is given as 8.66 units and 5.1.
We have already concluded that the triangle is a right-angle triangle, so all the three sides of the triangle must be different.
This implies that the triangle is scalene also.
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A letter in the word ACCEL is chosen 50 times. Results are shown in the table below
What is the experimental probability of choosing a C?
Answer:
Step-by-step explanation:
C is chosen 12 times (7 + 5)
You have 50 total picks.
So the experimental probability is 12/50.