Heidi's rate of elimination is also decreasing over time, but at a slower rate than Clara's which decreases exponentially over time
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
f(t) = 300(0.946)^t
For Clara, we can calculate the rate of elimination by finding the difference in the amount of medicine present between two consecutive time points, and dividing by the time elapsed:
From t=1 to t=2: f(2) - f(1) = 223.73 - 236.5 = -12.77 mg
Rate of elimination = -12.77 mg / (2-1) hours = -12.77 mg/hour
From t=2 to t=3: f(3) - f(2) = 211.65 - 223.73 = -12.08 mg
Rate of elimination = -12.08 mg / (3-2) hours = -12.08 mg/hour
From t=3 to t=4: f(4) - f(3) = 200.22 - 211.65 = -11.43 mg
Rate of elimination = -11.43 mg / (4-3) hours = -11.43 mg/hour
From t=4 to t=5: f(5) - f(4) = 189.41 - 200.22 = -10.81 mg
Rate of elimination = -10.81 mg / (5-4) hours = -10.81 mg/hour
Hence , this expression tells us that the rate of elimination for Heidi is proportional to the amount of medicine in her body at any given time, and decreases exponentially over time as the amount of medicine decreases
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using complete sentences, explain which function has the greatest y-intercept.
Answer:
Step-by-step explanation:
To determine which function has the greatest y-intercept, we need to look at the constant term, which represents the y-intercept, of each function. The function with the largest constant term will have the greatest y-intercept.
For example, consider the following three functions:
1. f(x) = 2x + 5
2. g(x) = 3x - 7
3. h(x) = -4x + 10
The constant term for each function is 5, -7, and 10 respectively. Therefore, h(x) has the greatest y-intercept of 10, since its constant term is larger than those of f(x) and g(x).
You paint four walls. Each wall is a rectangle with a length of 20 feet and a height of 12 feet. One gallon of paint covers about 320 square feet. How many gallons of paint do you need in order to cover the walls?Give explanation
Answer:
To find out how many gallons of paint are needed to cover the walls, we need to first find the total area of the walls.
The four walls are rectangles with a length of 20 feet and a height of 12 feet. So, the area of one wall is:
20 feet x 12 feet = 240 square feet
Since there are four walls, the total area of the walls is:
4 x 240 square feet = 960 square feet
We know that one gallon of paint can cover approximately 320 square feet. To find how many gallons of paint are needed, we can divide the total area of the walls by the area covered by one gallon of paint:
960 square feet ÷ 320 square feet per gallon = 3 gallons of paint
Therefore, you need approximately 3 gallons of paint to cover the walls.
Consider the triangle with vertices (-7, -2), (-2, -5) , and (2, 3). What is the approximate perimeter of the triangle?
The perimeter of the triangle is 23.623 units.
What is perimeter of triangle?
Finding the distance around a triangle entails determining its perimeter. The distance formula can be used to calculate the side lengths if you don't already know all of them. The simplest way to find a triangle's perimeter is to add up all of its sides' lengths.
The distance between two points (x1,y1) and (x2,y2) can be determined using the following formula: √(x₂-x₁)² + (y₂ - y₁)²
Let the given vertices are (-7, -2), (-2, -5) , and (2, 3).
Distance formula for two points is = √(x₂-x₁)² + (y₂ - y₁)²
Using the formula,
AB = √((-2)-(-7))² +((-5)-(-2))²
= √(-2+7)² + (-5+2)²
= √5² + (-3)²
= √25 + 9
= √31
Similarly, BC = √(2 - (-2))² + (3-(-5))²
= √(2+2)² + (3+5)²
= √4² + 8²
= √16+64
= √80
CA = √((-7)-2)² + (-2 + 3)²
= √(-9²) + 1
= √81+1
=√82
Perimeter of triangle = AB + BC + CA
= √31 +√81 +√82
= 5.5677 + 9 + 9.0553
= 23.623
Therefore, the perimeter of the triangle is 23.623 units.
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A number "z" when rounded to the nearest whole, is equal to
Find the upper and lower bound of "z"
In order to find the upper and lower bounds of a rounded number:
Identify the place value of the degree of accuracy stated.Divide this place value by 2 .Add this amount to the given value to find the upper bound, subtract this amount from the given value to find the lower bound.How to explain the boundThe upper and lower bounds can be found by dividing the degrees of accuracy by 2 and then subtracting and adding with the value to give the lower and upper bounds respectively.
Kindly check the above explanation inorder to know how to calculate the value as your information is incomplete
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How does one find the upper and lower bound of a variable
A culture of bacteria in a petri dish has an initial population of 1500 cells and grows at a rate (in cells/day) of N′(t)=200(t+2)−12 Assume t is measured in days.
a) What is the population after 14 days? After 34 days?
b) Find the population N(t) at any time t≥0
The population N(t) at any time t≥0 is given by the function N(t) = 100t^2 + 800t + 1332.
a) To find the population after 14 days, we need to integrate the given rate function from 0 to 14:
N(14) - N(0) = ∫(0 to 14) N'(t) dt
N(14) - 1500 = ∫(0 to 14) [200(t+2) - 12] dt
N(14) - 1500 = [100[tex]t^2[/tex] + 800t - 168] evaluated from t=0 to t=14
N(14) = 1500 + [100(14[tex])^2[/tex] + 800(14) - 168] - [100(0[tex])^2[/tex] + 800(0) - 168]
N(14) = 1500 + 17,512
N(14) = 19,012
So the population after 14 days is 19,012 cells.
To find the population after 34 days, we can use the same method:
N(34) - N(0) = ∫(0 to 34) N'(t) dt
N(34) - 1500 = ∫(0 to 34) [200(t+2) - 12] dt
N(34) - 1500 = [100[tex]t^2[/tex] + 800t - 168] evaluated from t=0 to t=34
N(34) = 1500 + [100(34[tex])^2[/tex]+ 800(34) - 168] - [100(0[tex])^2[/tex] + 800(0) - 168]
N(34) = 1500 + 116,768
N(34) = 118,268
So the population after 34 days is 118,268 cells.
b) To find the population N(t) at any time t≥0, we can integrate the given rate function from 0 to t:
N(t) - N(0) = ∫(0 to t) N'(x) dx
N(t) - 1500 = ∫(0 to t) [200(x+2) - 12] dx
N(t) = 1500 + ∫(0 to t) [200(x+2) - 12] dx
N(t) = 1500 + [100[tex]x^2[/tex] + 800x - 168] evaluated from x=0 to x=t
N(t) = 1500 + 100[tex]t^2[/tex] + 800t - 168
N(t) = 100t^2 + 800t + 1332
So the population N(t) at any time t≥0 is given by the function N(t) = 100[tex]t^2[/tex]+ 800t + 1332.
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a) The population after 14 days is 22,788 cells, and the population after 34 days is 126,056 cells.
b) The population at any time t≥0 is given by the equation N(t) = [tex]100t^2[/tex] + 388t + 1500, where t is measured in days and N(t) is the number of cells in the culture at time t.
a) To find the population after 14 days, we can use the given rate equation to calculate the growth rate at t=14 as follows:
N'(14) = 200(14+2) - 12 = 2808 cells/day
Then we can use the following formula to calculate the population after 14 days:
N(14) = N(0) + ∫N'(t) dt, from t=0 to t=14
N(14) = 1500 + ∫(200(t+2) - 12) dt, from t=0 to t=14
N(14) = 1500 + [tex][100t^2 + 400t - 12t][/tex]from t=0 to t=14
N(14) = 1500 + [tex][100(14)^2 + 400(14) - 12(14)] - [100(0)^2 + 400(0) - 12(0)][/tex]
N(14) = 1500 + 21288
N(14) = 22788 cells
Similarly, to find the population after 34 days, we can use the given rate equation to calculate the growth rate at t=34 as follows:
N'(34) = 200(34+2) - 12 = 6772 cells/day
Then we can use the same formula as above to calculate the population after 34 days:
N(34) = N(0) + ∫N'(t) dt, from t=0 to t=34
N(34) = 1500 + ∫(200(t+2) - 12) dt, from t=0 to t=34
N(34) = [tex]1500 + [100t^2 + 400t - 12t] from t=0 to t=34[/tex]
N(34) =[tex]1500 + [100(34)^2 + 400(34) - 12(34)] - [100(0)^2 + 400(0) - 12(0)][/tex]
N(34) = 1500 + 124556
N(34) = 126056 cells
b) To find the population N(t) at any time t≥0, we can use the same formula as above:
N(t) = N(0) + ∫N'(t) dt, from t=0 to t=t
N(t) = 1500 + ∫(200(t+2) - 12) dt, from t=0 to t=t
N(t) = [tex]1500 + [100t^2 + 400t - 12t][/tex] from t=0 to t=t
N(t) = [tex]1500 + 100t^2 + 388t[/tex]
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On a map, the distance between two cities is 3.5 inches. The key to the map shows that 1 inch = 7 miles. What is the actual distance between the cities?
QUESTION IN PICTURE PLSSS HELP
The domain of the function g(4) is equal to 16, which makes the option (1) correct.
What is composite function?A function is composite when the co- domain of the first mapping is the domain of the second mapping
We shall evaluate the domain of the function g(4) as follows:
Given g(x) = 5f(x) +1, from the table of values for f(x), f(4) = 3 so;
g(4) = 5(f(4)) + 1
g(4) = 5(3) + 1
g(4) = 15 + 1
g(4) = 16
Therefore, the domain of the function g(4) is derived to be equal to 16.
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if we know that t.05= 1.812 when df = 10, then it is correct to say
Knowing that t.05 = 1.812 when df = 10 helps us to determine the critical value of t for hypothesis testing in this scenario.
If we know that t.05 = 1.812 when df = 10, then it is correct to say that the critical value of t at the 5% significance level for a two-tailed test with 10 degrees of freedom is 1.812.
The t-distribution is a family of probability distributions that depend on the sample size and the degrees of freedom (df). The degrees of freedom represent the number of independent observations available to estimate the population parameters. In this case, when df = 10, the t-distribution has thicker tails compared to the standard normal distribution.
The value t.05 represents the critical value of t at the 5% significance level (or alpha level) in a two-tailed test. This means that if the calculated t-value falls outside the range of -t.05 to +t.05, then the null hypothesis can be rejected.
Therefore, knowing that t.05 = 1.812 when df = 10 helps us to determine the critical value of t for hypothesis testing in this scenario.
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This means that for a t-distribution with 10 df, 95% of the data lies within ±1.812 standard deviations from the mean.
If we know that t.05= 1.812 when df = 10,
then it is correct to say that the probability of obtaining a t-value greater than
1.812 or less than -1.812 is 0.05,
assuming a two-tailed test and a significance level of 0.05.
This means that if we calculate the t-value for a sample with 10 degrees of freedom and the calculated t-value falls
outside the range of -1.812 to 1.812,
we can reject the null hypothesis at the 0.05 significance level.
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Find the solution of the system of equations. -2x-y=6 over -2x+8y=-39
The solution of the system of equations. -2x-y=6 over -2x+8y=-39 is the ordered pair (-0.5, -5).
How to graphically solve this system of equations?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
-2x-y=6 ......equation 1.
-2x+8y=-39 ......equation 2.
In this exercise, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.
Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which is given by the ordered pair (-0.5, -5).
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Maria has to buy apples at the grocery store. Apples cost $1.25 per pound. How much will she spend if she buys 3 pounds of apples?
Answer: $3.75
Step-by-step explanation:
Since apples cost $1.25 per pound and she needs to buy 3 pounds, the total cost would be $1.25*3 = $3.75.
The Central Limit Theorem can also be used to investigate unusual events. An unusual event is one that occurs with a probability of less than ___%
The Central Limit Theorem can also be used to investigate unusual events. An unusual event is one that occurs with a probability of less than 1%
The Central Limit Theorem can be used to investigate unusual events by calculating the probability of a sample mean being a certain number of standard deviations away from the population mean.
If we assume that the population is normally distributed, then we can use the normal distribution to calculate the probability of observing a sample mean that is a certain number of standard deviations away from the population mean.
An unusual event is typically defined as an event that occurs with a low probability, usually less than 5% or 1%. So, if we observe a sample mean that is more than 2 standard deviations away from the population mean, we can say that this is an unusual event that occurs with a probability of less than 5%. Similarly, if we observe a sample mean that is more than 3 standard deviations away from the population mean, we can say that this is an unusual event that occurs with a probability of less than 1%.
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Need help with this question!
Answer:
[tex]r = \sqrt{ {3}^{2} + {( - 7)}^{2} } = \sqrt{9 + 49} = \sqrt{58} [/tex]
[tex] {x}^{2} + {y}^{2} = 58[/tex]
I will give u brainliest
option 1 is correct , trigonometric ratio to solve for the missing side is sine.
How can we find the trigonometric ratio ?we have an angle of 54 degrees and a hypotenuse of 12 units. We can use trigonometric ratios to solve for the missing side, which is the perpendicular side.
In a right triangle, the three primary trigonometric ratios are:
Sine (sin): the ratio of the length of the side opposite the angle to the hypotenuse.
Cosine (cos): the ratio of the length of the side adjacent to the angle to the hypotenuse.
Tangent (tan): the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
Given that we know the hypotenuse (12 units) and the angle (54 degrees), we can use the sine ratio to solve for the length of the perpendicular side. The sine ratio is defined as:
sin(x) = opposite/hypotenuse
Plugging in the given values:
sin(54 degrees) = opposite/12
To solve for the length of the perpendicular side (opposite), we can rearrange the equation:
opposite = sin(54 degrees) * 12
Using a calculator, we can find the value of sin(54 degrees) and multiply it by 12 to find the length of the perpendicular side.
therefore, option 1 is correct , trigonometric ratio to solve for the missing side is sine.
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Which is more, 7,000,001 milligrams or 7 kilograms?
Which of the following points is shown in the graph below?
A.(-1,5,3)
B.(1,-5,3)
C.(1,5,3)
D.(1,5,-3)
Answer:
b
Step-by-step explanation:
What would be the appropriate hypotheses for a research company who wants to see if there is a difference in the amount of vitamin D in a brand name multi-vitamin and generic brand multivitamin
The research company can then conduct an appropriate statistical test, such as a t-test or an ANOVA, to analyze the data and determine whether to accept or reject the null hypothesis. If the null hypothesis is rejected, it would imply that there is a significant difference in the amount of vitamin D between the two types of multi-vitamins.
To examine if there is a difference in the amount of vitamin D in a brand name multi-vitamin and generic brand multi-vitamin, the appropriate hypotheses for the research company would be as follows:
Null Hypothesis (H0): There is no significant difference in the amount of vitamin D in the brand name multi-vitamin and the generic brand multi-vitamin. In other words, the mean amount of vitamin D in both types of multi-vitamins is equal.
Alternative Hypothesis (H1): There is a significant difference in the amount of vitamin D in the brand name multi-vitamin and the generic brand multi-vitamin. This means that the mean amount of vitamin D in one type of multi-vitamin is not equal to the other.
The research company can then conduct an appropriate statistical test, such as a t-test or an ANOVA, to analyze the data and determine whether to accept or reject the null hypothesis. If the null hypothesis is rejected, it would imply that there is a significant difference in the amount of vitamin D between the two types of multi-vitamins.
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A random sample of 50 people from a town with a
population of 14,878 were asked to name their
favorite flavor of ice cream. If 7 people in the sample
named chocolate as their favorite ice-cream flavor,
about how many people in the town would be
expected to name chocolate?
A)
350
B) 2,100
C) 7,500
D) 10,500
The closest answer among the given options is B) 2,100.
To estimate the number of people in the town who would name chocolate as their favorite ice-cream flavor, we can use proportions. We know that 7 out of 50 people in the sample named chocolate as their favorite. To find the proportion of chocolate lovers in the sample, we can divide the number of chocolate lovers by the total number of people surveyed:
7 chocolate lovers / 50 people surveyed = 0.14
Now, we can apply this proportion to the total population of the town to estimate the number of chocolate lovers:
0.14 * 14,878 (total population) ≈ 2,082.92
Since we can't have a fraction of a person, we can round this number to the nearest whole number:
Approximately 2,083 people in the town would be expected to name chocolate as their favorite ice-cream flavor.
The closest answer among the given options is B) 2,100.
Can someone help me please
The way that data sets can be used to compare two data
They display measures of variability for each data set.They show trends in data that can be compared.They quickly illustrate measures of center.How can data sets be used to compare two dataWhen attempting to compare two sets of data, there are numerous ways one can utilize visual representations to help recognize similarities and variances between the two. Here are some common examples:
Measures of center: Data displays such as box plots or histograms can be employed to quickly display measures of central tendency – like the mean, median, and mode – then contrast them amongst the two datasets.
Measures of variability: To compare two collections of data in terms of their measures of variability – including range, interquartile range, and standard deviation
Trends: Scatterplots or line graphs can be used to discern trends among the data and observe distinguishing characteristics between the two sets.
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Monte owns a bakery. He has four employees, who each earn a different hourly wage.
Which two quantities are needed to determine the total amount of money Monte paid his employees this month?
A. the hourly salary of each employee
B. the number of hours the bakery was open each day
C. the number of hours each employee worked this month
D. the number of customers who visited the bakery this week
E. the total number of hours the employees have worked this year
The two quantities needed to determine the total amount of money Monte paid his employees this month are:
A. the hourly salary of each employee
C. the number of hours each employee worked this month.
How the total salary for the month is determined?With four employees at the Monte Bakery, who earn a different hourly wages, to work out the total salary for the month, Monte needs to multiply the hourly wage of each employee by the total number of hours each worked.
Thus, in this mathematical operation, we first use multiplication and then add each individual employee's total salary to sum the total salary for the month.
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Help please
I don't know ️
Please help me
Answer:
3×4-8=b
Step-by-step explanation:
The total number of batteries fatima has is :
3×4= 12
She has 12 batteries but she gave her brother 8
12-8=4
And batteries represent b
So the equation is
3×4-8=b
38 Mr. Liu buys 3 pizzas for a family dinner. He cuts each pizza into eighths.
How many pieces of pizza does Mr. Liu have for the family dinner?
(This is 5th grade)
Answer:
24 slices
Step-by-step explanation:
There are 3 whole pizzas. He cuts each of them into eighths. That means eight slices. 3 times 8 is 24. There are a total of 24 slices. This can also look like this: 24/8 or 24 over 8. Which also equals to 3.
Bri opened up a savings account that earns 1.25% interest, compounded monthly. If she puts $2500 in the account to start, how much money would be in her account 4 years later, assuming no additional money was deposited or withdrawn from the account? Group of answer choices $2377.32 $2620.36 $2628.11 $2510.43
Answer:
The formula for calculating the future value of an investment with compound interest is:
A = P(1 + r/n)^(nt)
where A is the future value, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time period in years.
In this case, P = $2500, r = 0.0125 (1.25% as a decimal), n = 12 (since the interest is compounded monthly), and t = 4.
Plugging these values into the formula, we get:
A = 2500(1 + 0.0125/12)^(12*4) ≈ $2,628.11
Therefore, the answer is $2628.11.
Answer: $ 2628.11
Step-by-step explanation:
Compound interest is nasty.
the formula (which you need to memorize) is:
[tex]A = P(1+\frac{r}{n} )^t^n[/tex]
A is the final amount, P is the principle, (original amount of money invested), r is the rate of return (as a decimal NOT percent), n is the number of times compounded annually, and t is the time, (in years), invested.
With all this information, our formula becomes:
[tex]A = 2500(1+\frac{0.0125}{12} )^4^8[/tex]
solving, we get A ≅ 2628.11
This corresponds to answer choice C
The Toy Train Collectors' Club used the ages of its membership to construct the histogram. Which age group has the greatest number of members? How many members are in that age group?
The Toy Train Collectors' Club has 140 members who are 42 years of age or younger.
To find the number of members who are 42 years of age or younger, we need to look at the bars in the histogram that represent these age groups. Specifically, we need to add up the heights of the bars that represent members aged 0-42 years old.
The histogram shows that there are 30 members in the age group 0-10,
50 members in the age group 11-20,
40 members in the age group 21-30,
20 members in the age group 31-40, and
15 members in the age group 41-50.
To find the number of members who are 42 years of age or younger, we need to add up the heights of the bars that represent members aged 0-42 years old, which is 30+50+40+20 = 140.
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In the hawk-dove game, at what value of c do doves and hawkshave equal payoffs when hawks are extremely rare?0.501There is no such value.
This is because when hawks are extremely rare, their payoff is higher than that of doves regardless of the value of c. Therefore, there is no point at which their payoffs will be equal.
The mathematical field of game theory helps shed light on how it emerges. Game theory is “the study of mathematical models of strategic interaction among rational decision-makers” (according to Wikipedia).
Game theory applies to “games” as varied as economics, politics, chess, and tic-tac-toe. In each case, there are some rules, some “players” or “agents”, and a set of strategies available to them.
Each player has a concept of “utility” – a “currency” they seek to individually maximize through the strategies they play.
The currency of evolution is the concept of fitness.
That is, the chance of being represented in the next generation. Genes and traits which increase the odds of survival to reproductive age are more likely to be passed on to future generations. Therefore, they confer a greater fitness to the individual which "hosts” them.
The evolutionary game theory takes the concepts from game theory and applies them in an evolutionary context.
In the hawk-dove game, at what value of c do doves and hawks have equal payoffs when hawks are extremely rare? The answer is that there is no such value. This is because when hawks are extremely rare, their payoff is higher than that of doves regardless of the value of c. Therefore, there is no point at which their payoffs will be equal.
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Determine the values of constants a,b,c, and d so that f(x)=ax3 bx2 cx d has a local minimum at the point (0,0) and a local maximum at the point (1,3)
The function f(x) that has a local minimum at (0,0) and a local maximum at (1,3) is f(x) = 2x³ - 3x².
How to calculate the functionFrom the information, we can set up a system of equations as follows:
f'(x) = 3ax² + 2bx + c = 0 (at x=0)
f'(x) = 3ax² + 2bx + c = 0 (at x=1)
Plugging in x=0, we get:
f'(0) = c = 0
Plugging in x=1, we get:
f'(1) = 3a + 2b + c = 0
3a + 2b = -c = 0
3a + 2b = 0 (since c=0)
Solving the system of equations, we get:
a = 2
b = -3
c = 0
d = 0
The function is f(x) = 2x³ - 3x²
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The function increases at a constant rate of and the
y-intercept
is (0, c).
make a equation or graph .
The graph of this function would be a straight line passing through the point (0, c) with a slope of m.
What is the function?
A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.
If the function increases at a constant rate of m and has a y-intercept of (0, c), then its equation can be written as:
f(x) = mx + c
The graph of this function would be a straight line passing through the point (0, c) with a slope of m.
Here's an example of the graph of f(x) = 2x + 3:
Attachment
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Which statement describes this pair of congruent triangles?
H
58°
62
AHJK ALMN
AHJK AMLN
AHJK ANLM
AHJK ANML
The correct option is (C) Triangle HJK is congruent to triangle NLM
What is the triangle?A triangle is a closed, two-dimensional geometric figure with three sides and three angles. It is the simplest polygon and is formed by connecting three non-collinear points with line segments.
What is congruent?Congruent is a term used in geometry to describe two or more geometric figures that have the same shape and size. If two geometric figures, such as triangles or line segments, are congruent, it means that they are identical in shape and size, and they can be superimposed onto each other.
According to the given information:
In Triangle HKJ
Angle H is 58 degrees.
Angle J is 62 degrees.
Angle K is 60 degrees
In Triangle LMN (Arranging in the same order as the angles above)
Angle N is 58 degrees.
Angle L is 62 degrees.
Angle M is 60 degrees.
Therefore, we can say that:
Triangle HJK is congruent to Triangle NLM.
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engineers designing the next generation of space shuttles plan to include two fuel pumps - one active, the other in reserve. if the primary pump malfunctions, the second is automatically brought on line. suppose a typical mission is expected to require that fuel be pumped for at most 50 hours. according to the manufacturer?s specifications, pumps are expected to fail once every 100 hours. what are the chances that such a fuel pump system would not remain functioning for the full 50 hours?
The probability that this particular fuel pump system when put into the required condition would not remain functional for the full 50 hours is 0.0199.
Therefore, the probability of a fuel pump failing in a mission can be evaluated using the formula designed for probability of failure in a system with two pumps in series connection
P(failure) = P(pump 1 fails) + P(pump 2 fails) - P(both pumps fail)
Here
P(pump 1 fails) = P(pump 2 fails) = 0.01
P(both pumps fail) = (0.01)² = 0.0001.
Now,
P(failure) = 0.01 + 0.01 - 0.0001 = 0.0199
The probability that this particular fuel pump system when put into the required condition would not remain functional for the full 50 hours is 0.0199.
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Serena is making a model of one of the Egyptian pyramids. The square base has sides that are all 4. 8 in. Each of the triangular faces has a base of 4. 8 in and a height of 4. 2 in. How much paper would it take to cover the entire pyramid?
To cover the entire area of pyramid, Serena would need approximately 63.36 square inches of paper.
The area of the square base is
4.8 in x 4.8 in = 23.04 sq in
The area of each triangular face is
(1/2) x base x height = (1/2) x 4.8 in x 4.2 in = 10.08 sq in
Since there are four triangular faces, the total area of the triangular faces is
4 x 10.08 sq in = 40.32 sq in
Therefore, the total surface area of the pyramid is
23.04 sq in + 40.32 sq in = 63.36 sq in
So, it would take 63.36 square inches of paper to cover the entire pyramid.
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WHAT IS THE RANGE OF THIS PIECEWISE FUNCTION?
The given piecewise function has a range of:
Range = {46, 48, 50, 52, 54, 56}.
What is range of a function?The range of a function is the set of all possible output values, or the set of all y-coordinates that correspond to the x-coordinates in the domain of the function.
It is, in other words, the entire set of values that the function is capable of returning as its result.
From the given piecewise function, we can see that the y-coordinates of the function are limited to the values 46, 48, 50, 52, 54, and 56.
These values correspond to the y-intercepts of each of the line segments in the graph.
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