Answer:
We have the equation:
-3 + sin(-3x) = -7/2
Adding 3 to both sides gives:
sin(-3x) = -1/2
The solutions for sin(x) = -1/2 are x = 7π/6 and x = 11π/6 in the interval [0, 2π).
We need to find the solutions for -3x in the interval [0, π).
For x = 7π/18, we get -3x = -7π/6, which is not in the given interval.
For x = 5π/18, we get -3x = -5π/2, which is not in the given interval.
For x = π/18, we get -3x = -π/2, which is in the given interval.
Therefore, the solution to the equation in the given interval is:
-3x = -π/2
x = π/6
Write a rule for g that represents a translation 2 units down, followed by a reflection in the y-axis of the graph of f(x)=5^x
Answer:
Assuming that g(x) represents the transformed function, the rule for g can be obtained by applying the translation and reflection operations in the correct order.
To translate the graph of f(x) down by 2 units, we need to subtract 2 from the function. This gives us:
h(x) = f(x) - 2 = 5^x - 2
Next, we need to reflect the graph of h(x) in the y-axis. To do this, we replace x with -x in the function. This gives us:
g(x) = h(-x) = 5^(-x) - 2
Therefore, the rule for g(x) that represents a translation 2 units down, followed by a reflection in the y-axis of the graph of
f(x) = 5^x is:g(x) = 5^(-x) - 2
I just need the answers please
The evaluations of the composite functions expressions and operations are presented as follows;
1. (f + g)(x) = 2·x² + 7·x + 3
(f - g)(x) = 7·x + 21
(f · g)(x) = x⁴ + 7·x³ + 3·x² - 63·x - 108
(f/g)(x) = f(x)/g(x) = (x² + 7·x + 12)/(x² - 9)
2. (f + x)(x) = 3·x - 2
(f - g)(x) = x + 4
(f · g)(x) = f(x) × g(x) = (2·x + 1) × (x - 3) = x⁴ + 7·x³ + 3·x² - 63·x - 108
(f/g)(x) = (2·x + 1)/(x - 3)
3. f[h(-9)] = 25
4. h[f(4)] = 20
5. g[h(-2)] = 10
6. The composite function that converts inches into miles is; n/63360
What are composite functions?Composite function is a function that is applied to the result of another function.
Part 1: Operations of Functions
1. f(x) = x² + 7·x + 12 and g(x) = x² - 9, therefore;
(f + g)(x) = f(x) + g(x) = (x² + 7·x + 12) + (x² - 9) = 2·x² + 7·x + 3
(f - g)(x) = f(x) - g(x) = (x² + 7·x + 12) - (x² - 9) = 7·x + 21
(f · g)(x) = f(x) × g(x) = (x² + 7·x + 12) × (x² - 9) = x⁴ + 7·x³ + 3·x² - 63·x - 108
(f/g)(x) = f(x)/(g(x)) = (x² + 7·x + 12)/(x² - 9)
2. f(x) = 2·x + 1 and g(x) = x - 3
(f + g)(x) = f(x) + g(x) = 2·x + 1 + (x - 3) = 3·x - 2
(f - g)(x) = f(x) - g(x) = 2·x + 1 - (x - 3) = x + 4
(f · g)(x) = f(x) × g(x) = (2·x + 1)·(x - 3) = 2·x² - x - 3
(f/g)(x) = f(x)/(g(x)) = (2·x + 1)/(x - 3)
Part 2; 3. f(x) = x², g(x) = 5·x, and h(x) = x + 4
f[h(-9)] = (h(-9))² = (-9 + 4)² = 25
4. f(x) = x², g(x) = 5·x, and h(x) = x + 4
h[f(4)] = (f(4) + 4) = (16 + 4) = 20
5. f(x) = x², g(x) = 5·x, and h(x) = x + 4
g[h(-2)] = (h(-2) × 5) = (-2 + 4) × 5 = 10
6. The formula F = n/12 converts n inches into feet f, and m = f/5280 converts feet to miles m.
Let F(N) represent the function that converts inches to feet and let G(F) represent the function that converts feet to miles. Then the composition function that converts inches to miles is G(F(N))
G(F(N)) = G(n/12) = (n/12)×(1/5280) = n/63360
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The functions f(x), g(x), and h(x) are shown below. Select the option that
represents the ordering of the functions according to their average rates of change on
the interval 1
HELP!!!
Arrange the functions according to the average rate of change in the interval 1<1. ×< 3 is: g(x) < f(x) = h(x)
In other words, g(x) has the smallest average rate of change, while f(x) and h(x) have the same largest average rate of change.
What is function?A function is a mathematical rule that takes an input (or inputs) and produces a corresponding output.
It describes a relationship between two quantities, where each input is associated with exactly one output.
Since the interval of interest is not provided, I will assume that the interval is 1 < x < 3, based on the graphs of the functions given.
To determine the ordering of the functions according to their average rates of change on the interval 1 < x < 3, we can use the following formula:
Average rate of change = (f(b) - f(a)) / (b - a)
where a and b are the endpoints of the interval.
Using this formula, we can calculate the average rates of change of the three functions on the interval 1 < x < 3. Here are the results:
f(x): average rate of change = (f(3) - f(1)) / (3 - 1) = (2 - (-2)) / 2 = 2
g(x): average rate of change = (g(3) - g(1)) / (3 - 1) = (-3 - (-1)) / 2 = -1
h(x): average rate of change = (h(3) - h(1)) / (3 - 1) = (0 - (-4)) / 2 = 2
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The complete question is given below:
Arrange the functions in the period 1 according to the average rate of change. 3 is: g(x) f(x) = h(x)
In other words, g(x) has the lowest average rate of change, whereas f(x) and h(x) both have the highest average rate of change.
What is a Function?A function is a mathematical rule that accepts an input (or inputs) and generates an output.
It defines a relationship among two quantities in which each input corresponds to only one output.
Because the interval of interest is not specified, I will assume that it is 1 x 3 based on the graphs of the functions supplied.
We can use the formula that follows to find the ordering of the functions based on their average frequencies of change on the interval 1 x 3:
Change at an Average Rate = (f(b) - f(a)) / (b - a)
where a and b are the interval's ends.
We can compute the average rates of change of all three functions on the interval 1 x 3 using this formula. Here are the outcomes:
f(x): average rate of change = (f(3) - f(1)) / (3 - 1)
= (2 - (-2)) / 2
= 2
g(x): average rate of change = (g(3) - g(1)) / (3 - 1)
= (-3 - (-1)) / 2
= -1
h(x): average rate of change = (h(3) - h(1)) / (3 - 1)
= (0 - (-4)) / 2
= 2
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Please help me ill give
Brainliest
Answer:
A
Step-by-step explanation:
Since both the x and y coordinates changed signs, this is a reflection over the origin. A reflection over the origin is a reflection across both axes.
Answer: A
A random sample of patients at a medical office found that 40% were in the age range 13–21. There are 1,100 patients in total. Use the experimental probability from the survey to predict about how many patients are in the age range 13–21
we can estimate that about 440 patients in the medical office are in the age range 13-21. The experimental probability of finding a patient in the age range 13-21 is 40%, which means that for every 10 patients in the medical office, 4 are in the age range 13-21.
To estimate how many patients are in the age range 13-21, we can use the proportion of the sample in the age range 13-21 and apply it to the entire population. In this case, we can use the proportion of patients in the age range 13-21 in the sample to estimate the number of patients in the age range 13-21 in the population.
The sample size is not given in the problem, but we are told that there are 1,100 patients in the medical office. Let's assume that the sample size is large enough to make a reasonable estimate.
So, if 40% of the sample is in the age range 13-21, then we can estimate that about 40% of the total population of 1,100 patients are also in the age range 13-21.
To calculate this, we can use the following formula:
estimated number of patients in the age range 13-21 = proportion in sample x total population
= 0.40 x 1,100
= 440
Therefore, we can estimate that about 440 patients in the medical office are in the age range 13-21.
It's important to note that this is just an estimate based on the experimental probability from the sample. The actual number of patients in the age range 13-21 may vary from this estimate due to sampling error or other factors. However, this estimate can still provide a useful approximation for planning and decision-making purposes.
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Use the following information to answer questions 10 - 13. (You will be following the steps to calculate the finance charge on an unpaid balance, and find the new balance.)
• Previous Balance: $678.98
• Payment: $150
• Purchases: $147.20
• APR: 14.24%
• Period: Monthly
10. What is the unpaid balance?
11. What is the periodic rate?
12. What is the finance charge?
13. What is the new balance?
The periodic rate is the annual percentage rate (APR) divided by the number of periods per year. The periodic rate is 1.1867%
What is the finance charge?The finance charge is the cost of borrowing money, and it is typically expressed as a percentage of the outstanding balance. In the given scenario, the finance charge is the interest that is charged on the unpaid balance.
According to question:10) The unpaid balance is the previous balance minus the payment, which is:
Unpaid balance = Previous balance - Payment
= $678.98 - $150
= $528.98
Therefore, the unpaid balance is $528.98.
11) The periodic rate is the annual percentage rate (APR) divided by the number of periods per year. Since the period is monthly, we divide the APR by 12. The periodic rate is:
Periodic rate = APR / 12
= 14.24% / 12
= 1.1867%
Therefore, the periodic rate is 1.1867%.
12) The finance charge is the unpaid balance multiplied by the periodic rate. The finance charge is:
Financial charge = Unpaid balance times the periodic rate
= $528.98 × 1.1867%
= $6.28 (rounded to the nearest cent)
Therefore, the finance charge is $6.28.
13) The new balance is the sum of the unpaid balance, the finance charge, and the purchases. The new balance is:
New balance = Unpaid balance + Finance charge + Purchases
= $528.98 + $6.28 + $147.20
= $682.46
Therefore, the new balance is $682.46.
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what can be said about the coefficients of the polynomial obtained by multiplying out when both and are odd integers? when both and are even integers? when one of and is even and the other is odd?
Odd coefficients of the polynomial are obtained by multiplying both odd integers.
Even coefficients of the polynomial are obtained by multiplying both even integers.
Even and odd coefficients of the polynomial are obtained by multiplying both odd integers.
Lets take two integer m and n,
If both 'm' and 'n' are odd integers, then the coefficients of the polynomial obtained by multiplying out will be odd.
If both 'm' and 'n' are even integers, then the coefficients of the polynomial obtained by multiplying out will be even.
If one of 'm' and 'n' is even and the other is odd, then the coefficients of the polynomial obtained by multiplying out will be even and odd.
There are no other cases.
The general form of the polynomial obtained by multiplying out a binomial is:
[tex](a+b)^n = nC_0a^n + nC_1a^{(n-1)}b + nC_2a^{(n-2)}b^2 + .....+ nC_n-1ab^{(n-1)} + nC_nb^n[/tex]
where [tex]nC_k[/tex] is a binomial coefficient.
In general, for a polynomial [tex](a+b)^n[/tex], the coefficient of the term of degree k is [tex]nC_k[/tex].
The binomial coefficients are defined as: [tex]nC_k = n! / (k!\times(n-k)!)[/tex]
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The logarithmic equation log(-x)+log(x+11)=1 has two solutions, -1 and -10. Determine if these are reasonable or extraneous solutions.
A) -1 and -10 are both reasonable (valid) solutions
B) -1 is a reasonable solution but -10 is an extraneous solution
C) -1 is an extraneous solution but -10 is a reasonable solution
D) -1 and -10 are both extraneous solutions
In the expression D) -1 and -10 are both extraneous solutions.
What is expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
The given logarithmic expression is
=> log(-x)+log(x+11) = 1 .
Here the given expression solution is -1 and -10.
Now put x=-1 into given expression then,
=> log(-(-1))+log(-1+11) =1
=> log(1)+log(10) =1
=> 0+1=1
=> 1=1
Then -1 is extraneous solution.
Now put x=-10 then,
=> log(-1(-10))+log(-10+11)=1
=> log(10)+log(1)=1
=> 1+0=1
=> 1=1
Then x=-10 is also extraneous solution.
Hence the correct option is D) -1 and -10 are both extraneous solutions.
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a woman is phenotypically normal, but her father had the sex-linked recessive condition of hemophilia, a blood-clotting disorder. if she has children with a man with a normal phenotype, what is the probability that their two sons will both have hemophilia?
The probability that their two sons will both have hemophilia is 0%.
Hemophilia is a sex-linked recessive disorder, which means that it is passed from mother to son. Since the woman does not have the disorder, she does not carry the gene for it and therefore her sons would not be affected by the disorder.
However, her daughters could be carriers of the disorder and could pass it on to their sons.
In order for a son to be affected by hemophilia, his mother must carry the gene for the disorder and the father must also have the gene. If the father does not have the gene, then the son will not have hemophilia.
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Hellppppppppppppppppp
lara ran the first leg of a relay race in 14.06 seconds. sheela ran the second leg. the total time it took both girls to run the race was 27.89 seconds. how long did it take sheela to run the second leg of the race?
it takes Sheela to run the second leg of the race: Ascertain the total or contrast: x = 13.83.
In view of the given circumstances, plan:: 14.06+ x = 27.89
Modify variables to the left half of the situation: x = 27.89 - 14.06
Ascertain the total or contrast: x = 13.83
Speed = Distance/Time - This lets us know how slow or quick an article moves. It portrays the distance voyaged partitioned when taken to cover the distance.
Speed is straightforwardly Relative to Distance and Conversely corresponding to Time. Thus,
Distance = Speed X Time, and
Time = Distance/Speed, as the speed builds the time taken will diminish as well as the other way around.
Utilizing these recipes any fundamental issues can be settled. Nonetheless, the right utilization of units is additionally something essential to consider while utilizing equations.
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Mr. Steiner purchased a car for about $14,000. Assuming his loan was compounded monthly at an interest rate of 4.9% for 6 years. How much will he pay for the car in total? (Use the formula below. Round to TWO decimal places and include $ in front)
Answer: His car was $415.18 in total
Step-by-step explanation: The calculation of the present value of a cash flow or other income stream that produces $1 in income over so many periods of time.
Amount borrowed = $12,500
Annual interest rate = 12.00%
Monthly interest rate = 1.00%
Period = 36 months
Let monthly payment be x
12,500 = x/1.01 + x/1.01^2 + x/1.01^3 … + x/1.01^35 + x/1.01^36
12,500 = x * (1 - (1/1.01)^36) / 0.01
12,500 = x * 30.107505
x = 12,500/30.107505
x = 415.18
So, the monthly payment is $415.18
WHATS THE ANSWER????
Answer:
They are congruent by AA- because the only thing they have in common is the 65 degree angles but the sides are all different
Step-by-step explanation:
R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
Find the values of a and b that complete the mapping diagram.
An effective visual representation of a function or a mapping between two sets is a mapping diagram. It consists of two vertical columns, one of which represents the domain set items and the other of which represents the range set elements. The items in the range set that match to those in the domain set are listed in the right column, and vice versa.
I assume you are given a mapping rule that relates elements in a set to other elements in another set, and you are asked to complete a mapping diagram based on this rule.
If the mapping rule is not specified, we cannot determine the values of a and b. However, assuming that the mapping rule is such that each element (x, y) in the set R is mapped to [tex](x + a, y + b)[/tex], we can complete the mapping diagram as follows:
The given set R is:
R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
If we apply the mapping rule to each element in R, we get:
(-3, -2) → (-3 + a, -2 + b)
(-3, 0) → (-3 + a, 0 + b)
(-1, 2) → (-1 + a, 2 + b)
(1, 2) → (1 + a, 2 + b)
To complete the mapping diagram, we need to find the values of a and b such that each mapped element is in the set R. That is, we need to find a and b such that:
(-3 + a, -2 + b) ∈ R
(-3 + a, 0 + b) ∈ R
(-1 + a, 2 + b) ∈ R
(1 + a, 2 + b) ∈ R
Substituting the values of R into each of these equations, we get:
(-3 + a, -2 + b) = (-3, -2), which gives a = 0 and b = 0
(-3 + a, 0 + b) = (-3, 0), which gives a = 0 and b = 0
(-1 + a, 2 + b) = (-1, 2), which gives a = 0 and b = 0
(1 + a, 2 + b) = (1, 2), which gives a = 0 and b = 0
Therefore, the values of a and b that complete the mapping diagram are a = 0 and b = 0.
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6 Quincy bought a variety-pack that contained 20 game dice. He sorted the dice by color and found that 15% of the dice were red. How many red dice were in the pack?
Answer:
If 15% of the dice were red, then the proportion of red dice is 0.15.
To find out how many red dice are in the pack, we can multiply this proportion by the total number of dice:
0.15 x 20 = 3
Therefore, there are 3 red dice in the variety pack.
Step-by-step explanation:
If 15% of the dice in the variety-pack are red, then the proportion of red dice to total dice is 0.15.
Let's represent the number of red dice as "x".
We know that the total number of dice in the pack is 20. Therefore, the number of non-red dice must be 20 - x.
We can set up an equation using the proportion of red dice:
x/20 = 0.15
To solve for x, we can multiply both sides by 20:
x = 20 * 0.15
x = 3
Therefore, there are 3 red dice in the pack.
trough is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across at the top and have a height of 1 ft. if the trough is being flled with water at a rate of 12 ft 3 ymin, how fast is the water level rising when the water is 6 inches deep?
The water level is rising at a rate of 32 ft/min when the water is 6 inches deep.
How to solve rise of water level?
Let's first draw a diagram to better understand the problem:
/|\
/ | \
/ | \
/ |h \
/ | \
/ | \
/ | \
/ | \
/ | \
/ | \
/_________|
b
where h is the height of the water, b is the width of the trough at water level, and 10 is the length of the trough.
Since the trough is being filled at a rate of 12 ft³/min, the volume of water in the trough is increasing at a rate of 12 ft³/min. Let's use this to find the rate at which the water level is rising.
The volume of water in the trough is given by the formula:
V = (1/2)bh²
where b is the width of the trough at water level, h is the height of the water, and 1/2 is the area of the triangular cross-section of the trough. We want to find the rate at which h is changing when h = 6 inches = 0.5 ft.
Differentiating both sides of the formula with respect to time t, we get:
dV/dt = (1/2)(db/dt)(h^2) + (1/2)(b)(2h)(dh/dt)
where db/dt is the rate at which the width of the trough at water level is changing, and dh/dt is the rate at which the water level is changing (i.e., the rate we want to find).
We know that dV/dt = 12 ft³/min and h = 0.5 ft. We also know that the width of the trough at the water level is 3 ft. To find db/dt, we need to use similar triangles. The triangle formed by the water and the sides of the trough is similar to the isosceles triangle at the end of the trough. Therefore, the ratio of the width of the trough at the water level to the height of the water is constant:
b/h = 3/1
Solving for b, we get:
b = 3h
on diffrentiating
db/dt = 3(dh/dt)
Substituting the values we know into the formula for dV/dt, we get:
12 = (1/2)(3h)(h²) + (1/2)(3h)(2h)(dh/dt)
12 = (3/2)h³+ 3h²(dh/dt)
4 = h²(dh/dt)
Solving for dh/dt, we get:
Therefore, the water level is rising at a rate of 32 ft/min when the water is 6 inches deep.
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Can someone pls help me with this
A. The equation of the line that passes through the point (4,3) and has a slope of -5/2 is y = (-5/2)x + 13.
B. The x-intercept of the equation is x = 26/5 or 5.2
How to Find the Equation of a Line?A. To find the equation of a line that passes through the point (4,3) and has a slope of -5/2, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is the given point.
Substituting the values, we get:
y - 3 = (-5/2)(x - 4)
Expanding the right side:
y - 3 = (-5/2)x + 10
Adding 3 to both sides:
y = (-5/2)x + 13
B. To find the x-intercept of this equation, we need to set y = 0 and solve for x:
0 = (-5/2)x + 13
Multiplying both sides by -2/5:
0 = x - (26/5)
Adding (26/5) to both sides:
x = 26/5
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What is the area of the parallelogram
Base is 8 height is 5 and width is 5.1:
I NEED AN ASWER ASAP
abc and def are similar. Find the missing side length.
According to the given information EF = 8 and DF = 7.
What is triangle ?A triangle is a three-sided polygon made up of three line segments that connect at three endpoints, called vertices. The study of triangles is an important part of geometry, and it has applications in various fields such as engineering, architecture, physics, and computer graphics.
According to the given information :Since triangle ABC and triangle DEF are similar, their corresponding sides are proportional. That is:
AB/DE = BC/EF = AC/DF
We are given AB = 40, BC = 64, AC = 56, and DE = 5. We can use the ratio AB/DE = BC/EF to find EF:
AB/DE = BC/EF
40/5 = 64/EF
8 = 64/EF
EF = 64/8
EF = 8
So EF = 8.
Similarly, we can use the ratio AC/DF to find DF:
AC/DF = AB/DE
56/DF = 40/5
56/DF = 8
DF = 56/8
DF = 7
So DF = 7.
Therefore,according to the given information EF = 8 and DF = 7.
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9. What is the volume of the triangular prism
below?
5 cm
3 cm
4 cm
3 cm
Answer:
Step-by-step explanation:
The radical form for each expression is given as follows:
How to obtain the radical form of each expression?
The general format of the exponential expression is given as follows:
To obtain the radical form, we have that:
a is the radicand.
n is the exponent.
m is the root.
Hence the radical form of the exponential expression is given as follows:
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Tough problem: Aisha bought a rectangular field. The perimeter of
the field is 240m. If the length of the field is increased by 8m and the
width is decreased by 5m, the area is decreased by 42m2
. Find the
length and the width of the field. Hint: If you set things right one of the
equations you get is not actually a linear equation, however it is
solvable.
Answer:
let W =with of field (M)
L=length of field=(7/5)×W
P=perimeter of field =2×(L+W) =240m
substiting L as fungtion of w in last equation:
2×(7/5)×W+W=240m
(12/5×w=120m
W=(5×+20m)/12=50m
L=(7/5×50m)=70m
What would be the new coordinates of W' after a dilation of 3? W
The new coordinates would be
W' (12 , 6)
X'( 24 , 18 )
Z'(24 ,6 )
What exactly does coordinate geometry mean?
The term "coordinate geometry" refers to the study of geometry using coordinate points (or analytic geometry). Calculating distances between points, segmenting lines into m:n pieces, finding a line's midpoint, figuring out a triangle's area in the Cartesian plane, and other operations are all achievable with coordinate geometry.
Remember that the rule for a dilation by a factor of k about the origin is
(x,y) = (kx, ky)
Identify the coordinates of the points W, X and Z. Then, apply a dilation by a factor of 3 about the origin to find W', X' and Z', the new coordinates after the dilation.
w = (4,2)
x = ( 8, 6 )
z = ( 8,2)
Apply a dilation by a factor of 3:
W(4,2) ⇒ W'(3 * 4, 3 * 2) = W' (12 , 6)
X(8 ,6 ) ⇒ X'(3 * 8 , 3 * 6 ) = X' ( 24 , 18 )
Z(8 , 2 ) ⇒ Z'(3*8 , 3 * 2) = Z'(24 ,6 )
Therefore, the new coordinates would be
W' (12 , 6)
X'( 24 , 18 )
Z'(24 ,6 )
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Which can cover a greater area, 2 quarters, each with a diameter of 1 inch, or 1 half dollar, with a diameter of 1. 2 inches?
The area of the half-dollar coin with a diameter of 1.2 inches is greater.
Both the given objects have a circular shape with a different diameter.
One of the objects is made up of two separate quarters of a circle, each with a diameter of 1 inch.
On the other hand, the second object is one half-dollar coin with a diameter of 1.2 inches.
We will use the formula of the area of a circle that is : A = πr²
Where A is the area of the circle.
π is the constant value (3.14)
r is the radius of the circle.
Let's calculate the area of 2 quarters each with a diameter of 1 inch.
The radius will be half of the diameter.
So, the radius is 1/2 inch for each quarter of the circle.
A = πr²A = π × (1/2)²A = π × 1/4A = 0.7854 square inches.
The total area of both quarters will be = 2 × 0.7854 square inches
The total area of both quarters = 1.5708 square inches
Now, let's calculate the area of the half-dollar coin with a diameter of 1.2 inches.
The radius will be half of the diameter.
The radius of the half-dollar coin = 1.2 / 2 = 0.6 inch
A = πr²A
= π × 0.6²A
= π × 0.36A
= 1.1318 square inches
The half-dollar coin has a greater area as compared to the two quarters of a circle.
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the simple regression equation assumes that while the error is not observable, it has a distribution with a mean equal to
The simple regression equation assumes that while the error is not observable, it has a distribution with a mean equal to 0 and a constant variance.
A simple regression equation describes how a single variable relates to another variable. It is one of the most widely used statistical tools. Simple regression is used when one predictor variable, often referred to as an independent variable, is used to explain the variance in a dependent variable.There are two types of simple regression equations, linear and nonlinear.
A linear regression equation is a straight line with a constant slope that represents the relationship between two variables, while a nonlinear regression equation is a curve that represents the relationship between two variables.According to the simple regression equation, while the error is not observable, it has a distribution with a mean equal to 0 and a constant variance. The error is the difference between the actual and predicted values of the dependent variable, and it measures the accuracy of the regression equation's predictions.
The mean of the error is zero, which indicates that the predicted values are equal to the actual values on average. The variance of the error is constant, which indicates that the error is distributed evenly throughout the dataset.
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please help me solve this i’ll mark brainliest
As the two triangles are congruent by AAS congruence rule, the segments AB is equivalent to FG.
What are congruent triangles?If two triangles are the same size and shape, they are said to be congruent.
To establish that two triangles are congruent, not all six matching elements of either triangle must be located.There are five requirements for two triangles to be congruent, according to studies and trials.
The congruence properties are SSS, SAS, ASA, AAS, and RHS.
Now in the given figure,
D is the midpoint, so CE = BG.
∠ABC ≅ ∠FGE
That gives us, AB ≈ FG as sides corresponding to equivalent sides are also equivalent to each other.
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calculate the value of the interquartile range for the following subsample: 24, 27, 35, 31, 21, 22, 28, 18, 25, 24, 36, 20.
The value of the interquartile range for the given subsample is 8.
The interquartile range (IQR) is a measure of the dispersion of a set of observations. It is defined as the difference between the third quartile and the first quartile (Q3-Q1). The subsample data is as follows: 24, 27, 35, 31, 21, 22, 28, 18, 25, 24, 36, 20. The interquartile range for the subsample data can be computed as follows:
Step 1: Arrange the data in ascending order: 18, 20, 21, 22, 24, 24, 25, 27, 28, 31, 35, 36.
Step 2: Find the median of the lower half of the data, which is called the first quartile, Q1. Here, the lower half of the data is 18, 20, 21, 22, 24, and 24. Hence, the median of the lower half of the data is the average of the two middle values, which is Q1 = (22 + 21)/2 = 21.5.
Step 3: Find the median of the upper half of the data, which is called the third quartile, Q3. Here, the upper half of the data is 24, 25, 27, 28, 31, 35, and 36. Hence, the median of the upper half of the data is the average of the two middle values, which is Q3 = (28 + 31)/2 = 29.5.
Step 4: Calculate the interquartile range as the difference between the third quartile and the first quartile: IQR = Q3 - Q1 = 29.5 - 21.5 = 8.
Therefore, the value of the interquartile range for the given subsample is 8.
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PLEASE HELP ME SOMEONE its due tomorrow.
The analysis of the data to obtain the best fit line equations that model the data, indicates;
5. a. Quadratic
b. y = -0.1179·x² + 2.1124·x + 4.215
c. Please find the completed chart showing the predicted values and the in the residuals in the following section.
6. a. A linear model may not be appropriate for the data in the residual plot
b. 4
c. 5
4. a. The exponential model of the function is; y = 100·e^(-0.124·t)
b. The weight after 8 weeks is about 37.1 grams
c. The sample will be 4 grams in about 26 weeks
5. a. The equation is; y = 22.703·x + 2.5733
b. The predicted y-value at x = 10 is; y = 229.60
c. The first time is about x ≈ 3.54
What is the best fit line?The best fit line is a line that is drawn through a set of data points in such a way that it minimizes the sum of squared errors of the data.
5. The best fit model can be obtained by plotting a scatter plot of the graph, which indicates that the best fit line resembles the shape of a parabola.
Therefore;
a. The best fit equation is; Quadratic
b. The best fit equation, obtained using technology is; y = -0.1179·x² + 2.1124·x + 4.215
The square of the correlation coefficient is; R² = 0.9584
The chart can be filled with the best fit equation as follows;
[tex]\begin{tabular}{ | c | c | c | c | c | }\cline{1-4}Distance (foot) & Height (foot) & Predicted Value &Residual \\ \cline{1-4}0 & 4 & 4.215 & -0.215 \\\cline{1-4}2 & 8.4 & 8.16588 & 0.23412 \\\cline{1-4}6 & 12.1 & 13.23804 & -1.13804 \\\cline{1-4}9 & 14.2 & 14.56626 & -0.36626\\\cline{1-4}12 & 13.2 & 13.77228 & -0.57228 \\\cline{1-4}13 & 10.5 & 13.03602 & -2.53602 \\\cline{1-4}15 & 9.8 & 10.8561 & -1.0561 \\\cline{1-4}\end{tabular}[/tex]
The predicted value are obtained by plugging in the x-value into the best fit equation and the residuals is the difference between the actual value and the predicted value.
6. a. A residual plot can be used to as assessment with regards to meeting the assumptions of a linear regression model.
A residual plot that is randomly scattered about zero indicates that a linear model is appropriate for the data.
The data points in the residual plot are not expressed as being randomly scattered around zero.
The pattern that exists in the residual plot indicates that the values are positive for x-values that are either low or high, and the middle x-values have a negative residuals. Therefr;
The pattern indicates that a linear regression model may not be appropriate for the datab. The number of positive residuals = 4
c. The number of negative residuals = 5
4. The general form of the exponential model of a function, y = A × e^(-k·t) can be used to find the function for the data as follows;
A = The initial amount = The value at 0 = 100
y = The amount of radioactive material at a given time t
e = Euler's number = 2.71828
The datapoints in the table indicates;
88.3 = 100 × e^(-k × 1)
k = -㏑(0.883) ≈ 0.124
The exponential model is therefore; y = 100 × e^(-0.124·t)
b. The weight of the sample after 8 weeks can be obtained by plugging in t = 8 in the exponential function for the weight of the radioactive substance as follows;
y = 100 × e^(-0.124 × 8) ≈ 37.1
The weight of the sample after 8 weeks is about 37.1 grams
c. When the sample is 4 grams we get;
y = 4
4 = 100 × e^(-0.124 × t)
e^(-0.124 × t) = 4/100 = 1/25
-0.124 × t = ln(1/25) = -ln(25)
t = ln(25)/0.124 ≈ 26
t ≈ 26 weeks
Therefore; The weight will be 4 grams after approximately 26 weeks
5. A linear regression can be performed using MS Excel to obtain the equation that models the data as follows;
y = 22.703·x + 2.5733
The square of the regression coefficient is; R² = 0.9995
a. The most appropriate equation to model the data in the table is; y = 22.703·x + 2.5733
b. The y-value when x = 10 can be predicted by plugging in x = 10 into the model equation for the data as follows;
y = 22.703 * 10 + 2.5733 ≈ 229.60
Therefore;
The predicted y-value when x is 10 is 229.60 (rounded to the nearest tenth)c. The first time the y-value is 83, can be found by setting y = 83 in the equation and solve for x as follows;
83 = 22.703·x + 2.5733
22.703·x = (83 - 2.5733)
x = (83 - 2.5733)/22.703 ≈ 3.54
Therefore, the first time the y-value is 83 is when x is approximately 3.54
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in a certain shipment of 18 18 computers, 6 6 are defective. 9 9 of the computers are selected at random without replacement. what is the probability that 4 4 of the 9 9 computers are defective? express your answer as a fraction or a decimal number rounded to four decimal places.
The probability that 4 of the 9 computers are defective is given by expression 0.3665.
It may be calculated by dividing the number of positive outcomes by the total number of potential outcomes. It is the attribute or state of being probable, the degree to which something is likely to happen. In other words, it is a way to gauge how likely an event is to occur.
out of 18 phones, 6 are defective. 9 of the phones are selected at random without replacement.
the probability that 4 of the 9 phones are defective
18 phones- 6 defective , 12 non-defective
9 phones- 4 defective , 5 non-defective
Required probability = [tex]\frac{^6 C_4*^1^2C_5 }{^1^8C_9}[/tex]
= 15x1188 / 48620
P = 0.3665
after rounding we get 0.3665.
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Complete question:
in a certain shipment of 18 computers, 6 are defective. 9 of the computers are selected at random without replacement. what is the probability that 4 of the 9 computers are defective? express your answer as a fraction or a decimal number rounded to four decimal places.
Describe each using a double inequality.
Answer:
Give me time to figure this out hold on
Step-by-step explanation:
12
I NEED HELP ON THIS ASAP!
Answer:
Step-by-step explanation:
The solution (16, 2) means 16 small gloves and 2 large gloves can be made in less than or equal to 16 hours and cost less than or equal to $40 in materials to make.