The first term of the GP is 4 and the common ratio is 3. We can now substitute these values into the formula for the sum of the first 10 terms to get 118096.
What is Geometric Progression?
A progression of numbers with a constant ratio between each number and the one before
Let the first term of the geometric progression be denoted by "a" and the common ratio be denoted by "r".
We know that the 4th term is 108, so we can use the formula for the nth term of a GP to write:
a*r³ = 108 .....(1)
We also know that the 8th term is 8748, so we can write:
a*r⁷ = 8748 .....(2)
To find the sum of the first 10 terms, we can use the formula for the sum of a finite geometric series:
S = a(1 - rⁿ)/(1 - r)
where S is the sum of the first n terms of the GP. We want to find the sum of the first 10 terms, so we plug in n = 10:
S = a(1 - r¹⁰)/(1 - r)
We now have two equations (1) and (2) with two unknowns (a and r). We can solve for a and r by dividing equation (2) by equation (1) to eliminate a:
(ar⁷)/(ar³) = 8748/108
r⁴ = 81
r = 3
Substituting r = 3 into equation (1) to solve for a, we have:
a*3³ = 108
a = 4
Therefore, the first term of the GP is 4 and the common ratio is 3. We can now substitute these values into the formula for the sum of the first 10 terms to get:
S = 4(1 - 3¹⁰)/(1 - 3)
S = 4(1 - 59049)/(-2)
S = 4(59048)/2
S = 118096
Therefore, the sum of the first 10 terms of the GP is 118096.
118096.
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Help me find the value of x
Answer:
x = 30
Step-by-step explanation:
We know
The three angles must add up to 180°. We know one is 20°, so the other two must add up to 160°.
2x + 3x + 10 = 160
5x + 10 = 160
5x = 150
x = 30
Suppose an unknown radioactive substance produces 16000 counts per minute on a Geiger counter at a certain time, and only 1000 counts per minute 13 days later. Assuming that the amount of radioactive substance is proportional to the number of counts per minute, determine the half-life of the radioactive substance.
The radioactive substance has a half-life of __ days.
The radioactive material has a half-life of roughly 11.8 days.
What exactly does half-life mean?The amount of time it takes for an active component of a medication to degrade by half in your body is referred to as the half-life.
Let's apply the exponential decay formula:
N(t) = N0 e(-kt)
Let's calculate the decay constant using the information provided:
At time t=0, the number of counts per minute is N0 = 16000.
At time t=13 days, the number of counts per minute is N(13) = 1000.
When we enter these numbers into the equation, we obtain:
N(13) = N0 e(-k*13)
1000 = 16000 e(-k*13)
e(-k*13) = 1000/16000
When we take the natural logarithm of both sides, we obtain:
ln(e(-k*13)) = ln(1000/16000)
-k*13 = ln(1000/16000)
k = -ln(1000/16000)/13
k ≈ 0.0585
We may use the half-life formula now that we know the decay constant:
t1/2 = ln(2)/k
Substituting k = 0.0585, we get:
t1/2 = ln(2)/0.0585
t1/2 ≈ 11.8
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Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than 0.28°C. Round your answer to 4 decimal places
The probability of obtaining a reading greater than 0.28°C is 0.3897.
What is standard normal distribution ?
The standard normal distribution is a specific type of probability distribution that has a mean of 0 and a standard deviation of 1. It is also called the Z-distribution or the Gaussian distribution.
The standard normal distribution is commonly used in statistics and probability theory to make comparisons and calculations across different normal distributions. To use the standard normal distribution for calculations involving a normal distribution with a different mean and standard deviation, the data must be standardized by subtracting the mean and dividing by the standard deviation.
According to the question:
To solve this problem, we need to standardize the value of 0.28°C using the standard normal distribution formula:
z = (x - mu) / sigma
where:
x = 0.28°C
mu = 0°C
sigma = 1.00°C
Substituting the values, we get:
z = (0.28 - 0) / 1.00
z = 0.28
Now, we need to find the probability of obtaining a reading greater than 0.28°C, which is the same as finding the area to the right of z = 0.28 on the standard normal distribution curve. We can use a standard normal distribution table or calculator to find this area.
Using a calculator or software, we find that the probability of obtaining a reading greater than 0.28°C is 0.3897, rounded to 4 decimal places.
Therefore, the probability of obtaining a reading greater than 0.28°C is 0.3897.
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Tutorial Exercise Find all the points at which the direction of fastest change of the function f(x, y) = x2 + y2 _ 8x 16y is i +j_ Step The direction in which the maximum rate of change of f(x, y) occurs at a point (a, b) is given by the vector Vfla, b) For flx,y) = x2 + y2 _ 8x - 16y, we have Vf(x, y) 2x 8)i + (2y - 16)jl (2x 8. 2y 16) Step 2 We need to find all points (x, Y) for which (2x 8)i + (2y 16)j is parallel to +j. So we must solve (2x 8)i + (2y 16)j k[i + j]- This means that k = 2x 8 and k = 2y 16. Equating these gives uS Submit
There are no points at which the function has its direction of fastest change along the vector i + j. This is because the equations lead to a contradiction.
The exercise asks to find all the points at which the function f(x, y) = x^2 + y^2 - 8x - 16y has its direction of fastest change along the vector i + j.
To find the points, we need to solve the equation:
(2x - 8)i + (2y - 16)j = k(i + j)
where k is a constant. Since the direction of fastest change is along the vector i + j, we know that the left-hand side of the equation represents the gradient vector of f(x, y).
Equating the x and y components of the gradient vector to the corresponding components of the vector i + j, we get:
2x - 8 = k
2y - 16 = k
Equating these two expressions for k, we get:
2x - 8 = 2y - 16
Solving for y in terms of x, we get:
y = x - 4
Substituting this expression for y into the equation of the gradient vector, we get:
2x - 8 = k
2(x - 4) - 16 = k
Simplifying, we get:
2x - 8 = k
2x - 24 = k
Substituting the first equation into the second, we get:
2x - 24 = 2x -
Simplifying, we get:
16 = 0
This is a contradiction, which means there are no points at which the function has its direction of fastest change along the vector i + j.
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A boat can travel 29mph in still water. If it travels 342 miles with the current in the same length of time it travels 180 miles against the current, what is the speed of the current?
29 = speed of the boat in still water
c = speed of the current
t = time it took each way
when going Upstream, the boat is not really going "29" fast, is really going slower, is going "29 - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "29" fast, is really going faster, is going "29 + c", because the current is adding its speed to it.
[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&180&29-c&t\\ Downstream&342&29+c&t \end{array}\hspace{5em} \begin{cases} 180=(29-c)(t)\\\\ 342=(29+c)(t) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{180=(29-c)t\implies \cfrac{180}{29-c}=t} \\\\\\ \stackrel{\textit{substituting on the 2nd equation from above}}{342=(29+c)\left( \cfrac{180}{29-c} \right)}\implies \cfrac{342}{29+c}=\cfrac{180}{29-c} \\\\\\ 9918-342c=5220+180c\implies 4698-342c=180c\implies 4698=522c \\\\\\ \cfrac{4698}{522}=c\implies \boxed{9=c}[/tex]
There are 450 seats in the lower level of a concert hall with b balcony seats in the upper level. So far, 170 tickets have been sold, which is 1/5 if the total number of seats in the concert hall. How many tickets sold are balcony seats?
Answer:
400 balcony seats
Step-by-step explanation:
We know 170 tickets have been sold which is 1/5 of the total tickets
We have to find the total number of seats by doing 170x5
Now we know that there are 850 seats (170x5)
We have to subtract the lower seats from the total number of seats to find b (balcony seats)
850-450 = 400
Therefore, b is equal to 400 balcony seats
ASAP PLEASE FOR A TEST!!!A line passes through (-1, 7) and (2, 10).
Which answer is the equation of the line?
O-3x+y=4
Ox+y=12
O = x+y=8
-3x+y=16
Answer:
i think this is the answer!! good luck
nction value. n=4 -1,4, and 2+2i are zeros; f(1)=-30
The polynomial function with the given zeros and numeric value at x = 1 is given as follows:
f(x) = x^4 - 7x³ + 16x² - 8x - 32
How to define the polynomial function?The zeros of the polynomial function are given as follows:
x = -1.x = 4.x = 2 + 2i.x = 2 - 2i. -> complex-conjugate theorem, when a complex number is a root of a polynomial function, it's conjugate also is.Then the linear factors of the function are given as follows:
x + 1.x - 4.x - 2 - 2i.x - 2 + 2i.According to the Factor Theorem, the function with leading coefficient a can be defined as a product of it's linear factors are follows:
f(x) = a(x + 1)(x - 4)(x - 2 - 2i)(x - 2 + 2i).
f(x) = a(x² - 3x - 4)(x² - 4x + 8)
f(x) = a(x^4 - 7x³ + 16x² - 8x - 32).
When x = 1, y = -30, hence the leading coefficient a is obtained as follows:
-30 = a(1 - 7 + 16 - 8 - 32)
-30a = -30
a = 1.
Hence the function is:
f(x) = x^4 - 7x³ + 16x² - 8x - 32
Missing InformationThe problem asks for the polynomial function with the given zeros and numeric value at x = 1.
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A salesperson earns 4% commission on furnace sales.
What is the commission that the salesperson earns on the sale of $33,000 worth of furnaces.
The commission earned 4 percentage on the salesperson on the sale of furnaces is $1320.
What is percentage?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. The word per cent means per 100. The letter "%" stands for it. The term "percentage" was adapted from the Latin word "per centum", which means "by the hundred". Percentages are fractions with 100 as the denominator.
by the question.
the commission that the salesperson earns on the sale of $33,000 worth of furnaces= 4% of 33,000 = 4× 330 = $1320
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the annual rainfall in 2017 in opuwo was 420mm.
the annual rainfall in 2018 was 12% more than in 2017.
Answer:
470.4 mm
Step-by-step explanation:
Given: the annual rainfall in 2017 in opuwo was 420 mm, the annual rainfall in 2018 was 12% more than in 2017.
First, find 12% of 420 mm:
12% of 420 mm
[tex]\frac{12}{100}[/tex] x 420 mm
1.2 x 420 mm
= 50.4 mm
Then add 50.4 mm to the previous annual rainfall of 420 mm:
50.4 mm + 420 mm
= 470.4 mm
Therefore, the annual rainfall in opuwo in 2018 is 470.4 mm.
If you start a bank account with N$15,000 and your bank compounds the interest monthly at
an interest rate of 9% p.a, how much money do you have at the year's end?
(Assume that you do not add or withdraw any money to/from the account).
Answer:
Step-by-step explanation:
16350$
Answer:
16 407.1
Step-by-step explanation:
Evaluate the expression for h = 6 and j = 5.
hj - h² =
Submit
Therefore, when h = 6 and j = 5, the value of hj - h² is -6.
What are arithmetic operations:Arithmetic operations are basic mathematical operations that involve manipulating numbers to perform calculations. There are four main arithmetic operations:
Addition: Adding two or more numbers together. The symbol used to represent addition is "+", and the result is called the sum.
Subtraction: Subtracting one number from another. The symbol used to represent subtraction is "-", and the result is called the difference.
Multiplication: Multiplying two or more numbers together. The symbol used to represent multiplication is "×" or "*", and the result is called the product.
Division: Dividing one number by another. The symbol used to represent division is "÷" or "/", and the result is called the quotient.
These operations can be combined to perform more complex calculations. Additionally, there are other arithmetic operations, such as exponentiation (raising a number to a power) and finding roots, which involve using arithmetic principles.
by the question.
To evaluate the expression hj - h² for h = 6 and j = 5, we simply substitute these values into the expression and perform the arithmetic operations:
hj - h² = (6)(5) - 6²
= 30 - 36
= -6
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factorise completely.
3x²-12xy
Answer:
Hence, factors are 3x,(x−4y).
Step-by-step explanation:
We need to factorise 3x 2 −12xy
Here we can take 3x common.
Thus we have 3x 2−12xy=3x(x−4y)
Hence, factors are 3x,(x−4y).
Answer: 3x ( x - 4y )
Step-by-step explanation:
Factorizing 3x²-12xy
3x ( x - 4y )
23. What are the digits which can be put in the box in 806 so that the four digit number is divisible by 8? 3 marks
6, 14, 22, 30, 38, 46, 54, 62, 70, 78, 86, 94
Untuk Konsultasi Tugas Lainnya: WA 0813-7200-6413
What is the code to this I need help asap.
Based on the information in the image, the values of the symbols in order would be: 5, 9.86, 9.93, 7.91. 10.56.
How to find the equivalent value of each symbol?To find the equivalent value of each symbol we must apply the Pythagorean theorem and find the value of the hopotenuse of all triangles as shown below:
Triangle 1:
4² + 3² = c²16 + 9 = c²c = 5Triangle 2:
5² + 8.5² = c²25 + 72.25 = c²c = 9.86Triangle 3:
9.86² + b² = 14²b² = 14² - 9.86²b² = 98.78b = 9.93Triangle 4:
a² + 6² = 9.93²a² = 9.93² - 6²a² = 62.60a = 7.91Triangle 5:
7.91² + 7² = c²62.56 + 49 = c²111.56 = c²10.56 = cAccording to the above, the values of the symbols in order would be:
5, 9.86, 9.93, 7.91. 10.56.
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The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 360 grams and a standard deviation of 9 grams Find the weight that corresponds to each event(use excel or appendix c to calculate the z value round your final answers to the 2 decimal places)
URGENT
The weight that corresponds to this event are approximately 344.03 grams and 375.97 grams.
How to deal with normally distribution?To find the weight that corresponds to each event, we need to use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can convert the given mean and standard deviation to z-scores using the formula:
z = (x - μ) / σ
where x is the weight we want to find, μ is the mean (360 grams), and σ is the standard deviation (9 grams).
Then, we can use a standard normal distribution table or calculator to find the probability of each event, and convert it back to a weight using the inverse of the z-score formula:
x = μ + z * σ
where z is the z-score that corresponds to the desired probability.
Event 1: The weight is less than 345 grams.
z = (345 - 360) / 9 = -1.67
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -1.67 is approximately 0.0475.
x = 360 + (-1.67) * 9 = 344.03 grams
Therefore, the weight that corresponds to this event is approximately 344.03 grams.
Event 2: The weight is between 355 and 365 grams.
First, we need to find the z-scores that correspond to the two boundaries:
z1 = (355 - 360) / 9 = -0.56
z2 = (365 - 360) / 9 = 0.56
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -0.56 is approximately 0.2123, and the probability of a z-score less than 0.56 is approximately 0.7123. Therefore, the probability of a z-score between -0.56 and 0.56 is:
0.7123 - 0.2123 = 0.5
x1 = 360 + (-0.56) * 9 = 355.16 grams
x2 = 360 + (0.56) * 9 = 364.84 grams
Therefore, the weight that corresponds to this event is any weight between 355.16 and 364.84 grams.
Event 3: The weight is greater than 375 grams.
z = (375 - 360) / 9 = 1.67
Using a standard normal distribution table or calculator, we find that the probability of a z-score greater than 1.67 is approximately 0.0475.
x = 360 + (1.67) * 9 = 375.97 grams
Therefore, the weight that corresponds to this event is approximately 375.97 grams.
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A regular hexagon is inscribed into a circle. Find the length of the side of the hexagon, if the radius of the circle is 12 cm.
A. 20 cm
B. 18 cm
C. 16 cm
D. 12 cm
E. None of these
In response to the stated question, we may respond that As a result, the fraction length of the hexagon's side is roughly 16.97 cm, which is closest to option C. (16 cm).
what is fraction?A fraction is a number that represents a portion of a whole or a ratio between two quantities in mathematics. It is represented as a top number (numerator) over a bottom number (denominator) divided by a horizontal line, also known as a vinculum. The fraction 3/4, for example, represents three-quarters of a whole that has been divided into four equal parts. Proper fractions, improper fractions , and mixed numbers are all ways to express a fraction. A suitable fraction is one in which the numerator is less than the denominator, for example, 2/5.
We can calculate the length of the other leg of the right triangle, which is also half the side of the hexagon, using the Pythagorean theorem:
[tex]$(fracs2 )2 + (fracs2 )2 = 122$\\$fracs244 + fracs244 = 144$\\$\frac{s^2}{2} = 144$\\$s^2 = 288$\\$s = sqrt288 = about 16.97$[/tex]
As a result, the length of the hexagon's side is roughly 16.97 cm, which is closest to option C. (16 cm).
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A line with a slope of -8/7 passes through the points (6, -10) and (-8, f). What is the
value of f?
Answer: -18
Step-by-step explanation:
Answer:
value of f is 6
Step-by-step explanation:
100% correct
the work is in the image below. Hope this help!
determine, without actually computing the z transform, the rocs for the z transform of the following signals:
The ROC of a given signal's Z-transform can be determined without actually computing the Z-transform by identifying the maximum and minimum magnitude of the signal and checking for any poles of the Z-transform within the resulting annular region.
Let's take a signal as an example, suppose x[n] = {1, -2, 3, -4, 5}. In order to determine the ROC of its Z-transform, we are firstly required to first look for any regions in the complex plane where the sum of the absolute values of the Z-transform is found finite. It can be done by looking for the maximum and minimum magnitude of x[n] and denote them as R1 and R2 respectively. Then, the ROC of the Z-transform will be the annular region between R1 and R2, excluding any poles of the Z-transform that lie within this annular region.
In this case, the maximum absolute value of x[n] is 5 and the minimum is found being 1. So, the ROC of the Z-transform will be the annular region between |z| = 1 and |z| = 5. We can denote this as 1 < |z| < 5. We also need to check if there are any poles of the Z-transform within this annular region. Since we haven't actually computed the Z-transform, we cannot determine the exact location of any poles.
However, we can check for any values of z that would make the Z-transform infinite. For example, if x[n] is a causal signal (i.e., x[n] = 0 for n < 0), then the ROC cannot include any values of z for which |z| < 1, since this would make the Z-transform infinite.
So, the ROC of the Z-transform for the given signal x[n] can be written as 1 < |z| < 5, assuming that x[n] is a causal signal.
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The complete question is :
Can you explain how to determine the ROCs (regions of convergence) for the Z-transform of a given signal without actually computing the Z-transform? Please provide an example signal with random data and demonstrate how to find its ROCs using this method.
work out minimum and maximum of hikers who could of have walked between 6 and 17 miles
The minimum number of hikers who could have walked between 6 miles and 17 miles is 9 as it lies in the common interval of 10 ≤ x ≤ 15.
What is minimum and maximum value?The minimum value of a set of numbers or a function is the smallest value within that set or range, while the maximum value is the largest value within the same set or range.
According to question:a) The minimum number of hikers who could have walked between 6 miles and 17 miles is 9 as it lies in the common interval of 10 ≤ x ≤ 15.
b) The maximum number of hikers who could have walked between 6 miles and 17 miles is 19.
a) The least value inside the target range is attained. when:
The two hikers in the 5 x 10 interval cover fewer than 6 miles.
The 8 hikers in the range 15-20-20 cover a distance of more than 17 miles.
As a result, the minimum is 9, or somewhere between 10 and 15 persons.
b) The maximum number in the desired range will be obtained when:
The two hikers in the 5 x 10 interval cover fewer than 6 miles.
Less than 17 miles are covered by the 8 hikers in the period of 15 to 20.
The maximum number is then determined as follows:
2 + 9 + 8 = 19 hikers.
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LaShawn’s class raised $500 for a fundraiser.
They used 10% of the money to cover the cost of materials, saved 20% for the next fundraising project, and donated the rest.
How much money did LaShawn’s class donate?
LaShawn's class donated $350 for the fundraiser.
How to find Percent of amount of money?LaShawn's class raised $500 for the fundraiser, and they used 10% of the money to cover the cost of materials. That means they spent:
[tex]$$0.1 \times 500 = 50$$[/tex]
So they spent $50 on materials. Next, they saved 20% of the money for the next fundraising project. That means they saved:
[tex]$$0.2 \times 500 = 100$$[/tex]
So they saved $100 for the next project. To find out how much money they donated, we can subtract the amount spent on materials and the amount saved from the total amount raised:
500 - 50 - 100 = 350
Therefore, LaShawn's class donated $350 for the fundraiser.
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What is the perimeter, P, of the rectangle?
Answer:
P = x(4x+7)/(x+2)(x+1)
Step-by-step explanation:
P = 2l + 2w. If x/x+2 = l and x/x+1 = w:
P = (2x/x+2) + (2x/x+1)
P = (2x(x+1)/(x+2)(x+1)) + (2x(x+2)/(x+1)(x+2))
P = (2x(x+1) + 2x(x+2))/(x+2)(x+1)
P = (4x squared + 7x)/(x+2)(x+1)
P = x(4x+7)/(x+2)(x+1)
0.00063 / (9*10^-4)
Please answer QUIKLYYYY!!!!
Answer: .70
Step-by-step explanation:
10^-4 = .0001
.0001 x 9= .0009
.00063/ .0009= .70
Isaiah is a high school basketball player. In a particular game, he made some free throws (worth one point each) and some two point shots. Isaiah scored a total of 12 points and made 4 times as many free throws as two point shots. Write a system of equations that could be used to determine the number of free throws Isaiah made and the number of two point shots he made. Define the variables that you use to write the system.
In equation 1, 4t + t = 12, so t = 8.
In equation 2, 4f = 8, so f = 2.
Isaiah made two free throws and eight two point shots.
What is equation?Equations usually contain an equation symbol, such as an equals sign (=) or an inequality symbol, such as a less than sign (<).
We can define the variables as ‘f’ for the number of free throws and ‘t’ for the number of two point shots.
The system of equations for this problem is as follows:
f + t = 12 (Equation 1)
f = 4t (Equation 2)
Equation 1 states that the total number of points that Isaiah scored is equal to the sum of the number of free throws and the number of two point shots. Equation 2 states that the number of free throws is four times the number of two point shots.
To solve this system of equations, we can use the substitution method. First, substitute 4t for f in equation 1 and solve for t. 4t + t = 12, so t = 8. Then substitute 8 for t in equation 2 and solve for f. 4f = 8, so f = 2.
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In equation 1, 4t + t = 12, so t = 2.4≈3
In equation 2, f = 4t, so f = 9.6≈10
Isaiah made three free throws and ten two point shots.
What is equation?Equations usually contain an equation symbol, such as an equals sign (=) or an inequality symbol, such as a less than sign (<).
We can define the variables as ‘f’ for the number of free throws and ‘t’ for the number of two point shots.
The system of equations for this problem is as follows:
f + t = 12 (Equation 1)
f = 4t (Equation 2)
Equation 1 states that the total number of points that Isaiah scored is equal to the sum of the number of free throws and the number of two point shots.
Equation 2 states that the number of free throws is four times the number of two point shots.
To solve this system of equations, we can use the substitution method. First, substitute 4t for f in equation 1 and solve for t.
4t + t = 12
so t = 2.4
Then substitute 2.4 for t in equation 2 and solve for f.
f = 4t
so f = 9.6.
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1. Find an equation for the line with the given properties.
Perpendicular to the line x = 5; containing the point (5,6)
y =
2. Find an equation for the line with the given properties. Use lowercase letter x for the variable.
Parallel to the line 7x - y = -7; containing the point (0,0)
y =
3. Find an equation for the line with the given properties.
Slope undefined; containing the point (8,2)
For the first question, the equation for the line is y = -x + 11. This comes from the fact that the slope for a line perpendicular to the line x = 5 is -1. From there, we can use the point (5,6) to calculate the y-intercept, which is 11.
For the second question, the equation for the line is y = 7x. This comes from the fact that the slope for a line parallel to the line 7x - y = -7 is 7. Since the point (0,0) is already on the line, the equation is already solved.
For the third question, the equation for the line is x = 8. This comes from the fact that the slope for a line with an undefined slope is 0. Since the point (8,2) is already on the line, the equation is already solved.
Find the area A of the sector shown in the picture
76 degrees
6
Answer:
Find the area A of the sector shown in the picture
76 degrees
6
Step-by-step explanation:
To find the area of a sector, we need to know the measure of the central angle and the radius of the circle.
If the central angle of the sector is 76 degrees, and the radius of the circle is 6, we can use the formula for the area of a sector:
A = (θ/360) * π * r^2
where θ is the central angle in degrees, r is the radius of the circle, and π is a constant approximately equal to 3.14.
Plugging in the given values, we get:
A = (76/360) * π * 6^2
Simplifying:
A = (0.2111) * π * 36
A = 7.57 square units (rounded to two decimal places)
Therefore, the area of the sector is approximately 7.57 square units.
solve the following system of equations: 2x - y =7, 3x + 4y = -6
Answer:
(2, -3)
Step-by-step explanation:
You must choose from the 3 ways to solve the system of equations:
1. Substitution
2. Elimination
3. Graphing (least recommended)
My example is going to be substitution, as folllows:
2x - y = 7
(Add y to both sides)
2x = y + 7
(Subtract 7 from both sides)
y = 2x - 7
Now, we are able to use substitution in the next equation with the other equation!
3x + 4y = -6
(Replace y with what y equals -- other equation)
3x + 4(2x -7) = -6
(Simplify the parantheses)
3x + 8x - 28 = -6
(Add 28 to both sides)
3x + 8x = -6 +28
3x + 8x = 22
(CLT - Combine like terms)
11x = 22
(Divide 11 from both sides)
x = 2
Now, we will find what y is by plugging x into the other equation.
y = 2x - 7
x = 2
y = 2(2) - 7
y = 4 - 7
y = -3
y = -3
x = 2
Since we found both of the variables' values, we found our coordinate pairs to solve this equation!
Answer: (2, -3)
do you mind helping me with this?
Answer:
125
Step-by-step explanation:
We Take
625 / 5 = 125
So, the answer is 125
i need help on these 2 !!!
The length of RS is 13 units and the length of the hypotenuse XY is approximately 16.4 units.
15) In ΔTSR
TR² = TS² + RS²
Substituting the given values, we get:
(5√10)² = 9² + RS²
250 = 81 + RS²
RS² = 169
Taking the square root of both sides, we get:
RS = 13 units
16)In ΔYZX
XY² = YZ² + XZ²
Substituting the given values, we get:
XY² = 10² + 13²
XY² = 169 + 100
XY² = 269
Taking the square root of both sides, we get:
XY = √269
XY=16.4 units
What is Pythagorean theorem?
In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
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In a double slit experiment, it is observed that the distance between adjacent maxima on a remote screen is 1.0cm. The distance between adjacent maxima when the slit separation is cut in half decreases to 0.50cm. The speed of light in a certain material is measured to be 2.2x10^8 m/s.
The index of refraction of the material used in double slit experiment is 1.36.
The distance between adjacent maxima on a screen in a double-slit experiment is given by:
d sinθ = mλ
where d is the slit separation, θ is the angle between the screen and the line connecting the slits and the maxima, m is the order of the maximum, and λ is the wavelength of light.
The distance between adjacent maxima changes from 1.0cm to 0.50cm when the slit separation is cut in half, which means that the wavelength of light is also halved. Therefore, the ratio of the two wavelengths is:
λ1/λ2 = 2/1 = 2
The speed of light in the material is given as 2.2x10^8 m/s. The speed of light in a vacuum is c, so the index of refraction of the material is given by:
n = c/v
where v is the speed of light in the material. Therefore:
n = c/2.2x10^8 m/s = 1.36
The index of refraction of the material is 1.36.
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_____The given question is incomplete, the complete question is given below:
In a double slit experiment, it is observed that the distance between adjacent maxima on a remote screen is 1.0cm. The distance between adjacent maxima when the slit separation is cut in half decreases to 0.50cm. The speed of light in a certain material is measured to be 2.2x10^8 m/s. what is the index refraction of this material?