When asked to find the distance, you should think of the Pythagorean Theorem.
Option C is the correct answer.
W have,
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
This theorem can be applied to find the distance between two points in a coordinate plane or in three-dimensional space.
The distance between two points is the length of the line segment connecting them, which is also the hypotenuse of a right triangle formed by the two points and the origin or another reference point.
Thus,
To find the distance between two points, you can use the Pythagorean Theorem by treating the coordinates of the two points as the lengths of the legs of a right triangle and finding the length of the hypotenuse.
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given the sse, ssr, and sst, find the variance in the dependent variable that can be explained by the variance in the independent variable. sse 12 ssr 24 sst 36 provide your answer below:
The variance in the dependent variable can be explained by the variance in the independent variable 66.67%.
To find the variance in the dependent variable that can be explained by the variance in the independent variable, we need to first calculate the coefficient of determination (R-squared).
The R-squared value is a statistical measure that determines the proportion of the variation in the dependent variable that can be explained by the independent variable.
R-squared is calculated as the ratio of the explained variation (SSR) to the total variation (SST).
Therefore, we can calculate the R-squared as follows:
R-squared = SSR/SST = 24/36 = 0.67
This means that 67% of the variation in the dependent variable can be explained by the variation in the independent variable.
To find the variance in the dependent variable that can be explained by the variance in the independent variable, we need to multiply the R-squared value by the total variance in the dependent variable (SST).
Therefore, we can calculate the variance explained by the independent variable as follows:
Variance explained = R-squared * SST = 0.67 * 36 = 24.12
Therefore,
The variance in the dependent variable that can be explained by the variance in the independent variable is 24.12.
This means that the independent variable can explain 24.12 units of variation in the dependent variable, while the remaining 11.88 units of variation are due to other factors not accounted for by the independent variable.
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if calls to your cell phone are a poisson process with a constant rate of 2 calls per hour, what is the probability that, if you forget to turn your phone off during a 1.5-hour movie, your phone rings during that time? how many calls do you expect to get during that movie?
we can expect to receive approximately 3 phone calls during the 1.5-hour movie, on average.
The probability of your phone ringing during a 1.5-hour movie can be calculated using the Poisson distribution formula:
P(X = k) = (e^-λ * λ^k) / k!
Where X is the number of phone calls, λ is the average rate of calls per unit time (in this case, 2 calls per hour), and k is the number of calls during the 1.5-hour period.
So, for k = 0 (no calls), the probability is: P(X = 0) = (e^-2 * 2^0) / 0! = e^-2 ≈ 0.1353
Therefore, the probability that your phone rings at least once during the movie is: P(X ≥ 1) = 1 - P(X = 0) = 1 - e^-2 ≈ 0.8647
To calculate the expected number of calls during the movie, we use the formula: E(X) = λ * t
Where t is the duration of the period (1.5 hours in this case). So, the expected number of calls during the movie is: E(X) = 2 * 1.5 = 3
Therefore, we can expect to receive approximately 3 phone calls during the 1.5-hour movie, on average.
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Compute dy/dx using the chain rule. State your answer in terms of x only. y=u/7 + 7/u, u=x-x^3
To compute dy/dx using the chain rule, we first need to find du/dx using the power rule.
du/dx = d/dx(x-x^3) = 1 - 3x^2
Next, we can use the chain rule to find dy/dx:
dy/dx = dy/du * du/dx
dy/du = 1/7 - 7/u^2
So,
dy/dx = (1/7 - 7/u^2) * (1 - 3x^2)
Substituting u = x - x^3, we get:
dy/dx = (1/7 - 7/(x-x^3)^2) * (1 - 3x^2)
Thus, the answer in terms of x only is:
dy/dx = (1/7 - 7/(x-x^3)^2) * (1 - 3x^2)
Let's compute dy/dx using the chain rule. Given the function y = u/7 + 7/u, where u = x - x^3, we will first differentiate y with respect to u, then differentiate u with respect to x, and finally multiply the two results together using the chain rule.
Here are the steps:
1. Differentiate y with respect to u:
dy/du = (1/7) - (7/u^2)
2. Differentiate u with respect to x:
du/dx = 1 - 3x^2
3. Apply the chain rule:
dy/dx = dy/du * du/dx
Now substitute the expressions we found in steps 1 and 2 into the chain rule formula:
dy/dx = [(1/7) - (7/u^2)] * (1 - 3x^2)
Since we need the answer in terms of x only, substitute the expression for u (x - x^3) back into the equation:
dy/dx = [(1/7) - (7/(x - x^3)^2)] * (1 - 3x^2)
This is the final expression for dy/dx using the chain rule in terms of x only.
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You are trying to compare health insurance plans provided by your company. The plan you would like has a premium of $125 per paycheck. How much are you paying for insurance per year if you get paid every two weeks? Please enter your answer without a dollar sign or spaces.
You would be paying $3000 per year for the health insurance plan.
How to how much are you paying for insurance per year if you get paid every two weeksIf the premium for the health insurance plan is $125 per paycheck, and you get paid every two weeks, then the cost of the insurance per month is:
2 paychecks x $125 per paycheck = $250 per month
To find the cost per year, we need to multiply the monthly cost by 12:
$250 per month x 12 months = $3,000 per year
hence, you would be paying $3000 per year for the health insurance plan.
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A store receives a delivery of 2 cases of perfume. Each case contains 10 bottles. Each bottle contains 80 millimeters of perfume.
How many milliliters of perfume in all does the store receive in this delivery?
Responses
94 mL
94 mL
160 mL
160 mL
800 mL
800 mL
1,600 mL
The total number of milliliters of perfume is 1,600 mL. Then the correct option is D.
Two cases of perfume are delivered to a retailer. There are ten bottles in each case. There are 80 millimeters of perfume in each bottle.
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The total number of milliliters of perfume is calculated as,
⇒ 2 x 10 x 80
⇒ 1,600 mL
Thus, the correct option is D.
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Can someone please help me ASAP? It’s due tomorrow!! I will give brainliest if it’s correct
In a box and whisker plot, the third quartile represents C. the middle data point of the upper half of the data set.
What is the third quartile?The third quartile represents the median of the data points to the right of the median of the box and whisker plot.
The third quartile is also described as the upper quartile, showing the value under which 75% of data points are found when arranged in increasing order.
Thus, the correct option for the third quartile is C.
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n the library of a small town, the mean cost of new books is the same as the median cost of new books. the distribution of book costs is: multiple choice question. negatively skewed symmetrically distributed positively skewed
If the mean cost of new books is the same as the median cost of new books, then the distribution of book costs is symmetrically distributed.
This means that the data is evenly distributed around the mean and median, and there are an equal number of values on both sides of the central point. In a symmetric distribution, the mean and median are the same, and the data is evenly spread out around them.
A negatively skewed distribution would have a longer tail on the left side, indicating that the majority of the values are higher. A positively skewed distribution would have a longer tail on the right side, indicating that the majority of the values are lower.
A symmetric distribution, on the other hand, has no long tail on either side, and the majority of the values cluster around the central point. Therefore, the distribution of book costs is symmetrically distributed.
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Solve the following boundary value problem. if there is no solution, write none for your answer. y″−3y′=0; y(0)=2−2e3; y(1)=0
The solution to the boundary value problem is
y(x) = -(2 - 2e^3)e^3/(1 - e^3) + (2 - 2e^3)/(1 - e^3) * e^(3x).
The characteristic equation is r^2 - 3r = 0, which has roots r = 0 and r = 3. Thus, the general solution to the differential equation is y(x) = c1 + c2e^(3x).
Using the initial condition y(0) = 2 - 2e^3, we have y(0) = c1 + c2 = 2 - 2e^3.
Using the boundary condition y(1) = 0, we have y(1) = c1 + c2e^3 = 0.
We can solve for c1 and c2 by solving the system of equations:
c1 + c2 = 2 - 2e^3
c1 + c2e^3 = 0
Subtracting the second equation from the first, we get c2(1 - e^3) = 2 - 2e^3, which gives us c2 = (2 - 2e^3)/(1 - e^3).
Substituting c2 into the second equation, we get c1 = -c2e^3 = -(2 - 2e^3)e^3/(1 - e^3).
Thus, the solution to the boundary value problem is y(x) = -(2 - 2e^3)e^3/(1 - e^3) + (2 - 2e^3)/(1 - e^3) * e^(3x).
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Dome Fuji, in Antarctica, is the ________ place in the world with a record low of –92 degrees.
colder
coldest
more cold
most cold
Answer: Dome Fuji, in Antarctica, is the coldest place in the world with a record low of –92 degrees.
Step-by-step explanation:
Isabella's Ice Cream Parlor uses waffle cones that have a diameter of 4.5 in. and a height of 6 in.
What is the exact volume of ice cream that completely fills one cone to the top?
Enter your answer as a decimal in the box. Use 3.14 for pi.
Answer:
31.7925 [tex]in^{3}[/tex]
Step-by-step explanation:
V = 1/3[tex]\pi r^{2}[/tex]h
v = 1/3 (3.14)([tex]2.25^{2}[/tex])(6) The radius is 1/2 of the diameter
v = 1/3 (3.14)(5.0625)(6)
v = [tex]\frac{95.3775}{3}[/tex]
v = 31.7925
Helping in the name of Jesus.
Let X have an exponential probability density function with B = 500.
a. Compute Pr[X > 500).
b. Compute the conditional probability Pr[X > 1000 | X > 500).
a. The probability that X is greater than 500 is approximately 0.368.
b. The conditional probability that X is greater than 1000 is approximately 0.368.
a. To compute Pr[X > 500), we use the cumulative distribution function (CDF) of the exponential distribution, which is:
F(x) = 1 - e^(-x/B)
Plugging in B = 500 and x = 500, we get:
Pr[X > 500) = 1 - F(500) = 1 - (1 - e^(-500/500)) = e^(-1) ≈ 0.368
Therefore, the probability that X is greater than 500 is approximately 0.368.
b. To compute Pr[X > 1000 | X > 500), we use the definition of conditional probability:
Pr[X > 1000 | X > 500) = Pr[(X > 1000) ∩ (X > 500)] / Pr[X > 500)
Since X is a continuous random variable, we can rewrite the probability of the intersection using the minimum of X:
Pr[(X > 1000) ∩ (X > 500)] = Pr[X > max(1000, 500)] = Pr[X > 1000]
Plugging in B = 500 into the CDF, we have:
Pr[X > 1000] = 1 - F(1000) = 1 - (1 - e^(-1000/500)) = e^(-2) ≈ 0.135
We already know from part a that Pr[X > 500) = e^(-1) ≈ 0.368.
Putting it all together, we have:
Pr[X > 1000 | X > 500) = Pr[X > 1000] / Pr[X > 500) = (e^(-2)) / (e^(-1)) = e^(-1) ≈ 0.368
This result shows that the conditional probability that X is greater than 1000, given that it is already greater than 500, is the same as the probability that X is greater than 500 on its own. In other words, knowledge of the fact that X is already greater than 500 does not change our prediction about whether it will be greater than 1000 or not.
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Find the sum of the series: M8 3 re 7 a) 0 3 a) of 21 ) b) O 2 c) [ ܬ .o 21 d) 4 e) 07
The sum of the series [tex]\sum_{k=0}^\infty \frac{3}{7^{k} }[/tex] is 7/2. Therefore, the correct answer is option C. The sum of a geometric series can be found only if the ratio is between -1 and 1.
To find the sum of the series [tex]\sum_{k=0}^\infty \frac{3}{7^{k} }[/tex], we can use the formula for the sum of an infinite geometric series, which is [tex]\frac{a}{1-r}[/tex], where a is the first term and r is the common ratio.
In this case, the first term is [tex]\frac{3}{7^0}=3[/tex] and the common ratio is [tex]\frac{1}{7}[/tex]. Substituting these values into the formula, we get:
[tex]\frac{3}{1-\frac{1}{7}}=\frac{3}{\frac{6}{7}}=\frac{7}{2}[/tex]
Therefore, the sum of the series is c. 7/2. Alternatively, we can also find the sum of the series by adding up the terms:
[tex]\frac{3}{1}+\frac{3}{7}+\frac{3}{49}+\frac{3}{343}+...\approx 4.5[/tex]
This method involves adding up an infinite number of terms, so it may not always be practical or accurate. Using the formula for the sum of an infinite geometric series is a more efficient and reliable method. Therefore, the correct answer is option C.
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Complete Question:
Find the sum of the series:
[tex]\sum_{k=0}^\infty \frac{3}{7^{k} }[/tex]
a. 7/3
b. 21/2
c. 7/2
d. 21/4
e. 7
The photographer takes the planned number of photos in sessions B
and C. At session D, the customer requests that she take the pictures
with a higher resolution. These photos will take up 3.4 megabytes of
space on the card.
Part C: Does the photographer have enough space left on her
memory card to take all the planned photos for session D at
a higher resolution? Explain how you know you are correct.
It will be impossible to know if the photographer has enough space left on her memory card without knowing the capacity of the card and the size of the planned photos for session D.
Main answer:
It is impossible to determine if the photographer has enough space left on her memory card without knowing the capacity of the card and the size of the planned photos for session D.
How can we determine if the photographer has enough space?We must know capacity of the card and the size of the planned photos for session D. If combined size of the planned photos for session B and C is less than remaining space on the card after accounting for the 3.4 megabytes needed for session D, then, the photographer would have enough space.
But if combined size of the planned photos for session B and C is greater than the remaining space on the card after accounting for the 3.4 megabytes needed for session D, then, the photographer would not have enough space.
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the sscp exam consists of ____ multiple-choice questions, and must be completed within three hours.
Answer:
125 questions
Answer:
125 questions
Step-by-step explanation:
Please show your work
The value of the fractions is 10.
We know,
A fraction is described as the part of a whole.
The different types of fractions are;
Mixed fractionsProper fractionsImproper fractionsSimple fractionsComplex fractionsHere, we have,
Given the fractions;
3 1/4 + 2 1/8 +2 7/8+1 3/4
convert to improper fractions, we have;
13/4 + 17/8 + 23/8 + 7/4
Find the LCM
26 + 17 + 23 + 14 /8
Find the values
80/8
divide the values
10
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complete question:
What is the answer 3 1/4 + 2 1/8 +2 7/8+1 3/4+1 3/4 +? Show the work
The growth rate of a population of size N at time t, denoted by the function N(t), is determined by four processes: birth, death, immigration, and emigration. Write and solve a differential equation model for N that reflects the following assumptions:
• There is constant immigration of 100 individuals every year.
• Birth rates are proportional to the population density. The more individuals there are the more births there are.
The per capita birth rate 0.15. • Death rates are proportional to the population density. The per capita death rate is 0.3.
A differential equation is an equation that relates an unknown function to its derivatives, or differentials, with respect to one or more independent variables. Therefore, N(t) = 666.67 - 566.67 * exp(-0.15*t + 0.7102)
The differential equation model for the population size N at time t is:
dN/dt = (birth rate - death rate + immigration rate) * N
where birth rate = per capita birth rate * N, death rate = per capita death rate * N, and immigration rate = constant immigration rate = 100.
Substituting the given values, we get:
dN/dt = (0.15N - 0.3N + 100) * N
Simplifying, we get:dN/dt = (-0.15*N + 100) * N
To solve this differential equation, we can use the method of separation of variables:dN / (-0.15*N + 100) = dt
Integrating both sides, we get:-6.6667 ln(-0.15*N + 100) = t + C
where C is the constant of integration.
Solving for N, we get:N(t) = (100/0.15) - (100/0.15) * exp(-0.15t - 6.6667C)
where (100/0.15) = 666.67.
To determine the value of the constant C, we need an initial condition. Let's assume that the initial population size N(0) = 1000. Substituting this in the above equation, we get:
1000 = 666.67 - (666.67 * exp(-6.6667*C))
Solving for C, we get: C = -0.1057
Substituting this value of C in the equation for N(t), we get:
N(t) = 666.67 - 566.67 * exp(-0.15*t + 0.7102)
Therefore, the model for the population size N at time t, reflecting the given assumptions, is:
N(t) = 666.67 - 566.67 * exp(-0.15*t + 0.7102)
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a circular sidewalk is being constructed around the perimeter of a local park a brick pathway will be added through the diameter of the circle as shown on the coordinate plane below and a tree will be planted in the sidewalk at the center of the circle what is the x coordinate where the tree will be planted
The x-coordinate where the tree will be planted in a circular sidewalk constructed around a park, with a brick pathway through its diameter from (-1,4) to (9,10), is 4, which is the x-coordinate of the center of the circle.
To find the center of the circle, we need to find the midpoint of the diameter. We can use the midpoint formula
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
where (x₁, y₁) and (x₂, y₂) are the endpoints of the diameter.
Using the coordinates (-1, 4) and (9, 10), we get
Midpoint = ((-1 + 9)/2, (4 + 10)/2) = (4, 7)
So the center of the circle is at the point (4, 7).
Since the tree will be planted at the center of the circle, its x-coordinate will be the same as the x-coordinate of the center of the circle, which is 4.
Therefore, the x-coordinate where the tree will be planted is 4.
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--The given question is incomplete, the complete question is given
" a circular sidewalk is being constructed around the perimeter of a local park a brick pathway will be added through the diameter of the circle is from (-1,4) and (9,10) coordinate plane and a tree will be planted in the sidewalk at the center of the circle what is the x coordinate where the tree will be planted "--
How do you predict a linear regression score?
To predict a linear regression score, you first need to train a linear regression model using a set of training data.
Once the model is trained, you can use it to make predictions on new data points. The predicted score will be based on the linear relationship between the input variables and the target variable,
A higher regression score indicates a better fit, while a lower score indicates a poorer fit.
To predict a linear regression score, follow these steps:
1. Gather your data: Collect the data p
points (x, y) for the variable you want to predict (y) based on the input variable (x).
2. Calculate the means: Find the mean of the x values (x) and the mean of the y values (y).
3. Calculate the slope (b1): Use the formula b1 = Σ[(xi - x)(yi - y)] Σ(xi - x)^2, where xi and yi are the individual data points, and x and y are the means of x and y, respectively.
4. Calculate the intercept (b0): Use the formula b0 = y - b1 * x, where y is the mean of the y values and x is the mean of the x values.
5. Form the linear equation: The linear equation will be in the form y = b0 + b1 * x, where y is the predicted value, x is the input variable, and b0 and b1 are the intercept and slope, respectively.
6. Predict the linear regression score: Use the linear equation to predict the value of y for any given value of x by plugging in the x value into the equation. The resulting y value is your predicted linear regression score.
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Freya drove from Bournemouth to Gloucester at an average speed of 50 mph for 2 hours and 30 minutes.
She then drove from Gloucester to Anglesey at an average speed of 65 mph for 3 hours.
Work out how many miles freya travelled in total.
The number of miles that Freya traveled in total is 320 miles.
Given that:
Bournemouth to Gloucester: v = 50 mph and t = 2.5 h
Gloucester to Anglesey: v = 65 mph and t = 3 h
We know that the speed formula
Speed = Distance/Time
The number of miles that Freya traveled in total is calculated as,
Distance = 50 x 2.5 + 65 x 3
Distance = 125 + 195
Distance = 320 miles
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I need to show my work, can someone help w this?
Cross multiplying
20 × 5 = t × t
100 = 2t
Dividing 2 on the opposite side
100/2 = t
t = 50
Drag the tiles to the correct boxes to complete the pairs.
Match each irrational number with the number line on which it is represented.
Each irrational number with the number line:
a) First number line = 2.1829391321..
b) Second number line = 2.364125..
c) Third number line = 2.18112..
d) Fourth number line = 2.1823912..
a) Here, we can obseve that between 2.182 and 2.183 a number line is divided into 10 equal segments.
So, each unit length represents (2.183 - 2.182) / 10 = 0.0001 unit
The required irrational number (represented by red dot) lie between 2.1829 and 2.183.
So, the irrational number would be 2.1829391321..
b) Here, we can obseve that between 2 and 3 a number line is divided into 10 equal segments.
So, each unit length represents (3 - 2) / 10 = 0.1 unit
The required irrational number (represented by red dot) lie between 2.3 and 2.4
So, the irrational number would be 2.364125..
c) Here, we can obseve that between 2.11 and 2.21 a number line is divided into 10 equal segments.
So, each unit length represents (2.21 - 2.11) / 10 = 0.01 unit
The required irrational number (represented by red dot) lie between 2.18 and 2.19
So, the irrational number would be 2.18112..
d) Here, we can obseve that between 2.18 and 2.19 a number line is divided into 10 equal segments.
So, each unit length represents (2.19 - 2.18) / 10 = 0.001 unit
The required irrational number (represented by red dot) lie between 2.182 and 2.183
So, the irrational number would be 2.1823912..
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Solve the proportion for a.
36
18
C2
2 =
a = [?]
Enter the number that belongs in the
green box.
Enter
Answer:
4
Step-by-step explanation:
a/2 = 36/18
Reduce the right fraction.
a/2 = 2/1
Multiply both sides by 2.
a = 4
Answer: 4
I really need help real fast please help with these three
Imagine that researchers measured resting heart rates on a large number of U.S. adults (n=5000) and found the following statistics:
PercentileResting Heart Rate (beats per minute)54510X25605070758090Y9595
If resting heart rate follows a normal distribution, what is the value of X above? Round to the nearest whole number.
Based on the given percentiles, we can determine that the value of X represents the resting heart rate at the 25th percentile. To estimate the value of X, we can use the z-score formula for a normal distribution. The z-score corresponding to the 25th percentile is approximately -0.674.
The formula for the z-score is: (X - mean) / standard deviation. We have the mean (70 bpm) and the z-score (-0.674), but we need to estimate the standard deviation. To do this, we can use the 50th and 75th percentiles. The z-score for the 50th percentile is 0, so the mean equals the 50th percentile value (70 bpm). The z-score for the 75th percentile is 0.674, so we can set up the equation:
(80 - 70) / standard deviation = 0.674
10 / standard deviation = 0.674
Standard deviation ≈ 10 / 0.674 ≈ 14.8 bpm
Now we can solve for X:
-0.674 = (X - 70) / 14.8
-0.674 * 14.8 ≈ X - 70
-9.9 ≈ X - 70
X ≈ 60.1
Rounding to the nearest whole number, the value of X is approximately 60 bpm.
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What ratios are equal to 4:6?
The ratio that is equivalent to 4:6 is 40:60
What are ratios?A ratio is a mathematical expression of comparing two similar or different quantities by division.
For examples if the ratio of cow to sheep In a farm is 3: 4, this means that for 3 cows in the farm there will be 4 sheeps
Equivalent ratios are the ratios that are the same when we compare them. Examples of equivalent ratios are 4:5 and 8 :10.
The equivalent of 4:6 can also be 2:3 but in the options we don't have that, another equivalent can be obtained by multiplying 10 to both sides
=4×10: 6× 10
= 40:60
therefore the equivalent of the ratio 4:6 is 40:60
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white cylindrical silo has a diameter of 30 feet and a height of 80 feet. a red stripe with a horizontal width of 3 feet is painted on the silo, as shown, making two complete revolutions around it. what is the area of the
The white cylindrical silo has a diameter of 30 feet, which means the radius is 15 feet. The height of the silo is 80 feet. The area of the red stripe on the cylindrical silo is approximately 565.5 square feet.
A red stripe with a horizontal width of 3 feet is painted on the silo, making two complete revolutions around it. This means the total length of the red stripe is 2 times the circumference of the base of the silo plus 2 times the circumference of the top of the silo. The circumference of the base of the silo is 2 times pi times the radius, which is 2 x 3.14 x 15 = 94.2 feet.
The circumference of the top of the silo is also 94.2 feet
So the total length of the red stripe is 2 x 94.2 + 2 x 94.2 = 376.8 feet. The horizontal width of the red stripe is 3 feet, so the area of the red stripe is 376.8 x 3 = 1130.4 square feet.
To find the total surface area of the silo, we need to find the area of the two circular ends and the area of the curved surface. The area of each circular end is pi times the radius squared, which is 3.14 x 15 x 15 = 706.5 square feet.
The area of the curved surface is the product of the height, the circumference, and 2 (since there are two sides), which is 80 x 94.2 x 2 = 15,088 square feet.
So the total surface area of the silo is 2 x 706.5 + 15,088 = 15,501 square feet.
Therefore, the area of the red stripe as a percentage of the total surface area of the silo is (1130.4/15,501) x 100% = 7.29%.
A white cylindrical silo has a diameter of 30
feet and a height of 80
feet. A red stripe with a horizontal width of 3
feet is painted on the silo, as shown, making two complete revolutions around it. What is the area of the stripe in square feet?
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Which expression represents the inverse of the matrix below? 1 2321 -1 2 1115 -2 -3 1 -1 -|T -2 -3 1 -1 2 -3 3(2-3] 1 2 -3
An expression that represent the inverse of the matrix below include the following: D. [tex]\frac{1}{5} \left[\begin{array}{ccc}2&-3\\1&1\end{array}\right][/tex]
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In this exercise, you are required to determine the inverse of the matrix below. This ultimately implies that, we would determine the determinant of the matrix as follows;
Determinant of A = detA = (1 × 2) - (-1)(3)
Determinant of A = detA = 2 - (-3)
Determinant of A = detA = 2 + 3
Determinant of A = detA = 5 ≠ 0
Since the determinant of A is not equal to zero (detA ≠ 0), we can logically deduce that, the inverse of A (A⁻¹) exist;
Adj(A) = [tex]\left[\begin{array}{ccc}2&-3\\1&1\end{array}\right][/tex]
A⁻¹ = [tex]\frac{1}{detA}[/tex][Adj(A)]
A⁻¹ = [tex]\frac{1}{5} \left[\begin{array}{ccc}2&-3\\1&1\end{array}\right][/tex]
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a quadrilateral has vertices A = (0,0), B = (1,3), C = (0,4), and D = (-1,1). Prove that ABCD is a parallelogram.
Answer:
To prove that ABCD is a parallelogram, we need to show that opposite sides are parallel. We can do this by calculating the slopes of each side and showing that they are equal.
The slope of a line passing through two points (x1,y1) and (x2,y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Using this formula, we can calculate the slopes of AB, BC, CD, and DA as follows:
Slope of AB:
slope_AB = (3 - 0) / (1 - 0) = 3
Slope of BC:
slope_BC = (4 - 3) / (0 - 1) = -1
Slope of CD:
slope_CD = (1 - 4) / (-1 - 0) = 3
Slope of DA:
slope_DA = (0 - 1) / (0 - (-1)) = 1
We can see that the slopes of AB and CD are equal, and the slopes of BC and DA are equal. Therefore, opposite sides of ABCD have equal slopes, which means they are parallel.
Hence, ABCD is a parallelogram.
Step-by-step explanation:
Question 4 (0.5 points) = y A function is given by z = f(x, y) = +y?sin(x). Suppose x= ne*sin(s), y = 152 + 42. Use Chain Rule to find the partial derivative when s t = 0. Round your answer to two decimal places.
Rounding to two decimal places, we get ∂z/∂s = 42.00 as answer.
Using Chain Rule, we have:
∂z/∂s = (∂z/∂x) * (∂x/∂s) + (∂z/∂y) * (∂y/∂s)
∂z/∂x = -y*cos(x), and ∂z/∂y = sin(x)
∂x/∂s = ne*cos(s), and ∂y/∂s = 42
Substituting these values, we get:
∂z/∂s = (-ycos(x)) * (necos(s)) + (sin(x)) * (42)
At s=0, x = ne*sin(s) = 0 and y = 152, so:
∂z/∂s = (-152cos(0)) * (necos(0)) + (sin(0)) * (42) = 42
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What is an equation of the linear relationship in slope-intercept form?
(nevermind i solved it)
The equation of the linear relationship in slope-intercept form is expressed as: y = 3x - 4.
How to Find the Equation of a Line in Slope-intercept Form?To find the equation, pick two points on the line and find the slope (m), then find the y-intercept (b) of the line.
Using, (0, -4) and (1, -1):
Slope (m) = (-1 -(-4)) / (1 - 0)
m = 3/1
m = 3
The y-intercept (b) is -4.
Substitute m = 3 and b = -4 into y = mx + b:]
y = 3x - 4
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