The least squares line equation is: y = 0.168x + 23.039. The slope of the line to three decimal places is 0.168.
Calculated the linear regression line using the least squares method.
The data points are as follows:
x (age in months): [73, 84, 98, 112, 116, 132, 150, 160, 164, 180]
y (taps/10 sec): [35, 40, 50, 42, 46, 41, 52, 52, 51, 66]
The least squares line for this data can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept. After performing the calculation, I found:
Slope (m): 0.168
Y-intercept (b): 23.039
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The figure shown at the right is known as Pascal's Triangle. Make a conjecture for the numbers in the 6th row.
Pascal's Triangle
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
What is the last row?
The pascals row triangle is solved and the last row is A = 1 5 10 10 5 1
Given data ,
Let the pascals triangle be represented as A
Now , the value of A is
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
Based on the pattern observed in Pascal's Triangle, the conjecture for the numbers in the 6th row would be:
1 5 10 10 5 1
Each integer in Pascal's Triangle equals the sum of the two numbers immediately above it. The numbers in the row are added to the first and last number, which is 1, to get the numbers in the middle.
This pattern is repeated in the sixth row, where the intermediate numbers are 5, 10, 10, 5, and the first and last digits are 1.
Hence , the pascals triangle is solved
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Geometry: Transformations
The point (-4, -1), is the bottom of a triangle. Which point would it map to if the triangle was translated right 5 units and reflected about the x-axis.
A) (2, 1)
B) (1, 1)
C) (-4, -4)
D) (-9, 1)
Answer: Ur answer will be A.
Which expression represents the phrase 5+ the quotient of 12. 8 and 3. 2
Expression 5 + (12.8 ÷ 3.2) represents the phrase 5 + the quotient of 12. 8 and 3. 2 and option (a) is the correct answer.
Expressions refer to a phrase with at least two numbers or variables with any mathematical operations such as addition, exponents, etc. x - 6, 9 + 4y, and 6a are all examples of mathematical expressions.
Equations refer to a sentence when two expressions are equated with the help of '='. x - 6 = 6a is an example of an equation.
In phrase 5+ the quotient of 12. 8 and 3. 2
We divide the phrase into different mathematical operations.
The first operation is of addition with 5, we can write the beginning as 5 + ...
The next operation is division in the phrase the quotient of 12. 8 and 3. 2 which is added to the expression and we get 5 + (12.8 ÷ 3.2)
And we get our answer.
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The complete question might be :
Which expression represents the phrase 5+ the quotient of 12. 8 and 3. 2?
a. 5 + (12.8 ÷ 3.2)
b. 5 - (12.8 + 3.2)
c. 5 + (12.8 * 3.2)
d. none of the above
If you take out a loan that costs 561.60 over eight years at an interest rate of 9%, how much was the loan for
The original loan amount by the given rate was 38,000.
We are given that;
Cost of loan= 561.60
Rate= 9%
Now,
To use the PV function, we need to convert the interest rate and the loan term to monthly values.
The interest rate per month is 9% / 12 = 0.75%.
The number of payments is 8 * 12 = 96.
The payment amount is 561.60
The PV function would be:
=PV(0.75%, 96, -561.60)
=38,000.
Therefore, by the simple interest the answer will be 38,000.
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14 ft NET OF ΤΟΥ BOX 12 ft 15 ft What is the surface area, in square feet, of the toy box?
The surface area, in square feet, of the toy box is 1116
What is the surface area, in square feet, of the toy box?From the question, we have the following parameters that can be used in our computation:
Dimensions 14 ft, 12 ft and 15 ft
The surface area, in square feet, of the toy box is calculated as
Surface area = 2 * (lw + lh + wh)
substitute the known values in the above equation, so, we have the following representation
Surface area = 2 * (14 * 12 + 14 * 15 + 12 * 15)
Evaluate
Surface area = 1116
Hence, the surgface area is 1116
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According to the 2010 Census, 11.4% of all housing units in the US were vacant. A county supervisor wonders if her count is different from this. She randomly selects 850 housing units in her county and finds that 120 of them are vacant. Use a significance level of a = 0.05.
a) State the hypotheses in symbols. (2 points)
b) Write the letter next to each assumption and condition that must be present in order to run the 1-Proportion z-Test. (2 points) A. Randomization Condition: The county supervisor conducts the survey randomly. B. 10% Condition: I will assume that this county has more than 8500 housing units. C. Independence Assumption: I will assume that one housing unit being vacant does not affect whether another housing unit is vacant, but I need to be careful here. D. Success/Failure Condition: Both N ∙ P = 850 ∙ 0.114 = 96.9 and n times q = 850 ∙ 0.886 = 753.1 are greater than 10. E. The Nearly Normal Condition: The sample size is 850 so it’s reasonable to say that this condition has been met.
c) Use your calculator to perform a 1-Proportion z-Test and report the test statistic and p-value. Do not make these calculations by hand. Instead, use the 1-PropZTest command in your graphing calculator found under STAT – TESTS. Write out what you entered in your calculator. (3 points)
d) Make a sketch of the test distribution. Your graphing calculator will make this sketch for you if your choose "Draw" instead of "Calculate" in the test input screen. However, your calculator will not label the graph for you. You must label the test statistic along the x-axis and the area under the curve as the p-value. For a two-tailed test such as this one, you will need to divide the pvalue in half and use that value to label each half of the area under the curve. (2 points)
e) Write a full conclusion for this test in the context of the problem (See #2b for format). (4 points)
a) State the hypotheses in symbols:
H₀: p = 0.114 (null hypothesis: the county's proportion of vacant housing units is equal to the national proportion)
H₁: p ≠ 0.114 (alternative hypothesis: the county's proportion of vacant housing units is different from the national proportion)
b) Assumptions and conditions for 1-Proportion z-Test:
A. Randomization Condition
B. 10% Condition
D. Success/Failure Condition
E. Nearly Normal Condition
c) To perform a 1-Proportion z-Test, enter the following in your calculator:
1-PropZTest(0.114, 120/850, 850)
Test statistic (z): ≈ 2.24
P-value: ≈ 0.025
d) Sketch of the test distribution:
- Label the x-axis with the test statistic (z ≈ 2.24)
- For a two-tailed test, divide the p-value in half (0.025/2 = 0.0125) and label each half of the area under the curve
e) Conclusion:
Since the p-value (0.025) is less than the significance level (α = 0.05), we reject the null hypothesis. There is sufficient evidence to conclude that the proportion of vacant housing units in the county is different from the national proportion of 11.4%.
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In Mrs. Hogan's kindergarten class, children make handprints in a round clay mold for their parents. The mold has a radius of 4 centimeters. What is the mold's area?
Answer: A ≈ 201.06 cm²
Step-by-step explanation:
We can use the given formula for a sphere's area to solve.
Given formula:
A = 4πr²
Subsiute given radius:
A = 4π(4 cm)²
Square:
A = 4π(16 cm²)
Multiply:
A = 201.0619298 cm²
Round:
A ≈ 201.06 cm²
which function best models the data in the graph? what does the slope of the function represent in this situation?
The slope of a function represents the rate of change and steepness of the line.
What the slope of a function represents in a general sense?Without seeing the graph, it is difficult to determine which function best models the data. However, I can explain what the slope of a function represents in a general sense.
In a linear function of the form y = mx + b, where m is the slope and b is the y-intercept, the slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x).
In other words, the slope tells us how much y changes for each unit increase in x. If the slope is positive, then y increases as x increases. If the slope is negative, then y decreases as x increases.
The magnitude of the slope also tells us how steep the line is. A larger slope (in absolute value) means that the line is steeper, while a smaller slope means that the line is flatter.
In summary, the slope of a function represents the rate of change and steepness of the line.
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Excel wants to increase the productivity of its line workers. four different programs have been suggested to help increase productivity. twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day's work has been recorded. you are given the results in the file name ahmadi. State the null and alternative hypotheses.
The null hypothesis would be that there is no significant difference in productivity between the four programs. The alternative hypothesis would be that there is a significant difference in productivity between at least two of the programs.
In this scenario, Excel is trying to increase the productivity of its line workers and is testing four different programs. A sample of twenty employees has been randomly assigned to one of the programs, and their daily output has been recorded in the file named "ahmadi." We will use these data to determine if any of the programs are effective in increasing productivity. The null and alternative hypotheses can be stated as follows:
Null Hypothesis (H0): There is no significant difference in productivity between the four programs. In other words, none of the programs have a meaningful impact on the productivity of the line workers.
Alternative Hypothesis (H1): At least one of the four programs has a significant impact on the productivity of the line workers, leading to increased output compared to the other programs.
To test these hypotheses, you would typically perform an analysis of variance (ANOVA) on the data provided in the "ahmadi" file. If the ANOVA result is significant, you would reject the null hypothesis and accept the alternative hypothesis, indicating that at least one program effectively increases productivity.
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Once you solve for ONE of the variables in a system, then...
*
you must determine the inverse of the corresponding matrix.
you must see that it works for all equations of the system.
you must involuntarily lubricate your corneas.
you must substitute the value of that variable in an equation to solve for the remaining variable.
The complete sentence is,
Once you solve for ONE of the variables in a system, then you must substitute the value of that variable in an equation to solve for the remaining variable.
We have to given that;
To find the method after, Once you solve for ONE of the variables in a system,
Hence, We get;
The correct method is,
Once you solve for ONE of the variables in a system, then you must substitute the value of that variable in an equation to solve for the remaining variable.
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if the coefficient of determination is 0.298, what percentage of the variation in the data about the regression line is unexplained? g
Therefore, approximately 70.2% of the variation in the data about the regression line is unexplained.
The coefficient of determination, denoted as R², is the proportion of the variation in the dependent variable that is explained by the independent variable(s). Therefore, the percentage of the variation in the data about the regression line that is unexplained can be found by subtracting the coefficient of determination from 1 and then multiplying the result by 100.
Percentage of variation unexplained = (1 - R^2) x 100%
Substituting R² = 0.298, we get:
Percentage of variation unexplained = (1 - 0.298) x 100%
Percentage of variation unexplained = 0.702 x 100%
Percentage of variation unexplained = 70.2%
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Simplify:
(-10x²) (-2x¹)
Ms. Hernandez began her math class by saying:
I'm thinking of 5 numbers such that their mean is equal to their median. If 4 of the numbers are 14, 8, 16, and 14, what is the 5th number?
What is the 5th number Ms. Hernandez is thinking of?
A. 13
B. 14
C. 15
D. 16
E. 18
The missing fifth number in the set of data given is option E: 18, solved by using the fact that median and mean are equal.
Mean and median are the two measures of central tendency in which median can be found by arranging the data in ascending or descending order. The given data can be arranged in ascending order as follows:
8, 14, 14, 16, x. (we need to find x, we are still unaware)
As the median is the mid value of the given data. Here, median must be 14.
Next, the mean of the data can be calculated by adding all the values together and dividing them by the total number of values: The formula for finding the mean is:
Mean = ∑X/n
where, X is the sample value, and n is the total number of values in the data.
Thus, Mean= 14 + 8 + 16 + 14/5
= 52 + x/ 5.
Now, we have been told that mean and median are equal. Using this fact:
Mean = Median
=52 + x/ 5 = 14
Solving for x in this case, we get
x = 18
Therefore, the possible values for the missing fifth number is 18.
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What is the distance, in units, between the points (−3, 1) and (2, −1)?
\sqrt{x} 3\\
\\
\sqrt{x} 5\\
\sqrt{x} 21\\
\\
\sqrt{x} 29
Answer:
[tex] \sqrt{ { (- 3 - 2)}^{2} + {(1 - ( - 1))}^{2} } [/tex]
[tex] \sqrt{ {( - 5)}^{2} + {2}^{2} } [/tex]
[tex] \sqrt{25 + 4} = \sqrt{29} [/tex]
carson city cinemas charges $15 per adult, $12 per child, and $10 for senior citizens to purchase movie tickets. write an equation relating a, c, and s if the theater collected a total of $1515 in ticket sales last month.
Carson City cinemas charge $15 per adult, $12 per child, and $10 for senior citizens to purchase movie tickets. The equation relating a, c, and s for Carson City Cinemas' ticket sales is 15a + 12c + 10s = 1515.
To write an equation relating to a, c, and s, we can use the information given in the question. Let a be the number of adult tickets sold, c be the number of child tickets sold, and s be the number of senior citizen tickets sold.
The price for an adult ticket is $15, so the total amount collected from adult tickets is 15a. Similarly, the total amount collected from child tickets is 12c, and the total amount collected from senior citizen tickets is 10s.
Since the theatre collected a total of $1515 in ticket sales, we can set up the equation:
15a + 12c + 10s = 1515
This equation relates the number of adults, children, and senior citizen tickets sold to the total amount collected in ticket sales.
To solve for a, c, and s, we would need more information. However, we can use this equation to analyze different scenarios. For example, we could plug in different values for a, c, and s to see how it affects the total amount collected.
In summary, the equation relating a, c, and s for Carson City Cinemas' ticket sales is 15a + 12c + 10s = 1515.
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The manager of a computer retail store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.3 years and a standard deviation of 0.5 years. He then randomly selects records on 32 laptops sold in the past and finds that the mean replacement time is 3.1 years.
Find the probability that 32 randomly selected laptops will have a mean replacement time of 3.1 years or less.
The probability that 32 randomly selected laptops will have a mean replacement time of 3.1 years or less is 0.0122 or approximately 1.22%. This suggests that it is unlikely that the manager's suppliers have been giving him laptop computers with lower-than-average quality.
To find the probability that 32 randomly selected laptops will have a mean replacement time of 3.1 years or less, we can use the central limit theorem. This theorem states that as sample size increases, the sampling distribution of the sample means approaches a normal distribution, regardless of the shape of the population distribution.
First, we need to calculate the standard error of the mean, which is the standard deviation of the sampling distribution. We can use the formula:
standard error = standard deviation / square root of sample size
Substituting the given values, we get:
standard error = 0.5 / sqrt(32) = 0.0884
Next, we need to standardize the sample mean using the formula:
z = (x - mu) / standard error
where x is the sample mean, mu is the population mean (given as 3.3 years), and standard error is the calculated value.
Substituting the given values, we get:
z = (3.1 - 3.3) / 0.0884 = -2.26
Finally, we need to find the probability that a standard normal distribution is less than or equal to -2.26. Using a standard normal table or calculator, we find this probability to be 0.0122 or approximately 1.22%.
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Answer these reflection
questions.
4
1. What does it mean for a
point to be a solution to a
system of equations?
2. When would you use the
substitution method instead
of the elimination method?
When a point is the solution of a system of equations, it means that all of the equations in the system are simultaneously satisfied by the values of the variables.
What is a linear equation?Use the substitution method to solve the system of equations when one of the variables in one of the equations can be easily isolated or solved for.
The system's remaining equations can then be modified to reflect the variable's expression, creating a new set of equations with one less variable. The system might be easier to manually solve as a result.
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an art supply company's sales this year were 180% of what they were 5 years ago. if sales 5 years ago were $25,000. what were this years sales?
If the sales 5 years ago were $25,000, then we can calculate this year's sales as follows:
Calculate the percentage increase from 5 years ago to this year:
Percentage increase = 180% - 100% = 80%
Calculate the amount of increase in sales:
Amount of increase = Percentage increase x Sales 5 years ago
Amount of increase = 0.8 x $25,000 = $20,000
Add the amount of increase to the sales 5 years ago to find this year's sales:
This year's sales = Sales 5 years ago + Amount of increase
This year's sales = $25,000 + $20,000 = $45,000
Therefore, this year's sales for the art supply company were $45,000.
a tank with a base of 4 feet by 5 feet and a height of 4 feet is full of water. the water weighs 62.4 pounds per cubic foot. how much work is done in pumping water out over the top edge in order to empty all of the tank. round your answer to one decimal place and show your drawing
The work done in pumping water out over the top edge to empty the tank is approximately 9984 foot-pounds, rounded to one decimal place.
To calculate the work done in pumping water out of the tank, we will use the formula:
Work = weight of water × height to be lifted
First, let's find the volume of the tank:
Volume = base × height Volume = (4 feet × 5 feet) × 4 feet Volume = 80 cubic feetNext, find the total weight of the water in the tank:
Total weight = volume × weight per cubic foot Total weight = 80 cubic feet × 62.4 pounds/cubic foot Total weight = 4992 poundsSince the height of the tank is 4 feet, and we need to pump the water over the top edge, we can assume the average height the water needs to be lifted is half the height of the tank, which is 2 feet.
Now, we can calculate the work done:
Work = total weight × average height to be lifted Work = 4992 pounds × 2 feet Work = 9984 foot-poundsSo, the work done in pumping water out over the top edge to empty the tank is approximately 9984 foot-pounds, rounded to one decimal place. Here is the visualization:
_______
| |
| | 4 feet
| |
|_______|
5 feet
|\
| \
h \
|___\____
5 feet
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If two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85, and standard deviations 12 and 15, respectively, then probability that the mean of the 1st sample will be larger than the mean of the 2nd sample is:__________
The probability that the mean of the first sample will be larger than the mean of the second sample is approximately 0.976 or 97.6%.
To find the probability that the mean of the first sample will be larger than the mean of the second sample, we can use the central limit theorem and the formula for the standard error of the difference between two means:
SE = sqrt[(s1^2/n1) + (s2^2/n2)]
Where SE is the standard error, s1 and s2 are the standard deviations of the two populations, n1 and n2 are the sample sizes, and ^2 represents squared.
Plugging in the given values, we get:
SE = sqrt[(12^2/30) + (15^2/36)]
SE = 3.535
Next, we need to standardize the difference between the two sample means by dividing it by the standard error:
z = (x1 - x2) / SE
Where z is the z-score, x1 and x2 are the sample means, and SE is the standard error.
In this case, we want to find the probability that the mean of the first sample is larger than the mean of the second sample, so we are interested in the area to the right of the z-score we calculate. Using a standard normal distribution table or calculator, we can find this probability to be:
P(z > -1.971) = 0.976
Therefore, the probability that the mean of the first sample will be larger than the mean of the second sample is approximately 0.976 or 97.6%.
For your question about the probability that the mean of the 1st random sample (size 30, mean 78, standard deviation 12) will be larger than the mean of the 2nd random sample (size 36, mean 85, standard deviation 15) from two different populations, we need to calculate the difference in the means and the standard error of the difference.
First, we find the difference in means: μ1 - μ2 = 78 - 85 = -7
Next, we calculate the standard error of the difference: SE = sqrt[(σ1²/n1) + (σ2²/n2)] = sqrt[(12²/30) + (15²/36)] ≈ 3.39
Now we need to find the z-score associated with the difference in means: z = (X1 - X2 - (μ1 - μ2)) / SE = (0 - (-7)) / 3.39 ≈ 2.06
Finally, we look up the probability associated with this z-score in a standard normal table or use a calculator. For z = 2.06, the probability that the mean of the 1st sample will be larger than the mean of the 2nd sample is approximately 0.0197, or 1.97%.
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Find a 3Ã3 matrix with exactly one (real) eigenvalue -4, such that the -4-eigenspace is a line.
The solution to this system is `x = [1, 1/4, 1/16]`, which is a nonzero vector in the -4-eigenspace.
One possible solution is the following matrix:
```
A = [[-4, 0, 0],
[1, -4, 0],
[0, 1, -4]]
```
We can verify that the eigenvalue -4 has algebraic multiplicity 3 by computing the characteristic polynomial:
```
det(A - lambda*I) = (-4 - lambda) * (-4 - lambda) * (-4 - lambda)
```
where `I` is the 3x3 identity matrix. Therefore, the eigenvalue -4 has geometric multiplicity 1, since the -4-eigenspace is a line.
To find the eigenvector associated with this eigenvalue, we solve the equation `(A - (-4)*I)x = 0`, or equivalently, `Ax = (-4)x`. This gives us the following system of equations:
```
-4x1 = 0
x1 - 4x2 = 0
x2 - 4x3 = 0
```
The solution to this system is `x = [1, 1/4, 1/16]`, which is a nonzero vector in the -4-eigenspace.
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Which equation is modeled on the number line below?
A
B
C
D
-12-11-10
3 x 4 = 12
-3x (-4)=12
3x (-4)=-12
4x (-3)=-12
HHHH>
89101112
4
7:5
Answer: equation 3x (-4) = -12 has a solution of x = 1, which can be represented on the number line between -2 and -3.
Step-by-step explanation: Based on the number line and the answer choices provided, it appears that the equation modeled on the number line is:
C) 3x (-4) = -12
This equation can be interpreted as "what number multiplied by 3 and then multiplied by -4 will give a result of -12". Solving for x, we get:
3x (-4) = -12
-12x = -12
x = -12/-12
x = 1
Therefore, the equation 3x (-4) = -12 has a solution of x = 1, which can be represented on the number line between -2 and -3.
let f be the function that satisfies the given differential equation (dy/dx = xy/2). write an equation for the tangent line to the curve y = f(x) through the point (1,1). then use your tangent line equation to estimate the value of f(1.2).
Our estimate for f(1.2) is 1.1 which satisfies differential equation.
To find the equation of the tangent line to the curve y = f(x) through the point (1,1), we first need to find the value of f(1) at x = 1. To do this, we can solve the differential equation given:
[tex]dy/dx = xy/2[/tex]
Separating the variables, we get:
[tex]dy/y = x/2 dx[/tex]
Integrating both sides, we get:
[tex]ln|y| = x^2/4 + C[/tex]
Where C is the constant of integration. To find the value of C, we can use the initial condition that f(1) = 1:
ln|1| = 1/4 + C
C = -1/4
So our equation for f(x) is:
[tex]ln|y| = x^2/4 - 1/4[/tex]
Simplifying, we get:
[tex]y = e^(x^2/4 - 1/4)[/tex]
To find the equation of the tangent line through the point (1,1), we need to find the slope of the tangent line at x = 1. To do this, we take the derivative of f(x) and evaluate it at x = 1:
[tex]f'(x) = (1/2)x e^(x^2/4 - 1/4)f'(1) = (1/2)(1) e^(1/4 - 1/4) = 1/2[/tex]
So the slope of the tangent line at x = 1 is 1/2. Using the point-slope form of a line, we get:
[tex]y - 1 = 1/2(x - 1)[/tex]
Simplifying, we get:
y = 1/2 x + 1/2
To estimate the value of f(1.2), we can use our tangent line equation. Plugging in x = 1.2, we get:
[tex]y = 1/2(1.2) + 1/2 = 1.1[/tex]
So our estimate for f(1.2) is 1.1.
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A zombie infection in Duluth High School grows by 15% per hour. The initial group of
zombies was a group of 4 freshmen. How many zombies are there after 6 hours?
Growth or decay situation?
What is the rate of growth or decay?
What is the growth or decay factor?
Initial amount?
What is the equation?
How many zombies are there after 6 hours?
Multiply and simplify.
x-1
2-1
x2+2x+1 X+1
01
X + 1
X - 1
X-1
X + 1
(x - 1)²
(x + 1)²
Answer:
try to get am math tutor........
The circumference of a circle is 12π m. Find its diameter, in meters.
Reason:
circumference = pi*diameter
Its diameter in meters is 12 meters.
What numbers multiply to 10 and add up to -10
Using algebra, the numbers multiply by 10 and add up to -10 are -5 - √(15) and -5 + √(15).
To find two numbers that multiply to 10 and add up to -10, we can use algebra. Let's call the two numbers we're looking for x and y. We know that:
xy = 10
We also know that:
x + y = -10
Now we can solve for one of the variables in terms of the other. For example, we can solve for x in terms of y by rearranging the second equation:
x = -y - 10
Now we can substitute this expression for x into the first equation:
(-y - 10)y = 10
Expanding and simplifying, we get:
-y² - 10y - 10 = 0
Solving for y using the quadratic formula, we get:
y = (-(-10) ± √((-10)² - 4(-1)(-10))) / (2(-1))
y = (10 ± √(60)) / 2
So the two possible values for y are:
y = 5 + √(15)
y = 5 - √(15)
Finally, we can plug each of these values for y back into x = -y - 10 to get the corresponding values for x:
x = -5 - √(15)
x = -5 + √(15)
Therefore, the two numbers that multiply by 10 and add up to -10 are approximately -5 - √(15) and -5 + √(15).
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Help with the two questions please!
The values of x and y are y = 27 and x = 18 & x = 3 and y = 12
The triangles are similar by SAS and SSS
Calculating the values of x and yGiven that the triangles are similar
So, we have
12/y = 4/9 and x/12 = 6/4
When evaluated, we have
4y = 12 * 9 and 4x = 12 * 6
Divide both sides by the coefficients of x and y
So, we have
y = 27 and x = 18
For the similar trapezoid, we have
(2x + 1)/3 = (4x + 9)/9 and 3/4 = 9/y
So, we have
6x + 3 = 4x + 9 and 3y = 4 * 9
Evaluate
2x = 6 and 3y = 36
So, we have
x = 3 and y = 12
The similarity of the trianglesFor the first pair of triangles, the triangles are similar by SAS because of the following corresponding sides and angles
QE corresponds to DC∠Q corresponds to ∠DQR corresponds to DRFor the second pair of triangles, the triangles are similar by SSS because the corresponding sides have the same scale factor of 1.5
i.e. RP/NM = 3/2 = 1.5, PN/LM = 6/4 = 1.5 and RN/LN = 9/6 = 1.5
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An online pet store offers the hamster house shown in the figure below.
Choose all of the expressions that could be used to find the volume of the hamster house.
A solid shape is shown; two rectangular prisms are attached. The total length of the shape is 6 feet. One rectangular prism has a length of 1 foot, width of 3 feet and height of 4 feet. The second rectangular prism has a length as 6 feet, width as 3 feet and height as 2 feet.
A.
(
1
×
3
×
4
)
+
(
2
×
5
×
3
)
B.
(
1
×
3
)
+
(
4
×
2
)
+
(
5
×
3
)
C.
(
1
×
3
×
2
)
+
(
6
×
3
×
2
)
D.
3
×
(
1
+
4
)
+
2
×
(
5
+
3
)
E.
(
3
×
4
)
+
1
×
(
2
×
5
)
+
3
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10 of 14 Answered
All the correct expressions that could be used to find the volume of the hamster house are,
⇒ (1 × 3 × 4) + (6 × 3 × 2)
How to solveGiven that;
One rectangular prism has a length of 1 foot, a width of 3 feet and a height of 4 feet.
And, The second rectangular prism has a length as 6 feet, a width as 3 feet, and a height of 2 feet.
Hence, the Volume of first rectangular prism is,
⇒ 1 × 3 × 4
And, Volume of a second rectangular prism is,
⇒ 6 × 3 × 2
Thus, All the correct expressions that could be used to find the volume of the hamster house are,
⇒ (1 × 3 × 4) + (6 × 3 × 2)
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The ratio of rookies to veterans in the camp was 2 to 7. Altogether there were 252 rookies and veterans in the camp.
How many of them were rookies?
Answer:
56 of them were rookies.
Step-by-step explanation:
Let x = the number of rookies; y = the number of veterans.
We have the total number of people:
x + y = 252 (1)
The ratio x/y = 2/7 is equal to:
7x = 2y, so x = 2y/7
Substituting x into (1):
2y/7 + y = 252
9y/7 = 252
y = 252 × 7/9 = 196
So substituting y into (1):
x + 196 = 252
x = 252 - 196 = 56.
There were 56 rookies in the camp.
To find the number of rookies in the camp, we will use the given ratio and the total number of people in the camp.
Step 1: Write down the ratio of rookies to veterans, which is 2:7.
Step 2: Add the two parts of the ratio together: 2 + 7 = 9 parts.
Step 3: Divide the total number of people in the camp by the total number of parts. In this case, there are 252 people and 9 parts: 252 / 9 = 28. This means each part represents 28 people.
Step 4: Multiply the number of people per part by the number of parts for rookies to find the total number of rookies: 2 parts (rookies) * 28 people per part = 56 rookies.
So, there were 56 rookies in the camp.
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