Answers
Hi there!
Your job, at least on this triangle, is pretty simple. This is a 45-45-90 triangle.
Because this is a 45-45-90 triangle, both legs are 5. That leaves us to find the hypotenuse, x.
And a 45-45-90 triangle's hypotenuse is easy. You just take the measure of one of the legs, or 5 in this case, and stick a \(\sqrt{2\\}\) right next to it. So your answer will be:
\(5\sqrt{2}\)
I hope this helps! :)
Related Questions
for which values of a is the matrix singular? (enter your answers as a comma-separated list.) a 3
2 6
a=
Answers
The matrix is singular when a = 4.
To determine when the matrix is singular, we need to find the determinant of the matrix and see when it is equal to zero.
The determinant of the matrix is:
| 3 2 |
| 6 a |
= 3(a) - (6)(2)
= 3a - 12
The matrix is singular when the determinant is equal to zero. Therefore, we need to solve the equation:
3a - 12 = 0
Solving for a, we get:
a = 4
Therefore, the matrix is singular if and only if a = 4. If a = 4, the determinant of the matrix is zero, which means the matrix is singular. If a is any other value, the determinant of the matrix is non-zero, which means the matrix is not singular.
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Question 2 20 pts A p-value for correlation which is statistically significant implies the correlation is due to random chance. True O False Question 5 20 pts For each one unit increase in X we expect Y to increase by b1 units, on average. Interpretation of the intercept Interpretation of a residual Interpretation of r-squared Interpretation of the slope
Answers
A p-value for correlation which is statistically significant implies the correlation is due to random chance. The correct solution to this is False.
A p-value for correlation which is statistically significant implies that it is unlikely that the observed correlation is due to random chance alone. In other words, it suggests that there is evidence to support the presence of a true correlation between the two variables being studied. The p-value is a measure of the strength of evidence against the null hypothesis (i.e., that there is no correlation between the two variables), and a smaller p-value indicates stronger evidence against the null hypothesis.
Interpretation of the intercept: The intercept in a linear regression model represents the value of the dependent variable when all independent variables are equal to zero. It is the value of the dependent variable when there is no effect of the independent variable(s) on it. For example, in a regression model predicting height based on age, the intercept would represent the expected height of a person at age zero (which is not a realistic scenario).
Interpretation of a residual: A residual is the difference between the actual observed value of the dependent variable and the predicted value of the dependent variable based on the regression model. It represents the part of the dependent variable that the model was not able to explain. A positive residual means that the actual value is greater than the predicted value, while a negative residual means that the actual value is smaller than the predicted value.
Interpretation of r-squared: R-squared is a measure of how much of the variation in the dependent variable is explained by the independent variable(s) in the regression model. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data. Specifically, it represents the proportion of the total variation in the dependent variable that is explained by the independent variable(s) in the model. For example, if r-squared is 0.75, it means that 75% of the variability in the dependent variable is explained by the independent variable(s) in the model.
Interpretation of the slope: The slope in a linear regression model represents the change in the dependent variable that is associated with a one-unit increase in the independent variable, holding all other variables constant. It reflects the average change in the dependent variable for each unit change in the independent variable. For example, in a regression model predicting height based on age, the slope would represent the average change in height for each additional year of age.
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match each table to an equation that represents the relationship.
table a Equation 1 400 + x = y
table b Equation 2 x - 400 = y
table c Equation 3 x + y = 400
table d Equation 4 400 X x = y
Answers
The equation y = 400x represents the relationship as shown in the table.
The correct option is table d.
What is the proportional relationship?
A proportional relationship is a relationship between two expressions, where changes in one expression mean some constant change in another expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
A table is shown in the attached image.
To find the relationship:
We will find the common ratio,
y/x = k, where k is the proportionality constant,
400/1 =400
800/2 = 400
1200/3 = 400.
That means, the equation is,
y = 400x
Therefore, y = 400x is the equation.
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The complete question is given in the attached image.
what are the major methods of recording unstructured observational data
Answers
The major methods of recording unstructured observational data are Narrative Description, Field Notes, Audio or Video Recording, Photography, Diagrams or Maps.
The major methods of recording unstructured observational data are:
1. Narrative Description: This method involves writing a detailed, chronological account of the observed events or behaviors, capturing the context and interactions as they occur naturally.
2. Field Notes: In this method, the observer takes brief, concise notes during the observation, focusing on key events, behaviors, or interactions. These notes can be expanded and organized later for further analysis.
3. Audio or Video Recording: Using audio or video equipment, the observer captures the events and interactions in their entirety. This allows for a more accurate record and the ability to review and analyze the data multiple times.
4. Photography: Taking photographs during the observation can provide a visual record of the events and behaviors. These images can supplement other data collection methods and help to illustrate specific aspects of the observation.
5. Diagrams or Maps: Drawing diagrams or maps of the observation setting can help capture the spatial relationships between individuals and objects, as well as the overall layout of the environment.
These methods can be used individually or in combination, depending on the research question and the specific needs of the study. Remember to always respect participants' privacy and obtain informed consent when necessary.
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which is closer to -3/5 … 2/5, -0.2, -4/5, 0.6
Answers
-3 : 5 = - 0,6
so it will be - 4/5 (= - 0,8)
Write the equation of the line that passes through the points (8,-1) and (2,-5) in standard form, given that the point-slope form is y+1=3/3(x-8)
Answers
The equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.
The given coordinate are (8, -1) and (2, -5).
What is the slope of an equation?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
The slope of the equation is \(m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}\).
The standard form of an equation is Ax + By = C.
The given the point-slope form is \(y+1=\frac{2}{3} (x-8)\).
Multiply each term by 3 of the equation.
\((y+1) \times3=\frac{2}{3} (x-8) \times3\)
⇒3y + 3 = 2x - 16
Subtract 2x from both sides of a equation.
That is, -2x + 3y + 3 = - 16
Subtract 3 from both sides of a equation.
That is, -2x + 3y = - 19
Multiply each term by - 1 from both sides of an equation.
That is, 2x - 3y = 19
Therefore, the equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.
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Fill in the table so that every row and every column sums to zero.
Answers
Answer:
Step-by-step explanation:
wheres the table
plsss answer this asap
Answers
Answer:
Aliyah started with eighteen (18) pieces.
Step-by-step explanation:
10+ 4(2)= 18
consider the following diagram. point Q is equidistant from a and b. if the distance from A to the perpendicular line is 3/4x+6 and distance from B to the same perpendicular line is 5x-4/5. what is the value of x
Answers
Answer: 1.6
Step-by-step explanation: just did it
In a typical month, the BBC Corporation receives 30 checks totaling $250,000. These are delayed five (5) days on average What is the average daily float? Assume 30 days per month. 0 $1,250,000 0 $1,500,000 O $41,667
Answers
The average daily float for the BBC Corporation, based on receiving 30 checks totaling $250,000 with an average delay of five days, is $41,667.
To calculate the average daily float, we need to determine the total amount of funds in transit and divide it by the average number of days the funds are delayed.
In this case, the BBC Corporation receives 30 checks totaling $250,000 in a typical month. The average delay for these checks is five days.
To calculate the total amount of funds in transit, we multiply the average daily amount by the average delay:
Total funds in transit = Average daily amount × Average delay
= ($250,000 / 30 days) × 5 days
= $8,333.33 × 5
= $41,666.67
Rounding to the nearest whole number, the average daily float is $41,667.
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The total length of these planks is 92 metres. Work out the number of planks of length 2 metres in Ben workshop.
Answers
Answer: 13
Step-by-step explanation:
X
f(x)
-10
-2
-1
-8
0
-6
1
-4
2
-2
3
0
Mark this and return
Which is an x-intercept of the continuous function in the
table?
O (0, -6)
O (3,0)
O (-6,0)
O (0, 3)
Save and Exit
Submit
Answers
The x intercept of the continuous function in the table is (3, 0).
What is an x Intercept?x intercept of a function or a graph is the point where the value of the function is 0.
In other words, it is the point where the graph of the function touches the X axis.
Given is a table values for the function.
From the given table, it can be seen that the value of the function is 0 in more than one point.
So x intercept will be all those values where the function value is 0.
This is because that, the function value is 0 when the graph touches the X axis.
So the points are (-1, 0), (2, 0) and (3, 0).
From the option, it is (3, 0).
Hence the x intercept is (3, 0).
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An airplane has an airspeed of 500 kilometers per hour (k/hr) in a
northerly direction (N 0˚ E). The wind velocity is 60 k/hr in a southeasterly (S45˚E)
direction. Let Va be the velocity of the plane relative to the air and Vw be the velocity
of the wind (both in terms of i and j).
1. Find vg = va + vw, the path of the plane relative to the ground. Round coefficients to the nearest tenth.
2. Find the actual speed and direction of the airplane relative to the ground. Round to the nearest tenth.
Answers
Mr. Jone bought a car that had 2,342. 5 mile on the odometer. When he old the car it had 25,452. 9 mile on the odometer. Which equation repreent how many mile Mr. Jone put on the car?
Answers
The equation which represent the number of miles Mr Jones put on the car is x = 25,452.9 miles - 2,342.5 miles
How to write equation about number of miles Mr Jones put on the car?Number of miles on the odometer of a car when Mr Jones bought it = 2,342.5 milesNumber of miles on the odometer of a car when Mr Jones sold it = 25,452.9 milesNumber of miles Mr Jones put on the car = xNumber of miles Mr Jones put on the car = Number of miles on the odometer of a car when Mr Jones sold it - Number of miles on the odometer of a car when Mr Jones bought it
x = 25,452.9 miles - 2,342.5 miles
x = 23,110.4 miles
In conclusion, the number of miles Mr Jones put on the car is 23,110.4 miles
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Given that f(x)=16x+4 and g(x)= x+9
f(g(12))=
g(f(12))=
Answers
For the expression f(g(12)), the result is 344. For the expression g(f(12)), the result is 205.
To find f(g(12)), we substitute the value of 12 into the g(x) function first. Plugging in x=12 into g(x) gives us g(12) = 12 + 9 = 21.
Next, we substitute the result of g(12) into the f(x) function.
Plugging in x=21 into f(x) gives us f(21) = 16(21) + 4 = 340 + 4 = 344. Therefore, f(g(12)) = 344.
To find g(f(12)), we substitute the value of 12 into the f(x) function first. Plugging in x=12 into f(x) gives us f(12) = 16(12) + 4 = 192 + 4 = 196.
Next, we substitute the result of f(12) into the g(x) function.
Plugging in x=196 into g(x) gives us g(196) = 196 + 9 = 205.
Therefore, g(f(12)) = 205.
Hence, f(g(12)) evaluates to 344, while g(f(12)) evaluates to 205.
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1/4 > 1. Order the following rational numbers from greatest to least: 25% - 0.17 3 5 1.2 - 12 First convert these numbers to decimal form. Show your work below. You can write on the screen! Next, grab the numbers in the list and place them in order from GREATEST to LEAST!
Answers
Answer:
1.2, 3/5, 25%, 0.17, -12
Step-by-step explanation:
In order to put these from greatest to least, you must put these in like terms.
Since there are more decimals that other terms, we're going to convert them all to decimals.
25%= 0.25
0.17= 0.17
3/5= 0.60
1.2= 1.20
-12= -12.00
Now that we see which numbers are greater, we convert them back to their original terms and place them in order from greatest to least.
1.2, 3/5, 25%, 0.17, -12
1/2 x 12 divided 2 - 2 +11
Please leave a explanation
Answers
Answer:
12
Step-by-step explanation:
1/2*12=6
6/2=3
11+2=13
13-3=10
10+2=12
P.E.M.D.A.S
Hope this helps!
Answer:
12
Step-by-step explanation:
Multiply 1/2 by 12 and get 6, divide 6 by 2 and get 3, 3-2 is 1, then add 1 and 11 to get the answer 12
(05.05 MC)
The area of a triangle is 24 square inches. What is the height of the triangle if the base length is 6 inches? (5
points)
Answers
Answer:
h = 8 inches
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = \(\frac{1}{2}\) bh ( b is the base and h the height )
given A = 24 and b = 6 , then
\(\frac{1}{2}\) × 6 × h = 24 , that is
3h = 24 ( divide both sides by 3 )
h = 8 inches
Find f¹(z) for the following function: f(x)= 6 x+2 3 f¹(z) = k
Answers
Answer: If I did this correctly, it is 6
Step-by-step explanation:
f¹(z) = k, where k is a constant.
To find f¹(z), we need to solve the equation z = 6f¹(z) + 2/3 for f¹(z). Let's proceed step by step.
Start with the equation z = 6f¹(z) + 2/3.
Subtract 2/3 from both sides of the equation: z - 2/3 = 6f¹(z).
Divide both sides of the equation by 6: (z - 2/3)/6 = f¹(z).
Simplify the expression on the left side: f¹(z) = (z - 2/3)/6.
Thus, f¹(z) = (z - 2/3)/6, where f¹(z) represents the inverse function of f(x).
In summary, the inverse function f¹(z) of f(x) = 6x + 2/3 is given by (z - 2/3)/6.
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Start by finding the scale of this map. At the actual gym, one side length of the snack stand is 60 feet. On the scale map, it is 20 cm. What is the scale?
Answers
Answer:
I actual foot represents 0.01093 foot on paper
Step-by-step explanation:
Given that :
Actual side length of snack stand = 60 feets
Length of side on map = 20cm
Scaie :
60 feet = 20cm
1 foot = (20/60) cm
1 foot = 0.333 cm
1cm = 0.0328084 foot
0.333cm = (0.33 * 0.0328084) = 0.01093 feets
Scale :
I actual foot represents 0.01093 foot on paper
Use number sense to solve the equation. 3x + 14 = 23 A. 3 B. 6 C. 9 D. 4
Answers
Answer:
x=3
Step-by-step explanation:
3x + 14 = 23
3x=23-14
3x=9
x=9/3
x=3
option A is the correct answer
my best friend doesn't know the answer i aaint answering it for him help him help this dumbo
Answers
Answer:
5 batches
Step-by-step explanation:
michael arranged all his books in a bookcase with 10 books on each shelf and no books left over. after michael acquired 10 additional books, he arranged all his books in a new bookcase with 12 books on each shelf and no books left over. how many books did michael have before he acquired the 10 additional books? before michael acquired the 10 additional books, he had fewer than 96 books. before michael acquired the 10 additional books, he had more than 24 books.
Answers
Michael had 72 books before he acquired the 10 additional books.
STEPS FOR CALCULATION THE ADDITIONAL BOOKSLet's call the number of books Michael had before he acquired the 10 additional books x.The number of books Michael had after he acquired the 10 additional books is x + 10.We are told that x + 10 can be divided into 12 books per shelf with no books left over, so x + 10 must be divisible by 12.We are also told that x is fewer than 96 and more than 24, so x must be a multiple of 12 that is between 24 and 96.The multiples of 12 between 24 and 96 are 36, 48, 60, 72, 84, so the number of books Michael had before he acquired the 10 additional books is one of these numbers.Out of these numbers, only 72 can be divided into 10 books per shelf with no books left over, so Michael had 72 books before he acquired the 10 additional books.Learn more about equation here:
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The nth term of an arithmetic sequence is given by an
an= 4 + 5(n-1). If you were to graph ordered pairs where x is the term number and y is the term, what linear equation would describe the line that passes through the points?
Answers
Answer:
y = 5x - 1Step-by-step explanation:
aₙ = y n = x
aₙ = 4 + 5(n-1)
y = 4 + 5(x - 1)
y = 4 + 5x - 5
y = 5x - 1
There are 10 people taking part in a raffle.
Ann, Bob, Elsa, Hans, Jim, Kira, Lena, Omar, Ravi, and Soo.
Suppose that prize winners are randomly selected from the 10 people.
Compute the probability of each of the following events.
Event A: The first three prize winners are Soo, Ann, and Jim, regardless of order.
Event B: Ann is the first prize winner, Lena is second, and Bob is third.
Write your answers as fractions in simplest form.
P(A) =
?
P (B) =
Answers
The probabilities are:
\(P(A) = \frac{1}{120}\) and \(P(B) = \frac{1}{720}\).
To calculate the probabilities, we need to consider the total number of possible outcomes and the number of favorable outcomes for each event.
Event A: The first three prize winners are Soo, Ann, and Jim, regardless of order.
There are 10 people, so the total number of possible outcomes is 10P3 (permutations of 10 people taken 3 at a time).
This is calculated as 10! / (10-3)! = 10! / 7! = 10 * 9 * 8 = 720.
The number of favorable outcomes is 3! (permutations of 3 people), as the order doesn't matter.
So, the number of favorable outcomes is 3! = 3 * 2 = 6.
P(A) = favorable outcomes / total outcomes = 6 / 720 = 1 / 120.
Event B: Ann is the first prize winner, Lena is second, and Bob is third.
Similarly, there are 10P3 total outcomes, which is 720.
The number of favorable outcomes is 1, as there is only one specific arrangement where Ann is first, Lena is second, and Bob is third.
P(B) = favorable outcomes / total outcomes = 1 / 720.
Therefore, the probabilities are:
P(A) = 1 / 120
P(B) = 1 / 720.
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Find how much interest $10,000 earns in 4 years in a certificate of deposit paying 4.5% interest compounded quarterly. The interest earned in 4 years is $ (Do not round until the final answer. Then round to the nearest cent as needed.)
Answers
According to the Question, The interest earned in 4 years is $1,954.83.
What is compounded quarterly?
A quarterly compounded rate indicates that the principal amount is compounded four times over one year. According to the compounding process, if the compounding time is longer than a year, the investors would receive larger future values for their investment.
The principal is $10,000.
The annual interest rate is 4.5%, which is compounded quarterly.
Since there are four quarters in a year, the quarterly interest rate can be calculated by dividing the annual interest rate by four.
The formula for calculating the future value of a deposit with quarterly compounding is:
\(P = (1 + \frac{r}{n})^{nt}\)
Where P is the principal
The annual interest rate is the number of times the interest is compounded in a year (4 in this case)
t is the number of years
The interest earned equals the future value less the principle.
Therefore, the interest earned can be calculated as follows: I = FV - P
where I = the interest earned and FV is the future value.
Substituting the given values,
\(P = $10,000r = 4.5/4 = 1.125n = 4t = 4 years\)
The future value is:
\(FV = $10,000(1 + 1.125/100)^{4 *4} = $11,954.83\)
Therefore, the interest earned is:
\(I = $11,954.83 - $10,000= $1,954.83\)
Thus, the interest earned in 4 years is $1,954.83.
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a film distribution manager calculates that 9%9% of the films released are flops. if the manager is right, what is the probability that the proportion of flops in a sample of 506506 released films would differ from the population proportion by greater than 3%3%? round your answer to four decimal places.
Answers
The probability that the proportion of flops in a sample of 506 released films would differ from the population proportion by greater than 3% is approximately 0.0192 or 1.92% (rounded to four decimal places).
Given:
Population proportion of flops: p = 9% = 0.09
Sample size: n = 506
First, let's calculate the standard deviation (σ) of the sampling distribution, which represents the standard error of the proportion:
σ = √[(p * (1 - p)) / n]
= √[(0.09 * (1 - 0.09)) / 506]
≈ √[(0.0819) / 506]
≈ √[0.000161955]
≈ 0.012736
Next, we need to find the z-score associated with a difference of 3% from the population proportion:
z = (0.03 - 0) / σ
= 0.03 / 0.012736
≈ 2.3542
Using a standard normal distribution table or calculator, we can find the probability associated with the z-score of 2.3542. However, since we are interested in the probability that the proportion differs from the population proportion by greater than 3%, we need to consider both tails of the distribution.
The probability of a difference greater than 3% is equal to the probability of a z-score less than -2.3542 or greater than 2.3542.
P(z < -2.3542) + P(z > 2.3542)
Looking up the values in the standard normal distribution table or using a calculator, we find:
P(z < -2.3542) ≈ 0.0096
P(z > 2.3542) ≈ 0.0096
Adding these probabilities:
0.0096 + 0.0096 ≈ 0.0192
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A researcher who is evaluating the significance of a multiple regression equation with two predictor variables, obtains an F-ratio with df = 2, 18. How many individuals were needed to produce the sample data used to find the regression equation?
Answers
The number of individuals needed to produce the sample data used to find the regression equation is 21.
Given,
In the question:
A researcher who is evaluating the significance of a multiple regression equation with two predictor variables, obtains an F-ratio with df = 2, 18.
To find the regression equation.
Now, According to the question:
F test:
In the multiple regression, the relationship between the variables is statistically significant can be check by F-test. The F-test used to determine the statistical regression models which is best suited for the population.
A value of 2 represents the degrees of freedom due to regression.
and, the value 18 represents the degrees of freedom due to or residuals.
The formula of degree of freedom due to residual is:
\(df_r_e_s_i_d_u_a_l\) = n - k - 1
The number of individuals in the sample data (n) can be calculated as:
\(df_r_e_s_i_d_u_a_l\) = n - k - 1
18 = n - 2 - 1
18 = n - 3
18 + 3 = n
21 = n OR
n = 21
Hence, The number of individuals needed to produce the sample data used to find the regression equation is 21.
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a car travels at a distance of 450 kilometers in 6 hours. What speed did the car travel at?
Answers
Speed = Distance ÷ Time
Here, the distance traveled by the car is 450 kilometers and the time taken is 6 hours. Substituting these values in the formula we get:
Speed = 450 km ÷ 6 hours
Simplifying this expression gives:
Speed = 75 km/hour
Therefore, the car traveled at a speed of 75 kilometers per hour.
The value of a rare baseball card issued in 1989 is represented by the function )-0.2-252+3x +4 where x represents the number of years since the baseball card was issued. Use the Remainder Theorem to find the value of the card in 1999
Answers
The correct format of the question is
The value of a rare baseball card issued in 1989 is represented by the function f(x) = \(0.2x^3- 0.25x^2+3x +4\) where x represents the number of years since the baseball card was issued. Use the Remainder Theorem to find the value of the card in 1999
Answer:
The value of the card in 1999 is 209
Step-by-step explanation:
The remainder theorem says that
If you divide a Polynomial by f(x) be a Linear factor of the form (x-a) the remainder will be equal to F(a).
f(x) = \(0.2x^3- 0.25x^2+3x +4\)
So we need to find from 1989 to 1999 which is 10 years
so our a = 10
Factor will be x-10
Applying remainder theorem
\(\frac{ 0.2x^3 -0.25x^2+3x+4}{x-10}\)
we will get
Quotient = \(0.2x^2 + 1.75x +20.5\)
Remainder = 209
Verifying our result
F(10) = \(0.2(10)^3 -0.25(10)^2 + 3(10) + 4\)
= 200 -25 + 30 + 4
= 209