swhat happens to the diagonal of a rectangle when the rectangle is reflected across a line of symmetry? what does this suggest about the diagonals of rectangles?
Answers
When reflected across a line of symmetry, a shape having that line of symmetry will fall on itself. These are the actual claims:
(1) The rectangle's diagonals will line up exactly with one another.
(2) A rectangle's diagonals are symmetry lines.
We deduce from the question that the rectangle is mirrored across the symmetry line.
When done, the rectangle's half will fall directly on the other half.
This indicates that the rectangle's diagonal will line up perfectly with the opposite diagonal.
According to the aforementioned claim, a rectangle's diagonal is also its line of symmetry.
To learn more about lines of symmetry and diagonals link is here
brainly.com/question/1045307
#SPJ4
Related Questions
Use the Distributive Property to expand the expression you obtained in part B.
The expression is 2(100 − x).
Answers
Answer:
The expression 2(100 − x) expands to 200 − 2x.
Step-by-step explanation:
2(100) − 2(x).
Multiply within each term:
200 − 2x.
Answer:
2(100 − x)
Distribute the 2:
2(100) − 2(x).
Multiply within each term:
200 − 2x.
The expression 2(100 − x) expands to 200 − 2x.
Step-by-step explanation:
Mark me brainliest please?
An equation is shown: x2 + 4x + 4 = 0
What are the x intercepts? Show your work using a method of your choice.
What is an alternate method you could use to find the x intercepts (other than the method you used)?
What is the vertex? Is it a minimum or maximum? How do you know by looking at the equation?
What steps would you take to graph using the information you have already calculated? How would you use symmetry to help you graph?
Answers
Answer:
x intercepts are (-2, 0).
Step-by-step explanation:
X intercepts: The x intercepts are the points where the graph of the equation crosses the x-axis. In order to find the x intercepts, we can set the equation equal to 0 and solve for x.
x^2 + 4x + 4 = 0
(x + 2)^2 = 0
x + 2 = 0
x = -2
Therefore, the x intercepts are (-2, 0).
\(\hrulefill\)
Alternate method: Another method to find the x intercepts is to use the quadratic formula. The quadratic formula is:
\(x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}\)
Comparing x^2 + 4x + 4 = 0 with ax^2=bx+c=0,
In this case, we get a = 1, b = 4, and c = 4.
Substituting these values into the quadratic formula, we get:
\(x = \frac{-4 \± \sqrt{4^2 - 4 * 1 * 4} }{2 * 1}\\x =\frac{-4}{2}\\x=-2\)
Therefore, the x intercepts are still (-2, 0).
\(\hrulefill\)
Vertex: The vertex is the point of the parabola that is highest or lowest.
In order to find the vertex, we can use the formula:
\((h, k) = (\frac{-b}{2a}, \frac{-(b^2-4ac)}{4a})\)
Comparing x^2 + 4x + 4 = 0 with ax^2=bx+c=0,
In this case, we get a = 1, b = 4, and c = 4.
Substituting these values into the formula, we get:
\((h, k) = (\frac{-4}{2*1}, \frac{-(4^2-4*1*4)}{4*1})\\(h, k) =(-2,0)\)
Therefore, the vertex is (-2, 0).
Minimum or maximum: The vertex is a minimum because the coefficient of x^2 is positive. This means that the parabola opens upwards, and the vertex is the lowest point of the parabola.
\(\hrulefill\)
Graphing: In order to graph the equation, we can first plot the x intercepts.
Graph: Attachment
Then, we can draw a parabola that passes through the x intercepts and the vertex. We can use symmetry to help us graph the parabola.
The graph can be drawn by inputting values of x into the function f(x) = x² + 4x + 4,
The parabola is symmetric about the vertical line that passes through the vertex. This means that if we reflect the parabola over this line, we will get the same parabola.
As you can see, the parabola opens upwards and has a minimum vertex at (-2, 0).
Answer:
x-intercept: x = -2
Alternative method: Quadratic formula
Vertex: (-2, 0)
Minimum as the leading coefficient is positive.
Step-by-step explanation:
x-interceptsThe x-intercepts are the points at which the curve crosses the x-axis, so the x-values when y = 0.
As the quadratic equation is already equal to zero, to find the x-intercepts, factor and solve for x.
\(x^2+4x+4=0\)
\(x^2+2x+2x+4=0\)
\(x(x+2)+2(x+2)=0\)
\((x+2)(x+2)=0\)
\((x+2)^2=0\)
\((x+2)=0\)
\(x=-2\)
Therefore, the x-intercept of the given quadratic equation is x = -2.
\(\hrulefill\)
Alternative methodAn alternative method to use to find the x-intercept(s) is the quadratic formula.
\(\boxed{\begin{minipage}{4 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\\\when $ax^2+bx+c=0$ \\\end{minipage}}\)
\(\hrulefill\)
VertexThe vertex of a quadratic function is the turning point of the parabola. It is the point where the graph reaches its minimum or maximum value
As there is only one x-intercept of the given quadratic equation, and the equation can be rewritten in the form (x + 2)² = 0, we can identify that the vertex of the parabola is the x-intercept, (-2, 0).
Since the leading coefficient of the equation is positive, the parabola opens upwards. Therefore, the vertex represents a minimum.
\(\hrulefill\)
GraphingThe graph of a quadratic equation is a parabola.
A parabola is symmetric with respect to its axis of symmetry, which is a vertical line passing through its vertex. As the vertex of the given quadratic equation is (-2, 0), the axis of symmetry is x = -2.
To graph the equation using the information already calculated, first plot the vertex at (-2, 0) and draw the axis of symmetry through the vertex.
Find other points on the graph by inputting values of x into the function f(x) = x² + 4x + 4, then reflect those points across the axis of symmetry.
By connecting these points and considering the symmetry, we can sketch the graph of the equation.
Find the solution of the differential equation dydx=y2 4 that satisfies the initial condition y(7)=0
Answers
The particular solution to the differential equation with the initial condition y(7) = 0 is:
(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.
To solve the given differential equation, we can use the method of separation of variables. Here's the step-by-step solution:
Step 1: Write the given differential equation in the form dy/dx = f(x, y).
In this case, dy/dx = y² - 4.
Step 2: Separate the variables by moving terms involving y to one side and terms involving x to the other side:
dy / (y² - 4) = dx.
Step 3: Integrate both sides of the equation:
∫ dy / (y² - 4) = ∫ dx.
Let's solve each integral separately:
For the left-hand side integral:
Let's express the denominator as the difference of squares: y² - 4 = (y - 2)(y + 2).
Using partial fractions, we can decompose the left-hand side integral:
1 / (y² - 4) = A / (y - 2) + B / (y + 2).
Multiply both sides by (y - 2)(y + 2):
1 = A(y + 2) + B(y - 2).
Expanding the equation:
1 = (A + B)y + 2A - 2B.
By equating the coefficients of the like terms on both sides:
A + B = 0, and
2A - 2B = 1.
Solving these equations simultaneously:
From the first equation, A = -B.
Substituting A = -B in the second equation:
2(-B) - 2B = 1,
-4B = 1,
B = -1/4.
Substituting the value of B in the first equation:
A + (-1/4) = 0,
A = 1/4.
Therefore, the decomposition of the left-hand side integral becomes:
1 / (y² - 4) = 1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2)).
Integrating both sides:
∫ (1 / (y² - 4)) dy = ∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy.
Integrating the right-hand side:
∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy
= (1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁,
where C₁ is the constant of integration.
For the right-hand side integral:
∫ dx = x + C₂,
where C₂ is the constant of integration.
Combining the results:
(1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁ = x + C₂.
Simplifying the equation:
(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + (C₂ - C₁).
Combining the constants of integration:
C = C₂ - C₁, where C is a new constant.
Finally, we have the solution to the differential equation that satisfies the initial condition:
(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + C.
To find the value of the constant C, we use the initial condition y(7) = 0:
(1/4) * ln|0 - 2| - (1/4) * ln|0 + 2| = 7 + C.
Simplifying the equation:
(1/4) * ln|-2| - (1/4) * ln|2| = 7 + C,
(1/4) * ln(2) - (1/4) * ln(2) = 7 + C,
0 = 7 + C,
C = -7.
Therefore, the differential equation with the initial condition y(7) = 0 has the following specific solution:
(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.
Learn more about differential equations on:
https://brainly.com/question/25731911
#SPJ11
HELP PLEASE!!!!! I need help
Answers
Answer:
5 hours and 8 minutes is what I got, but i'm not really sure so only put that answer if someone else got that to. (The upcoming and this sentence is pre-written and copy and pasted in every brainly question or comment I write or answer.) If this answer helped you please consider giving it brainliest.
- •Trix•
( Yes I know my - •Trix• thingy is not my user but its what I would change it to if I could but I can't, please address me as Trix while commenting or talking to me here.)
Which of the following are compound events? Check all that apply.
A. drawing an ace and then a king from a deck of cards
B.drawing a red card from a deck of cards
C.rolling a 1 on a number cube and then tossing a coin and landing on tails
D.choosing a banana, then an apple, and then an orange from a fruit basket
E.choosing a dime from a piggy bank
Answers
Answer:
A, C and D
Step-by-step explanation:
In this question, we are asked to select which of the options is/are example(s) of compound event(s)
The easiest way to answer this is to have an idea of what we mean by a compound event. When we talk about a compound event, we are referring to an event that has more than one outcome. This is a direct contrast to a simple event where we have only one outcome. To find the probability of a compound event, we shall need to add up the probabilities of all the single events that lies there in
In answering this question, we shall be considering the options one after the other.
A. It is a compound event
This is because we are looking at more than one event happening
B. It is not a compound event
It is not a compound event as we have only one outcome
C. This is a compound event
We have more than one outcome here. In fact, we are dealing with more than one sample space here
D. It is a compound event
We are working on different simple events here
E. It is not a compound event
It is not because we are only focused on a particular type of outcome
Answer:
A, C, D
A: drawing an ace and then a king from a deck of cards
C: rolling a 1 on a number cube and then tossing a coin and landing on tails
D: choosing a banana, then an apple, and then an orange from a fruit basket
Step-by-step explanation:
just did it on edge 2020 hope it helps
:)
A is a set of factors of 12. Which one of the following is not member of A? *
A. 3
B. 4
C. 5
D. 6
Answers
Answer:
5
Step-by-step explanation:
3*4=12
4*3=12
6*2=12
but 12 is not factor of 5
Explanation:
3x4=12
4x3=12
6x2=12
But 5 does not equal 12
9 ft=_____ in Do y'all know the answer to this plz help me out plz and thanks
Answers
Answer:
108
Step-by-step explanation:
As 1 foot = 12 inches, 9 foot = 12*9 = 108.
Hope this helps! :)
Answer:
The answer is 108. 1 foot equals 12 inches. So, you just need to multiply 9 by 12. 9 x 12 = 108.
Which of the following describes the transformation from Figure 1
to Figure 2
Answers
The translation from figure 1 to figure 2 is 4 units to the left and one unit up.
Which transformation is applied from figure 1 to figure 2?Here we have two figures, the blue one is figure 1 and the orange one is figure 2.
Clearly we have a translation here, to identify the translation just analyze one of the vertices.
The top vertex at the blue figure is (2, 1)
The top vertex at the orange figure is (-2, 2)
The translation is given by:
T = (-2, 2) - (2, 1) = (-4, 1)
So we have a translation of 4 units to the left and one unit up.
Laern more about translations at:
https://brainly.com/question/24850937
#SPJ1
Answer:
Step-by-step explanation:
answer is a
According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0. 82.
a. Suppose a random sample of 100 Americans is asked, "Are you satisfied with the way things are going in your life?" Is the response to this question qualitative or quantitative? Explain.
A. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.
B. The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not.
C. The response is quantitative because the responses can be measured numerically and tho values added or subtracted, providing meaningful results
D. The response is qualitative because the response can be measured numerically and the value added or subtracted, providing meaningful results.
b. Explain why the sample proportion, p, is a random variable. What is the source of the variability?
c. Describe the sampling distribution of p, the proportion of Americans who are satisfied with the way things are going in their life. Be sure to verify the model requirements.
d. In the sample obtained in part (a), what is the probability the proportion who are satisfied with the way things are going in their life exceeds 0. 85?
e. Would it be unusual for a survey of 100 Americans to reveal that 75 or fewer are satisfied with the way things are going in their life? Why?
Answers
A. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.
B. The source of the variability is due to chance or sampling error, which arises from taking a sample instead of surveying the entire population.
C. The sampling distribution of p is approximately normal.
D. We find that the probability is 0.0912 or about 9.12%.
E. We get:z = (0.75 - 0.82) / sqrt[0.82(1-0.82)/100] = -2.29
a. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.
b. The sample proportion, p, is a random variable because it varies from sample to sample. The source of the variability is due to chance or sampling error, which arises from taking a sample instead of surveying the entire population.
c. The sampling distribution of p is approximately normal if the sample size is sufficiently large and if np ≥ 10 and n(1-p) ≥ 10, where n is the sample size and p is the population proportion. In this case, we have:
Sample size (n) = 100
Population proportion (p) = 0.82 Thus, np = 82 and n(1-p) = 18, both of which are greater than 10. Therefore, the sampling distribution of p is approximately normal.
d. To calculate the probability that the proportion who are satisfied with the way things are going in their life exceeds 0.85, we need to find the z-score and then look up the corresponding probability from the standard normal distribution table. The formula for the z-score is:
z = (p - P) / sqrt[P(1-P)/n]
where p is the sample proportion, P is the population proportion, and n is the sample size. Substituting the given values, we get:
z = (0.85 - 0.82) / sqrt[0.82(1-0.82)/100] = 1.33
Looking up the corresponding probability from the standard normal distribution table, we find that the probability is 0.0912 or about 9.12%.
e. Yes, it would be unusual for a survey of 100 Americans to reveal that 75 or fewer are satisfied with the way things are going in their life. To check if it is unusual or not, we need to calculate the z-score and find its corresponding probability from the standard normal distribution table. The formula for the z-score is:
z = (p - P) / sqrt[P(1-P)/n]
where p is the sample proportion, P is the population proportion, and n is the sample size. Substituting the given values, we get:
z = (0.75 - 0.82) / sqrt[0.82(1-0.82)/100] = -2.29
Looking up the corresponding probability from the standard normal distribution table, we find that the probability is 0.0106 or about 1.06%. Since this probability is less than 5%, it would be considered unusual to observe 75 or fewer Americans being satisfied with the way things are going in their life.
Learn more about distribution from
https://brainly.com/question/23286309
#SPJ11
On a test of 80 items, Ariel got 59 correct. What percent were correct? a. 73. 75% c. 135. 59322% b. 1. 3559322% d. 0. 7375%.
Answers
The percentage of correct items is 73.75%. Option A shows the percentage of correct items in the test.
What is the percentage?The percentage is defined as the relative value which represents the hundredth part of any quantity.
Given the total number of items in the test is 80. Ariel got 59 correct.
The percentage of the correct items is calculated as given below.
Total Items = 80
Correct Items = 59
Percentage of Correct Items = \(\dfrac {59}{80}\times 100\)
Percentage of Correct Items = \(73.75%\)
Hence we can conclude that the percentage of correct items is 73.75%. Option A shows the percentage of correct items in the test.
To know more about the percentage, follow the link given below.
https://brainly.com/question/8011401.
What is the measure of Angle HEG?
Answers
Answer:
angle HEG = 12 degrees
Step-by-step explanation:
A line is 180 degrees. Since there is a right angle there, you know that angleHEG and 78 added together is 90degrees
x + 78 = 90 >> subtract 78 from both sides
x = 12
angle HEG = 12 degrees
Answer:
18 degrees
Step-by-step explanation:
There is a little box on the left that indicates both angles together make a 90 degree angle so you just have to do 90 - 78 to get the answer.
Brainliest for correct awnser
Which of the following lists of ordered pairs is a function?A.(1, 1), (2, 3), (1, 5), (4, 7)B.(0, 2), (4, 2), (0, –4), (4, –2)C.(2, 4), (3, 9), (4, 16), (5, 25)D.(2, 4), (–2, 4), (3, 9), (–2, –4)
Answers
Please help please now help ASAP
Answers
Answer:
2
Step-by-step explanation:
If measure JKL=(8x-6) and arc measure JML= (25x-13) find arc measure JML
Answers
The measure of arc JML is -46/17.
To find the measure of arc JML, we need to equate it to the measure of angle JKL.
Given:
Measure of JKL = 8x - 6
Measure of JML = 25x - 13
Since angle JKL and arc JML correspond to each other, they have the same measure.
Therefore, we can set up the equation:
8x - 6 = 25x - 13
Next, we solve for x:
8x - 25x = -13 + 6
-17x = -7
x = -7 / -17
x = 7/17
Now, substitute the value of x back into the equation for the measure of JML:
Measure of JML = 25x - 13
Measure of JML = 25 × (7/17) - 13
Measure of JML = (175/17) - (221/17)
Measure of JML = -46/17
Therefore, the measure of arc JML is -46/17.
for such more question on measure
https://brainly.com/question/25716982
#SPJ11
Evaluate the numerical expression (5-4) 1/2
Answers
Answer:
I think the answer is 1/2
The value of the numerical expression (5 - 4) x 1/2 will be 0.50.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The expression is given below.
⇒ (5 - 4) x 1/2
Simplify the expression, then we have
⇒ (5 - 4) x 1/2
⇒ 1 x 1/2
⇒ 1 / 2
⇒ 0.50
The value of the numerical expression (5 - 4) x 1/2 will be 0.50.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
. Nick has a job delivering pizzas. He is paid $11.50 for each hour he works, then earns an extra $5 for each delivery he makes. Nick would like to earn more than $145 when he works his 7-hour shift on Saturday. What is the minimum number of deliveries he must make to do this?
Answers
Answer:
13
Step-by-step explanation:
11.50x7=80.50
5x13=65
80.50+65=145.50
The elevation of a city is 2633 feet above sea level.
Write a signed number to represent this elevation
Answers
Answer:
+2633 ft
Step-by-step explanation:
The city is above sea level meaning it is a positive number.
question 9 in r, which statistical measure demonstrates how strong the relationship is between two variables?
Answers
Correlation analysis is a statistical technique used to measure the strength of the relationship between two variables.
Correlation analysis in research is a factual strategy used to quantify the strength of the direct correlation between two factors and figure out their affiliation. It ascertains the degree of progress in one variable because of the change in the other. A high correlation focuses on a solid correlation between the two factors, while a low correlation implies that the factors are pitifully related.
With regard to statistical surveying, specialists use this strategy to break down quantitative information gathered through research strategies like reviews and live surveys. They attempt to recognize the correlation, designs, huge associations, and patterns between two factors or datasets.
There is a positive correlation between two variables when an increment in one variable prompts an increment in the other. Then again, a negative correlation implies that when one variable expands, different declines as well as the other way around.
Correlation analysis is used to study practical cases. Here, the researcher can't manipulate individual variables. For example, correlation analysis is used to measure the correlation between the patient's blood pressure and the medication used.
Marketers use it to measure the effectiveness of advertising. Researchers measure the increase/decrease in sales due to a specific marketing campaign.
Thus, Correlation analysis is a statistical technique used to measure the strength of the relationship between two variables.
To learn more about Correlation analysis, visit brainly.com/question/29785220
#SPJ4
the route used by a certain motorist in commuting to work contains two intersections with traffic signals. the copyright 2016 cengage learning. all rights reserved. may not be copied, scanned, or duplicated, in whole or in part. due to electronic rights, some third party content may be suppressed from the ebook and/or echapter(s). editorial review has deemed that any suppressed content does not materially affect the overall learning experience. cengage learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 66 chapter 2 probability probability that he must stop at the first signal is .4, the analogous probability for the second signal is .5, and the probability that he must stop at at least one of the two signals is .7. what is the probability that he must stop a. at both signals? b. at the first signal but not at the second one? c. at exactly one signal?
Answers
a. The probability that he must stop at both signals is 0.2.b. The probability that he must stop at the first signal but not at the second one is 0.2.
c. The probability that he must stop at exactly one signal is 0.5.
a. The probability that he must stop at both signals is equal to the product of the individual probabilities of stopping at each signal, which is 0.4 x 0.5 = 0.2.
b. The probability that he must stop at the first signal but not at the second one is equal to the probability of stopping at the first signal only, which is 0.4.
c. The probability that he must stop at exactly one signal is equal to the sum of the probability of stopping at the first signal and the probability of stopping at the second signal, which is 0.4 + 0.5 = 0.5.
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
1) A Freedom 35 financial planner claims you will need
$1,175,000 to retire in 15 years time. How much should you invest
today at 9% simple interest to reach your retirement goal?
2) How long will it
Answers
you should invest approximately $500,000 today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years.
To determine how much you should invest today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years, we can use the formula for simple interest:
A = P(1 + rt)
Where A is the future value, P is the principal (the amount you should invest today), r is the interest rate, and t is the time in years.
We can rearrange the formula to solve for P:
P = A / (1 + rt)
Plugging in the values, we have:
P = 1,175,000 / (1 + 0.09 * 15)
P = 1,175,000 / (1 + 1.35)
P = 1,175,000 / 2.35
P ≈ $500,000
Therefore, you should invest approximately $500,000 today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years.
To learn more about interest click here:brainly.com/question/1040694
#SPJ11
Use an equation to write 3 x 3/4 as a multiple of a unit fraction
Answers
The equation which represents 3 x 3/4 as a unit fraction is; 3 × 3/4 = 9 × 1/4.
Multiple of a unit fractionA unit fraction by definition is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.
On this note, the given expression when expressed as a unit fraction is;
3 × 3/4 = (3×3) × 1/4= 9 × 1/4.Read more on unit fractions;
https://brainly.com/question/2929160
An engineer earns $108 000 annually. Deductions
of $3 975 are made each month.
Calculate:
(a) his gross monthly salary
(b) his net monthly salary
Answers
Answer:
9,000
5,025
Step-by-step explanation:
Please I really need help
Answers
Answer:
n = 10
Step-by-step explanation:
n! / 6!(n - 6)! = n! / 4!(n - 4)!
6!(n - 6)! = 4!(n - 4)!
6!(n - 6)! / 4!(n - 4)! = 1
6*5(n - 6)! / (n - 4)! = 1
30(n - 6)! = (n - 4)!
(10-6)! = 4 * 3 * 2 * 1 and
(10 -4)! = 6*5*4*3*2*1
Dividing (10-4)! / (10-6)! = 30
so n = 10.
In exercise 11-14 find the value of x for each one thank you whoever gets all of it right gets brainliest
Answers
The missing angles of the given quadrilaterals are 64°, 68°, 89° and 99°
What are quadrilaterals?A quadrilateral is a four-sided polygon, having four edges and four corners.
Given are quadrilaterals, we need to find the missing angles in them,
So, to find the missing angles, we will use the concept of sum of interior angles of a quadrilateral,
We know that, the sum of interior angles of a quadrilateral, is 360°
a) ∠ W + ∠ X + ∠ Y + ∠ Z = 360°
x + 100° + 130° + 66° = 360°
x = 360° - 296°
x = 64°
b) ∠ G + ∠ H + ∠ J + ∠ K = 360°
x + 103° + 133° + 58° = 360°
x = 360° - 294°
x = 68°
c) ∠ K + ∠ L + ∠ M + ∠ N = 360°
88° + 154° + x + 29° = 360°
x = 360° - 271°
x = 89°
d) ∠ A + ∠ B + ∠ C + ∠ D = 360°
x + 92° + 68° + 101° = 360°
x = 360° - 261°
x = 99°
Hence, the missing angles of the given quadrilaterals are 64°, 68°, 89° and 99°
Learn more about quadrilaterals, click;
https://brainly.com/question/29934291
#SPJ1
a bridge hand consists of 13 cards dealt at random from the deck of 52. the probability that a bridge hand will have exactly 2 queens is:
Answers
The probability that a bridge hand will have exactly 2 queens is 0.45%.
To find the probability of getting a bridge hand with exactly 2 queens, we need to use the binomial probability formula. The formula is:
P(exactly k successes) = (n choose k) * p^k * (1-p)^(n-k)
Where:
n is the total number of trials
k is the number of successes in the trials
p is the probability of success in a single trial
In this case, the total number of trials is 13 (since a bridge hand consists of 13 cards), and the number of successes we want is 2 (since we want exactly 2 queens). The probability of success in a single trial is the probability of drawing a queen, which is 4/52 (since there are 4 queens in a deck of 52 cards).
Plugging these values into the formula, we get:
P(exactly 2 queens) = (13 choose 2) * (4/52)² * (48/52)¹¹
= (78) * (1/169) * (4/13)¹¹
= (4/169) * (4/13)¹¹
This simplifies to:
P(exactly 2 queens) = (4/169) * (4/13)¹¹
= (4/169) * (4/169)¹¹
= (4/169)¹²
The final probability is approximately 0.0045 or 0.45%. This means that the probability of getting a bridge hand with exactly 2 queens is quite low.
Learn more about Probability at:
brainly.com/question/24756209
#SPJ4
Suppose x has a normal distribution with mean 80 and standard deviation 5. What is the 90th percentile of x?.
Answers
The distribution has a 90th percentile for the value of 86.45 of x.
Let the normal distribution be X.
Hence according to the problem,
X ~ N(80, 25)
where,
the mean = μ = 80
the variance = σ² = 5² = 25
To find the 90th percentile we need to find a variable whose CDF is equal to 90% or 0.9
Let the variable be x.
Then
P(X < x) = 0.9
Now to find this we will first transform this to the standard normal form Z.
Any distribution can be brought to the standard normal form by,
Z = (X - μ)/σ
where
μ is the mean of the distribution
σ is the standard deviation of the distribution
Here,
μ = 80
σ = 5
Hence we get,
Φ[(x - 80)/5] = 0.9
From the standard normal table we get that for Φ(1.29) the p-value is approximately 0.9
hence we get
Φ[(x - 80)/5] = Φ(1.29)
or, (x - 80)/5 = 1.29
or, x - 80 = 6.45
or, x = 86.45
To learn more about Normal Approximation visit
https://brainly.com/question/13073518
#SPJ4
Make h the subject of the formula E = 1 -\pi \sqrt{x} (h -0.5/1 -h)
Answers
To make h subject of the formula, the other expressions in the equation is expressed to equal h as follows:
h = (1 + E + 0.5π√x/)(π√x + 1 + E)How can h in the equation, \(E = 1-\pi \sqrt{x} (\frac {h-0.5}{1-h})\) be made subject of the formula?The steps in making h subject of the formula in the given equation are as follows:
Step 1: Add \(pi \sqrt{x} (\frac {h-0.5}{1-h})\) to both sides
\(E + \pi \sqrt{x} (\frac {h-0.5}{1-h})= 1\)
Step 2: subtract E from both sides
\(\pi \sqrt{x} (\frac {h-0.5}{1-h}) = 1 + E\)
Step 3: divide both sides by π√x
h - 0.5/1 - h = 1 + E/π√x
Step 4: cross multiply
(h - 0.5)(π√x) = (1 + E)(1 - h)
hπ√x -0.5π√x = 1 - h + E - hE
Step 5: collect like terms
hπ√x + h + hE = 1 + E + 0.5π√x
h(π√x + 1 + E) = 1 + E + 0.5π√x
Step 6: divide both sides by (π√x + 1 + E)
h = (1 + E + 0.5π√x/)(π√x + 1 + E)
In conclusion, in making h subject of the formula, the other expressions in the equation is expressed to equal h.
Learn more about subject of the formula at: https://brainly.com/question/657646
#SPJ1
When he was 30, Kearney began investing $200 per month in various securities for his retirement savings. His investments averaged a 5. 5%
annual rate of return until he retired at age 68. What was the value of Kearney's retirement savings when he retired? Assume monthly
compounding of interest. (2 points)
$182,722. 38
$307,479. 35
$351,115. 71
$1,537. 40
Answers
The value of Kearney's retirement savings when he retired at age 68 is approximately $351,115.71
To calculate the value of Kearney's retirement savings when he retired, we can use the formula for the future value of an ordinary annuity with monthly compounding of interest:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value of the annuity (retirement savings)
P is the monthly payment or investment amount ($200)
r is the monthly interest rate (5.5% / 12)
n is the number of compounding periods (number of months from age 30 to age 68, which is 68 - 30 = 38 years * 12 months/year = 456 months)
Let's calculate the value of Kearney's retirement savings:
r = 5.5% / 12 = 0.0045833 (monthly interest rate)
n = 456 (number of months)
FV = 200 * [(1 + 0.0045833)^456 - 1] / 0.0045833
Calculating the value:
FV ≈ $351,115.71
To learn more about formula for the future value go to:
https://brainly.com/question/29071795#
#SPJ11
(-1, 16), (-13, 6)
Write an equation in slope-intercept form.
help
Answers
Answer:
y=5/6x+101/6
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(6-16)/(-13-(-1))
m=-10/(-13+1)
m=-10/-12
simplify
m=5/6
y-y1=m(x-x1)
y-16=5/6(x-(-1))
y-16=5/6(x+1)
y-16=5/6x+5/6
y=5/6x+5/6+16
y=5/6x+5/6+96/6
y=5/6x+101/6
Cross elasticity of demand is the percentage change in the quantity __________ of a good divided by the percentage change in __________. Group of answer choices demanded; the price of the good supplied; the price of the good demanded; the price of another good supplied; the price of another good demanded; income
Answers
Answer:
demanded;
the price of another good demanded
Step-by-step explanation:
Cross price elasticity of demand measures the responsiveness of quantity demanded of good A to changes in price of good B.
cross price elasticity of demand = percentage change in quantity demanded of good A / percentage change in price of good B
Price elasticity of demand measures the responsiveness of quantity demanded to changes in price of the good.
Income elasticity of demand measures the responsiveness of quantity demanded to changes in income.