point $p$ lies inside square $abcd$ such that triangle $abp$ is equilateral. find $\angle pcd$ in degrees.
Answers
The measurement of angle PCD in equilateral triangle is 67.38°.
Let $s$ be the side length of the square $abcd$, and let $O$ be the center of the square. Then $OP = s/\sqrt{2}$.
Since triangle $ABP$ is equilateral, we have $\angle ABP = 60^\circ$ and $AP=BP=s$. Let $E$ be the foot of the perpendicular from $P$ to $AB$. Then $AE=BE=s/2$ and $EP=s\sqrt{3}/2$.
Since $EP$ is perpendicular to $AB$ and $AB$ is parallel to $CD$, we have $\angle PCD = \angle ACE$.
Since $OP$ is perpendicular to $AB$, we have $\angle OEP = \angle AEP = 30^\circ$. Also, $OE=OP/\sqrt{2}=s/2$.
Using the Pythagorean theorem in triangle $OCE$, we have
CE= \(\sqrt{(OE)^{2} + (OC)^{2}} = \sqrt{(s/2)^{2} + s^{2}} = s\sqrt{5}/2\)
Therefore, $\sin \angle ACE = CE/CP = \sqrt{5}/2$. Thus,
∠PCD = ∠ACE = arcsin(√5/2) ≈ 67.38°
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Related Questions
Y=x^3-4x^2-20x+48 use the rational zero theorem
Answers
The roots of the given polynomial using the rational zero theorem are; 2, -4 and 6.
How to use the rational zero theorem?We are given the polynomial;
y = x³ - 4x² - 20x + 48
Since all coefficients are integers, we can apply the rational zeros theorem.
The trailing coefficient (the coefficient of the constant term) is 48
Find its factors (with the plus sign and the minus sign): ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.
These are the possible values for p.
The leading coefficient (the coefficient of the term with the highest degree) is 1.
These are the possible rational roots:
±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.
Checking the possible roots: if a is a root of the polynomial P(x), the remainder from the division of P(x) by x - a should equal 0 (according to the remainder theorem, this means that P(a)=0
Plugging in those values, the only ones that yield P(a) = 0 are; 2, -4 and 6.
Thus, these are the roots of the given polynomial.
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Examine the following graph of y=1/4x+2 Created using GeoGebra If the point (-4, b) is on this line, what is the value of b? Enter your answer
Answers
Answer:
1
Step-by-step explanation:
it's given that x=-4
so
y=¼×-4+2
y=-1+2
y=1
therefore
b=1
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If a cheeseburger weighs a half pound on Earth,
what will it weigh on Jupiter?
Answers
Answer:
47 pounds i think \/'_'\/
Step-by-step explanation:
screenshot shows questions HELP PLEASE ITS DUE TODAY
Answers
The operations between the data-sets are given as follows:
8. B ∩ A = {2,3}.
9. A ∩ U = {2,3,5,6}.
10. n(B) = {1,5,6,7}.
11. B x C = {{2,5}, {2, 1}, {2, 3}, {3, 5}, {3,1}, {3,3}}.
What is the intersection operation between two data-sets?The intersection operation between two data-sets is the set that is composed by all the elements that belong to both data-sets. The intersection operation is represented by the symbol ∩.
From the data-sets in this problem, we have that:
B ∩ A = {2,3}, as elements 2 and 3 both belongs to sets A and B.A ∩ U = {2,3,5,6}, as elements 2, 3, 5 and 6 both belongs to sets A and U.What is the negation of a data-set?The negation of a data-set is the set that contains all elements belonging to the universe set U but not to the data-set.
Hence, from the data-sets in this problem, we have that:
n(B) = {1,5,6,7}.
In which n(B) is the negation of set B.
What is the multiplication between two data-sets?The multiplication between two data-sets is given by all ordered pairs formed from the two data-sets.
Hence the solution for item 11 is given as follows:
B x C = {{2,5}, {2, 1}, {2, 3}, {3, 5}, {3,1}, {3,3}}.
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fill in the blank.when we have a___data set it is like the scrambled phrase. statistic is the process of using visual, numerical, and tabular display to unscramble the data and discover the message behind it
Answers
When we have a population data set it is like the scrambled phrase. statistic is the process of using visual, numerical, and tabular display to unscramble the data and discover the message behind it.
A collection of data is known as a data set (or dataset). In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable. The data set includes values for each of the variables, such as the object's height and weight, for each set member. Data sets can also be made up of a group of files or documents.
The analysis and manipulation of data is the essence of statistics. As we just covered in the introduction, statistics is the study of the calculation and analysis of numerical data. Let's examine other statistical definitions provided by various authors in this article.
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.................................................................................................
Answers
Answer:
m<B = 141 degrees
Step-by-step explanation:
This shape is a heptagon meaning its angles should have a sum of 900 degrees.
we are given the degrees and we need to ad them up
148+90+120+129+130+142=749
then we subtract 749 from 900 which looks like
900-749=141
from subtracting 749 from 900 we get 141 hence we get our answer that m<B = 141 degrees
Determine the probability of rolling a die and getting a 2
then a 5.
Answers
The probability of rolling a die and getting a 2, then a 5, is 1/36.
To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.
First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.
Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.
To find the probability of both events happening, we multiply the probabilities:
Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.
Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.
It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.
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In a sample of 560 adults, 336 had children. Construct a 95% confidence interval for the true population proportion of adults with children.
Give your answers as decimals, to three places
< p <
What is the expected value of �?
Answers
The confidence interval is 0.559 < p < 0.641 and expected value is 0.600
Confidence IntervalTo construct a confidence interval for the true population proportion, we can use the formula:
p ± Z * √((p × (1 - p)) / n)
Where:
p = sample proportion (336/560)
Z = critical value for the desired confidence level
95% confidence = Z-value of approximately 1.96
n = 560
Let's calculate the confidence interval:
p = 336/560 ≈ 0.600
Z ≈ 1.96 (for a 95% confidence level)
n = 560
Plugging these values into the formula:
p ± Z × √((p × (1 - p)) / n)
0.600 ± 1.96 × √((0.600 × (1 - 0.600)) / 560)
0.600 ± 1.96 × √((0.240) / 560)
0.600 ± 1.96 × √(0.0004285714)
0.600 ± 1.96 × 0.020709611
0.600 ± 0.040564459
The confidence interval is:
0.559 < p < 0.641
Therefore, the 95% confidence interval for the true population proportion of adults with children is 0.559 < p < 0.641.
The expected valueFor proportions, the expected value is simply the sample proportion, which is approximately 0.600.
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Please help with this math question!
Answers
Answer:
5. Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
A statistics class suspected that students at their school were getting less than 8 hours of sleep. They took a random sample of 42 students and asked them how many hours of sleep they get per night. The students in the sample reported sleep amounts that had a mean of 7.5 hours and a standard deviation of 1.6 hours. These results produced a test statistic of t -2.03 and a P-value of approximately 0.025. Assuming the conditions for inference were met, what is an appropriate conclusion at the a = 0.05 significance level?
Choose 1 answer: A. Fail to reject the null hypothesis. This isn't enough evidence to conclude that the mean amount of sleep is less than 8 hours. B. Fail to reject the null hypothesis. This is strong evidence that the mean amount of sleep is less than 8 hours. C. Reject the null hypothesis. This is strong evidence that the mean amount of sleep is less than 8 hours. D. Reject the null hypothesis. This isn't enough evidence to conclude that the mean amount of sleep is less than 8 hours.
Answers
The correct answer is to Reject the null hypothesis. This is strong evidence that the mean amount of sleep is less than 8 hours.
The test statistic of t = -2.03 and P-value of approximately 0.025 suggest that the mean amount of sleep for students is significantly less than 8 hours.
The P-value of 0.025 is less than the significance level of 0.05, which means that there is enough evidence to reject the null hypothesis that the mean amount of sleep is 8 hours.
Therefore, the appropriate conclusion at the a = 0.05 significance level is that the mean amount of sleep for students is less than 8 hours.
Hence, the correct answer is C.
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Someone please help
Answers
Answer:
4/3 (x) = 28/3
*divide both sides by 4/3
4/3 (x) ÷ 4/3 = 28/3 ÷ 4/3
x = 7
A clothing store is offering 40% off of any sale merchandise. Chester's subtotal is $128.00. What is his total after the discount?
Answers
Answer:
76.8
Step-by-step explanation:
(The rate is usually given as a percent.).
To find the discount, multiply the rate by the original price.
To find the sale price, subtract the discount from the original price.
Question 6 of 10
A line of best fit was drawn for 6 data points. What is the maximum number
of these data points that may not actually be on the line?
OA. 6
B. 3
O C. 4
OD. 5
SUBMIT
Answers
What is the formular for compound interest
Answers
Answer:
Compound interest is the interest imposed on a loan or deposit amount.
The most commonly used concept in our daily existence is compound interest.
The compound interest for an amount depends on both Principal and interest gained over periods.
Formula to calculate compound interest.
\({ \boxed{ \rm{C.I = P \bigg(1 + \dfrac{r}{n} \bigg) ^{nt} - P}}}\)
Here,
P is Principal
r is rate of interest
t is total time span.
n is number of times interest got compounded annually.
5. The circle graph shows last year's ticket
sales with a total of 842 tickets.
4%
17%
55%
24%
Adults
Students
Children Under 12
Seniors
This year 22 more tickets were sold to
seniors. How many senior tickets were
sold this year?
A 36 tickets
B 39 tickets
C 143 tickets
D 165 tickets
Answers
The total ticket were sold this year is 39 tickets.
What is arithmetic?
Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
The circle graph shows last year's ticket sales with a total of 842 tickets.
Adults =4%
Students =17%
Children Under 12 =55%
Seniors =24%
This year 22 more tickets were sold to seniors.
According to given question we have
Ticket sold to the senior
=24% *842
= 202.08 tickets.
Tickets were sold this year
= 202.08/12 tickets.
=16.84 tickets.
This year 22 more tickets were sold to seniors
=16.84 tickets+22 tickets
=38.84 ≈39 tickets
Therefore, the total ticket were sold this year is 39 tickets.
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Due to the tide, the water level rises and falls daily in Buzzard's Bay. D gives the depth of the water, in meters, t hours after midnight on a certain day. What is the best interpretation for the following statement? The value of the derivative of D at t = 8 is equal to -0.5. Choose 1 answer a. At 8 a.m. the water level decreased at a rate of 0.5 meters per hour. b. At 8 a.m. the water level decreased at a rate of 0.5 meters. c. At 8 a.m. the water level was 0.5 meters below sea level. d. Until 8 a.m. the water level decreased at a rate of 0.5 meters per hour.
Answers
The correct interpretation for the statement D'(8) = -0.5 is (c) At 8 a.m. the water level was 0.5 meters below sea level.
How to interpret the function notation D'(n)From the question, we have the following parameters that can be used in our computation:
The function D gives the depth of the water, in meters, t hours after midnight on a certain day
This means that
D = depth in meters
t = time in hours
From the question, we have
Notation = D(n)
Also, from the question, we have
D'(8) = -0.5
This is the inverse of the function D(t)
So, the values of the parameters are
D(t) = -0.5
t = 8
This means that the number of hours is 8 and the depth is -0.5 meters
Hence, the interpretation of D'(8) = -0.5 is (c) At 8 a.m. the water level was 0.5 meters below sea level.
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find lim x approaches 3
f(x) = x^2 - 2
f(x) = -3x + 15. x> 3
Answers
The value of the limit of the function f(x) = x² - 2 is 7.
The value of the limit of the function f(x) = -3x + 15 is -6.
We have,
To evaluate the limit as x approaches 3, we need to find the limit of function f(x) as x approaches 3 from both sides of 3.
First, let's evaluate the limit from the left side of 3:
lim x → 3⁻ f(x) = lim x → 3⁻ (x^2 - 2)
Substituting x = 3 - h (where h approaches zero) gives:
lim h → 0⁺ [(3 - h)^2 - 2]
= lim h → 0⁺ [9 - 6h + h^2 - 2]
= lim h → 0⁺ [h^2 - 6h + 7]
= 7
(since the limit of a quadratic function as h approaches zero is the constant term)
Next, let's evaluate the limit from the right side of 3:
lim x → 3⁺ f(x)
= lim x → 3⁺ (-3x + 15)
= -6
Since the limit from the left side is not equal to the limit from the right side, the limit of f(x) as x approaches 3 does not exist.
Thus,
The value of the limit of the function f(x) = x² - 2 is 7.
The value of the limit of the function f(x) = -3x + 15 is -6.
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In which direction must the graph of RX) = 2* be shifted to produce the graph of g(x) = 2(x-7)?
Answers
You will go down 7 and shifts left twice
Please help will mark Brainly
Answers
Answer:
A
Step-by-step explanation:
Blue = River Y
Red = River Z
River Y equation: y = 18
River Z equation: y = 10 + 2x
Graph A represents this system of equations.
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Find the value of a in the parallelogram. (6a - 4) (2a +68)
Answers
Answer:
8a×64
Step-by-step explanation:
This is right because you have to add the two numbers with the variable and add the regular numbers
representation of the function f(x)=-2x2+8x-6
Answers
Y-intercepts: (-6,0)
Calculate the surface area
Answers
To calculate the surface area of a rectangular prism, we need to find the area of each of its six faces and then add them up. In this case, the dimensions of the shape are:
Length = 8 cmWidth = 3 cmHeight = 6 cmRefer to the attachment below.
Three pairs of facesThere are three pairs of faces on a rectangular prism:
Two faces (top & bottom) with dimensions: Length × Width (8 cm × 3 cm).Two faces (front & back) with dimensions: Length × Height (8 cm × 6 cm).Two faces (left & right) with dimensions: Width × Height (3 cm × 6 cm).Finding the areaArea of Length × Width faces8 cm × 3 cm = 24 cm²
Since there are two of these faces, the total area is:
2 × 24 = 48 cm²
Area of Length × Height faces8 cm × 6 cm = 48 cm²
Since there are two of these faces, the total area is:
2 × 48 = 96 cm²
Area of Width × Height faces3 cm × 6 cm = 18 cm²
Since there are two of these faces, the total area is:
2 × 18 = 36 cm²
Adding the areas of the facesNow, add up the areas of all six faces:
Surface Area = 48 + 96 + 36 = 180 cm²
AnswerSo, the surface area of the rectangular prism is 180 cm².
________________________________________________________
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Imagine a clock with the hour hand at 12 and the minute hand at 2. Does the angle formed by the two hands have a measure greater than, less than, or equal to 1/4 turn?
Answers
The angle formed by the two hands have a measure less than 1/4 turn
How to relate the measure of the angle to 1/4 turn?From the question, we have the following parameters that can be used in our computation:
A clock with the hour hand at 12 and the minute hand at 2
The turn represented by the above is represened as
Turn = (2 * 30)/360
When simplified, we have
Turn = 1/6
Next, we have
Angle at the turn = 1/4
1/6 is less than 1/4
This means that the angle formed by the two hands have a measure less than 1/4 turn
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find the LCM
of
75, 5,3
Answers
Answer:
LCM = 75
Step-by-step explanation:
1: Multiply the factor by the greatest number
Description:
The least common multiple for 75,5,3 is 75.
LCM= Least common Multiple
Please mark brainliest
Hope this helps.
Answer:
75
Step-by-step explanation:
Break each number into prime factors
75 = 25*3 = 5*5*3
5 = 5*1
3 = 3*1
Multiply by the greatest number of each factor
3 = 1 time
5 = =2 times
The least common multiple = 3 * 5*5 = 75
select the correct answer from each drop down menu.  quadrilateral abcd is a parallelogram. complete the statements to prove that ab =cd and bc = ad
Answers
Due to the fact that the numbers 4 and 5 both refer to comparable triangles, the correct quadrilateral ABCD is a parallelogram.
What does a quadrilateral mean?The polygon consists of four vertices and four sides. Angles add up to 360. A form of quadrilateral with equal and parallel opposite sides is a parallelogram.
Given
A parallelogram is an ABCD quadrilateral.
Both AB and BC are parallel to CD and AD, respectively.
Consequently, it is a parallelogram's condition.
A form of quadrilateral with equal and parallel opposite sides is a parallelogram.
Here, CAB and ACD are congruent, and BCA and CAD are congruent.
Then ABC is comparable to ADC, CAB is to ACD, and BCA is to CAD.
Then ABC is comparable to ADC.
Yet AC is AC.
ADC and ABC are then congruent.
As a result, for the equivalent triangle, 4 and 5 have the same significance.
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Help !!
centimeters and millimeters <3
Answers
1 cm = 10 mm. Length of book : 28 cm. Length of book = 280 mm. This shows that measurements in mm are the same but look to have a higher number .
How to compare centimeters and millimeters ?The conversion factor provided states that 1 cm is equal to 10 mm, which means that 1 cm is made up of 10 individual millimeters.
The length of my book in when measured in millimeters is 280 mm.
In centimeters, this is therefore:
= 280 mm / 10 cm /mm
= 28 cm
Although the numerical value appears higher when expressed in millimeters, it is important to note that the actual length of the book remains the same.
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what is the area of the triangle 13,12,5
Answers
Answer:
area = 5
Step-by-step explanation:
Domain and range? Checking my work
My answer:
D:[-7,-1]
R:[-6,-3]
![Domain and range? Checking my workMy answer:D:[-7,-1]R:[-6,-3]](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/M1DHM2WbLoHN9AoOGLHqNwVNm8kP7k0H.png)
Answers
Answer:
Correct numbers, wrong format
Step-by-step explanation:
Remember the figure is continuous so it should be written as an inequality:
D:(-7<x<-1)
R:(-6<x<-3)
In a survey, the planning value for the population proportion is p*= 0.25. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.06? Round your answer up to the next
whole number.
Answers
The sample should be taken to provide a 95% confidence interval is 200.
What is a confidence interval?A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.
Confidence is another name for probability in statistics.
Given the planning value for the population proportion,
probability, p = 0.25
q = 1 - p = 1 - 0.25
q = 0.75
margin of error = E = 0.06
value of z at 95% confidence interval is 1.96,
the formula for a sample is,
n = (z/E)²pq
n = (1.96/0.06)²*0.25*0.75
n = 200.08
n = 200 approx
Hence sample size is 200.
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Write the equation of the line that is perpendicular to 3x+2y=8 and goes through the point (-5,2)
Answers
Answer:
\(\displaystyle y=\frac{2}{3}(x+5)+2\)
Step-by-step explanation:
We need to find the equation of the line perpendicular to the line 3x+2y=8 and passes through (-5,2).
The given line can be expressed as:
\(\displaystyle y=-\frac{3}{2}x+4\)
We can see the slope of this line is m1=-3/2.
The slopes of two perpendicular lines, say m1 and m2, meet the condition:
\(m_1.m_2=-1\)
Solving for m2:
\(\displaystyle m_2=-\frac{1}{m_1}\)
\(\displaystyle m_2=-\frac{1}{-\frac{3}{2}}\)
\(\displaystyle m_2=\frac{2}{3}\)
Now we know the slope of the new line, we use the slope-point form of the line:
\(y=m(x-h)+k\)
Where m is the slope and (h,k) is the point. Using the provided point (-5,2):
\(\boxed{\displaystyle y=\frac{2}{3}(x+5)+2}\)