The diagram shows a parallelogram ABCD and an equilateral triangle BDE.
CDE is a straight line.
(a) Work out angle BDE
Give a reason for your answer.
(b) Work out angle CDB
Give a reason for your answer.
Answers
Answer:
a) ∠BDE is 60° because ΔBDE is an equilateral triangle with all three angles = 60°.
b) ∠CDB = 120° because 180° - 60° = 120°
Step-by-step explanation:
Related Questions
Please prove the following trigonometric identity.
[tex]\cos^2(5x)-\sin^2(5x)=\cos(10x)[/tex]
Answers
Answer:
See Below.
Step-by-step explanation:
We want to verify the trigonometric identity:
[tex]\cos^2(5x)-\sin^2(5x)=\cos(10x)[/tex]
For simplicity, we can let u = 5x. Therefore, by substitution, we acquire:
[tex]\cos^2(u)-\sin^2(u)[/tex]
Recall the double-angle identity formula(s) for cosine:
[tex]\displaystyle \begin{aligned} \cos(2x)&=\cos^2(x)-\sin^2(x)\\&=2\cos^2(x)-1\\&=1-2\sin^2(x)\end{aligned}[/tex]
Therefore, our identity becomes:
[tex]=\cos(2u)[/tex]
Back-substitute:
[tex]=\cos(2(5x))=\cos(10x)\stackrel{\checkmark}{=}\cos(10x)[/tex]
Hence proven.
cos²A - sin²A = cos2A, this is a general indentity where A can have any random value x/2, y/3, 1/8, 8, 9 etc.
Replacing A with 5x:
=> cos²(5x) - sin²(5x) = cos²(10x)
Moreover,
cos(A + B) = cosAcosB - sinAsinB.
When A = B,
cos(A + A) = cosAcosA - sinAsinA
cos2A = cos²A - sin²A
You can do the same with 5x.
cos(10x) = cos(5x + 5x)
cos(10x) = cos(5x)cos(5x) - sin(5x)sin(5x)
cos(10x) = cos²(5x) - sin²(5x)
what is the next number in sequence -8 -4 0, 4,
Answers
Answer:
8
Step-by-step explanation:
You add 4 to get the next number.
(-8) + 4 = (-4)
(-4) + 4 = 0
0 + 4 = 4
4 + 4 = 8
Arletta built a cardboard ramp for
her little brother's toy cars. Find
the volume of this ramp.
-
Answers
Answer:
525
Step-by-step explanation:
25 x 6 = 150; 150 / 2 =75; 75 x 7 = 525
A market researcher analyzing the fast-food industry noticed the following: The historical average amount spent at an upscale restaurant was $150.30, with a standard deviation of $50. The researcher wishes to have a sampling error of $5 or less and be 95 percent confident of an estimate to be made about average amount spent at an upscale restaurant from a survey. What sample size should be used (round the number up)
Answers
Answer:
A sample size of 385 should be used.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
What sample size should be used (round the number up)
A sample of n should be used.
n is found when M = 5.
We have that [tex]\sigma = 50[/tex]
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]5 = 1.96\frac{50}{\sqrt{n}}[/tex]
[tex]5\sqrt{n} = 1.96*50[/tex]
Simplifying by 10
[tex]\sqrt{n} = 1.96*10[/tex]
[tex]\sqrt{n} = 19.6[/tex]
[tex](\sqrt{n})^2 = (19.6)^2[/tex]
[tex]n = 384.16[/tex]
Rounding up
A sample size of 385 should be used.
Find the missing angle of each triangle.
Answers
Answer:
1 is 64
2 is 85
3 is 56 hope this helps
Step-by-step explanation:
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6) Supplementary Exercise 5.51
A consumer advocate claims that 80 percent of cable television subscribers are not satisfied with their cable service. In an attempt to justify this claim, a randomly selected sample of cable subscribers will be polled on this issue.
(a)
Suppose that the advocate's claim is true, and suppose that a random sample of five cable subscribers is selected. Assuming independence, use an appropriate formula to compute the probability that four or more subscribers in the sample are not satisfied with their service. (Do not round intermediate calculations. Round final answer of p to 1 decimal place. Round other final answers to 4 decimal places.)
The answer for 6(a) is P( Xâ¥4) = P ( x = 4) + P (x = 5) = 5/4 * 0.84 * 0.21 + 5/5 * 0.85 * 0.20 = 0.737
(b)
Suppose that the advocate's claim is true, and suppose that a random sample of 25 cable subscribers is selected. Assuming independence, find each of the following: (Do not round intermediate calculations. Round final answer of p to 1 decimal place. Round other final answers to 4 decimal places.)
1.
The probability that 15 or fewer subscribers in the sample are not satisfied with their service.
The answer for 6(b)1 is P(Yâ¤15) = 1 - P( Y > 20) - X20, i = 16 P ( Y = i) = 1- 0.421 - 0.562 = 0.017
2.
The probability that more than 20 subscribers in the sample are not satisfied with their service.
The answer for 6(b)2 is
3.
The probability that between 20 and 24 (inclusive) subscribers in the sample are not satisfied with their service.
The answer for 6(b)3 is P(20 > Y < 24) = 1 - 0.421 - 0.1867 - 0.1358 - 0.0708 - 0.0236 = 0.1621
4.
The probability that exactly 24 subscribers in the sample are not satisfied with their service.
The answer for 6(b)4 is P( Y = 24) = 0.0236
(c)
Suppose that when we survey 25 randomly selected cable television subscribers, we find that 15 are actually not satisfied with their service. Using a probability you found in this exercise as the basis for your answer, do you believe the consumer advocate's claim? Explain. (Round your answer to 4 decimal places.)
Answers
Answer:
[tex]P(X \le 4) = 0.7373[/tex]
[tex]P(x \le 15) = 0.0173[/tex]
[tex]P(x > 20) = 0.4207[/tex]
[tex]P(20\ge x \le 24)= 0.6129[/tex]
[tex]P(x = 24) = 0.0236[/tex]
[tex]P(x = 15) = 1.18\%[/tex]
Step-by-step explanation:
Given
[tex]p = 80\% = 0.8[/tex]
The question illustrates binomial distribution and will be solved using:
[tex]P(X = x) = ^nC_xp^x(1 - p)^{n-x}[/tex]
Solving (a):
Given
[tex]n =5[/tex]
Required
[tex]P(X\ge 4)[/tex]
This is calculated using
[tex]P(X \le 4) = P(x = 4) +P(x=5)[/tex]
This gives:
[tex]P(X \le 4) = ^5C_4 * (0.8)^4*(1 - 0.8)^{5-4} + ^5C_5*0.8^5*(1 - 0.8)^{5-5}[/tex]
[tex]P(X \le 4) = 5 * (0.8)^4*(0.2)^1 + 1*0.8^5*(0.2)^0[/tex]
[tex]P(X \le 4) = 0.4096 + 0.32768[/tex]
[tex]P(X \le 4) = 0.73728[/tex]
[tex]P(X \le 4) = 0.7373[/tex] --- approximated
Solving (b):
Given
[tex]n =25[/tex]
i)
Required
[tex]P(X\le 15)[/tex]
This is calculated as:
[tex]P(X\le 15) = 1 - P(x>15)[/tex] --- Complement rule
[tex]P(x>15) = P(x=16) + P(x=17) + P(x =18) + P(x = 19) + P(x = 20) + P(x = 21) + P(x = 22) + P(x = 23) + P(x = 24) + P(x = 25)[/tex]
[tex]P(x > 15) = {25}^C_{16} * p^{16}*(1-p)^{25-16} +{25}^C_{17} * p^{17}*(1-p)^{25-17} +{25}^C_{18} * p^{18}*(1-p)^{25-18} +{25}^C_{19} * p^{19}*(1-p)^{25-19} +{25}^C_{20} * p^{20}*(1-p)^{25-20} +{25}^C_{21} * p^{21}*(1-p)^{25-21} +{25}^C_{22} * p^{22}*(1-p)^{25-22} +{25}^C_{23} * p^{23}*(1-p)^{25-23} +{25}^C_{24} * p^{24}*(1-p)^{25-24} +{25}^C_{25} * p^{25}*(1-p)^{25-25}[/tex]
[tex]P(x > 15) = 2042975 * 0.8^{16}*0.2^9 +1081575* 0.8^{17}*0.2^8 +480700 * 0.8^{18}*0.2^7 +177100 * 0.8^{19}*0.2^6 +53130 * 0.8^{20}*0.2^5 +12650 * 0.8^{21}*0.2^4 +2300 * 0.8^{22}*0.2^3 +300 * 0.8^{23}*0.2^2 +25* 0.8^{24}*0.2^1 +1 * 0.8^{25}*0.2^0[/tex]
[tex]P(x > 15) = 0.98266813045[/tex]
So:
[tex]P(X\le 15) = 1 - P(x>15)[/tex]
[tex]P(x \le 15) = 1 - 0.98266813045[/tex]
[tex]P(x \le 15) = 0.01733186955[/tex]
[tex]P(x \le 15) = 0.0173[/tex]
ii)
[tex]P(x>20)[/tex]
This is calculated as:
[tex]P(x>20) = P(x = 21) + P(x = 22) + P(x = 23) + P(x = 24) + P(x = 25)[/tex]
[tex]P(x > 20) = 12650 * 0.8^{21}*0.2^4 +2300 * 0.8^{22}*0.2^3 +300 * 0.8^{23}*0.2^2 +25* 0.8^{24}*0.2^1 +1 * 0.8^{25}*0.2^0[/tex]
[tex]P(x > 20) = 0.42067430925[/tex]
[tex]P(x > 20) = 0.4207[/tex]
iii)
[tex]P(20\ge x \le 24)[/tex]
This is calculated as:
[tex]P(20\ge x \le 24) = P(x = 20) + P(x = 21) + P(x = 22) + P(x =23) + P(x = 24)[/tex]
[tex]P(20\ge x \le 24)= 53130 * 0.8^{20}*0.2^5 +12650 * 0.8^{21}*0.2^4 +2300 * 0.8^{22}*0.2^3 +300 * 0.8^{23}*0.2^2 +25* 0.8^{24}*0.2^1[/tex]
[tex]P(20\ge x \le 24)= 0.61291151859[/tex]
[tex]P(20\ge x \le 24)= 0.6129[/tex]
iv)
[tex]P(x = 24)[/tex]
This is calculated as:
[tex]P(x = 24) = 25* 0.8^{24}*0.2^1[/tex]
[tex]P(x = 24) = 0.0236[/tex]
Solving (c):
[tex]P(x = 15)[/tex]
This is calculated as:
[tex]P(x = 15) = {25}^C_{15} * 0.8^{15} * 0.2^{10}[/tex]
[tex]P(x = 15) = 3268760 * 0.8^{15} * 0.2^{10}[/tex]
[tex]P(x = 15) = 0.01177694905[/tex]
[tex]P(x = 15) = 0.0118[/tex]
Express as percentage
[tex]P(x = 15) = 1.18\%[/tex]
The calculated probability (1.18%) is way less than the advocate's claim.
Hence, we do not believe the claim.
work out the value of angle x, 90 degrees
Answers
Answer:
x = 45
Step-by-step explanation:
In isosceles triangles (a triangle where two sides are equal), the two base angles are congruent.
The sum of angles in a triangle is 180°.
In this problem, x is a base angle, so the other base angle is equal to x.
So, adding up all the measures of the angles in this triangle,
90 + x + x = 180
Simplify.
2x + 90 = 180
Substract 90 from both sides
2x = 90
Divide both sides by 2
x = 45
A bucket has 16 tennis balls and 10 ping pong balls . What is the probability of selecting a ping pong ball , replacing it and then selecting a tennis ball
Answers
Answer:
40/169
Step-by-step explanation:
P(pp,tennis) = [tex]\frac{10}{26}[/tex] × [tex]\frac{16}{26}[/tex] = 40/169 in simplified form
The probability of selecting a ping pong ball, replacing it and then selecting a tennis ball is 40/169.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
Tennis ball = 16
Ping pong balls = 10
So, probability of selecting a ping pong ball, replacing it and then selecting a tennis ball
= 10/ 26 x 16/26
= 40/169
Learn more about Probability here:
https://brainly.com/question/11234923
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HELP ASAP!!!hahahahsna s densllalsjdnd dnsksk
Answers
Answer:
A = (-7,6)
B = (2,4)
C = (-6,0)
Step-by-step explanation:
A = (-9 + 2, 2 + 4)
B = (0 + 4, 0 + 4)
C = (-8 + 2, -4 + 4)
Which intervals are most appropriate for a histogram
displaying the mileage ratings?
The list shows the mileage rating (in mpg) for some 2019
vehicles with all-wheel or four-wheel drive.
11, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 18,
18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21,
21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 24, 24,
24, 24, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 27, 28, 29,
30, 31, 32, 33, 34
O 0-15, 15-30, 30-45
O 0–20, 20-40, 40-60
O 10-15, 15-20, 20-25, 25-30, 30-35
O 0-5,5–10, 10-15, 15-20, 25-25, 25-30
Answers
Answer:
C. 10–15, 15–20, 20–25, 25–30, 30–35
Step-by-step explanation:
What must the missing digit be so that the number rounds to 4 when rounding to the nearest whole number?
A. 5
B. 9
C. Any number greater than 5
D. The digit does not matter
Answers
Answer:
C. any number greater than 5
Step-by-step explanation:
when rounding numbers. 5 or more up the score. the number will be rounded to the next whole number
Answer:
Step-by-step explanation:
D the digit does not metter
The table shows the prices for the same cereal, sold in different weights. Which size box is the best buy, in terms of price per ounce?
A. 9 oz
B.18 oz
C.28 oz
D.38 oz
Answers
Answer:
c
Step-by-step explanation:
ESPERO TE A YDUE :)
please answer all the questions for 25 points and for brainliest if not answer correctly will report
Answers
Answer:
1) 56.52 in²
2) 565.2 ft²
3) 235.5yd²
4) 898.04 ft²
5) 942 yd²
6) 75.36 in²
Step-by-step explanation:
SA= πrS + πr²
1) (3.14)(2)(7) + (3.14)(2²) = 56.52 in²
2) (3.14)(9)(11) + (3.14)(9²) = 565.2 ft²
3) (3.14)(5)(10) + (3.14)(5²) = 235.5yd²
4) (3.14)(11)(15) + (3.14)(11²) = 898.04 ft²
5) (3.14)(10)(20) + (3.14)(10²) = 942 yd²
S =5 because 5² = 3² + 4²
6) (3.14)(3)(5) + (3.14)(3²) = 75.36 in²
write any odd number and find their sum product
Answers
Answer:
3?
Step-by-step explanation:
Jeremiah answered 20
out of 25 questions
correctly on the math test.
What percent of the
questions did Jeremiah
answer correctly?
Answers
Answer:
he got 80 percent correct
Simplify the numeric expression below. Show all
work.
8-12-(6 + 4)
Answers
Answer:
negative 14 or -14
Step-by-step explanation:
8-12-10
= 8-22
= -14
3/4 divided by 1/4 help can you teach me how to do it to
Answers
Answer:
3/4 divided by 1/4 = 3
Step-by-step explanation:
When we divide two fractions, such as 3/4 ÷ 1/4, we flip the second fraction and then we simply multiply the numerators with each other and the denominator with each other.
We also simplify the answers to fraction problems whenever possible.
Answer:
3
Step-by-step explanation:
=(3/4)(4/1)
kcf (keep, change, flip)
so we're keeping 3/4 the same then we're changing it from division to multiplication and fliping 1/4 to 4/1 (as shown above)
3*4=12 and 4*1=4
so our new fraction is 12/4
12/4 is an improper fraction and 12 divided by 4 is 3
good luck :)
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have a great day !!
The measure of an angle is 149.5°. What is the measure of its supplementary angle?
Answers
Answer:
30.5°
Step-by-step explanation:
Supplementary angles add up to 180°. You know one angle is 149.5°, so you can find the other angle.
Measure of its supplementary angle = 180° - 149.5°
= 30.5°
What is the explicit formula for the geometric sequence 15, 3, 0.6,
0.12, ...?
Answers
Answer:
A
Step-by-step explanation:
first num is 15
ratio is 0.2
formula is a.r^n-1
hi
The fair spinner shown in the diagram above is spun.
Work out the probability of getting a factor of 12.
Give your answer in its simplest form.
Answers
Answer:
hi.a..a.q.q.q.q..w.w.q.
Plss help me will mark brainliest
Answers
Answer:
45-degrees
Step-by-step explanation:
The triangle is a 90-degree triangle
Triangles = 180-degrees
90 + 45 + 45 = 180
On Triangle ABC, Angle A measures 30 degrees, Angle B measures 90 degrees, and Angle C measures 60 degrees. List the sides of Triangle ABC in order from shortest to longest.
Answers
Answer:
A=30 B=90 C=60
Step-by-step explanation:
A=30 C=60 B=90
Tayler works at a bicycle shop. When he sells a bicycle, he earns 6% of the sale price as a commission. One day Tayler sold 1 bicycle for $125 and 2 bicycles for $75 each. What was the total amount of commission he earned?
Answers
$72x2=$150
$150+125=$275
6% of 275= $16.5
Which statement best describes the values of x and y in the table
Answers
Answer:
Answer A
Step-by-step explanation:
As the value of x increases by 2 the value of y increases by 4
PLEASE HELP!!! WILL MARK BRAINLIEST!!! Answers only related to the question please!
Exponential functions have the form f(x)= b^x. What type of an exponential function would you have (increasing or decreasing) if the value of b is greater than one?
Answers
Answer:
x is form
Step-by-step explanation:
Carol has a choice of an account that compounds quarterly and an account that compounds daily.
If they both have the same interest rate, which will earn more interest?
The account that compounds quarterly.
The account that compounds daily.
They will both earn the same interest
Answers
Answer: The account that compounds daily.
Step-by-step explanation: If you reinvest your money more frequently, then you will also be able to earn interest on the interest that you earned the previous day and so on.
please help me
( - 3 ) ( a + x ) , if a + 8, x = - 10
Answers
Answer:
6
Step-by-step explanation:
-3 x (8 + [-10]) =
-3 x (8 - 10) =
-3 x -2 =
6
HOpe that helps!
Answer: 6
Step-by-step explanation:
finding the answer from an equation
replace the values of x and a in the equation:
(-3) * ( 8 + -10)
= (-3) * (-2)
recall :
(-) * (-) = +
hence -3 * -2
= 6
Hope this helps. Can u pls give me brainliest
4. What is an example of like terms in the expression below?
(2 points)
9x + 15y + 6 - 2 + x?
15y and 6
9x and x
z and x
30x and 10y
Answers
Answer:
9x and x since all of the others would be in different groups
9x+15y+6-2+x
10x+15y+4
Mr. Cox's round baler bales a 4-foot-wide bale having a 5.25 foot diameter. He wants to wrap
the bale in a white wrapper. He must allow an extra 10 percent for lapping. How many square
feet of wrapping does each bale require?
Answers
Answer:
109.27 ft²
Step-by-step explanation:
SA = face + face + curve
SA = 2πr² + 2πrw
= 2π(2.625)² + 2π(2.625)(4)
= ~43.3 + ~65.97 = 109.27 = SA
How can 26n - 7m +4(10n - 6m) be rewritten? A. 36n - 13m B. 40n - 9m C. 66n - 31m D. 35mn
Answers
Answer:
C. 66n - 31m
Step-by-step explanation:
26n - 7m + 4(10n - 6m)
26n - 7m + 40n - 24m
26n - 31m + 40n
66n - 31m