Answers
Step-by-step explanation:
By Sine rule, BC/sin93° = 11/sin42°.
Therefore BC = 16.4.
Related Questions
With domestic sources of building supplies running low several years ago, roughly 60,000 homes were built with imported Chinese drywall. According to an article federal investigators identified a strong association between chemicals in the drywall and electrical problems, and there is also strong evidence of respiratory difficulties due to the emission of hydrogen sulfide gas. An extensive examination of 58 homes found that 46 had such problems. Suppose these 58 were randomly sampled from the population of all homes having Chinese drywall.
(a) Does the data provide strong evidence for concluding that more than 50% of all homes with Chinese drywall have electrical/environmental problems? Carry out a test of hypotheses using a = 0.01.
Compute the test statistic value. Round your answer to two decimal places.
(b) Calculate a lower confidence bound using a confidence level of 99% for the percentage of all such homes that have electrical/environmental problems. (Round your answer to one decimal place.)
(c) If it is actually the case that 80% of all such homes have problems, how likely is it that the test of (a) would not conclude that more than 50% do? (Round your answer to four decimal places.)
Answers
Answer:
Step-by-step explanation:
Null hypothesis:
[tex]H_o : \mu = 0.50[/tex]
Alternative hypothesis:
[tex]H_a : \mu > 0.50[/tex]
The sample proportion [tex]\hat p = \dfrac{x}{n}[/tex]
[tex]\hat p = \dfrac{46}{58}[/tex]
[tex]\hat p = 0.7931[/tex]
The test statistics:
[tex]Z = \dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n} } }[/tex]
[tex]Z = \dfrac{0.7931 - 0.50}{\sqrt{\dfrac{0.5(1-0.5)}{58} } }[/tex]
[tex]Z = \dfrac{0.2931}{\sqrt{\dfrac{0.25}{58} } }[/tex]
[tex]Z = \dfrac{0.2931}{0.06565321643}[/tex]
Z = 4.46 (to two decimal places)
At 99% C.I
Level of significance is:
∝ = 1 - C.I
∝ = 1 - 0.99
∝ = 0.01
Thus, the lower confidence bound can be computed as:
[tex]= \hat p - Z_{\alpha} \sqrt{\dfrac{\hat p ( 1- \hat p )}{n} }[/tex]
Critical value of [tex]Z_{0.01/2} = 2.33[/tex]
[tex]= 0.7931 - 2.33 \sqrt{\dfrac{0.7931 (1-0.7931)}{58}}[/tex]
[tex]= 0.7931 - 2.33 (0.05319)[/tex]
= 0.7931 - 0.1239327
= 0.6691673
[tex]\simeq[/tex] 0.7 (to one decimal place)
(c)
Given:
[tex]P_o = 0.50[/tex] and [tex]\hat p = 0.80[/tex]
Then:
[tex]\beta (0.8) = \phi \Big [ \dfrac{p_o-\hat p + Z_{\alpha} \sqrt{\dfrac{p_o(1-p_o)}{n}}}{\sqrt{\dfrac{\hat p(1-\hat p)}{n} } } \Big][/tex]
[tex]\beta (0.8) = \phi \Big [ \dfrac{0.5-0.8 + 2.33 \sqrt{\dfrac{0.5(1-0.5)}{58}}}{\sqrt{\dfrac{0.8(1-0.8)}{58} }}\Big][/tex]
[tex]= \phi \Big [ \dfrac{-0.3+ 2.33 (0.06565)}{\sqrt{0.0027586 }} \Big][/tex]
[tex]= \phi \Big [ \dfrac{-0.3+ 0.1529645}{0.052522} \Big][/tex]
[tex]= \phi \Big [ \dfrac{-0.1470355}{0.052522 } \Big][/tex]
[tex]= \phi \Big [-2.799\Big][/tex]
= 0.0026 ( to four decimal place).
What is the common difference for this arithmetic sequence?
-6, -1,4,9, 14, ...
A. 5
B. 3
C. 6
D. 4
Answers
Answer:
A. 5
Step-by-step explanation:
-6 + 5 = -1
-1 + 5 = 4
4 + 5 = 9
9 + 5 = 14
g A nationwide survey of 17,000 college seniors by the University of Michigan revealed that almost 70% disapprove of daily pot smoking. If 18 of these seniors are selected at random and asked their opinion, what is the probability that more than 9 but fewer than 14 disapprove of smoking pot daily
Answers
Answer:
the probability that more than 9 but fewer than 14 disapprove of smoking pot daily is 0.608
Step-by-step explanation:
From the information given:
Let N represent the total number of senior students
N = 17000
and k to be the number of seniors disapproving of daily pot smoking
k = 17000 × 0.70
k = 11900
sample size n = 18
Suppose X represents the random variable...
Then,
X = 0,1,2,...,18
Thus X follows a hypergeometric distribution with parameters
(N = 17000, n = 18 & k = 11900)
Thus, the probability mass function is:
[tex]P(X =x) = \dfrac{(^k_n) (^{N-k}_{n-x} ) }{(^N_n) }; \ max \{0,(N-K) \} \le x \le min \{n,k\}[/tex]
[tex]P(X =x) = \dfrac{(^{11900}_n) (^{17000-11900}_{18-x} ) }{(^{17000}_{18}) }[/tex]
[tex]P(X =x) = \dfrac{(^{11900}_n) (^{51000}_{18-x} ) }{(^{17000}_{18}) }; \ 0\le x \le 18[/tex]
Now, the required probability is computed as:
[tex]P(9<X<14) = P(10 \le X \le13)[/tex]
[tex]P(9<X<14) = P(X =10) +P(X =11) +P(X=12) +P(X =13)[/tex]
[tex]P(9<X<14) = \left\{\begin{array}{c} \dfrac{(^{11900}_{10}) (^{5100}_{18-10}) }{(^{17000}_{18})} + \dfrac{(^{11900}_{11}) (^{5100}_{18-11}) }{(^{17000}_{18})}+ \dfrac{(^{11900}_{12}) (^{5100}_{18-12}) }{(^{17000}_{18})} + \dfrac{(^{11900}_{13}) (^{5100}_{18-13}) }{(^{17000}_{18})}\end{array}\right\}[/tex]P(9<X<14) = 0.0811 + 0.1377 + 0.1874 + 0.2018
P(9<X<14) = 0.608
Thus, the probability that more than 9 but fewer than 14 disapprove of smoking pot daily is 0.608
Serena bought 5 shirts for $6 each spent $7 on lunch. she paid for the shirts and lunch using her debit card. The change in the balance of serena’s checking account can be represented by the expression shown. 5(-6) + (-7) which integer represents the change in the balance of serena’s checking account from these purchases? A // -37. B // 23. C // -18. D // 4
Answers
Answer:
A -$37
Step-by-step explanation:
5×6=30
30 +7= 37
since your losing money its negatively
-37
Which equation represents the parabola shown on the
graph?
A. y2 = -2x
B. y2 = -8%
C. x2 = -2y
D. x2 = -8y
Answers
Answer:
y2=-8x is what's graphed so B.
Step-by-step explanation:
(I think you mistyped the choice)
Answer:
Which equation represents the parabola?
a) y2 = –2x
b) x2 = –2y
c) y2 = –8x
d) x2 = –8y
Step-by-step explanation:
C for edge 2021
How to write slope intercept form of
y = -5/4 (x+4)
Answers
Answer: y=−5/4x−5
Step-by-step explanation:
The ratio of fifth graders to sixth graders is 4 to 5. If one of the grade totals is 160,
select the possible totals for the other grade.
200
160
40
32
128
Answers
Answer:
Hi how are you doing today Jasmine
Answer:
40 and 32 i think
Step-by-step explanation:
i did it and im pretty sure its 40 and 32
The sum of two numbers is 48. Their difference is −4. Find the numbers.
Answers
Answer:
22 and 26
Step-by-step explanation:
So i need help with the question below.
Answers
Answer:
Option (1)
Step-by-step explanation:
Option (1)
[tex]3\frac{3}{9}+7\frac{6}{11}=10\frac{87}{99}[/tex]
[tex]3\frac{3}{9}+7\frac{6}{11}[/tex] [tex]=3+\frac{3}{9}+7+\frac{6}{11}[/tex]
[tex]=(3+7)+(\frac{3}{9}+\frac{6}{11})[/tex]
[tex]=10+(\frac{3}{9}\times \frac{11}{11})+(\frac{6}{11}\times \frac{9}{9})[/tex]
[tex]=10+(\frac{33}{99}+\frac{54}{99})[/tex]
[tex]=10+\frac{87}{99}[/tex]
[tex]=10\frac{87}{99}[/tex]
True.
Option (2)
[tex]2\frac{3}{8}+6\frac{4}{5}=8\frac{12}{40}[/tex]
[tex]2\frac{3}{8}+6\frac{4}{5}=2+\frac{3}{8}+6+\frac{4}{5}[/tex]
[tex]=(2+6)+(\frac{3}{8}+\frac{4}{5})[/tex]
[tex]=(8)+(\frac{3}{8}\times \frac{5}{5} +\frac{4}{5}\times \frac{8}{8})[/tex]
[tex]=8+(\frac{15}{40}+\frac{32}{40})[/tex]
[tex]=8+\frac{47}{40}[/tex]
[tex]=8+\frac{40}{40}+\frac{7}{40}[/tex]
[tex]=8+1+\frac{7}{40}[/tex]
[tex]=9+\frac{7}{40}[/tex]
[tex]=9\frac{7}{40}[/tex]
False.
Option(3)
[tex]3\frac{3}{7}+4\frac{2}{3}=7\frac{2}{21}[/tex]
[tex]3\frac{3}{7}+4\frac{2}{3}=(3+\frac{3}{7})+(4+\frac{2}{3})[/tex]
[tex]=(3+4)+(\frac{3}{7}+\frac{2}{3})[/tex]
[tex]=7+(\frac{3}{7}\times \frac{3}{3} +\frac{2}{3}\times \frac{7}{7})[/tex]
[tex]=7+(\frac{9}{21}+\frac{14}{21})[/tex]
[tex]=7+(\frac{23}{21})[/tex]
[tex]=7+(\frac{21}{21}+\frac{2}{21})[/tex]
[tex]=8+\frac{1}{21}[/tex]
[tex]=8\frac{1}{21}[/tex]
False.
Option (4)
[tex]4\frac{5}{6}+5\frac{5}{7}=9\frac{10}{13}[/tex]
[tex]4\frac{5}{6}+5\frac{5}{7}=4+\frac{5}{6}+5+\frac{5}{7}[/tex]
[tex]=(4+5)+(\frac{5}{6}+\frac{5}{7})[/tex]
[tex]=9+(\frac{5}{6}\times \frac{7}{7}+\frac{5}{7}\times \frac{6}{6})[/tex]
[tex]=9+(\frac{35}{42}+\frac{30}{42})[/tex]
[tex]=9+\frac{65}{42}[/tex]
[tex]=9+(\frac{42}{42}+\frac{23}{42})[/tex]
[tex]=9+1+\frac{23}{42}[/tex]
[tex]=10\frac{23}{42}[/tex]
False.
Therefore, Option (1) is the answer.
what is the incline slope of the ramp?
Rise= 2 feet
run = 10 feet
Answers
To go on a summer trip, Ravi borrows $800. He makes no payments until the end of 3 years, when he pays off the entire loan. The lender charges simple interest at an annual rate of 5%. Answer the following questions. If necessary, refer to the list of financial formulas. (a) How much total interest will Ravi have to pay? Х 5 ? s) (b) What will the total repayment amount be (including interest)?
Answers
Answer:
srry but search 12 z6xs
Step-by-step explanation:
(a) The total interest that Ravi will have to pay is $120. (b) The total repayment amount will be $920.
a) The interest rate is 5% per year, so Ravi will pay 5% * 800 = $40 per year in interest.
Since he borrowed the money for 3 years, he will pay a total of 3 * 40 = $120 in interest.
b) The total repayment amount will be the principal amount of $800 plus the interest of $120, for a total of 800 + 120 = $920.
Simple interest formula: I = P * r * t
Where:
I is the interest
P is the principal amount
r is the interest rate
t is the time in years
Interest per year: 5% * 800 = $40
Total interest: 3 * 40 = $120
Total repayment amount: 800 + 120 = $920
To learn more about interest here:
https://brainly.com/question/31135293
#SPJ2
Solve each system by elimination.
1) –10x – 15y = 30
-9x - 5y=-24
Answers
Answer:
(6,-6)
Step-by-step explanation:
1. -10x-15y=30
-10x-15y+15y=30+15y
-10x/-10=30+15y/-10
x=-3 -3/2
plug in the other equation and solve for y
-9x-5y=-24
-9(-3-3/2)-5y=-24
y=-6
plug -6 in for y in one of the original equations
-9x-5y=-24
-9x-5(-6)=-24
solve for x
x=6
wonderful
Simplify the expression:
9g - 9g
Answers
Answer:
0
Step-by-step explanation:
How do you write 0.0704 in scientific notation?
Answers
Answer:
well for me I think it's
Step-by-step explanation:
7.04×10^-2
Here are the monthly charges for Jo's mobile phone
Monthly charge 616
150 free minutes, then 18p per minute
150 free texte, then 18p per text
During one month, Jo makes 170 minutes of calls and sends 182 texte,
Work out the total charge for the month
Answers
Fixed monthly charge = £16
Monthly 150 free minutes, post that 13p (or £0.13) per minute,
Monthly 150 free texts, post that 15p (or £0.15) per text
Jo's mobile phone usage details:
170 minutes of calls
182 texts
Total Charges for Jo = Fixed Monthly Charge + Charges for Calls + Charges for Texts
⇒ Total Charges for Jo = 16 + (170-150) × 0.13 + (182-150) × 0.15
⇒ Total Charges for Jo = 16 + (20) × 0.13 + (32) × 0.15
⇒ Total Charges for Jo = 16 + 2.6 + 4.8
⇒ Total Charges for Jo = 23.4
Hence, Jo should be charged £23.4 for the month.
Hope this helps !
A 128 inch board is cut into 3 pieces. The second piece is 33 inches longer than the first piece, and the third is three times as long as the first. Set up an equation and solve it to determine the length of the three pieces.
Answers
Answer:
The first piece is 19 inches, the second is 52, and the third piece is 57.
Step-by-step explanation:
Solve for x using (x) + (x + 33) + (3x) = 128.
How do you do this? is geometry please help this define my grade
Answers
Answer:
x = 21.287
Step-by-step explanation:
Use:
SOH CAH TOA
Cos(37) = 17.3/x
x = 21.287
Answer:
x = 21.287
Step-by-step explanation:
Use:
SOH CAH TOA
Cos(37) = 17.3/x
x = 21.287
Charles received a $3.00 tip from a customer who had a $12.00 bill. Which decimal represents the fraction of the bill Charles received as a O 0.12 0 0.25 O 0.3 O 0.4
Answers
Answer:
I think 0.4 would be the answer
Answer:
0.12 go to places to the left
this has me a bit confused...can anyone help?
Answers
Answer:
x = 3b/2 + 3y/2
Step-by-step explanation:
Goal: Find x
To do that we must isolate x on one side of the equation.
2/3x - y = b
2/3x - y + y = b + y
2/3x = b + y
2/3x ÷ 2/3 = b + y ÷ 2/3
(When we divide fractions we multiply by its reciprocol.)
x = 3b/2 + 3y/2
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
In a quadrilateral, all four of the angles are right angles. if the figure doe isn’t have four congruent sides, what is it?
rectangle
quadrilateral
rhombus
square
Answers
Answer:
rectangle
Step-by-step explanation:
The value of y is directly proportional to the value of x. If y = 35 when & = 140, what is the value of y when 3 = 70
answer choices -
17,5
280
70
35
Answers
How can you tell the diffrence between horizontal and vertical translation in an equation?
Answers
Vertical:
y=f(x) + k : graph shifts k units up
y=f(x) - k : graph shifts k units down
Horizontal:
y=f(x - k) : graph shifts k units right
y= f(x+k) : graph shifts k units left
If one term of a proportion is not known, what can be used to find the value of that term?
A: Substitution
B: Graphing
C: Cross-multiplication
D: Adding all the numbers together
Please select the best answer from the choices provided.
Answers
Answer:
cross multification is correct answer
use the table of values to explain if x and y are in a proportional relationship.
Answers
Answer:
Yes, they are in a porpotional relationship.
Step-by-step explanation:
solve for x! show your work please :)
Answers
Answer:
x= 12
Step-by-step explanation:
16=24
2x-6= 18
2x= 18+6= 24
2x= 24
x= 24/2= 12
hope it helps!
Answer:
x=12
Step-by-step explanation:
Line AC and line PR are congruent.
2x-6=18
2x=24
x=12
6. An ice cream costs 15 more than a cold drink. If the cost of
buying 5 ice creams is 125, find the price of a cold drink.
Answers
Answer:
The price of a cold drink is 10 dollars.
Step-by-step explanation:
We can use proportion.
[tex] \frac{5 \: ice \: creams}{125 \: dollars} = \frac{1 \: ice \: cream}{x} \\ \\ \frac{5x}{5} = \frac{125}{5} \\ \\ x = 25[/tex]
So we found out that one ice-cream costs $25.00.
The statement said, "An ice cream costs 15 more than a cold drink"
In other words, A cold drink costs 15 dollars less than an ice cream.
So we would subtract.
[tex]25 - 15 = 10[/tex]
So a cold drink costs $10.00.
A varsity boy's basketball team has ratio of seniors to juniors that is 7:4. The varsity girl's basketball team has a ratio of seniors to juniors that is 3 to 2. If each team has 12 juniors, which team has more seniors?
Answers
Answer:
Girl's basketball team has more seniors
Step-by-step explanation:
A varsity boy's basketball team has ratio of seniors to juniors that is 7:4.
Let there are 7x seniors and 4x juniors in boy's basketball team.
ATQ,
7x+4x = 12
11x = 12
x = 12/11
Seniors = [tex]7\times \dfrac{12}{11}=7.63[/tex]
The varsity girl's basketball team has a ratio of seniors to juniors that is 3 to 2.
Let there are 7x seniors and 4x juniors in girl's basketball team.
3x+2x = 12
5x = 12
x = 12/5
Seniors = [tex]7\times \dfrac{12}{5}=16.8[/tex]
As we can see that girl's basketball team has more seniors as compared to the boy's team.
Write the equation in POINT-SLOPE FORM of the line that passes throught (5,9) and has a slope of -7.
Answers
Answer:
The equation of line with slope -7 passing through (5,9) in point-slope form is:
[tex]y-9 = -7(x-5)[/tex]
Step-by-step explanation:
Given
Slope of line = m = -7
Point = (5,9)
The point slope form of equation is obtained from a point and slope. It is given by the equation:
[tex]y-y_1 = m(x-x_1)[/tex]
We know that (x1,y1) = (5,9)
Putting the values we get
[tex]y-9 = -7(x-5)[/tex]
Hence,
The equation of line with slope -7 passing through (5,9) in point-slope form is:
[tex]y-9 = -7(x-5)[/tex]
Which system has exactly one solution?
A. 3x - y =8
6x - 2y = 16
B. Y = 4x + 9
Y = 4x - 9
C. -6x + y = 2
Y = 6x + 2
D. 3x + 2y = 4
x - y = 3
Answers
Answer:
D
Step-by-step explanation:
A. when using elimination all number cancel out making it infinite solutions
B. has the same slope meaning the lines are parallel and will never intersect
C. when you isolate the y on 1 side for the 1st equation the equations are the same meaning infinite solutions
so d is the only one left
Hope this helps or makes sense.
what is the value of tan(arccos(-sqrt2/2)
Answers
Answer:
i think is -1 because the value is -1
Answer:
D. -1
Step-by-step explanation:
ed2021