Answer: Rs. 40,000
Step-by-step explanation:
Let say Marked price of the Watch
= M Rs
Discount = 20 %
Discount = (20/100)M = 0.2M Rs
Price after Discount = M - 0.2M =
Rs 0.8M
13 % Value added tax
=> VAT = (13/100) * 0.8M = 0.104M Rs
Value of Watch = 0.8M + 0.104M = 0.904M Rs
0.904M = 36160
=> M = 40000
Marked Price of Watch = Rs 40,000
All the angles in the diagram are measured to the nearest degree. Work out the upper bound and lower bound of angle x 59 degree 108 degree 81 degree X degree ??????
Answer: lower bound, x = 110.5°
upper bound, x = 113.5°
Step-by-step explanation:
There is no diagram but I am going to assume it is a quadrilateral since it has 4 angles. The sum of the angles of a quadrilateral is 360°.
Upper Lower
59° 58.5° ≤ a < 59.5
108° 107.5° ≤ b < 108.5°
81° 80.5° ≤ c < 81.5°
Total: 246.6° ≤ x < 249.5°
Subtract the lower and upper bound totals from 360° :
360.0 360.0
- 246.5 - 249.5
x = 1 1 3.5 1 1 0.5
↓ ↓
upper lower
bound bound
Find the value of x and the value of y.
A r= 15, y = 10/3
B. r=20, p=10/3
C. x=20/3, y = 513
D. r=15, y =53
Answer:
Step by step solution:
The commute time for people in a city has an exponential distribution with an average of 0.66 hours. What is the probability that a randomly selected person in this city will have a commute time between 0.55 and 1.1 hours? Answer: (round to 3 decimal places)
Answer:
[tex] P(0.55 <X<1.1)= F(1.1) -F(0.55) [/tex]
And replacing we got:
[tex] P(0.55 <X<1.1)= (1-e^{-\frac{1}{0.66} *1.1}) -(1-e^{-\frac{1}{0.66} *0.55})[/tex]
[tex] P(0.55 <X<1.1)=e^{-\frac{1}{0.66} *0.55}- e^{-\frac{1}{0.66} *1.1}=0.2457[/tex]
And rounded the answer would be 0.246
Step-by-step explanation:
For this case we can define the random variable X as "The commute time for people in a city" and for this case the distribution of X is given by:
[tex] X \sim exp (\lambda = \frac{1}{0.66}= 1.515)[/tex]
And for this case we want to find the following probability:
[tex] P(0.55 <X<1.1)[/tex]
And we can use the cumulative distribution function given by:
[tex] F(x) =1- e^{-\lambda x}[/tex]
And using this formula we got:
[tex] P(0.55 <X<1.1)= F(1.1) -F(0.55) [/tex]
And replacing we got:
[tex] P(0.55 <X<1.1)= (1-e^{-\frac{1}{0.66} *1.1}) -(1-e^{-\frac{1}{0.66} *0.55})[/tex]
[tex] P(0.55 <X<1.1)=e^{-\frac{1}{0.66} *0.55}- e^{-\frac{1}{0.66} *1.1}=0.2457[/tex]
And rounded the answer would be 0.246
To assess the accuracy of a laboratory scale, a standard weight known to weigh 1 gram is repeatedly weighed a total of n times How large should n be so that a 95% confidence interval for µ has a margin of error of ± 0.0001?
Answer:
[tex]n=(\frac{1.960(1)}{0.0001})^2 =384160000[/tex]
So the answer for this case would be n=384160000 rounded up to the nearest integer
Step-by-step explanation:
We know the following info:
[tex] ME = 0.0001[/tex] represent the margin of error desired
[tex] \sigma= 1[/tex] we assume that the population deviation is this value
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =0.0001 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 95% of confidence interval now can be founded using the normal distribution. If we use the normal standard distribution or excel we got: [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.960(1)}{0.0001})^2 =384160000[/tex]
So the answer for this case would be n=384160000 rounded up to the nearest integer
by what rational number should we divide 22/7 so as to get the number -11/13?
Answer:
7/54
Step-by-step explanation:
let thenumber be x
then 22/7 /x = -11/27
= 22x/7 = -11/27
= x = -11*7/27*22 = 7/54
Hope it helps!!
You are standing 5 miles away from the peak. You look up at a 47-degree angle to the peak. How tall is the mountain? Hint: 5280 feet = 1 mile. Round your answer to the nearest foot.
Answer:
19272 feet
Step-by-step explanation:
We are given that the distance between the person and peak is 5 miles.
and angle is [tex]47^\circ[/tex] when we look up at the mountain peak.
The given situation is best represented as a right angled triangle as shown in the attached figure.
[tex]\triangle[/tex]IKJ where [tex]\angle K = 90^\circ[/tex]
IK is the mountain.
J is the point where we are standing.
Distance JI = 5 miles
[tex]\angle J = 47^\circ[/tex]
To find: Distance IK = ?
We can use trigonometric identities to find IK.
[tex]sin\theta = \dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]sinJ = \dfrac{IK}{JI}\\\Rightarrow sin47 = \dfrac{IK}{5}\\\Rightarrow IK = sin47^\circ \times 5\\\Rightarrow IK = 0.73 \times 5\\\Rightarrow IK = 3.65\ miles \\\Rightarrow IK = 3.65 \times 5280\ ft\\\Rightarrow IK = 19272\ ft[/tex]
Hence, height of mountain = 19272 ft
What is the answer to this question?
32
\y-step explanation:
Answer: 9.20 am
Step-by-step explanation:
Every hour the difference between the two watches increases by 3 minutes 3x3=9
That gives us 3 hours and then divide 60 into 3 to make 20 minutes
3hours + 20mins = 3 20mins
6:00 a.m. + 3hrs 20 mins = 9:20 a.m.
Rearrange the following steps in the correct order to locate the last occurrence of the smallest element in a finite list of integers, where the integers in the list are not necessarily distinct.
a. return location
b. min ≔a1 and location ≔1
c. min ≔ai and location≔i
d. procedure last smallest(a1,a2,...,an: integers)
e. If min >= ai then
Answer:
The rearranged steps is as follows:
d. procedure last smallest(a1,a2,...,an: integers)
b. min ≔a1 and location ≔1
e. If min >= ai then
c. min ≔ai and location≔i
a. return location
Step-by-step explanation:
The proper steps to perform the task in the question above is dbeca
Here, the procedure (or function) was defined along with necessary parameters
d. procedure last smallest(a1,a2,...,an: integers)
The smallest number is initialized to the first number on the list and its location is initialized to 1
b. min ≔a1 and location ≔1
The next line is an if conditional statement that checks if the current smallest number is greater than a particular number
e. If min >= ai then
If the above condition is true, the smallest value is assigned to variable min; it's location is also assigned to variable location
c. min ≔ai and location≔i
The last step returns the location of the smallest number
a. return location
Which fraction is equivalent to 2/-6? -2/6 2/6 -2/-6 6/2
Please answer this correctly
Answer:
6 ties
Step-by-step explanation:
At least 37 but fewer than 63 makes it 37-62
So,
37-62 => 6 ties
12x - y = -4
4x - 3y = -6 (1 point)
Answer:
Step-by-step explanation:
12x - y = -4 ----------------------(I)
4x - 3y = -6 ---------------------(II)
Multiply equation (I) by (-3)
(I)*(-3) -36x + 3y = 12
(II) 4x - 3y = - 6 {Add and y will be eliminated}
- 32x = 6
x = 6/-32
x = -3/16
Plugin the value of x in equation (I)
[tex]12*\frac{-3}{16} -y=-4\\\\3*\frac{-3}{4}-y=-4\\\\\frac{-9}{4}-y = -4\\\\-y=-4+\frac{9}{4}\\\\-y=\frac{-4*4}{1*4}+\frac{9}{4}\\\\-y=\frac{-16}{4}+\frac{9}{4}\\\\-y=\frac{-7}{4}\\\\y=\frac{7}{4}\\\\y=1\frac{3}{4}[/tex]
A piece of wire of length 7070 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) minimize and (b) maximize the combined area of the circle and the square?
Answer:
a.x=39.2
b.Use whole wire as a circle
Step-by-step explanation:
We are given that
Length of piece of wire=70 units
Let length of wire used to make a square =x units
Length of wire used in circle=70- x
Side of square=[tex]\frac{perimeter\;of\;square}{4}=\frac{x}{4}[/tex]
Circumference of circle=[tex]2\pi r[/tex]
[tex]70-x=2\pi r[/tex]
[tex]r=\frac{70-x}{2\pi}[/tex]
Combined area of circle and square,A=[tex](\frac{x}{4})^2+\pi(\frac{70-x}{2\pi})^2[/tex]
Using the formula
Area of circle=[tex]\pi r^2[/tex]
Area of square=[tex](side)^2[/tex]
a.[tex]A=\frac{x^2}{16}+\frac{4900+x^2-140x}{4\pi}[/tex]
Differentiate w.r.t x
[tex]\frac{dA}{dx}=\frac{x}{8}+\frac{2x-140}{4\pi}[/tex]
[tex]\frac{dA}{dx}=0[/tex]
[tex]\frac{x}{8}+\frac{2x-140}{4\pi}=0[/tex]
[tex]\frac{\pi x+4x-280}{4\pi}=0[/tex]
[tex]\pi x+4x-280=0[/tex]
[tex]x(\pi+4)=280[/tex]
[tex]x=\frac{280}{\pi+4}[/tex]
x=39.2
Again differentiate w.r.t x
[tex]\frac{d^2A}{dx^2}=\frac{1}{8}+\frac{1}{2\pi}[/tex]>0
Hence, the combined area of circle and the square is minimum at x=39.2
b.When the wire is not cut and whole wire used as a circle . Then, combined area is maximum.
Rebecca is a real estate agent who would like to find evidence supporting the claim that the population mean market value of houses in the neighborhood where she works is greater than $250,000. To test the claim, she randomly selects 35 houses in the neighborhood and finds that the sample mean market value is $259,860 with a sample standard deviation of $24.922. The test statistic t for a hypothesis test of H0 : μ = 250.000 versus Ha : μ > 250.000 is t 2.34 , which has 34 degrees of freedom. If 0.01
A) Fail to reject the null hypothesis that the true population mean market value of houses in the neighborhood where Rebecca works is equal to $250,000.
B) Reject the null hypothesis that the true population mean market value of houses in the neighborhood where Rebecca works is equal to $250,000.
C) There is enough evidence at the α-: 0.05 level of significance to support the claim that the true population mean market value of houses in the neighborhood where Rebecca works is greater than $250,000.
D) There is not enough evidence at the α-_ 0.05 level of significance to suggest that the true population mean market value of houses in the neighborhood where Rebecca works is not equal to $250,000.
Answer:
There is enough evidence at the α-: 0.05 level of significance to support the claim that the true population mean market value of houses in the neighborhood where Rebecca works is greater than $250,000.
Step-by-step explanation:
We are given that Rebecca randomly selects 35 houses in the neighborhood and finds that the sample mean market value is $259,860 with a sample standard deviation of $24.922.
Let [tex]\mu[/tex] = population mean market value of houses in the neighborhood.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = $250,000 {means that the population mean market value of houses in the neighborhood where she works is equal to $250,000}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $250,000 {means that the population mean market value of houses in the neighborhood where she works is greater than $250,000}
The test statistics that would be used here One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean market value = $259,860
s = sample standard deviation = $24,922
n = sample of houses = 35
So, the test statistics = [tex]\frac{259,860-250,000}{\frac{24,922}{\sqrt{35} } }[/tex] ~ [tex]t_3_4[/tex]
= 2.34
The value of t-test statistic is 2.34.
Also, P-value of the test statistics is given by;
P-value = P([tex]t_3_4[/tex] > 2.34) = 0.0137
Since our P-value is less than the level of significance as 0.0137 < 0.05, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the population mean market value of houses in the neighborhood where she works is greater than $250,000.
please help and please show your work
Answer:
The volume of all 9 spheres is 301.6 [tex]in^3[/tex]
Step-by-step explanation:
Notice that three of the identical spheres fit perfectly along the 12 in side box, therefore we know that the diameter of each is 12 in/3 = 4 in.
Then the radius of each sphere must be 2 inches (half of the diameter). Now that we know the radius of each sphere, we use the formula for the volume of a sphere to find it:
[tex]V=\frac{4}{3} \pi R^3\\V=\frac{4}{3} \pi (2\,in)^3\\V=\frac{4}{3} \pi\, 8\,\,in^3\\V=\frac{32}{3} \pi\,\,in^3[/tex]
Now, the total volume of all nine spheres is the product of 9 times the volume we just found:
[tex]V_{all \,9}=9\,*\frac{32}{3} \pi\,\,in^3\\V_{all \,9}=96 \pi\,\,in^3\\V_{all \,9}\approx \,301.6\,\,in^3[/tex]
the graph of y=-4x7 is:
Answer:
(0,7)
Step-by-step explanation:
28
Step-by-step explanation:
how many nickels equal $18.45? (show your work)
Answer:
369
Step-by-step explanation:
One nickel = 0.05
0.05x=18.45
x=369
All math teachers are smart. Ms. Smith is your math teacher, so she is smart. What type of reasoning is this? inductive or deductive
Answer:
I believe it is Inductive Reasoning.
Step-by-step explanation:
Inductive Reasoning is a type of logical thinking that involves forming generalizations based on specific incidents you've experienced, observations you've made, or facts you know to be true or false.
Deductive Reasoning is a basic form of valid reasoning.
A File that is 242 megabytes is being downloaded.If the download is 12.9%complete,how many megabytes have been downloaded?Round your answer to the nearest tenth.
Answer:31
Step-by-step explanation: Since you are trying to find a percentage of a number all you have to do is multiply 242 by 12.9% and because you have to round to the nearest tenth it will be 31
There are 5 gallons of distilled water in science supplies. If 8 students each use an equal amount of distilled water and there is 1 gallon left in supplies, how much will each student get?
Answer:
0.5 gallon
Step-by-step explanation:
let x refer to students
5 = 8x + 1
8x = 4
x= 0.5 gallon
Kyle has 3 cards 6, 1, 2, what is all the numbers he can make using these cards, including one, two and three digit numbers
Answer: he can make 21 different numbers.
Step-by-step explanation:
If he uses only one card, the numbers are:
1, 2 and 6, so here we have 3 combinations.
If he uses two cards, for the first digit he has 3 options (because he has 3 cards) and for the second digit he has two options (because he already selected one of the cards) then he has:
3*2 = 6 different options
If uses the 3 cards, then he has 3 options for the first card, 2 options for the second card and one option for the third card, then the number of combinations is:
c = 3*2*1 = 6 combinations.
Adding all together we have C = 3 + 6 + 6 = 21 combinations.
Based on the following construction which statement below
must NOT be true?
Answer:
B. AC = 2AB
hope it helps!
Step-by-step explanation:
AC is half of AB
so if the statement says AC is 2AB it suggests that AC is greater than AB
this is definitely false..
The population of a community is known to increase at a rate proportional to the number of people present at time t. If an initial population P0 has doubled in 3 years, how long will it take to triple
To the nearest tenth, which is the perimeter of ABC. Geometry
Answer:
23.6
Step-by-step explanation:
Finding AC:
Cos 61 = [tex]\frac{adjacent}{hypotenuse}[/tex]
0.48 × 10 = Adjacent
AC = 4.8
Now, CB:
Cos 29 = [tex]\frac{adjacent}{hypotenuse}[/tex]
0.87 × 10 = CB
CB = 8.8
The perimeter:
=> 10+4.8+8.8
=> 23.6
Answer:
23.6
Step-by-step explanation:
Brand name producers of aspirin claim that one advantage of their aspirin over generic aspirin is that brand name aspirin is much more consistent in the amount of active ingredient used. This in turn means that users can expect the same results each time they use the brand name aspirin, while the effects of the generic aspirin can be a lot more variable. A random sample of 200 brand name aspirin tablets had a mean and standard deviation of active ingredient of 325.01 and 10.12 mg. A second independent sample of 180 generic aspirin tablets was measured for the amount of active ingredient, and the mean standard deviation were 323.47 and 11.43 mg. Given that the amount of active ingredient is normally distributed for both the brand name and the generic aspirin, do these data support the brand name producers claim? Let alpha = 0.025.
Answer:
Step-by-step explanation:
The claim here is that the brand name aspirin is more consistent in the amount of active ingredient used than the generic aspirin.
This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean amount of active ingredients in brand name aspirin and μ2 be the mean amount of active ingredients in generic name aspirin
The random variable is μ1 - μ2 = difference in the mean amount of active ingredients between the brand name and generic aspirin
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 ≥ μ2 H0 : μ1 - μ2 ≥ 0
The alternative hypothesis is
H1 : μ1 < μ2 H1 : μ1 - μ2 < 0
This is a left tailed test
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
From the information given,
x1 = 325.01
x2 = 323.47
s1 = 10.12
s2 = 11.43
n1 = 200
n2 = 180
t = (325.01 - 323.47)/√(10.12²/200 + 11.43²/180)
t = 1.24
1.237877
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [10.12²/200 + 11.43²/180]²/[(1/200 - 1)(10.12²/200)² + (1/180 - 1)(11.43²/180)²] = 1.53233946713/0.00537245359
df = 285
We would determine the probability value from the t test calculator. It becomes
p value = 0.108
Since alpha, 0.025 < than the p value, 0.108, then we would fail to reject the null hypothesis. Therefore, at 2.5% level of significance, these data support the brand name producers claim
Describe the steps to solve a rational equation. Create your own example and solve it following your steps. Then, provide an additional example for other people to try to solve as they reply to your post.
Answer:
Here is an exampls
Step-by-step explanation:
3.249 thousandths rounded to the nearest tenth
Answer:
3.2
Step-by-step explanation:
Rounded to the nearest 10
What is the area of a shape with points a 5 -8 b 11, -8 c 11,0 d 6,-3 e 4,-3
Answer:
Area of the given figure is 51.5 square units.
Step-by-step explanation:
Area of rectangle OCBH = Length × width
= 11 × 8
= 88 square units
Area of trapezoid OGEF = [tex]\frac{1}{2}(b_1+b_2)\times h[/tex]
= [tex]\frac{1}{2}(\text{GE+OF)}\times (\text{OG})[/tex]
= [tex]\frac{1}{2}(3+6)\times 4[/tex]
= 18 units²
Area of trapezoid GCDE = [tex]\frac{1}{2}(\text{GC+DE)}\times (\text{GE})[/tex]
= [tex]\frac{1}{2}(7+2)\times 3[/tex]
= 13.5 units²
Area of triangle AFH = [tex]\frac{1}{2}(\text{Base})\times (\text{Height})[/tex]
= [tex]\frac{1}{2}(5)(2)[/tex]
= 5 units²
Area of polygon ABCDEF = Area of rectangle CBHO - (Area of trapezoid OGEF + Area of trapezoid GCDE + Area of triangle AFH)
= 88 - (18 + 13.5 + 5)
= 88 - 36.5
= 51.5 units²
Therefore, area of the given polygon is 51.5 units²
this is a grade 4 maths question. i need help with doing a model from this question as well. thank you! —————————————————- a rope was cut into 2 pieces. The first piece was twice the length of the second piece. If the first piece was 5m 50cm long what was the length of the rope before it was cut
Answer:825cm
Step-by-step explanation:550cm/2=275cm
275*3=825cm
In two or more complete sentences, explain how to use ordered pairs of points in and to determine if and are inverses of each other.
Brainliest to whoever gets this correct Which of the following is equal to the rational expression when x ≠ -3? x^2-9/x+3
Answer:
see below
Step-by-step explanation:
We presume you want to simplify ...
[tex]\dfrac{x^2-9}{x+3}=\dfrac{(x-3)(x+3)}{x+3}=\boxed{x-3}[/tex]
__
The numerator is the difference of squares, so is factored accordingly. One of those factors cancels the denominator.