The number of houses are 180, and the number of flats are 100.
It is given that the number of houses and the number of flats ratio is 9:5 the number of flats and the number of bungalows ratio is 10:3.
It is required to find the number of houses in the village if the number of bungalows is 30.
What is a fraction?Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The ratio of the number of houses and the number of flats:
= 9:5 and
The ratio of the number of flats and the number of bungalows :
=10:3
It means we can write the ratio of the number of houses and the number of flats = 18:10
And the ratio of the number of:
Houses : Flats : Bungalows = 18:10:3
But the number of bungalows are 30.
Then the ratios are:
180:100:30
Thus, the number of houses are 180, and the number of flats are 100.
Learn more about the fraction here:
brainly.com/question/1301963
In a grinding operation, there is an upper specification of 3.150 in. on a dimension of a certain part after grinding. Suppose that the standard deviation of this normally distributed dimension for parts of this type ground to any particular mean dimension LaTeX: \mu\:is\:\sigma=.002 μ i s σ = .002 in. Suppose further that you desire to have no more than 3% of the parts fail to meet specifications. What is the maximum (minimum machining cost) LaTeX: \mu μ that can be used if this 3% requirement is to be met?
Answer:
Step-by-step explanation:
Let X denote the dimension of the part after grinding
X has normal distribution with standard deviation [tex]\sigma=0.002 in[/tex]
Let the mean of X be denoted by [tex]\mu[/tex]
there is an upper specification of 3.150 in. on a dimension of a certain part after grinding.
We desire to have no more than 3% of the parts fail to meet specifications.
We have to find the maximum [tex]\mu[/tex] such that can be used if this 3% requirement is to be meet
[tex]\Rightarrow P(\frac{X- \mu}{\sigma} <\frac{3.15- \mu}{\sigma} )\leq 0.03\\\\ \Rightarrow P(Z <\frac{3.15- \mu}{\sigma} )\leq 0.03\\\\ \Rightarrow P(Z <\frac{3.15- \mu}{0.002} )\leq 0.03[/tex]
We know from the Standard normal tables that
[tex]P(Z\leq -1.87)=0.0307\\\\P(Z\leq -1.88)=0.0300\\\\P(Z\leq -1.89)=0.0293[/tex]
So, the value of Z consistent with the required condition is approximately -1.88
Thus we have
[tex]\frac{3.15- \mu}{0.002} =-1.88\\\\\Rrightarrow \mu =1.88\times0.002+3.15\\\\=3.15[/tex]
What’s the correct answer for this question?
Answer
A. 18(3/4)π
Explanation
In the attached file
Will pick brainliest! I need help with this, actual effort in answering is much appreciated.
Answer:
option 2
Step-by-step explanation:
4^2=16/8=2. 4^2=16/16=1. 2-1=1
(Bonus) A rectangular box has its edges changing length as time passes. At a par-ticular instant, the sides have lengthsa= 150 feet,b= 80 feet, andc= 50 feet.At that instant,ais increasing at 100 feet/sec,bis decreasing 20 feet/sec, andcisincreasing at 5 feet/sec. Determine if the volume of the box is increasing, decreasing,or not changing at all, at that instant.
Answer:
the volume of the box is increasing
dV = +310,000 ft^3/s
Step-by-step explanation:
Volume of a rectangular box with side a,b and c can be expressed as;
V = abc
The change in volume dV can be expressed as;
dV = d(abc)/da + d(abc)/db + d(abc)/dc
dV = bc.da + ac.db + ab.dc ......1
Given:
a= 150 feet,
b= 80 feet, and
c= 50 feet
ais increasing at 100 feet/sec,bis decreasing 20 feet/sec, andcisincreasing at 5 feet/sec
da = +100 feet/s
db = -20 feet/s
dc = +5 feet/s
Substituting the values into the equation 1;
dV = (80×50×+100) + (150×50×-20) + (150×80×+5)
dV = +400000 - 150000 + 60000 ft^3/s
dV = +310,000 ft^3/s
Since dV is positive, the volume of the box is increasing at that instant.
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Solution,
Radius=2 m
Area =pi r^2
= 3.142*(2)^2
=12.568 m^2
hope it helps
Good luck on your assignment
Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.5% of the 451 members of the 50 Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eight year period.
Construct a 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight–year period.
Define the random variable in X and P in words.
Which distribution should you use in this problem?
Answer:
Step-by-step explanation:
a) Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 451
x = 1.5/100 × 451 = 7
p = 7/451 = 0.02
q = 1 - 0.02 = 0.98
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.97 = 0.1
α/2 = 0.01/2 = 0.03
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.03 = 0.97
The z score corresponding to the area on the z table is 2.17. Thus, Thus, the z score for a confidence level of 97% is 2.17
Therefore, the 97% confidence interval is
0.02 ± 2.17√(0.02)(0.98)/451
= 0.02 ± 0.014
b) x represents the number of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.
P represents the proportion of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.
The distribution that should be used is the normal distribution
The perimeter of the shape is 28 cm. Find the value of radius.
Answer:
r = 4.2805cm
Step-by-step explanation:
ok first the shape its made of two slant height and and an arc of degree 70°
The total perimeter = 28cm
The formula for the total perimeter= 2l + 2πl(70/360)
Where l is the radius of the shape.
But l = 2r
So
= 2l + 1.2217l
= 3.2217l
28 = 3.2217l
l = 28/3.2217
l = 8.691
Recall that l = 2r
8.691= 2r
r = 8.691/2
r = 4.2805cm
The average of 12, 25 , 33 , and N is 120. Find N.
Answer:
So the formula for mean is you add up all of the numbers and divide by the number of numbers, that will give you the mean/average. So that means that (12+25+33+N)/4 = 120. We can simplify by first adding all of the numbers and multiplying both sides by 4 which will cancel out the four on the right side.
70+N/4 = 120
480 = 70+N
So then we subtract 70 from both sides. Then we get 410 = N.
The answer is
410 is AnswerAssume Shelley Kate decides to take her social security at age 63. What amount of social security benefit will she receive each month, assuming she is entitled to $720 per month
She will receive a lot more money because she is already retired from work already and will win as bit more money
A bookstore charges $4 for shipping, no matter how many books you buy. Irena makes a graph showing the shipping cost for I to 5 books. She claims that the points she graphed lie on a line. Does her statement make sense? Explain
Answer:
Yes
Step-by-step explanation:
1 book = $4
2 books = 2*$4
3 books = 3*$4
4 books = 4*$4
5 books = 5*$4
This can be shown as: y=4x
y=ax+b is linear function, Irena is right
For a super soaker water gun, a pump handle is moved back and forth to build up pressure in the water reservoir. The water is released by pulling a trigger and shooting the water a significant distance. Assuming that you can create an absolute pressure of 8 atm in the reservoir:
a) What is the velocity at which the water leaves the gun?
b) If the water exits the gun through a hole with a radius of 1-mm, what is the volume rate of flow in m3/s?
c) If the water gun is fired horizontally and held 1.2 meters above the ground, where does the water hit the ground? Pressure 8 cm water
Answer:
a) The velocity at which the water leaves the gun = 37.66 m/s
b) The volume rate of flow = (1.183 × 10⁻⁴) m³/s
c) The water hits the ground 18.64 m from the point where the water gun was shot.
Step-by-step explanation:
a) Using Bernoulli's equation, an equation that is based on the conservation of energy.
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
The two levels we are considering is just inside the water reservoir and just outside it.
ρgh is an extension of potential energy and since the two levels are at the same height,
ρgh₁ = ρgh₂
Bernoulli's equation becomes
P₁ + ½ρv₁² = P₂ + ½ρv₂²
P₁ = Pressure inside the water reservoir = 8 atm = 8 × 101325 = 810,600 Pa
ρ = density of water = 1000 kg/m³
v₁ = velocity iof f water in the reservoir = 0 m/s
P₂ = Pressure outside the water reservoir = atmospheric pressure = 1 atm = 1 × 101325 = 101,325 Pa
v₂ = velocity outside the reservoir = ?
810,600 + 0 = 101,325 + 0.5×1000×v₂²
500v₂² = 810,600 - 101,325 = 709,275
v₂² = (709,275/500) = 1,418.55
v₂ = √(1418.55) = 37.66 m/s
b) Volumetric flowrate is given as
Q = Av
A = Cross sectional Area of the channel of flow = πr² = π×(0.001)² = 0.0000031416 m²
v = velocity = 37.66 m/s
Q = 0.0000031416 × 37.66 = 0.0001183123 m³/s = (1.183 × 10⁻⁴) m³/s
c) If the height of gun above the ground is 1.2 m. Where does the water hit the ground?
The range of trajectory motion is given as
R = vT
v = horizontal component of the velocity = 37.66 m/s
T = time of flight = ?
But time of flight is given as
T = √(2H/g) (Since the initial vertical component of the velocity = 0 m/s
H = 1.2 m
g = acceleration due to gravity = 9.8 m/s²
T = √(2×1.2/9.8) = 0.495 s
Range = vT = 37.66 × 0.495 = 18.64 m
Hope this Helps!!!
Simplify this equation x2-5x-36
Answer:
[tex]=\left(x+4\right)\left(x-9\right)[/tex]
Step-by-step explanation:
[tex]x^2-5x-36\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(x^2+4x\right)+\left(-9x-36\right)\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+4x\mathrm{:\quad }x\left(x+4\right)\\\mathrm{Factor\:out\:}-9\mathrm{\:from\:}-9x-36\mathrm{:\quad }-9\left(x+4\right)\\=x\left(x+4\right)-9\left(x+4\right)\\\mathrm{Factor\:out\:common\:term\:}x+4\\=\left(x+4\right)\left(x-9\right)[/tex]
Please answer this question for me thank you !! 20 Points !! Will give brainliest !!
Answer:
b
Step-by-step explanation:
In a parralel graph, the slopes would always be the same. The intercept in the answer is 2, showing that the coordinate points are (0,2)
Hope this helps!:)
Answer:
B) y = 2x + 2
Step-by-step explanation:
Firstly, you have to know that parallel lines have congruent slopes. That means that the slope of this line will be 2.
Next, make a point slope form of the equation:
y - y1 = m(x - x1)
y - 2 = 2(x - 0)
y - 2 = 2x - 0
Now, we can make it into slope intercept form.
y - 2 = 2x
y = 2x + 2
Hope this helps :)
Please help! Will give Brainliest!
Steps 1-4 in attachment (#4 below)
Step 4: Use the equation you wrote in Step 3. Write the equation for the graph of g(x) that has also been shifted right 1 unit.
Answer:
g(x) = 2|x|g(x) = -2|x|g(x) = -2|x| -3g(x) = -2|x-1| -3Step-by-step explanation:
1) Vertical stretch is accomplished by multiplying the function value by the stretch factor. When |x| is stretched by a factor of 2, the stretched function is ...
g(x) = 2|x|
__
2) Reflection over the x-axis means each y-value is replaced by its opposite. This is accomplished by multiplying the function value by -1.
g(x) = -2|x|
__
3) As you know from when you plot a point on a graph, shifting it down 3 units subtracts 3 from the y-value.
g(x) = -2|x| -3
__
4) A right-shift by k units means the argument of the function is replaced by x-k. We want a right shift of 1 unit, so ...
g(x) = -2|x -1| -3
Each limit represents the derivative of some function f at some number a. State such an f and a in each case.
lim √9 + h - 3 / h
h-->0
Answer:
a = 0f(h) = [tex]\frac{\sqrt{9+h} - 3}{h}[/tex]limit of the function is 1/6Step-by-step explanation:
The general form representing limit of a function is expressed as shown below;
[tex]\lim_{h \to a} f(h)[/tex] where a is the value that h will take and use in the function f(h). It can be expressed in words as limit of function f as h tends to a. Comparing the genaral form of the limit to the limit given in question [tex]\lim_{h \to 0} \frac{\sqrt{9+h} - 3}{h}[/tex], it can be seen that a = 0 and f(h) = [tex]\frac{\sqrt{9+h} - 3}{h}[/tex]
Taking the limit of the function
[tex]\lim_{h \to 0} \frac{\sqrt{9+h} -3}{h}\\= \frac{\sqrt{9+0}-3 }{0}\\= \frac{0}{0}(indeterminate)[/tex]
Applying l'hopital rule
[tex]\lim_{h \to 0} \frac{\frac{d}{dh} (\sqrt{9+h} - 3)} {\frac{d}{dh} (h)}\\= \lim_{h \to 0} \frac{1}{2} (9+h)^{-1/2} /1\\=\frac{1}{2} (9+0)^{-1/2}\\= \frac{1}{2} * \frac{1}{\sqrt{9} } \\= 1/2 * 1/3\\= 1/6[/tex]
I NEED HELP WITH THIS PLEASE HELP ME
Answer:
156 minutes
Step-by-step explanation:
So we need to create an equation to represent how Frank's phone company bills him
I will denote "y" as the total for his billI will denote "x" as the number of minutes Frank usesSo the phone company charges an $8 monthly fee, so this value remains constant and will be our "y-intercept"
They then charge $0.06 for every minute he talks, this will be our "slope"
Combining everything into an equation, we have: y = 0.06x + 8
Now since we were given Franks phone bill total and want to figure out how many minutes he used, we just need to solve the equation for x and plug in our known y value
y = 0.06x + 8 → y - 8 = 0.06x → [tex]x=\frac{y-8}{0.06}[/tex] Then plugging in our y value we get [tex]x=\frac{17.36-8}{0.06}=\frac{9.36}{0.06}= 156[/tex]Frank used up a total of 156 minutes
At a gas station, 50% of the customers use regular gas, 30% use mid-grade gas and 20% use premium gas. Of those customers using regular gas, only 30% fill their tanks. Of those customers using mid-grade gas, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. What is the probability that the next customer will request mid-grade gas and fill the tank
Answer:
The probability that the next customer will request mid-grade gas and fill the tank is 0.1800
Step-by-step explanation:
In order to calculate the probability that the next customer will request mid-grade gas and fill the tank we would have to make the following calculation:
probability that the next customer will request mid-grade gas and fill the tank= percentage of the people using mid-grade gas* percentage of the people using mid-grade gas that fill their tanks
probability that the next customer will request mid-grade gas and fill the tank= 30%*60%
probability that the next customer will request mid-grade gas and fill the tank= 0.1800
The probability that the next customer will request mid-grade gas and fill the tank is 0.1800
Results of 99% confidence intervals are consistent with results of two-sided tests with which significance level? Explain the connection. A 99% confidence interval is consistent with a two-sided test with significance level alphaequals nothing because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval ▼ contains does not contain the value in the null hypothesis.
Answer:
Yes, they are consistent.
A 99% confidence interval is consistent with a two-sided test with significance level alpha=0.01 because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval does contains the value in the null hypothesis.
Step-by-step explanation:
Yes, they are consistent.
A 99% confidence interval is consistent with a two-sided test with significance level alpha=0.01 because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval does contains the value in the null hypothesis.
The critical values of the confidence level are equivalent to the critical values in the hypothesis test. In the case that the conclusion of the test is to not reject the null hypothesis, the test statistic falls within the acceptance region: its value is within the critical values of the two-sided test.
Then, it is also within the critical values of the confidence interval and the sample mean (or other measure) will be within the confidence interval bounds.
Function c(x) = 5x
If your input was 2, what is your output?