An inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours. How long will it take both pipes to fill the pool?
Answer:
It will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.
Step-by-step explanation:
Given that an inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours, to determine how long it will take both pipes to fill the pool, the following calculation must be performed:
1/5 + 1/4 = X
0.20 + 0.25 = X
0.45 = X
9/20 = X
9 = 60
2 = X
120/9 = X
13,333 = X
Therefore, it will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.
40% of what number is 16.6?
Prove the following identities : i) tan a + cot a = cosec a sec a
Step-by-step explanation:
[tex]\tan \alpha + \cot\alpha = \dfrac{\sin \alpha}{\cos \alpha} +\dfrac{\cos \alpha}{\sin \alpha}[/tex]
[tex]=\dfrac{\sin^2\alpha + \cos^2\alpha}{\sin\alpha\cos\alpha}=\dfrac{1}{\sin\alpha\cos\alpha}[/tex]
[tex]=\left(\dfrac{1}{\sin\alpha}\right)\!\left(\dfrac{1}{\cos\alpha}\right)=\csc \alpha \sec\alpha[/tex]
Question :
tan alpha + cot Alpha = cosec alpha. sec alphaRequired solution :
Here we would be considering L.H.S. and solving.
Identities as we know that,
[tex] \red{\boxed{\sf{tan \: \alpha \: = \: \dfrac{sin \: \alpha }{cos \: \alpha} }}}[/tex][tex] \red{\boxed{\sf{cot \: \alpha \: = \: \dfrac{cos \: \alpha }{sin \: \alpha} }}}[/tex]By using the identities we gets,
[tex] : \: \implies \: \sf{ \dfrac{sin \: \alpha }{cos \: \alpha} \: + \: \dfrac{cos \: \alpha }{sin \: \alpha} }[/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin \: \alpha \times sin \: \alpha }{cos \: \alpha \times sin \: \alpha} \: + \: \dfrac{cos \: \alpha \times cos \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]
[tex] : \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \times sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \: sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \: cos \: \alpha } } [/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha \: + \: cos {}^{2} \alpha}{cos \: \alpha \: sin \alpha} } [/tex]
Now, here we would be using the identity of square relations.
[tex]\red{\boxed{ \sf{sin {}^{2} \alpha \: + \: cos {}^{2} \alpha \: = \: 1}}}[/tex]By using the identity we gets,
[tex] : \: \implies \: \sf{ \dfrac{1}{cos \: \alpha \: sin \alpha} }[/tex]
[tex]: \: \implies \: \sf{ \dfrac{1}{cos \: \alpha } \: + \: \dfrac{1}{sin\: \alpha} }[/tex]
[tex]: \: \implies \: \bf{sec \alpha \: cosec \: \alpha}[/tex]
Hence proved..!!Please help
4. The equation of a curve is y = (3 - 2x)^3 + 24x.
(a) Find an expression for dy/dx
5. The equation of a curve is y = 54x - (2x - 7)^3.
(a) Find dy/dx
(4) y = (3 - 2x)³ + 24x
Use the power and chain rules:
dy/dx = 3 (3 - 2x)² d/dx [3 - 2x] + 24
dy/dx = 3 (3 - 2x)² (-2) + 24
dy/dx = -24x ² + 72x - 30
(5) y = 54x - (2x - 7)³
Same basic procedure:
dy/dx = 54 - 3 (2x - 7)² d/dx [2x - 7]
dy/dx = 54 - 3 (2x - 7)² (2)
dy/dx = -24x ² + 168x - 240
What is the chance of getting 3 of the same cards in a row in a 52 cards deck?
Answer:
1/425
Step-by-step explanation:
The first card can be any card, so we don’t have to evaluate the probability.
Now we can suppose that the exit card is a two
- For the second card we have 3/51 of possibilities that is a 2 = 1/17
- For the third card we have 2/50 of possibilities that is a 2 = 1/25
1/17 * 1/25 = 1/425
Consider the following results for two independent random samples taken from two populations.
Sample 1 Sample 2
n1=50 n2=35
x¯1=13.6 x¯2=11.6
σ1=2.2 σ2=3.0
Required:
a. What is the point estimate of the difference between the two population means?
b. Provide a 90% confidence interval for the difference between the two population means.
c. Provide a 95% confidence interval for the difference between the two population means.
Answer:
a. 2
b. The 90% confidence interval for the difference between the two population means is (1.02, 2.98).
c. The 95% confidence interval for the difference between the two population means is (0.83, 3.17).
Step-by-step explanation:
Before solving this question, we need to understand the central limit theorem and the subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Sample 1:
[tex]\mu_1 = 13.6, s_1 = \frac{2.2}{\sqrt{50}} = 0.3111[/tex]
Sample 2:
[tex]\mu_2 = 11.6, s_2 = \frac{3}{\sqrt{35}} = 0.5071[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 13.6 - 11.6 = 2[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.3111^2+0.5071^2} = 0.595[/tex]
a. What is the point estimate of the difference between the two population means?
Sample difference, so [tex]\mu = 2[/tex]
b. Provide a 90% confidence interval for the difference between the two population means.
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 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
The margin of error is:
[tex]M = zs = 1.645(0.595) = 0.98[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2 - 0.98 = 1.02
The upper end of the interval is the sample mean added to M. So it is 2 + 0.98 = 2.98
The 90% confidence interval for the difference between the two population means is (1.02, 2.98).
c. Provide a 95% confidence interval for the difference between the two population means.
Following the same logic as b., we have that [tex]Z = 1.96[/tex]. So
[tex]M = zs = 1.96(0.595) = 1.17[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2 - 1.17 = 0.83
The upper end of the interval is the sample mean added to M. So it is 2 + 1.17 = 3.17
The 95% confidence interval for the difference between the two population means is (0.83, 3.17).
X+34>55
Solve the inequality and enter your solution as an inequality comparing the variable to a number
Answer:
x > 21
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
x + 34 > 55
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 34 on both sides: x > 21
What are the zeros of f(x) = (x - 2)(x + 7)? Select all that apply.
A. X= -7
B. X = -2
C. X = 2
D. X = 7
Answer:
2 = x -7 = x
Step-by-step explanation:
f(x) = (x - 2)(x + 7)
y = (x - 2)(x + 7)
Set y = 0
0 = (x - 2)(x + 7)
Using the zero product property
0 = x-2 0 = x+7
2 = x -7 = x
Answer:
Zeros happen when f(x) = 0. There are two zeros in the given function:
when (x - 2) = 0when (x + 7) = 0Therefore solve both equations above and you'll get:
Zero #1 = 2Zero #2 = -7Please look at the file below. (No links will give brainiest)
Answer:
3.564 m^2
Step-by-step explanation:
The area of the original garden is
A = 5.4 * 1.5 = 8.1
The new garden is
5.4*1.2 = 6.48 by 1.5*1.2 =1.8
The area is
A = 6.48*1.8=11.664
The increase in area is
11.664-8.1=3.564
The given information is,
To find the increase in area of the garden.
Formula we use,
→ Area = Length × Width
Area of the real garden is,
→ 5.4 × 1.5
→ 8.1 m
The new garden will be,
→ 5.4 × 1.2 = 6.48 m
→ 1.5 × 1.2 = 1.8 m
The area of the new garden is,
→ 6.48 × 1.8
→ 11.664
Then the increase in area of the garden,
→ 11.664 - 8.1
→ 3.564 m²
Hence, 3.564 m² is the increase in area.
I really need help big time thank you
BRAINLIESTT A spinner is divided into 8 equal-sized sections, and each section is labeled with a number 1 through 8.
if Kathryn spins the arrow on the spinner twice, what is the probability that the arrow will land on a section with an odd number the first time
and a number greater than 6 on the second spln?
Answer:
The probability would be 1/8.
Step-by-step explanation:
The probability of the spinner landing on an odd number is 1/2, and the probability of the spinner landing on a number greater than 8 is 1/4. So we multiply those two probabilites to get our answer 1/8.
Which of the following is the differnce of two squares
!!!!Please Answer Please!!!!
ASAP!!!!!!
!!!!!!!!!!!!!
Answer:
False
Step-by-step explanation:
well i think that the answer from my calculations
An isosceles right triangle has a hypotenuse that measures 4√2 cm. What is the area of the triangle?
PLEASE HELP
Answer:
8
Step-by-step explanation:
As it's an isosceles right triangle, it's sides are equal, say x. x^2+x^2=(4*sqrt(2))^2. x=4, Area is (4*4)/2=8
PLEASE HELP AND BE RIGHT BEFORE ANSWERING
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Since point P is the center of dilation, it doesn't move. (It is "invariant.") The other points on the figure move to 1/4 of their original distance from P. On this diagram, it is convenient that the distances are all multiples of 4 units, so dividing by 4 is made easy.
Simplificar expresiones algebraicas
I need help with this
Answer:
below
Step-by-step explanation:
A AND C is the right option
congruent angles are angles with exactly the same measure
(4-1) + (6 + 5) = help plz
help please! i'm in class and i have 10 mins left. :)
Answer:
3:8
Step-by-step explanation:
i will gadit
that only
PLEASE HELPPPPP ASAPPPPPPPPPPPPP PLEASEEEE
Answer:
0.5679
Step-by-step explanation:
From. The table Given above :
The probability of female Given an advanced degree ;
P(F|A) = p(FnA) / p(A)
From the table, p(FnA) = 322
P(Advanced degree), P(A) = (245 + 322) = 567
Hence,
P(F|A) = p(FnA) / p(A) = 322 / 567 = 0.5679
A recipe calls for 2 1/2 tablespoons of oil and 3/4 tablespoons of vinegar. What is the ratio of oil to vinegar in this recipe?
Answer:
10:3
Step-by-step explanation:
Make 2 1/2 an improper fraction, you will get 5/2. You dont have to do anything to the 3/4.
For you to find the ratio of an fraction, you have to take the numerator but the denominator has to be the same.
So make 5/2 to a 10/4.
Take the numerator 10 & 3.
Your answer will be 10:3
No problem.
which choice are equivalent to the expression below? Check all that apply
I could not get the expressions to type correctly because I am new so I am sending a picture. I am having trouble working backwards to figure out which once to choose.
Answer:
A, B, and E apply
Step-by-step explanation:
One thing we can do is to make everything in the same format, under one square root, with no non-square roots.
First, we can say that 6 is equal to √36 as 6² =36, and 6 ≥ 0. Therefore, 6√3 = √36 * √3 = √108
For A, √3 * √36 = √108, so this applies
For B, √18 * √6 = √108, so this applies
For C, 108² = √something bigger than 108 = √11664, so this does not apply
For D, √54 ≠ √108, so this does not apply
For E, √108 = √108, so this applies
For F, √3 * √6 = √18, so this does not apply
A cylindrical piece of iron pipe is shown below. The wall of the pipe is 1.25 inches thick: The figure shows a cylinder of height 14 inches and diameter 8 inches What is the approximate inside volume of the pipe?
332 cubic inches
69 cubic inches
703 cubic inches
99 cubic inches
Answer: 332 cubic inches
Step-by-step explanation:
You can eliminate 69 and 99 as those answers don't make any sense. This leaves you with 703 and 332.
It says the wall of the pipe is 1.25 inches thick so you multiply that by 2 and subtract it by the diameter to get the insider diameter of 5.5
Now you just use the equation V = (3.14)(r^2)(14) where the radius is half of 5.5.
So to finalize the equation you get V = (3.14)(5.5)^2(14) which comes out to 332 cubic inches
The best choice is 332 cubic inches.
69 cubic inches and 99 cubic inches are less and 703 cubic inches is a large approximation.
Diameter = d= 8 inches
Height= Length = l= 14 inches
Thickness= 1.25 inches
Outer Radius= R= diameter/2= 8/2=4 inches
Inner radius = r= Radius - thickness
= 4- 1.25= 2.75 inches
Volume of the cylinder = Area × length
= π r²× l
= 22/7 × (2.75)² × 14
= 332. 616 inches cube
So the best answer is 332 cubic inches
https://brainly.com/question/21067083
If a + b = s and a - b = t, then which of the following expresses the value of ab in terms of s and t?
Please help me out
Answer:
=(s^2 - t^2)/4
Step-by-step explanation:
a + b = s and a - b = t,
Add the two equations together
a + b = s
a - b = t
----------------
2a = s+t
a = (s+t)/2
Subtract the two equations
a + b = s
- a + b = -t
-------------------
2b =(s-t)
b = (s-t)/2
We want to find ab
ab = (s+t)/2 * (s-t)/2
FOIL
=(s^2 - t^2)/4
Help! Given that tanθ=-1, what is the value of secθ, for 3π/2<θ<2π?
Answer: Choice B) [tex]\sqrt{2}[/tex]
Work Shown:
[tex]\sec^2(\theta) = \tan^2(\theta) + 1\\\\\sec^2(\theta) = (\tan(\theta))^2 + 1\\\\\sec^2(\theta) = (-1)^2 + 1\\\\\sec^2(\theta) = 2\\\\\sec(\theta) = \sqrt{2}\\\\[/tex]
Note: secant is positive in quadrant Q4, when theta is between 3pi/2 radians and 2pi radians (270 degrees and 360 degrees). So that's why we don't consider the minus form of the plus minus.
Pleaseee Help. What is the value of x in this simplified expression?
(-1) =
(-j)*
1
X
What is the value of y in this simplified expression?
1 1
ky
y =
-10
K+m
+
.10
m т
9514 1404 393
Answer:
x = 7
y = 5
Step-by-step explanation:
The applicable rule of exponents is ...
a^-b = 1/a^b
__
For a=-j and b=7,
(-j)^-7 = 1/(-j)^7 ⇒ x = 7
For a=k and b=-5,
k^-5 = 1/k^5 ⇒ y = 5
Bob's truck averages 23 miles per gallon. If Bob is driving to his mother's house, 72 miles away, how many gallons of gas are needed? Round to the nearest tenth.
Answer:
3.1 gallons
Step-by-step explanation:
To solve this, we need to figure out how many gallons of gas go into 72 miles. We know 23 miles is equal to one gallon of gas, and given that the ratio of miles to gas stays the same, we can say that
miles of gas / gallons = miles of gas / gallons
23 miles / 1 gallon = 72 miles / gallons needed to go to Bob's mother's house
If we write the gallons needed to go to Bob's mother's house as g, we can say
23 miles / 1 gallon = 72 miles/g
multiply both sides by 1 gallon to remove a denominator
23 miles = 72 miles * 1 gallon /g
multiply both sides by g to remove the other denominator
23 miles * g = 72 miles * 1 gallon
divide both sides by 23 miles to isolate the g
g = 72 miles * 1 gallon/23 miles
= 72 / 23 gallons
≈ 3.1 gallons
What is the complete factorization of the polynomial below?
x3 + 8x2 + 17x + 10
A. (x + 1)(x + 2)(x + 5)
B. (x + 1)(x-2)(x-5)
C. (x-1)(x+2)(x-5)
O D. (x-1)(x-2)(x + 5)
Answer: A (x+1)(x+2)(x+5)
Step-by-step explanation:
Which of the following exponential equations is equivalent to the logarithmic
equation below?
log 970 = x
A.x^10-970
B. 10^x- 970
C. 970^x- 10
D. 970^10- X
Given:
The logarithmic equation is:
[tex]\log 970=x[/tex]
To find:
The exponential equations that is equivalent to the given logarithmic equation.
Solution:
Property of logarithm:
If [tex]\log_b a=x[/tex], then [tex]a=b^x[/tex]
We know that the base log is always 10 if it is not mentioned.
If [tex]\log a=x[/tex], then [tex]a=10^x[/tex]
We have,
[tex]\log 970=x[/tex]
Here, base is 10 and the value of a is 970. By using the properties of exponents, we get
[tex]970=10^x[/tex]
Interchange the sides, we get
[tex]10^x=970[/tex]
Therefore, the correct option is B, i.e., [tex]10^x=970[/tex].
Note: It should be "=" instead of "-" in option B.
Describe the transformation of f(x) to g(x). Pleaseee helllp thank youuuu!!!
The transformation set of [tex]y[/tex] values for function [tex]f[/tex] is [tex][-1,1][/tex] this is an interval to which sine function maps.
You can observe that the interval to which [tex]g[/tex] function maps equals to [tex][-2,0][/tex].
So let us take a look at the possible options.
Option A states that shifting [tex]f[/tex] up by [tex]\pi/2[/tex] would result in [tex]g[/tex] having an interval [tex][-1,1]+\frac{\pi}{2}\approx[0.57,2.57][/tex] which is clearly not true that means A is false.
Let's try option B. Shifting [tex]f[/tex] down by [tex]1[/tex] to get [tex]g[/tex] would mean that has a transformation interval of [tex][-1,1]-1=[-2,0][/tex]. This seems to fit our observation and it is correct.
So the answer would be B. If we shift [tex]f[/tex] down by one we get [tex]g[/tex], which means that [tex]f(x)=\sin(x)[/tex] and [tex]g(x)=f(x)-1=\sin(x)-1[/tex].
Hope this helps :)
