Answer:
Your answer should be B.
One's intelligence quotient, or IQ, varies directly as a person's mental age and inversely as that person's chronological age.
A person with a mental age of 22 and a chronological age of 25 has an IQ of 132. What is the chronological age of a person
with a mental age of 20 and an IQ of 100?
The chronological age is
Answer:
The chronological age is 30 years
Step-by-step explanation:
Q= (kM)/C
132= (22k)/ 25
3300= 22k
k= 150
Q= (150M)/C
100= (150 x 20)/C
100= 3000/C
100C= 3000
C= 30
brainliest pls
Find the coefficient of the term containing y^8 in the expansion of [(x/2)-4y]^9
The coefficient of the term containing y^8 in the expansion of [(x/2)-4y]^9 is -126.
To find the coefficient of the term containing y^8, we can use the Binomial Theorem. According to the Binomial Theorem, the expansion of (a + b)^n can be written as:
(a + b)^n = C(n,0) * a^n * b^0 + C(n,1) * a^(n-1) * b^1 + C(n,2) * a^(n-2) * b^2 + ... + C(n,k) * a^(n-k) * b^k + ... + C(n,n) * a^0 * b^n
where C(n,k) is the binomial coefficient given by C(n,k) = n! / (k! * (n-k)!).
In our case, a = x/2 and b = -4y. Plugging these values into the formula, we have:
[(x/2)-4y]^9 = C(9,0) * (x/2)^9 * (-4y)^0 + C(9,1) * (x/2)^8 * (-4y)^1 + C(9,2) * (x/2)^7 * (-4y)^2 + ... + C(9,8) * (x/2)^(9-8) * (-4y)^8 + C(9,9) * (x/2)^0 * (-4y)^9
The term containing y^8 is C(9,8) * (x/2)^(9-8) * (-4y)^8 = C(9,8) * (x/2) * (-4y)^8.
The binomial coefficient C(9,8) is equal to 9, and the term (x/2) * (-4y)^8 simplifies to (-4)^8 * (x/2) * y^8 = 65536 * (x/2) * y^8.
Therefore, the coefficient of the term containing y^8 is 65536 * (x/2) = 32768x.
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Pls answer quickly, make sure to answer all parts
Find the area of the region bounded by the line y =3x -6 and line y=-2x+8 and
a) the x-axis. b) the y-axis. c) the line y=6. d) the line x=5.
The area of the region between line y =3x -6 and line y=-2x+8 and
the x-axis with the help of integration will be 2.88 sq units.
What exactly is integration?
The process of computing an integral is known as integration. Mathematicians utilise integrals to compute a variety of useful quantities such as areas, volumes, displacement, and so on. When we talk about integrals, we usually imply definite integrals. Antiderivatives are represented by indefinite integrals. Integration, along with differentiation, is one of the two major calculus concepts in mathematics (which measure the rate of change of any function with respect to its variables).
Integral Fundamental
A definite integral is one that has both upper and lower bounds. For X to lie, only a true line may be utilised. The Definite Integral is also known as a Riemann Integral.
From a to b, use ∫f(x)dx
indefinite integral
Integrals are defined without upper and lower limits. It looks like this:
A indefinite Integral is written as:
∫f(x)dx = F(x) + C
Where C might be any constant and the function f(x) is referred to as the integrand.
Now,
As given in image
Area of the region will be =∫3x-6 dx from x=2 to 2.8 +∫-2x+8 from x=2.8 to 4.
=(3x²/2-6x) from x=2 to 2.8 + (-2x²/2+8x) from x=2.8 to 4.
=3*0.8*0.8/2-6*0.8-2*1.2*1.2+8*1.2
=2.88 sq units.
Hence,
The area of the region between line y =3x -6 and line y=-2x+8 and the x-axis with the help of integration will be 2.88 sq units.
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what is the volume of the solid
Answer:
204 cubic feet
Step-by-step explanation:
The formula for the volume of a rectangular prism is simply to multiply together the length, width, and height. In this case, 6*17*2=204 cubic feet. Hope this helps!
Answer:
do 16x17 divided by 2
Step-by-step explanation:
:)
(3^5)^2/3^-2 simplified
Answer:
-20
Step-by-step explanation:
convert 2 Bigha into kattha
Answer:
To convert 2 Bigha into Kattha:
If 1 Bigha = 20 Kattha:
2 Bigha = 2 * 20 Kattha = 40 Kattha
If 1 Bigha = 16 Kattha:
2 Bigha = 2 * 16 Kattha = 32 Kattha
what is the lowest common denominator for 31/40 and 5/6?
answer : 31/40 = 93/120
5/6 = 100/120
Construct both a 98% and a 80% confidence interval for B₁. B₁=46, s=5.7, SSzz = 57, n = 12 98%:
To construct a 98% confidence interval for B₁, we can use the t-distribution since the sample size is small (n = 12).
Given the sample mean (B₁ = 46), sample standard deviation (s = 5.7), and sum of squares (SSzz = 57), we can calculate the confidence interval.
The formula for a confidence interval is:
Confidence Interval = Sample Mean ± (Critical Value * Standard Error)
For a 98% confidence level and n = 12, the critical value is approximately 2.681 (obtained from a t-distribution table).
The standard error is calculated as the sample standard deviation divided by the square root of the sample size (s / √n).
Plugging in the values:
Standard Error = 5.7 / √12 ≈ 1.647
Confidence Interval = 46 ± (2.681 * 1.647)
Therefore, the 98% confidence interval for B₁ is approximately (42.21, 49.79).
In conclusion, we can be 98% confident that the true value of B₁ falls within the range of 42.21 to 49.79 based on the given sample data.
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Find three rational numbers between -3 and -2.
Answer:
-2.2
-2.5
-2.8
cuz uhhhhhhhhhhhhhhh
Answer:
2.1
2.3
2.7
Step-by-step explanation:
Yes
What is Open Source GIS? How will this change spatial computing?
Open Source GIS stands for Open Source Geographic Information System. It refers to a type of software that allows users to create, manage, analyze, and visualize spatial data. Open source means that the source code of the software is freely available and can be modified and distributed by anyone.
The use of Open Source GIS has the potential to significantly change spatial computing in several ways:
1. Collaboration: Open Source GIS encourages collaboration among users. Since the source code is freely available, users can contribute to the development of the software by fixing bugs, adding new features, or improving existing ones. This collaborative approach leads to the rapid evolution and enhancement of the software.
2. Cost-effectiveness: Open Source GIS eliminates the need for expensive proprietary software licenses. Users can freely download and use the software without any financial burden. This makes it more accessible to individuals and organizations with limited resources.
3. Customizability: Open Source GIS allows users to customize the software according to their specific needs. They can modify the source code and add new functionalities or customize existing ones. This flexibility enables users to tailor the software to their unique requirements.
4. Community support: Open Source GIS has a large and active user community. This community provides support through forums, mailing lists, and online resources. Users can seek help, share ideas, and collaborate with others who have similar interests or challenges. The community support helps users overcome difficulties and enhances the overall user experience.
5. Innovation: Open Source GIS encourages innovation in spatial computing. The open nature of the software fosters experimentation and the development of new ideas and approaches. Users can contribute their innovations to the community, which benefits the wider user base.
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Find the value of X!!!
Answer:
3x7=21
11+17= 28
Step-by-step explanation:
The estimated standard error of the mean is to be used whenever you must estimate the __________ of the population.
The sign below shows how much a cafe
charges for each size of coffee that it sells.
a) Which size is the best value for money?
b) The ingredients cost the cafe 13p per
100 ml of coffee. Based on this cost, what
percentage of the price of a small coffee is
profit?
Give your answer to 3 s.f.
c) Despite the large coffee being twice the
size of the small coffee, the difference in
price is only 60p. Why do you think this
might be the case?
Write a sentence to explain your answer.
Volume
Price
Small
250 ml
£2.40
Medium
330 ml
£2.70
Large
500 ml
£3.00
a. The medium coffee is the best value for money.
b. The percentage profit is 40%
c The cafe is likely doing this because they know that many people will choose the small coffee because it is the cheapest option.
How to calculate the valuea) The cost per 100 ml of coffee is:
2.40 / 250 = 0.96p
The cost per 100 ml of coffee for the medium and large sizes is:
2.70 / 330 = 0.82p
3.00 / 500 = 0.60p
Therefore, the medium coffee is the best value for money.
b) The profit on a small coffee is:
2.40 - (0.96 x 250) = 0.96p
The percentage profit is:
(0.96 / 2.40) x 100 = 40%
c) The large coffee is twice the size of the small coffee, but the difference in price is only 60p. This is because the cafe is making a larger profit on the small coffee. The cafe is likely doing this because they know that many people will choose the small coffee because it is the cheapest option.
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PLZ HELP ME MARK AS BRAINLY HOWEVER ANSWERS FIRST!!!!
Answer:
115
Step-by-step explanation:
When multiplying a fraction by a fraction, you multiply the numerator by the numerator and same with the denominator. 13 times 4 =52, 7 times 9=63, 52+63=115. Hope this helps!
will give brainliest to quickest answer
Answer:
The vertex is option C: (-6, -2)
Step-by-step explanation:
The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)
Pls mark brainliest.
It is sufficient to test an analogy by asking what are its relevant similarities.
True or False
The statement that It is sufficient to test an analogy by asking what are its relevant similarities is false.
Analogy refers to the process of comparison of two or more items such that it explains some idea, or classification or familiarity and representativeness. Studying the analogies helps in enhancing, strengthening and reinforcing the skills in areas such as reading comprehension, homophones, deductive reasoning and logic.
Testing an analogy only by relevant similarities will produce partial results which might not be suitable to fully explain the reason. Hence, both relevant similarities and differences are to be considered for more detailed review. Different kind of analogies used to explain the differences or similarities are synonym and antonym, symbol and reference, degree of differences.
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Determine the force exerted by the jet on the wall when the angle between the jet and the house is 90
The equation P 5 0.00267sF gives the power P (in horsepower) needed to keep a certain bicycle moving at speed s (in miles per hour), where F is the force (in pounds) of road and air resistance. On level ground, the equation F 5 0.0116s 2 1 0.789 models the force F. Write a model (in terms of s only) for the power needed to keep the bicycle moving at speed s on level ground. How much power is needed to keep the bicycle moving at 10 miles per hour?
The pull of gravity is different on Earth than on the Moon. An object that weighs 25 pounds on Earth weighs about 4 pounds on the Moon. An astronaut, wearing all the necessary gear, weighs 500 pounds on Earth.
How many pounds would the astronaut with gear weigh on the Moon?
pounds
The weight of the astronaut with gear on the moon is 80 pounds.
The pull of gravity is different on Earth than on the Moon as gravity depends on factors such as the mass of the celestial body, the radius of the celestial body, and the density of the celestial body.
The pull of gravity on Earth = 10 m/s²
Thus, Given:
Weight of object on Earth: 25 pounds
Weight is described as the product of mass and the acceleration due to gravity
Thus, 25 = 10 * mass
mass = 2.5 unit
Weight of the object on the Moon: 4 pounds
4 = 2.5 * acceleration due to gravity on the moon
Acceleration due to gravity on the moon = 1.6 m/s²
Weight of astronaut with gear on earth = 500 pounds
500 = mass * 10
mass = 50 units
Weight of astronaut with gear on earth = 50 * 1.6
= 80 pounds
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What is the solution to -(4x-3) = -7(9+x) ???
Answer:
The solution is -22
Step-by-step explanation:
The solution of an equation is the value of the variable of the equation
∵ -(4x - 3) = -7(9 + x)
→ Simplify each side
∵ -(4x) - -(3) = -7(9) + -7(x)
∴ (-4x) - (-3) = -63 + (-7x)
→ Remember (-)(-) = (+) and (-)(+) = (-)
∴ -4x + 3 = -63 - 7x
→ Add 7x to both sides
∴ -4x + 7x + 3 = -63 - 7x + 7x
∴ 3x + 3 = -63
→ Subtract 3 from both sides
∵ 3x + 3 - 3 = -63 - 3
∴ 3x = -66
→ Divide both sides by 3
∴ x = -22
∴ The solution is -22
What is the value of m? m = 68 m = 78 m = 102 m = 112
The value of m in the image below which shows two parallel lines that are crossed by a transversal is: m = 102.
What are the Angles Formed When Two Parallel Lines are Crossed by a Transversal?Examining the image attached below, we have a transversal, line d, which crossed the two parallel lines, lines e and f, to form same-side interior angles, 78° and m°.
These two angles are said to be supplementary to each other based on the same-side interior angles theorem.
Therefore:
78 + m = 180
Subtract 78 from both sides:
78 + m - 78 = 180 - 78
m = 102°
Therefore, the value of m is: m = 102.
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Answer:
c. 102
Step-by-step explanation:
got it right on the review
180-78=102
Listen
The test scores of 10 students are listed below. Find the value of the first quartile.
67 67 69 70 70 74 75 78 79 79 80
A)69
B)69.5
C)68
D)70
Answer:
69
Step-by-step explanation:
67 67 69 70 70 74 75 78 79 79 80
______________
67 67 69 70 70 -> First Quartile
74 - Middle Quartile
75 78 79 79 80 -> Third Quartile
First Quartile -> 67 67 69 70 70
69 is middle
Answer = 69
For ax² + bx + c = 0 , the sum of the roots is -b/a and the product of the roots is c/a . Find a quadratic equation for each pair of roots. Assume a=1 .
2+5 i and 2-5 i .
The quadratic equation with roots 2 + 5i and 2 - 5i is: x² - 4x - 21 = 0.The quadratic equation with roots 3 + 4i and 3 - 4i is:x² - 6x - 7 = 0
The sum of the roots of the quadratic equation ax² + bx + c = 0 is -b/a and the product of the roots is c/a.
If a = 1, then the sum of the roots is -b and the product of the roots is c.
Given that the roots are 2 + 5i and 2 - 5i, the sum of the roots is 2 + 5i + 2 - 5i = 4.
The product of the roots is (2 + 5i)(2 - 5i) = 4 - 25 = -21.
Therefore, the quadratic equation with roots 2 + 5i and 2 - 5i is: x² - 4x - 21 = 0
Let the roots be 3 + 4i and 3 - 4i.
The sum of the roots is 3 + 4i + 3 - 4i = 6.
The product of the roots is (3 + 4i)(3 - 4i) = 9 - 16 = -7.
Therefore, the quadratic equation with roots 3 + 4i and 3 - 4i is:x² - 6x - 7 = 0
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HELP PLEASE!!!
Assume a class has 25 students.
a) If 80% of the class passed the test, how many students passed?
students
b) If 7 students got A’s on the test, what percent of students got A’s?
%
Answer:
A) 20
B) 28%
Step-by-step explanation:
A) In order to find percentages you need to make them in to decimals. 80% as a decimal is .8, if you multiply 25 by the decimal .8, you get 20.
B) To find the percentage all you do is divide, 7/25, this gives you the decimal .28, this as a percentage is 28%.
help please and thankyou 5
The angles x of the right angle triangle is 36.87 degrees.
How to find the angles of a right triangle?A right angle triangle is a triangle that has one angle as 90 degrees. The angles of a right angle triangle can be found using trigonometric ratios.
Therefore, let's find the angle M(x)
sin x = opposite / hypotenuse
where
opposite side = 6hypotenuse side = 10Therefore,
sin x = 6 / 10
sin x = 0.6
x = sin⁻¹ 0.6
x = 36.8698976458
x = 36.87 degrees.
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Simplify and then evaluate the equation
when a= 2 and b = 4.
b2 + 3(b – 62) – 2a= [?]
Answer:
-170
Step-by-step explanation:
First, you would substitute 2 and 4 for a and b. 4 times 2 + 3(4 - 62) - 2 times 2 = ?
Then, do 4 times 2 (8), 3(4-62)=3(-58)
8 + -174 - 4 = -170
If m<1 = 88 , find the m<3.
Answer:
use symbolab
Step-by-step explanation:
1. The temperature outside is -5°F.
Name the temperature that would make
the sum of the two temperatures 0°F.
I
Your anstver
Question 2
Answer:
1
Step-by-step explanation:
Question attached..
Answer:
I think the answer is 20
Step-by-step explanation:
to solve you take the number on the right, subtract it by one, then multiple the new number by the old one.
1-1=0x1=0
3-1=2x3=6
4-1=3x4=12
2-1=1x2=2
5-1=4x5=20
We will see that the pattern is defined by the function:
f(x) = (x - 1)*x
Such that:
f(5) = 20.
How to find the pattern?
Here we have the relations:
1 = 0
3 = 6
4 = 12
2 = 2
5 = ?
We can think this as a function, actually:
f(1) = 0
f(3) = 6
f(4) = 12
f(2) = 2
f(5) = ?
Now, one pattern that can be seen is that:
f(1) = (1 - 1)*1 = 0
f(2) = (2 - 1)*2 = 2
f(3) = (3 - 1)*3 = 6
And so on, so the function is actually:
f(x) = (x - 1)*x
Evaluating it in 5, we will see that:
f(5) = (5 - 1)*5 = 20
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3
Graph the line with slope
passing through the point (-1,-5).
4
Step-by-step explanation:
you use the graph's lines to count