Find a function y(x) such that 2yy' = x and y(2) = 7. y =
Answers
The function y(x) that satisfies the given differential equation and initial condition is:
\(y(x) = e^((1/2)x^2 + ln|7| - 2) or y(x) = -e^((1/2)x^2 + ln|7| - 2).\)
To find the function y(x) that satisfies the given differential equation 2yy' = x with the initial condition y(2) = 7, we can solve the differential equation using separation of variables.
Step 1: Separate the variables:
Divide both sides of the equation by 2y to isolate y' on one side and x on the other side:
y' = x / (2y)
Step 2: Integrate both sides:
Integrate both sides of the equation with respect to x:
∫(1/y) dy = ∫(x/2) dx
Step 3: Evaluate the integrals:
The integral on the left side can be evaluated as ln|y|, and the integral on the right side can be evaluated as (1/2)x² + C, where C is the constant of integration.
Step 4: Apply the initial condition:
Substitute the initial condition y(2) = 7 into the equation to find the value of the constant C:
ln|7| = (1/2)(2)² + C
ln|7| = 2 + C
Step 5: Solve for C:
Subtract 2 from both sides of the equation:
C = ln|7| - 2
Step 6: Write the final solution:
Substitute the value of C into the equation to obtain the final solution:
ln|y| = (1/2)x² + ln|7| - 2
Step 7: Exponentiate both sides:
Take the exponential function of both sides of the equation:
\(|y| = e^((1/2)x² + ln|7| - 2)\)
Step 8: Remove the absolute value:
Since the right side of the equation can be positive or negative, we can remove the absolute value by considering two cases:
\(For y > 0: y = e^((1/2)x^2 + ln|7| - 2)\\For y < 0: y = -e^((1/2)x^2 + ln|7| - 2)\)
Therefore, the function y(x) that satisfies the given differential equation and initial condition is:
\(y(x) = e^((1/2)x^2 + ln|7| - 2) or y(x) = -e^((1/2)x^2 + ln|7| - 2).\)
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Related Questions
An office building casts a shadow 107 ft long and at the same time a 7.0 ft post casts a shadow 6.0 ft long. What is the height of the building?
Answers
The height of the office building casting a shadow of 107ft is approximately 124.83 ft.
What is the height of the building?A ratio is simply the relation between two amounts showing how many times a value is contained within another value.
Given the data in the question;
Shadow of building = 107 ftHeight of post = 7.0 ftShadow of post = 6 ftHeight of building = xRatio of height of office building and its height = x / 107
Ratio of height of post and its height = 7 / 6
Equate the two to get the height of the office building.
x / 107 = 7 / 6
Solve for x
x × 6 = 7 × 107
6x = 749
x = 746 / 6
x = 124.83 ft
Therefore, the height of the building is 124.83 ft.
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Which number line shows the solution to the inequality
4x + 529?
Answers
Answer:
like the other person said! Where are the number lines?
Step-by-step explanation:
Find the square roots of these numbers by division method.
a-6090
Answers
1:the area of a rectangular floor is 32m².if it's breadth is half of its length find its perimeter
2:the perimeter of a square is 12cm
find its length find its area
3:the perimeter of a squared field is 60m. find its area
4: the perimeter of a rectangle is 28 cm and it's length is 8cm.
find its breadth find its area
Answers
Answer:
Step-by-step explanation:
1) length = x m
breadth = x/2 m
Area of rectangular floor = 32 square m
\(length * breadth = 32\\\\x*\dfrac{1}{2}x = 32\\\\\\x^{2}=32*2\\\\\\x^{2} = 64\\\\x=\sqrt{64}=\sqrt{8*8}\\\\x = 8 \ m\)
Length = 8 m
Breadth =8/2 = 4 m
Perimeter = 2*(length + breadth) = 2*(8 + 4)
= 2*12
= 24 m
2) Perimeter of square = 12 cm
Side of a square = perimeter ÷ 4 = 12 ÷ 4 = 3 cm
Area =side *side = 3*3 = 9 cm²
3) Perimeter of square field = 60 m
Side = Perimeter ÷ 4 = 60 ÷4 = 15 m
Area of square = 15 * 15 = 225 m²
4) Perimeter of rectangle = 28 cm
breadth = (Perimeter ÷ 2) - length
= (28 ÷2) - 8
= 14 - 8
Breadth = 6 cm
Area of rectangle = 8 * 6 = 48 cm
\(\bold{\huge{\pink{\underline{ Solutions }}}}\)
Answer 1 :-We have,
The area of rectangular floor is 32 m²Breath is half of its length Therefore,Let the length of the rectangular field be x
So,
Breath of the rectangular field will be x/2
We know that,
\(\bold{\red{Area \: of \: rectangle = length}}{\bold{\red{\times{ Breath}}}}\)
Subsitute the required values,
\(\sf{32 = x }{\sf{\times{\dfrac{x}{2}}}}\)
\(\sf{32 = }{\sf{\dfrac{x^{2}}{2}}}\)
\(\sf{ 32}\sf{\times{ 2 = x^{2}}}\)
\(\sf{ 64 = x^{2}}\)
\(\bold{ x = 8 m}\)
Thus, The length of rectanglular field is 8m
Therefore,
Breath of the rectangular field will be
\(\sf{=}{\sf{\dfrac{8}{2}}}\)
\(\bold{ = 4 m }\)
Now,We have to find the perimeter of the given rectangular field
We know that,
Perimeter of the reactangle
\(\bold{\blue{ = 2( L + W) }}\)
Subsitute the required values in the above formula :-
Perimeter of the rectangular field
\(\sf{ = 2( 8 + 4) }\)
\(\sf{ = 2}{\sf{\times{12}}}\)
\(\bold{ = 24 m}\)
Hence, The perimeter of the rectangular field is 24 m
Answer 2 :-We have
The perimeter of square is 12 cmLet the side of the square be x
We know that,
\(\bold{\pink{ Perimeter\: of\: square = 4 }}{\bold{\pink{\times{ side}}}}\)
Subsitute the required values in the above formula :-
\(\sf{12 = 4 }{\sf{\times{ x }}}\)
\(\sf{\dfrac{ 12}{4}}{\sf{ = x }}\)
\(\bold{ x = 3 cm}\)
Thus, The length of the square is 3 cm
Now,We have to find the area of square
We know that,
\(\bold{\red{Area \: of \: square = Side }}{\bold{\red{\times{ Side}}}}\)
Subsitute the required values,
Area of square
\(\sf{ = 3 }{\sf{\times{ 3 }}}\)
\(\sf{ = 9 cm^{2}}\)
Hence , The length and area of square is 3cm and 9 cm²
Answer 3 :-We have
The perimeter of square feild is 60 mLet the side of the square feild be x
We know that,
\(\bold{\pink{ Perimeter\: of\: square = 4 }}{\bold{\pink{\times{ side}}}}\)
Subsitute the required values,
\(\sf{60 = 4 }{\sf{\times{ x }}}\)
\(\sf{\dfrac{ 60}{4}}{\sf{ = x }}\)
\(\bold{ x = 15 m }\)
Thus, The side of the square feild is 15m
Now,We have to find the area of square
We know that,
\(\bold{\red{Area \: of \: square = Side }}{\bold{\red{\times{ Side}}}}\)
Subsitute the required values,
Area of square
\(\sf{ = 15 }{\sf{\times{ 15 }}}\)
\(\sf{ = 225 cm^{2}}\)
Hence, The area of square feild is 225 cm²
Answer 4 :-We have,
The perimeter of rectangle is 28 cmThe length of rectangle is 8 cmLet the breath of the rectangle be x
We know that,
\(\bold{\blue{Perimeter\:of\: rectangle= 2( L + W) }}\)
Subsitute the required values,
\(\sf{ 28 = 2( 8 + x) }\)
\(\sf{ 28 = 16 + 2x }\)
\(\sf{ 28 - 16 = 2x }\)
\(\sf{ 12 = 2x }\)
\(\sf{\dfrac{ 12}{2}}{\sf{ = x }}\)
\(\bold{ x = 6 cm}\)
Thus, The breath of the rectangle is 6 cm
Now,We have to find the area of rectangle
We know that,
\(\bold{\red{Area \: of \: rectangle = length}}{\bold{\red{\times{ Breath}}}}\)
Subsitute the required values,
Area of rectangle
\(\sf{= 8 }{\sf{\times{6}}}\)
\(\sf{ = 48 cm^{2}}\)
Hence, The breath and area of rectangle is 6cm and 48 cm² .
[ Note :- Kindly refer app for better understanding ]
What does it mean for a manufacturer’s warranty and an extended warranty to overlap?
a.
Both warranties cover the product against the same problems.
b.
Both warranties cover the product over the same period of time.
c.
Both warranties will pay separately in the event that the product breaks.
d.
Both warranties come from the same source.
Please select the best answer from the choices provided
Answers
Answer:
a What does it mean for a manufacturer’s warranty and an extended warranty to overlap? both warranties cover the same period.
Step-by-step explanation:
Find the measures of DX and DY
DX and DY:
Answers
The angle measures of X and Y are given as follows:
<X = <Y = 75º.
How to obtain the angle measures of X and Y?The sum of the interior angle measures of a polygon with n sides is given by the equation presented as follows:
S(n) = 180 x (n - 2).
The polygon for this problem has four sides, hence the sum of the measures is of:
S(4) = 180 x (4 - 2)
S(4) = 360º.
Adding the four measures, and considering the X and Y have equal measure, the measures are given as follows:
<X + <Y + 90º + 120º = 360º
<X + <X + 210º = 360º
2<X = 150º
<X = 150/2
<X = 75º.
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Question 4: 10 pts
Find whether the regular triangular pyramid has plane symmetry, symmetry about an axis, or neither.
Answers
Answer:2
Step-by-step explanation: but it was real
Answer:
Step-by-step explanation:
1) 2 + x = 22 3) -6 + p = -18 5) -29 = -20 + n 7) -5 + r = -23 9) 11 = x + 13 11) 101 = n +55 2) -15 = -18 + n 4) -18 + v = -9 6) -19 = n - 13 8) -12 = k +5 10) 11 = -1 + x 12) x - 36 = -68
Answers
Answer:
1)x=20
3)p=−12
5)n=−9
7)r=−18
9)x=−2
11)n=46
2)n = 3
4)v=9
6)n=−6
8)k=−17
10)x=12
12)x=−32
Step-by-step explanation:
Let's solve your equation step-by-step.
1) 2+x=22
Step 1: Simplify both sides of the equation.
x+2=22
Step 2: Subtract 2 from both sides.
x+2−2=22−2
x=20
3) −6+p=−18
Step 1: Simplify both sides of the equation.
p−6=−18
Step 2: Add 6 to both sides.
p−6+6=−18+6
p=−12
5) −29=−20+n
Step 1: Simplify both sides of the equation.
−29=n−20
Step 2: Flip the equation.
n−20=−29
Step 3: Add 20 to both sides.
n−20+20=−29+20
n=−9
7) −5+r=−23
Step 1: Simplify both sides of the equation.
r−5=−23
Step 2: Add 5 to both sides.
r−5+5=−23+5
r=−18
9) 11=x+13
Step 1: Flip the equation.
x+13=11
Step 2: Subtract 13 from both sides.
x+13−13=11−13
x=−2
11) 101=n+55
Step 1: Flip the equation.
n+55=101
Step 2: Subtract 55 from both sides.
n+55−55=101−55
n=46
2) −15=−18+n
Step 1: Simplify both sides of the equation.
−15=n−18
Step 2: Flip the equation.
n−18=−15
Step 3: Add 18 to both sides.
n−18+18=−15+18
n=3
4) −18+v=−9
Step 1: Simplify both sides of the equation.
v−18=−9
Step 2: Add 18 to both sides.
v−18+18=−9+18
v=9
6) −19=n−13
Step 1: Flip the equation.
n−13=−19
Step 2: Add 13 to both sides.
n−13+13=−19+13
n=−6
8) −12=k+5
Step 1: Flip the equation.
k+5=−12
Step 2: Subtract 5 from both sides.
k+5−5=−12−5
k=−17
10) 11=−1+x
Step 1: Simplify both sides of the equation.
11=x−1
Step 2: Flip the equation.
x−1=11
Step 3: Add 1 to both sides.
x−1+1=11+1
x=12
12) x−36=−68
Step 1: Add 36 to both sides.
x−36+36=−68+36
x=−32
Divides 2/10=/5 pleased give me an answer i need it i beg you
a
Answers
Answer:
2/10= 0.2
10/2= 5
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In the context of hypothesis testing, what is a test statistic?
a. The confidence level that is to be used to except or reject the null hypothesis.
b. A parameter determine from a sample, such as mean or standard deviation, used to test a hypothesis.
c. A value, determined from sample information, used to test the null hypothesis.
Answers
In the context of hypothesis testing, a test statistic is; c. A value, determined from sample information, used to test the null hypothesis.
How to Interpret Hypothesis Testing?Hypothesis testing is defined as the method that is used to find the probability of the hypothesis to be proved in the future on the basis of the small population sample. The null hypothesis is said to be a hypothesis where no important difference between the random variables
The test statistic is defined as a value that is computed from the sample data that is used when making a decision about whether or not to reject the null hypothesis.
Looking at the options and based on the definitions above, option C adequately describes the test statistic.
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if you traveled in space at a speed of 1000 miles per house, how far would you travel in 7.5*10^5 houes
Answers
Traveling at a speed of 1000 miles per hour for 7.5 * 10⁵ hours would result in traveling a distance of 7.5 * 10⁸ miles.
To calculate the distance traveled, we can multiply the speed by the time traveled.
Speed = 1000 miles per hour
Time = 7.5 * 10⁵ hours
Distance = Speed * Time
Distance = 1000 miles/hour * 7.5 * 10⁵ hours
To perform this calculation, we can multiply the numerical values and keep the scientific notation for the result:
Distance = 1000 * 7.5 * 10⁵ miles
Distance = 7.5 * 10⁸ miles
Therefore, traveling at a speed of 1000 miles per hour for 7.5 * 10⁵ hours would result in traveling a distance of 7.5 * 10⁸ miles.
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Math question on how to evaluate f(5)
Answers
The value of f(5) in the function are - 9 . Option B
What is function?A function can be defined as an expression, rule or law that shows the relationship between a dependent variable or independent variable.
Given the functions;
f(x) = 3x - 1 (1)f(x) = 1 - 2x (2)To determine the value f(5), substitute the value of x as 5
x > 1 , so we use equation 2
From function (2)
f(5) = 1 - 2x
f(5) = 1 - 2(5)
f(5) = 1 - 10
f(5) = - 9
Thus, the value of f(5) in the function are - 9 . Option B
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Adam plans to choose a video game from a section of the store where everything is 75% off. He writes the expression d−0.75d to find the sale price of the game if the original price is d dollars. Rena correctly writes another expression, 0.25d , that will also find the sale price of the game if the original price is d dollars. Drag each description to explain each part of both expressions.
Answers
In 1st part expression there is a subtraction of 75% of 0.75d from orignal price and in 2nd expression the discount of 75% of the orignal price.
What do you mean by an expression?In mathematics, an expression is a combination of symbols, numbers, and operators (such as +, −, ×, ÷, etc.) that represent a quantity or a mathematical operation.
Expressions can be simple or complex, and they can involve variables, constants, and functions. Expressions can be evaluated or simplified to obtain a numerical or symbolic result.
d: This represents the original price of the video game in dollars.
0.75d: This represents the price of the video game after the 75% discount has been applied. It is equivalent to subtracting 75% of the original price (0.75 times d) from the original price (d).
0.25d: This represents the amount of the original price that is discounted by 75%. It is equivalent to subtracting the sale price (d - 0.75d) from the original price (d), since the discount is 75% or 0.75 of the original price (d).
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what is the coefficient of (3y^2 + 9)5
Answers
The coefficient of (3y² + 9)5 is 15.
A polynomial is of the form a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ.
Here, x is the variable, aₙ is the constant term, and a₀, a₁, a₂, ..., and aₙ₋₁, are the coefficients.
a₀ is the leading coefficient.
In the question, we are asked to identify the coefficient of (3y² + 9)5.
First, we expand the given expression:
(3y² + 9)5
= 15y² + 45.
Comparing this to the standard form of a polynomial, a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ, we can say that y is the variable, 15 is the coefficient, and 45 is the constant term.
Thus, the coefficient of (3y² + 9)5 is 15.
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Please help me with this, no clue.
Answers
Problems 1 - 6, evaluate each expression for the given values of the variables.
1 5a + 4b - 3a - 7b+ 4a; a = -3 and b = 4
2. c6-1)-cm; b=5 and c= -2
3. 5x – 2xy + 3y: x=-5 and y=-2
4. -K -(7k - 4m); k=-2 and m = 4
5. 3(6x + 5y) - 2y: x = 3 and y=-3
6. 5(3m – n) – 4(2m- n); m=-8 and n=-11
Problems 7 - 14, combine like terms and simplify completely
Answers
Step-by-step explanation:
1) 5a+4b-3a-7b+4a
Add terms having 'a' and 'b' separately
=6a-3b
Now subtitute values of a and b :
=6(-3)-3(4)
=-18-12
=-30
2)c(6-b)-c²
=6c-bc-c²
Subtitute values of b and c:
= 6(-2)-(5)(-2)-(-2)²
=-12+10-4
=-6
3)5x²-2xy+3y
Subtitute values of x and y:
=5(-5)²-2(-5)(-2)+3(-2)
=5(25)-20-6
=125-20-6
=99
4)-k²-(7k-4m)
Subtitute values of m and k:
=-(-2)²-{7(-2)-4(4)}
=-4-(-14-16)
=-4-(-30)
=-4+30
=26
5)3(6x+5y)-2y
Subtitute values of x and y:
=3{6(3)+5(-3)}-2(-2)
=3(18-15)+4
=3(3)+4
=9+4
=13
6)5(3m-n)-4(2m-n)
Subtitue values of m and n:
=5{5(-8)-(-11)}-4{2(-8)-(-11)}
=5(-40+11)-4(-16+11)
=5(-29)-4(-5)
=-145+20
=-125
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a right triangle has sides measuring 10, 24, and 26cm. what is the measure of x to the nearest degree
Answers
Answer:
D. 67
Step-by-step explanation:
with respect to angle x.
perpendicular is 24.
hypotenuse is 26cm
since we have
sin angle=perpendicular / base
sin x=24/26
x=sin inverse(24/26)
x=67.38
in nearest degree x=67 degree
Solve |x + 4| - 5 =6.
Answers
Answer:
The answer is x =7 and x= - 15
Explanation
\( |x + 4| - 5 = 6 \\ |x + 4| = 6 + 5 \\ |x + 4| = 11 \\ x + 4 = 11 \: \:and \: \: x + 4 = - 11 \\ x = 11 - 4 \: \: and \: \: x = - 11 - 4 \\ x = 7 \: \: and \: \: x = - 15\)
A flower bed in the corner of your yard is in the shape of a right triangle. The perpendicular sides of the bed measure 7
feet and 9 feet. Calculate the area of the flower bed.
a. 39.5 sq.ft
C. 21.5 sq.ft
b. 31.5 sq.ft
d. 11.5 sq. ft
Answers
9 ft x 7 ft = 63ft, but since we are finding the area of a triangle, not a square, we would divide that answer by 2, so:
63ft / 2 = 31.5 sq ft
Given j(-8,-5) and l(6,-11) if k(r-4,2s) is the midpoint of jl which correctly gives the values of r and s?
Answers
The values of r and s is -1 and -4 respectively.
Given that:-
coordinates of j are (-8,-5)
coordinates of l are (6,-11)
coordinates of k are (r-4,2s)
Also, k is the mid-point of jl.
We have to find the values of r and s.
We know that, for (x,y) and (z,w), the mid-point is ((x+z)/2, (y+w)/2).
Here,
(x,y) = (-8.-5)
(z,w) = (6,-11)
(r-4,2s) = ((x+z)/2,(y+w)/2)
Hence,
(r-4,2s) = ((-8+6)/2,(-5-11)/2)
(r-4,2s) = (-1,-8)
Comparing the coordinates, we get:-
r - 4 = -1
r = -1+4 =3
2s = -8
s =-8/2 = -4
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An adult pass for a county fair costs $2 more than a children’s pass. When 378 adult and 214 children’s passes were sold, the total revenue was $2,348. Find the cost of an adult pass.
Answers
378A + 214C = 2384
An adults pass (A) cost two dollars ($2) more than a children’s pass (C).
378 adult passes and 224 children passes are sold. The revenue is 2384.
378(C+2) + 224C = 2384
378C + 2 x 378 + 214C = 2384
592C + 756 = 2384
593C = 2384 — 756 = 1628
C = 1628/592 = 11/4 = $2.75
A = $2.75 + $2 = $4.75
There are two equations with two unknowns.
In equation (1) A is already in terms of C so substitute equation (1) into equation (2) and solve for C.
Now that C is know, substitute C back into equation (1) to get A.
Results:
Adult’s cost: $4.75
Children cost: $2.75
brainliest??
The probability P(Z>1.28) is closest to: (a) −0.10
(b) 0.10
(c) 0.20
(d) 0.90
Answers
Answer:
Step-by-step explanation:
The probability P(Z>1.28) represents the area under the standard normal distribution curve to the right of the z-score 1.28.
Using a standard normal distribution table or a calculator, we find that the area to the right of 1.28 is approximately 0.1003.
Therefore, the answer is closest to option (b) 0.10. there is a 10% chance of obtaining a value above 1.28 in a standard normal distribution.
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Which of the following is a rational number?
√√12
√47
√22
√9
Answers
Answer:
√9
Step-by-step explanation:
First, it's important to know that a rational number is a number that can be expressed as a fraction. This means that all whole numbers are rational numbers. Knowing this, let's see if any of the radicals simplify into a fraction or whole number.
√12 = 3.464101615.....
NOT a rational number
√47 = 6.8556546.....
NOT a rational number
√22 = 4.69041576.....
NOT a rational number
√9 = 3
Rational number
So, √9 is a rational number.
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Have a GREAT day!!!
Expand the expressions and simplify. 5(x + 4) 3(x + 2) = Question 1 options: a. 8x + 4b. 6x + 18 c. 8x + 26d. 7x - 18
Answers
Answer:
(✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿)
To expand and simplify 5(x + 4) 3(x + 2), we can use the distributive property of multiplication over addition which states that a(b + c) = ab + ac.
So, we have:
5(x + 4) 3(x + 2) = (5x + 20)(3x + 6)
Now, we can use the distributive property again to expand this expression:
(5x + 20)(3x + 6) = 5x * 3x + 5x * 6 + 20 * 3x + 20 * 6
= 15x^2 + 90x + 60
Therefore, the answer is 15x^2 + 90x + 60.
I hope this helps!
(✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿)
Find the Inverse Function f(x)=x-5
Answers
Lily has a mask collection. She keeps some in a display case and the rest on the wall. 365 of her masks are on the wall, and 27% of her masks are in the display case. What is the total number of masks in Lily's collection?
Answers
Step-by-step explanation:
this answer is that correct
brain lest
If 365 of her masks are on the wall, and 27% of her masks are in the display case. Then 467 marks are the total number of masks in Lily's collection
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Lily keeps masks in a display case and the rest on the wall.
365 of her masks are on the wall.
27% of her masks are in the display case
We need to find what is 27% of 365 to solve this problem
27/100×365=0.27×365
=98.55
Now we need to find the total number of masks in Lily's collection
365+98.55
463.55
467
Hence, 467 are total number of masks in Lily's collection.
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How to write two hundred five million, four hundred thousand, six
Answers
Hey there!
“Two hundred five million, four hundred thousand six”
205,400,006
Because,
“two hundred five million” is
205,000,000
“Four hundred thousand” is
400,000
“Six” is simplify
6
The equation is:
205,000,000 + 400,000 + 0 + 0 + 6
Which converts to: 205,400,006
Answer: 205,400,006
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a newsletter publisher believes that less than 65% 65 % of their readers own a personal computer. for marketing purposes, a potential advertiser wants to confirm this claim. after performing a test at the 0.02 0.02 level of significance, the advertiser decides to reject the null hypothesis. what is the conclusion regarding the publisher's claim?
Answers
The conclusion regarding the publisher's claim is that it is incorrect if the potential advertiser rejects the null hypothesis. A newsletter publisher believes that less than 65% 65 % of their readers own a personal computer. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.02 0.02 level of significance, the advertiser decides to reject the null hypothesis.
What is a null hypothesis?
The null hypothesis is a fundamental idea in inferential statistics that represents the null assumption. It's frequently utilized to compare datasets and decide whether any differences between them are real or just by chance.
It is also called H0. It is the default theory that no difference exists between two tested populations or data sets.
A hypothesis test is a way of deciding whether the data supports or disproves the null hypothesis. If the null hypothesis is incorrect, it is referred to as a Type I error. If it is true and the data leads to its rejection, it is known as a Type II error.
Thus, after performing the test at the 0.02 level of significance, if the potential advertiser decides to reject the null hypothesis, the publisher's claim is incorrect.
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yeaahhhh help please i beg for your help -^-
Answers
Answer:
48
Step-by-step explanation:
Since it is a triangle, it should add up to be a total of 180 degrees.
I took 64 + 68 = 132
Since there's a missing angle, you can take 180 - 132 = 48
All the angles should add up to 180 so 64 + 68 + 48 = 180
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F
The table of values represents a linear function.
X Y
-4 21
-2 15
0
9
2
3
4 -3
Which of the following are the slope and y-intercept of the linear function?
O A. slope: 2
y-intercept: -6
O B. slope: -3
y-intercept: 9
O C. slope: -4
y-intercept: 21
O D. slope: -2
y-intercept: 6
C
Oll
hp
O
O
Answers
The slope of the linear function is -3, and the y-intercept = 9. Option B is the correct answer.
What is slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
Given that,
(x1, y1) = (-4, 21)
(x2, y2) = (-2, 15)
The slope is given as:
m = (y2 - y1) / (x2 - x1)
m = (15 - 21) / (-2 + 4)
m = -6 / 2
m = -3
The slope of the linear function is -3.
The y-intercept of the function is determined when the value of x = 0.
The value of y when x = 0 from the given table is 9.
Hence, the slope of the linear function is -3, and the y-intercept = 9. Option B is the correct answer.
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