The actual mean weight of the infants when they were 1 month old is 4.297
The residual plot doesn't show any obvious leftover pattern, confirming that a linear model is appropriate.
the equation of this line as ˆy=12x−1 with an accent on the y to indicate that the y-values computed using this equation
y = 4.88 + 0.267(1)
y = 5.147
residual = -0.85 = A - 5.147 + 5.147
residual = 4.297
the actual mean weight of the infants when they were 1 month old is 4.297
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Show ([tex]\frac{\sqrt{11} }{6} ,[/tex][tex]\frac{5}{6}[/tex]) is or is not on the unit circle. State the unit circle definitions and definitions in terms of other trig functions.
By using coordinates in rectangular form and Pythagorean theorem, we conclude that the point (x, y) = (√11 / 6, 5 / 6) is on the unit circle as its norm is equal to 1.
Is a given point on Cartesian plane lying on the unit circle?
We find a point in rectangular form, that is, a point of the form (x, y). Unit circles are circles with a radius 1 that are commonly used to represent graphically angles. The given point is in the units if and only if its norm is equal to 1. The norm of the point is determined by using the Pythagorean theorem:
r = √[(√11 / 6)² + (5 / 6)²]
r = √[(11 / 36) + (25 / 36)]
r = √(36 / 36)
r = √1
r = 1
By using coordinates in rectangular form and Pythagorean theorem, we conclude that the point (x, y) = (√11 / 6, 5 / 6) is on the unit circle as its norm is equal to 1.
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What is the converse of the following statement?
"If cows make milk, then chickens make eggs. "
Answer:
"If chickens make eggs, then cows make milk."
Step-by-step explanation:
Answer: A: If chickens make eggs, then cows make milk.
Step-by-step explanation: Hope that helped
pls help find interval notation
Step-by-step explanation:
-2x - 7 > 1
-2x > 8
-x > 4
x < -4
that is a continuous line from -4 all the way to the left, and the dot on -4 is empty (meaning : it is not included due to the "<" symbol).
x - 2 >= -1
x >= 1
that is a continuous line from +1 all the way to the right, and the dot on +1 is filled (meaning : is IS included due to the ">=" symbol.
3. Solve the formula v + f -e = 2 for e
O Ae-v-f-2
O BC v+f-2
O ce-v-f+2
O De-u+f+2
Answer:
B is the correct answer.
Step-by-step explanation:
Add -2+e to both sides
v + f − e -2+e = 2 -2+e
Which will give you v + f -2 = e.
Evaluate the expression 9^2 the two is small and on top of the nine
Answer:
81
Step-by-step explanation:
That's the squared symbol, it means to multiply the number by itself x amount of times. 9 times 9 = 81
solve each inequality
||x-4|-7|<5
The solution of the inequality is (x > - 8 and x < 2) or (x > 6 and x < 16).
How to find the solution set of an inequalityHerein we find an inequality that involves two absolute values. Absolute values are defined by the following piecewise functions:
|x - a| = x - a for x ≥ a|x - a| = - x + a for x < aNow we proceed to solve the inequality given:
||x - 4| - 7| < 5
- 5 < |x - 4| - 7 < 5
0 < |x - 4| - 2 < 10
|x - 4| - 2 > 0 and |x - 4| - 2 < 10
Case 1: |x - 4| - 2 > 0
|x - 4| > 2
x - 4 > 2 and x - 4 < - 2
x > 6 and x < 2
Case 2: |x - 4| - 2 < 10
|x - 4| < 12
x - 4 < 12 and x - 4 > - 12
x < 16 and x > - 8
The solution of the inequality is (x > - 8 and x < 2) or (x > 6 and x < 16).
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b) The angle of elevation of a tower at a distance of 27 meter from the foot of the tower is 60°, find the height of the tower. Speedy Additional Mathematics - Book VIII 98
The height of the tower is approximately 46.765 feet
Step-by-step explanation:
The given parameters are;
The distance from the foot of the tower where the angle of elevation is
measured = 27 feet
The angle of elevation to the top of the tower from a point 27 feet from the foot of the tower, θ = 60°
Therefore, by trigonometric ratio, we have;
tan 60= the height of tower / distance from foot of tower
[tex]\sqrt{3}[/tex]= height of tower /27
1.73205 *27 = height of tower
46.765 feet is the height of tower
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For the function g defined above, a is a constant and g(4)=8. What is the value of g(-4)?
The value of g(-4) is 8.
A set of inputs and outputs that are connected to one another in some way is referred to as a relation. We refer to the relations as a function when each input results in a single output. However, you must be certain that no input leads to more than one output in order to determine if a relation is a function or not.
Only when each element of a nonempty set M has a single range to a nonempty set N is a function a relation.
g(x) = ax^2 + 24
⇒ g(4) = a (4)^2 + 24
⇒ 8 = 16a + 24
⇒ 8 − 24 = 16a
⇒ −16 = 16a
⇒ a = −1
Since, g(−4) = a(−4) ^2 + 24
∴ g(−4) = 16(−1) + 24
⇒ g(−4) = 8
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Luis has 1/2 quart of grape juice. he pours the same amount into each of 5 glasses. which equation represents the fraction of a quart of grape juice n that is in each glass?ll
The equation n = (1/2)(1/5) represents the fraction of a quart of grape juice n that is in each glass option (A) is correct.
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 question is incomplete.
The complete question is:
Luis has 1/2 quart of grape juice. he pours the same amount into each of 5 glasses. which equation represents the fraction of a quart of grape juice n that is in each glass?
n = (1/2)(1/5)
n = (1/2)(5/1)
n = (1/2)(5)
n = (1/2)
From the data given in the question:
Let n be the fraction of a quart of grape juice n that is in each glass:
n = (1/2)(1/5)
Thus, the equation n = (1/2)(1/5) represents the fraction of a quart of grape juice n that is in each glass option (A) is correct.
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Which expression is equivalent to (4y²) ³ (3y²)?
O 12y8
12y12
192y8
192y12
Answer: It is 192y^8. Just solve each one seperately until the answers match. Reduce the expression to 192y^8. Feel free to message me for an explanation
Answer: C. 192y>8
Step-by-step explanation:
Mia uses the formula πr2 to find the area of a circle. What is πr2 an example of?.
πr² an example of a model.
What are mathematical models?A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
Here, the area of a circle is calculated by the use of formula πr² where π is a constant 3.14 and r is a variable. Therefore this formula is used to find the area.
Thus, πr² an example of a model.
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PLEASE HELP ASAPPP !!! WILL GIVE BRAINLIEST AND 5 STAR RATING
Answer:
12/15
Step-by-step explanation:
8. Olivia's brother is twice her age
minus 9 years. He is also as old
as half the sum of the ages of
Olivia and both of her 12 year-
old twin brothers. Write and
solve an equation to find the
ages of Olivia and her brother.
The ages of Olivia and her brother are 10 years and 11 years respectively
Let x₁, and x₂ be the ages of Olivia and her brother respectively.
Given that Olivia's brother is twice her age minus 9 years.
⇒ x₂ = 2x₁ - 9 → equation 1
Also given that Olivia's brother is as old as half the sum of the ages of Olivia and both of her 12-year-old twin brothers.
⇒ x₂ = 1/2 × (x₁ + 12) → equation 2
Using equation 1 in equation 2, we get
2x₁ - 9 = 1/2 × (x₁ + 12)
⇒ 4x₁ - 18 = x₁ + 12 (multiplying by 2 on both sides)
⇒ 4x₁ - x₁ = 12 + 18
⇒ 3x₁ = 30
⇒ x₁ = 10 (dividing by 3 on both sides)
Using the value of x₁, in equation 1,
⇒ x₂ = 2(10) - 9
⇒ x₂ = 20 - 9
⇒ x₂ = 11
Therefore the ages of Olivia and her brother are 10 years and 11 years respectively.
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If you want to use the sin function in the math library, as x = math.sin(3.14), how should you write the import statement?
We use import math when we want to use the sin function in the math library, x= math. sin(3.14).
Similar to #include header_file in C/C++, that how to import function in python. The import statement brings in code from one module into another program, where modules are files that contain python code, and modules are used to group related code in a program, instead of rewriting the code again, you can reuse the same code in different files. To import code from a module a parameter is to be followed import module name ( where the import word is the keyword and the module name is the module you want to import ).
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2y-4+5y=4-3y+5
How to solve this?
Answer:
You would first move all of the y numbers to one side so it should look like this: 2y-4+5y+3y=4+5. Then you would all the numbers that don't have y at the end to the other side: 2y+5y+3y=4+5+4.
Then you would add them all up: 10y=13
So your answer is 10y=13
Step-by-step explanation:
You invested a total of $50,000 in 2 funds earning 6.5% and 9% simple interest. during 1 year, the 2 funds earned a total of $3625 in interest. how much did you invest in each fund? amount at 6.5%
Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The person has invested $35,000 in the fund returning at a rate of 6.5%.
What is simple interest?Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
SI = PRT = (R% of P)T
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
Let the amount invested in the first fund be represented by x, then the amount invested in the second fund will be ($50,000 - x).
Now, if the 2 funds earn 6.5% and 9% simple interest. Also, in the first year, they earned a total of $3625 from the interest. Therefore, we can write the equation to represent the given situation as,
6.5% of x + 9% of ($50,000 - x) = $3625
0.065x + 0.09(50,000 - x) = 3625
0.065x + 4,500 - 0.09x = 3,625
0.065x - 0.09x = 3625 - 4500
0.025 = 875
x = 875/0.025
x = 35,000
Therefore, the person has invested $35,000 in the fund returning at a rate of 6.5%.
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From nine cards numbered 1 through 9, two cards are drawn. consider the selection and classification of the cards as odd or even as an experiment. how many sample points are there for this experiment?
Probability= 5/9
Even cards = 2,4,6,8
Odd cards = 1,3,5,7,9
The number of ways of choosing one odd and one even number is 5C1 * 4C1
( 5!/ 1!* 4!) * (4!/1! * 3!)
5* 4= 20
Total number of ways of choosing 2 cards out of 9 = 9C2
9!/ 2! * (9-2)!
= 9!/ 2! * 7!
= 9*8/2
= 9 *4= 36
Thus, Probability is = 20/ 36
= 5/9
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a line with a slope equal to -2/3 passes through (-1, -4) and (3,y) what’s the value of y
Answer:
-20/3
Step-by-step explanation:
Using point-slope form, the equation is
[tex]y+4=-\frac{2}{3}(x+1) [/tex]
Substituting x=3,
[tex]y+4=-\frac{2}{3}(3+1) \\ \\ y+4=-\frac{8}{3} \\ \\ y=-\frac{20}{3}[/tex]
please help i’m literally so stressed out
Luis has $420 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
• He buys a new bicycle for $209.67.
•He buys 2 bicycle reflectors for $6.04 each and a pair of bike gloves for $25.77.
•He plans to spend some or all of the money he has left to buy new biking outfits
for $37.16 each.
Which inequality can be used to determine x, the maximum number of outfits Luis
can purchase while staying within his budget?
The inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4
How to solve inequality?Luis has $420 to spend at a bicycle store for some new gear and biking outfits.
He buys a new bicycle for $209.67.He buys 2 bicycle reflectors for $6.04 each and a pair of bike gloves for $25.77.He plans to spend some or all of the money he has left to buy new biking outfits for $37.16 each.Therefore,
x = maximum number of outfits Luis can purchase while staying within his budget.
Hence, the inequality that can be used to represent the situation is as follows;
209.67 + 6.04(2) + 25.77 + 37.16x ≤ 420
235.44 + 12.08 + 37.16x ≤ 420
247.52 + 37.16x ≤ 420
37.16x ≤ 420 - 247.52
37.16x ≤ 172.48
divide both sides by 37.16
x ≤ 4.64155005382
x ≤ 4
Therefore, the inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4
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I need help on this one question, anyone know the answer?
solve 2x-9y=14 for y
The value of y in expression is 14-2x/-9
How to calculate the value of y ?The expression is written as
2x - 9y = 14
We are asked to calculate the value of y in the expression
2x - 9y = 14
-9y= 14-2x
Divide by the coefficient of y which is -9
y= 14-2x/-9
Hence the value of y is 14-2x/-9
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Is the statement the solution set of a linear system involving variables is a list of numbers that makes each equation in the system a true statement when the values are substituted for respectively true or false? explain.
False, because The singles answer fits the description. All potential solutions are included in the solution set.
There might not be a solution to a set of linear equations that makes sense. False. There is at least one answer for a consistent system.What makes up a linear system's solution set?
The answer to a system of equations is a set of values for a variable that concurrently satisfy each equation. Finding every feasible combination of the variable values that make up the system's solutions is necessary to solve an equation system.Is it true that a linear system's existence and uniqueness are two key issues? False or true?
In a linear system, existence and uniqueness are crucial considerations. Both conceptually and practically, it is frequently essential to know whether a system has a solution (exists) and, if it does, whether this solution is the only one available (uniqueness).Learn more about linear system.
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What is the side length of a square with an area of 121 square centimeters?
In centimeters
The answer to this question is:
Size of a square's side = 11 cm
A Square is a flat geometric shape with four right angles and equal sides. The square's four sides are equal to one another or congruent. The square's opposing sides run parallel to one another. The square's diagonals form a 90° angle with one another. The two diagonals of the square are equivalent to one another. The square is made up of four vertices and four sides.
Area of square = ( Side )²
Given that:
Area of square = ( Side )² = 121 cm²
Dimensions of a square's side = √ Area
so, the length of the square's side = √ 121
= √ 11*11
= √ ( 11 )²
= 11
Thus, side of the square = 11 cm
Therefore, side length of square = 11cm
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i’m confused please help
c. Write an equation for which every real number is a solution. Choose the correct answer below.
OA. 7(x-2)=2(x-7)
OB. 2(x-7)=2(x-7)
OC. x+2=x+7
Mia uses the formula πr2 to find the area of a circle. What is πr2 an example of?.
πr2 is an example of (D) a model.
What is a model?A mathematical model is a system description that employs math ideas and language. Mathematical modeling is the process of creating a mathematical model. Mathematical models are used in the natural sciences (physics, biology, earth science, chemistry), engineering disciplines (computer science, electrical engineering), and non-physical structures such as the social sciences (such as economics, psychology, sociology, political science). A large part of the field of operations research is the use of statistical equations to solve problems in business or military operations. Music, linguistics, and philosophy all use mathematical models (for example, intensively in analytic philosophy). A model is, for example, the method for the area of a circle, πr2.Therefore, πr2 is an example of (D) a model.
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The complete question is given below:
Mia uses the formula πr2 to find the area of a circle. What is πr2 an example of?
A. a robot
B. a car
C. a telescope
D. a model
find the measure of angle B.
Answer:
m <B = 41°
Step-by-step explanation:
Fact: complementary angles measures add to 90 degrees
Given: m < A = 2x-19, and m <B = x+7
Find: m <B = ?
Find x
2x-19 + x+7 = 90
2x+x = 90 +19-7
3x = 102
x = 34
Find m <B
m <B = x+7
m <B = 34+7
m <B = 41
The recipe calls for 1 1/2 lbs. of ground beef. how much ground beef will jenny need to make enough meat loaf for everyone?
Total amount of ground beef is 7.5 lbs
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
a) The recipe for the meat loaf used by Jenny can serve a total of 8 people.
Total people = 40
Number of each ingredient
= 40 / 8
= 5
b) As, recipe contains 1 1/2 lb (1.5 lbs) of ground beef,
So, Total amount of ground beef = 1.5 lbs * 5 = 7.5 lbs
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Your question is incomplete, probably the complete question/missing part is:
Jenny is throwing a surprise birthday party for her best friend Katie. She has decided to make Katie’s favorite dish, meat loaf. There will be a total of 40 people at the party. Answer the following questions:
• The recipe says it serves 8 people. By what number should Jenny multiply each ingredient to make enough meat loaf for everyone? 5
• The recipe calls for 1 1/2 lbs. of ground beef. How much ground beef will Jenny need to make enough meat loaf for everyone?
Find the average rate of change for the function f(x)=3^x+17
Using the intervals x=3 to x=6
Answer:
234
Step-by-step explanation:
the average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [3, 6 ] , then
f(b) = f(6) = [tex]3^{6}[/tex] + 17 = 729 + 17 = 746
f(a) = f(3) = 3³ + 17 = 27 + 17 = 44 , then
average rate of change = [tex]\frac{746-44}{6-3}[/tex] = [tex]\frac{702}{3}[/tex] = 234
HELP me ill give brainlist or whatever its called
Answer:
1 cm
Step-by-step explanation:
you multiply 3 by 1/3 and you get 3/3 which is 1