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Related Questions
Jalal weighs twice as much as Meena. Meena's weight is 60% of Bahar's weight. Dolly weighs 50% of Laila's weight. Laila weighs 19% of Jalal's weight. Who among these 5 persons weighs the least
Answers
Dolly weighs the least among Jalal, Meena, Bahar, Dolly, and Laila. This is based on the given information regarding their relative weights.
To determine this, let's analyze the given information. We know that Meena's weight is 60% of Bahar's weight, which implies that Bahar weighs more than Meena. Additionally, Laila's weight is 19% of Jalal's weight, indicating that Jalal weighs significantly more than Laila.
Since Jalal weighs twice as much as Meena, it means that Jalal's weight is even greater than Bahar's weight. Considering these relationships, Dolly's weight, which is 50% of Laila's weight, is the smallest among the mentioned individuals.
In conclusion, based on the given information, Dolly weighs the least among Jalal, Meena, Bahar, Dolly, and Laila.
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What do we do to both sides of this equation to solve?
x−10=8
Question 2 options:
Subtract 10 from both sides
Add 10 to both sides
Multiply both sides by 10
Divide both sides by 10
Answers
Add 10 to both sides
Step-by-step explanation:
x-10 = 8
x - 10 + 10 = 8+ 10
x = 18
Step-by-step explanation:
Add 10 to both sides
or,x-10+10=8+10
or,x=18
graph each linear inequality (3.)x-y>5 m= , b=(5.) y ≥ -5/3 x + 1. m=. b= -2x+y<5 m=. b=(7.) 4x-2y -8. m=. b=2x-y<4 5. m=. b=
Answers
For a equation of the form:
\(\begin{gathered} y=mx+b \\ or \\ ymx+b \\ or \\ y\le mx+b \\ or \\ y\ge mx+b \end{gathered}\)m = slope
b = y-intercept
for:
\(\begin{gathered} x-y>5 \\ \text{solve for y:} \\ y-------(5)
\(\begin{gathered} y\ge-\frac{5}{3}x+1 \\ m=-\frac{5}{3} \\ b=1 \\ ----- \\ y<2x+5 \\ m=2 \\ b=5 \end{gathered}\)(7)
\(\begin{gathered} y<2x+4 \\ so\colon \\ m=2 \\ b=4 \\ ------- \\ y<2x+5 \\ so\colon \\ m=2 \\ b=5 \end{gathered}\)
write a formula for a linear function f(x) that models the situation, where x is the number of years after 2007. in 2007 the average adult ate 52 pounds of chicken. this amount will increase by 0.8 pounds per year until 2012.
Answers
Step-by-step explanation:
x = number of years after 2007.
x = 0 for 2007.
PC(x) is a function that calculates how many pounds of chicken the average adult will eat every year (x) after 2007 (up to 2012).
PC(x) = 0.8x + 52
0 <= x <= 5
in 2007 (x = 0) the average adult ate 52 pounds.
in every year after 2007 until 2012 0.8 pounds get added to the amount of the previous year.
so, in 2012 (x = 5) the average adult will eat
PC(5) = 0.8×5 + 52 = 4 + 52 = 56 pounds of chicken.
A company selis a seasonal product. The revenue R (in dollars) generated by sales of the product can be modeled by R=430.5t 2
e −t/30
+45,000,0≤t≤365 where t is the time in days. (Round your answers to two decimal places.) (a) Find the average dally revenue during the first quarter, which is given by 0≤t≤90. 5 (b) Find the average dally revenue during the fourth quarter, which is given by 274≤t≤365. 5 (c) Find the total dally revenue during the year. 3
Answers
The total daily revenue during the year is $10,131,607.29
The formula for the revenue of a product is given as R=430.5t^2e^(−t/30)+45,000, where t is the time in days. We have to find the average daily revenue during the first quarter, average daily revenue during the fourth quarter and total daily revenue during the year
To find the average daily revenue during the first quarter which is given by 0 ≤ t ≤ 90.5First, we have to find the revenue generated on the first day which is t = 0 R = 430.5 × (0)^2e^(-0/30) + 45,000R = 45,000 The revenue generated on the 90th day of the first quarter is R = 430.5 × (90.5)^2e^(-90.5/30) + 45,000R = 633,318.23 Therefore, the total revenue during the first quarter = 633,318.23 - 45,000 = 588,318.23Average daily revenue during the first quarter is given by total revenue/number of days.
Therefore, Average daily revenue during the first quarter = 588,318.23/90.5= $6491.70b) To find the average daily revenue during the fourth quarter which is given by 274 ≤ t ≤ 365.5First, we have to find the revenue generated on the first day which is t = 274 R = 430.5 × (274)^2e^(-274/30) + 45,000R = 163,443.32The revenue generated on the last day of the fourth quarter which is t = 365.5 is R = 430.5 × (365.5)^2e^(-365.5/30) + 45,000R = 4,636,614.36Therefore, the total revenue during the fourth quarter = 4,636,614.36 - 163,443.32 = 4,473,171.04Average daily revenue during the fourth quarter is given by total revenue/number of days.
Therefore, Average daily revenue during the fourth quarter = 4,473,171.04/91= $49,210.01c) The total daily revenue during the year is the sum of revenue during the first quarter, second quarter, third quarter and fourth quarter.Total daily revenue during the year = Revenue during Q1 + Revenue during Q2 + Revenue during Q3 + Revenue during Q4Total daily revenue during the year = 588,318.23 + 1,686,599.94 + 4,383,518.08 + 4,473,171.04Total daily revenue during the year = $10,131,607.29
Therefore, the average daily revenue during the first quarter is $6491.70. The average daily revenue during the fourth quarter is $49,210.01. The total daily revenue during the year is $10,131,607.29.
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(15 points!!) Which transformation forms a mirror image of a figure on a coordinate plane?
Answers
Answer:
BLUEE
Step-by-step explanation:
IM HOPING THIS IS CORRECT
A video game randomly chooses your car color and type. The probability of
getting a red car is 0.25, and the probability of getting a convertible is 0.40.
Event A = You get a red car.
Event B = You get a convertible.
A and B are independent events if
A. The probability of getting a red car or a convertible is 0.10.
B. The probability of getting a red car or a convertible is 0.65.
C. The probability of getting a red convertible is 0.10.
D. The probability of getting a red convertible is 0.
Answers
The correct option regarding the probabilities of the two events when they are independent are given by:
C. The probability of getting a red convertible is 0.10.
What is the probability of independent events?If two events, A and B, are independent, the probability of both events happening is the multiplication of the separate probabilities of each event happening, that is.
P(A and B) = P(A) x P(B).
For this problem, the separate probabilities are given by:
P(A) = 0.25.P(B) = 0.40.Then, for them to be independent, we need that:
P(A and B) = 0.25 x 0.40 = 0.10.
A and B means a red convertible car, hence the correct option is:
C. The probability of getting a red convertible is 0.10.
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Shelly sleeps for 7 hours 30 minutes in a day. For how many hours did she sleep in the month of January?
Answers
Answer:
Shelly slept 232 hours and 30 minutes in the month of January
Step-by-step explanation:
31 days in January, so the equation will be
31 x 7.5 ( I wrote 0.5 because 30 minutes is half a day)
= 232.5 hours
Shelly slept 232 hours and 30 minutes in the month of January
Answer:
232.5 hours
Step-by-step explanation:
Well, the month of January has 31 days.
If shelly sleeps for 7.5 hours a day, and she sleeps 31 days, we need to do multiplication!
7.5*31=232.5 hours!
Simplify: 3•6 - 42 ÷ 2
Answers
Answer:
-3
Step-by-step explanation:
3 x 6 - 42/2 =
18 - 42/2 =
18 - 21 =
-3
Answer:
18-21=x
Step-by-step explanation:
18-21=x
x= -3(this is just extra)
many fire stations handle emergency calls for medical assistance as well as calls requesting firefighting equipment. a particular station says that the probability that an incoming call is for medical assistance is 0.67. this can be expressed as
Answers
The probability that an incoming call is for firefighting equipment (or any other reason besides medical assistance) is 0.33 or 33%.
The statement "the probability that an incoming call is for medical assistance is 0.67" can be expressed as:
P(Medical Assistance) = 0.67
This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.67 or 67%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:
P(Not Medical Assistance) = 1 - P(Medical Assistance) = 1 - 0.67 = 0.33
In science, the probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability
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Find f. f '(t) = sec(t)(sec(t) + tan(t)), − π/2 < t < π/2 , f (π/4)= −2
Answers
We used integration to find the function f given \(f'(t) = sec(t)[sec(t) + tan(t)]\), \(-\pi /2 < t < \pi /2\) and \(f(\pi /4) = -2\). The solution is \(f(t) = tan(t) + ln|sec(t) + tan(t)| - 3 - ln(2)\).
To find the function f given f'(t), we need to integrate f'(t) with respect to t. In this case, we have:
\(f'(t) = sec(t)[sec(t) + tan(t)]\)
We can simplify this expression by using the identity \(sec^2(t) = 1 + tan^2(t)\)to get:
\(f'(t) = sec^2(t) + sec(t)tan(t)\)
We can then integrate f'(t) to obtain f(t):
\(f(t) = \int [sec^2(t) + sec(t)tan(t)] dt\)
Using the identity \(\int sec^2(t) dt = tan(t) + C\), we can simplify the integral to:
\(f(t) = tan(t) + ln|sec(t) + tan(t)| + C\)
To find the value of C, we use the initial condition \(f(\pi /4) = -2\):
\(-2 = tan(\pi /4) + ln|sec(\pi /4) + tan(\pi /4)| + C\)
-2 = 1 + ln(2) + C
C = -3 - ln(2)
Therefore, the solution to the initial value problem is:
\(f(t) = tan(t) + ln|sec(t) + tan(t)| - 3 - ln(2)\)
In summary, we used integration to find the function f given \(f'(t) = sec(t)[sec(t) + tan(t)]\), \(-\pi /2 < t < \pi /2\) and \(f(\pi /4) = -2\). The solution is \(f(t) = tan(t) + ln|sec(t) + tan(t)| - 3 - ln(2)\).
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Let V be the set of all ordered pairs of real numbers, and consider the following addition and scalar multiplication operations on u=(u1,u2) and v=(v1,v2) : u+v=(u1+v1+2,u2+v2+2),ku=(ku1,ku2) Show whether V is a vector space or not. (Hint: Try Axiom's 7 or 8 )
Answers
The set V with the defined addition and scalar multiplication operations is a vector space.
To determine if V is a vector space, we need to verify if it satisfies the vector space axioms. Let's check Axioms 7 and 8:
Axiom 7: Scalar multiplication distributes over vector addition.
For any scalar k and vectors u, v in V, we need to check if k(u + v) = ku + kv.
Let's consider:
k(u + v) = k((u1 + v1 + 2, u2 + v2 + 2))
= (k(u1 + v1 + 2), k(u2 + v2 + 2))
= (ku1 + kv1 + 2k, ku2 + kv2 + 2k)
On the other hand:
ku + kv = k(u1, u2) + k(v1, v2)
= (ku1, ku2) + (kv1, kv2)
= (ku1 + kv1, ku2 + kv2)
= (ku1 + kv1 + 2k, ku2 + kv2 + 2k)
Since k(u + v) = ku + kv, Axiom 7 holds.
Axiom 8: Scalar multiplication distributes over scalar addition.
For any scalars k1, k2 and vector u in V, we need to check if (k1 + k2)u = k1u + k2u.
Let's consider:
(k1 + k2)u = (k1 + k2)(u1, u2)
= ((k1 + k2)u1, (k1 + k2)u2)
= (k1u1 + k2u1, k1u2 + k2u2)
On the other hand:
k1u + k2u = k1(u1, u2) + k2(u1, u2)
= (k1u1, k1u2) + (k2u1, k2u2)
= (k1u1 + k2u1, k1u2 + k2u2)
Since (k1 + k2)u = k1u + k2u, Axiom 8 also holds.
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Solve the system of equations :-6x - y = -16-6x -5y = -8
Answers
The given system of equation are :
-6x - y = -16
-6x -5y = -8
On subtracting both the equation we get :
-6x -y -(-6x -5y) = -16 -(-8)
-6x -y +6x +5y = -16 +8
-6x + 6x +5y -y = -8
4y = -8
4y = -8
Divide both side by 4:
4y/4 = -8/4
y = -2
Substitute the value of y =- 2 in the any one equation:
-6x - y = -16
-6x - (-2)= -16
-6x + 2 = -16
-6x = -16 -2
-6x = -18
x = 3
Answer : x = 3, y = -2
When fingerprinting a person who is missing fingers, what are the two notations you should use on the fingerprint card
Answers
Fingerprinting is a technique used by forensic experts and crime scene investigators to identify individuals based on their unique fingerprints. Fingerprints are unique to each individual and have distinct ridge patterns that are used to identify individuals.
It is an effective way of identifying people because fingerprints remain the same throughout a person's life, unlike other physical characteristics.
When fingerprinting a person who is missing fingers, two notations that should be used on the fingerprint card are "amputation" and "absent." The notations on the fingerprint card should indicate that the fingers are missing due to amputation or absence.
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When fingerprinting a person missing fingers, the two notations that should be used on the fingerprint card are tented arch for a missing middle finger and amputation notation for a completely missing finger.
Explanation:When fingerprinting a person who is missing fingers, two notations should be used on the fingerprint card:
Tented arch: If the person is missing the middle finger, the missing finger should be notated as a tented arch. This means that the ridges of the fingertip start on one side of the finger and end on the other, creating a tent-like shape.Amputation: If a person is missing a finger completely, the notation should indicate the specific finger that is missing and the level of the amputation, such as 'Amputation of left index finger at the proximal phalanx'.Learn more about Fingerprinting here:https://brainly.com/question/34652657
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Enzymes : Fish that been dried in the sun keeps longer than wet fish.
Answers
1. Consider the following problem:
Maximize Z=2x1+5x2
subject to
x1+2x2≤10 (resource 1)
x1+3x2≤12 (resource 2)
and
x1≥0,x2≥0.
(a) The objective function changes to Z=cx1+5x2. What is the range of c, when the optimal solution does not change?
Answers
The range of c for which the optimal solution does not change is c = 2.
To determine the range of c for which the optimal solution does not change, we need to identify the values of c for which the objective function remains parallel to the original objective function 2x1 + 5x2.
In the original problem, the objective function is Z = 2x1 + 5x2.
If we change the coefficient of x1 to c, the new objective function becomes Z = cx1 + 5x2.
To keep the optimal solution unchanged, we need the direction of the objective function to remain the same. This means that the slope of the new objective function should be the same as the original objective function (2x1 + 5x2).
The slope of the new objective function is equal to the coefficient of x1, which is c. Therefore, for the optimal solution to remain the same, the value of c must be equal to 2.
So, the range of c for which the optimal solution does not change is c = 2.
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3. Audrey measures the distance around the lid of her aquarium. The picture shows the shape of the lid. If the perimeter of the lid is 56 inches, what is the missing side length? * Brainliest and 20 points
Answers
Answer:
18 in
Step-by-step explanation:
At university A, 46% of the undergraduate students are female. At university B, 52% of the undergraduate students are female. Suppose a random sample of 100 students from both schools was selected. Assume the sampling distribution of p hat Subscript Upper A Baseline minus p hat Subscript Upper B is approximately Normal.
What is the probability that the proportion of females selected from university A is greater than the proportion of females selected from university B?
If needed, use the z-table to answer the question.
Report your answer to 3 decimal places.
Answers
Answer: .198
Step-by-step explanation:
got it right on edg
an experiment consists of tossing 4 unbiased coins simultaneously. the number of simple events in this experiment is question 20answer a. 10 b. 8 c. 16 d. 25
Answers
The number of simple events in this experiment is 16.
The correct answer to the given question is option c.
The probability of an event can be calculated by dividing the number of favorable outcomes by the number of possible outcomes. A simple event is one in which only one of the outcomes can occur. For example, if a coin is tossed, a simple event would be the outcome of the coin being heads or tails.
The total number of possible outcomes in the experiment of tossing 4 unbiased coins simultaneously is 2⁴, since there are two possible outcomes for each coin. Thus, the total number of possible outcomes is 16.
Each coin has two possible outcomes: heads or tails. If all four coins are flipped, there are two possible outcomes for the first coin, two possible outcomes for the second coin, two possible outcomes for the third coin, and two possible outcomes for the fourth coin. Therefore, the total number of possible outcomes is 2 × 2 × 2 × 2 = 16.
Therefore, the number of simple events in this experiment is 16, which is option (c).
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WILL MARK BRAINLIEST ( if the answer contains DETAILS, and NOT the ANSWER or a LINK
Answers
Answer:
answer
Step-by-step explanation:
details
-------------------------
brainliest now? ;)
What does the coefficient of determination equal if r = 0.89?A) 0.94B) 0.89C) 0.79D) 0.06E) None of the above
Answers
Main Answer:The correct answer would be C)0.79.
Supporting Question and Answer:
How is the coefficient of determination related to the correlation coefficient?
The coefficient of determination measures the proportion of the variance in the dependent variable that can be explained by the independent variable(s). It ranges from 0 to 1, where 0 indicates no relationship and 1 indicates a perfect fit.
Since the coefficient of determination is the square of the correlation coefficient, squaring the correlation coefficient (r) will give us the value of r².
Body of the Solution:The coefficient of determination, denoted as R^2, is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). It ranges between 0 and 1.
The relationship between the coefficient of determination (R^2) and the correlation coefficient (r) is given by the equation:
R^2 = r^2
Given that r = 0.89, we can find the value of R^2:
R^2 = (0.89)^2
= 0.7921
So, the coefficient of determination (R^2) equals 0.7921, which is approximately 0.79.
Final Answer:Therefore,the coefficient of determination (R^2) equals 0.7921, which is approximately 0.79.
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The coefficient of determination (R^2) equals 0.7921, which is approximately 0.79.
How is the coefficient of determination related to the correlation coefficient?The coefficient of determination measures the proportion of the variance in the dependent variable that can be explained by the independent variable(s). It ranges from 0 to 1, where 0 indicates no relationship and 1 indicates a perfect fit.
Since the coefficient of determination is the square of the correlation coefficient, squaring the correlation coefficient (r) will give us the value of r².
The coefficient of determination, denoted as R^2, is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). It ranges between 0 and 1.
The relationship between the coefficient of determination (R^2) and the correlation coefficient (r) is given by the equation:
R^2 = r^2
Given that r = 0.89, we can find the value of R^2:
R^2 = (0.89)^2
= 0.7921
So, the coefficient of determination (R^2) equals 0.7921, which is approximately 0.79.
Therefore, the coefficient of determination (R^2) equals 0.7921, which is approximately 0.79.
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Two cards are dealt from a shuffled standard deck of cards. This means the cards are sampled uniformly at random without replacement. What is the probability that both cards are aces and one of them is the ace of spades
Answers
The Probability that both cards are spades and one of them is ace of the spade is 0.0026.
Total number of cards = 52
Number of ace cards = 4
Number of ace of spade = 1
a). Probability that both cards are spades and one of them is ace of spade is:
p=(1׳C₁)/⁵²C₂
= 0.0026
Here, ³C₁ is the number of ways of selecting one ace from the rest 3 aces (club, diamond, heart) and ⁵²C₂ is the number of ways of selecting 2cards from 52 cards and 1 is the sole way of selecting an ace of spade.
Therefore, the Probability that both cards are spades and one of them is ace of the spade is 0.0026.
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y=4x-16. Please Show work
Answers
Answer: x=4
Step-by-step explanation:
Step 1. turn you y into a 0
0=4x-16
Step 2. get x alone
a.
0 = 4x -16
+16 +16
*what you do to one side of the equal sign you must to the other.
b.
0 + 16 = 4x
(divide by 4) 16 = 4x (divide by 4)
*divide by 4 to get rid of the 4 next to the x, remeber to do both sides of the equal sign
4 = x
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(4, 5) , B (12, 9) ; 3 to 1
The coordinates of P are…?
Answers
For the line segment AB with coordinates A( 4,5) and B(12, 9) divided by point P in the ratio AP : PB = 3 : 1 then coordinates of P are ( 10,8).
As given in the question,
Given:
Line segment AB with coordinates A( 4,5) and B(12, 9)
Line segment AB divided by point P in the ratio AP : PB = 3: 1
Let (x ,y) be the coordinates of point P .
Coordinates of A(4,5) = ( x₁, y₁)
B(12,9) = (x₂ , y₂)
Ratio m : n = 3 : 1
Coordinates of point P is given by:
x = (mx₂ + nx₁)/ ( m+ n)
= [3(12) + 1(4)] / (3+1)
= ( 36 +4)/ 4
= 40 /4
= 10
x = (my₂ + n y₁)/ ( m+ n)
= [3(9) + 1(5)] / (3+1)
= ( 27 +5)/ 4
= 32/4
= 8
P(x ,y) = P(10, 8)
Therefore, For the line segment AB with coordinates A( 4,5) and B(12, 9) divided by point P in the ratio AP : PB = 3 : 1 then coordinates of P are ( 10,8).
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Is 2 a happy number?
Answers
No, 2 is not a happy number because 2 can not become 1 after a series of stages in which each step 2 is replaced by the sum of its squares
Let's try to first comprehend what numbers are.
An arithmetic value that is calculated and utilized to represent a quantity is called a number. Numeral symbols, such as "3" are used in writing to represent numbers. A number system is a methodical technique to express numbers using digits or other symbols. The numerical system is a helpful collection of numbers that illustrates the number's algebraic and mathematical structure. presents an example that is typical.
Happy numbers If a number leads to 1 after a series of stages in which each step's number is replaced by the sum of its squares, it is said to be happy. For example, if we start with a happy number and keep replacing it with the sum of its squares, we eventually reach 1.
So 2 is not a happy number.
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Find m angle Y
(6x – 23)
(4х + 9)
m angle Y = ?
a
54
b
34
C
73
d
16
Answers
Answer:
m<y= 34
Step-by-step explanation...
6x-23=4x+9
2x=32
x=16
m<y+m<z=180
m<y=73+73=180
m<y=34
An isosceles triangle is a two-dimensional figure which has two equal sides and the two angles opposite to the equal sides are equal.
The sum of the three angles is equal to 180 degrees.
The value of angle m∠Y is 34°.
Option B is the correct answer.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Isosceles triangle:
Two sides are equal.
The angles opposite to the equal sides are also equal.
So,
From the figure we have,
6x - 23 = 4x + 9
Add 23 on both sides.
6x - 23 + 23 = 4x + 9 + 23
6x = 4x + 32
Subtract 4x on both sides.
6x - 4x = 4x + 32 - 4x
2x = 32
Divide both sides by 2.
x = 32/2
x = 16
The sum of the three angles of the Isosceles triangle given must be 180 degrees.
6x - 23 + 4x + 9 + m∠Y = 180
Put x = 16
6x16 - 23 + 4x16 + 9 + m∠Y = 180
96 - 23 + 64 + 9 + m∠Y = 180
146 + m∠Y = 180
Subtract 146 on both sides.
m∠Y = 180 - 146
m∠Y = 34
Thus,
The value of angle m∠Y is 34°.
Option B is the correct answer.
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If k (x) = x^2 and p (x) = k (x) + n, what is the value of n?
Answers
The equation k(x) = x^2 is quadratic equation, and the value of n in p (x) = k (x) + n is -6
How to determine the value of n?The equations are given as:
k(x) = x^2
p (x) = k (x) + n
From the graph, we can see that the graph of k(x) is shifted down by 6 units.
This means that the equation of p(x) is
p (x) = k (x) - 6
By comparison;
n = -6
Hence, the value of n in p (x) = k (x) + n is -6
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A square could be called a _____ since it has four right angles.
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A square could be called a rectangle since it has four right angles.
A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.
A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°. Observe the rectangle given below to see its shape, sides and angles.
So, Every square is a rectangle because it is a quadrilateral with all four angles right angles.
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for a perfectly symmetrical distribution with µ = 30, what is the mode?
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In a perfectly symmetrical distribution with a mean (µ) of 30, there is no specific mode because all values occur with equal frequency.
In a perfectly symmetrical distribution, such as a symmetric bell-shaped curve or a uniform distribution, each value occurs with the same frequency. This means that there is no value that occurs more frequently than others, resulting in multiple modes or no mode at all.
The mode is typically used to identify the most common value in a dataset, but in a perfectly symmetrical distribution, all values have equal frequency, and there is no single mode. Instead, the distribution is characterized by its symmetry around the mean (µ). The mean represents the central tendency of the distribution, indicating the balance point of the data. In this case, with a mean of 30, the distribution is centered around this value, with equal numbers of observations on either side.
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By now you are adept at calculating averages and intuitively can estimate whether something is "normal" (a measurement not too far from average) or unusual (pretty far from the average you might expect). This class helps to quantify exactly how far something you measure is from average using the normal distribution. Basically, you mark the mean down the middle of the bell curve, calculate the standard deviation of your sample and then add (or subtract) that value to come up with the mile markers (z scores) that measure the distance from the mean.
For example, if the average height of adult males in the United States is 69 inches with a standard deviation of 3 inches, we could create the graph below.
Men who are somewhere between 63 and 75 inches tall would be considered of a fairly normal height. Men shorter than 63" or taller than 75" would be considered unusual (assuming our sample data represents the actual population). You could use a z score to look up exactly what percentage of men are shorter than (or taller than) a particular height.
Think of something in your work or personal life that you measure regularly (no actual calculation of the mean, standard deviation or z scores is necessary). What value is "average"? What values would you consider to be unusually high or unusually low? If a value were unusually high or low—how would it change your response to the measurement?
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Understanding the concept of average and what values are considered unusually high or low in measurements helps inform decision-making and prompts appropriate responses based on deviations from the norm.
In various aspects of life, such as work or personal activities, there are measurements that we regularly encounter. For example, in the context of sales performance, the average number of monthly sales could be considered the "average" value. Sales figures significantly higher than the average would be considered unusually high, while significantly lower figures would be considered unusually low.
Identifying unusually high or low values can have different implications depending on the situation. In the case of sales performance, unusually high sales could indicate exceptional performance or success, leading to rewards or recognition. Conversely, unusually low sales might signal underperformance, prompting the need for investigation or corrective measures.
By understanding what values are considered normal or unusual within a specific context, we can adjust our responses accordingly. This knowledge allows us to set benchmarks, identify outliers, and make informed decisions based on the measurements we encounter in our work or personal lives.
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