Answers
3x-1 = 4x-2
x=1
she had 1 hit
21)
2(3t+1) =4(2t-1)
6t+2 = 8t-4
6=2t
t=3
3 fish
Related Questions
A student has some 1 bills and $5 bills in his wallet. he has a total of 15 bills that are worth $47. how many of each type of bill does he have?
Answers
Total number of bills - 15
Total value of the bills - $47
Bills - $1 and $5
*Solution
Let:
x - number of $1 bills
y - number of $5 bills
1. The total number of bills comprising of $1 and $5 bills is 15. Thus,
x + y = 15 (EQUATION 1)
2. The total value of the bills is $47. Thus,
$1 (x) + $5 (y) = $47 (EQUATION 2)
3. There are 2 ways to solve this (system of linear equations) mathematically. You can use the elimination method or the substitution method. Using the elimination method to eliminate the variable x... (subtract Equation 1 from Equation 2)
1x + 5y = 47
_
x + y = 15
0 + 4y = 32
4. Thus, the value of y, which is the number of $5 bills is,
4y = 32
4 4
y = 8
5. The number of $1 bills (x) can then be solved using either Equations 1 or 2. Using Equation 1 to determine x,
x + y = 15
x = 15 - y
x = 15 - 8
x = 7
From the solution, we have determined that there are 8 pieces of $5 bills and 7 pieces of $1 bills.
Answer:
B. seven $1 bills and eight $5 bills.
Step-by-step explanation:
n = number of $1 bills
m = number of $5 bills
Given:
n + m = 15
n($1) + m($5) = $47
Just solve 2 equations in 2 unknowns n and m:
(i) n + m = 15
(ii) n + 5m = 47
Subtract (i) from (ii) and get
4m = 32
m = 32/4 = 8
Then from (i) get
n = 15 - m = 15 - 8 = 7
There are 7 $1 bills and 8 $5 bills.
If a microscope has a series of three lenses that magnify individually 5x, 5x, and 7x, what is the total magnification of the microscope
Answers
Hope this helps!
The total magnification of the microscope is 175x.
Given that,
If a microscope has a series of three lenses that magnify individually 5x, 5x, and 7x.Based on the above information, the calculation is as follows:
[tex]= 5 \times 5 \times 7[/tex]
= 175x
Therefore we can conclude The total magnification of the microscope is 175x.
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Anthony has 115 book in his room .He is storing them in boxes .Each box holds 17 book .How many boxes does Anthony need?
Answers
Anthony need 7 boxes to hold 115 books.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Anthony has 115 books in his room.
And, He is storing them in boxes.
Each box holds 17 books.
Now,
Since, Total number of books = 115
And, Each box holds 17 books.
Hence, Number of boxes to cover 115 books = 115 ÷ 17
= 7
Since, We get the quotient after divide 115 by 17 is 13.
So, Anthony use 1 box extra to keep 13 remaining books.
Thus, Anthony need 7 boxes to hold 115 books.
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Write an equation in point-slope form of the line through point J(-8,10) with slope -5.
A. y + 10 = -5(x + 8)
B. y - 10 = 5(x + 8)
C. y - 10 = -5(x + 8)
D. y - 10 = -5(x - 8)
Answers
Hope this helps! :)
REVISE: I accidently put y instead of x in the -5(x + 8) part. It's fixed now.
Identify the degree of the polynomial 6xy2 − xy + 8 + 12y.
Answers
the product of two consecutive odd integers is one less than four times their sum. Find the two integers.
Answers
x^2 + 2x = 8x + 8 - 1
x^2 - 6x - 7 = 0
(x-7)(x+1) = 0
x = 7 and x = -1
the two integers are 7 and 9
or
two integers are - 1 and 1
Which choices are equivalent to the fraction below? Check all that apply.
Answers
answer is C and E
Which of the following disjunctions is false ?
A. 4 - 3 = 2 or 6 · 3 = 9
B. 5 · 6 = 30 or 3 + 4 = 7
C. 8 + 3 = 11 or 5 · 4 = 23
D. 7 + 6 = 13 or 5 · 2 = 10
Answers
----------------------------------------------
Choice A
4-3=2 is false
6*3=9 is false
both parts are false, so overall the entire disjunction is false
----------------------------------------------
Choice B
5*6=30 is true
3+4=7 is true
Neither part is false, so overall the entire thing is true
----------------------------------------------
Choice C
8+3=11 is true
5*4=23 is false
While second piece is false, the overall disjunction is true. The first part (true) makes the whole thing true.
----------------------------------------------
Choice D
7+6=13 is true
5*2=10 is true
Neither part is false, so overall the entire thing is true
----------------------------------------------
----------------------------------------------
In summary, we have
A. False
B. True
C. True
D. True
Making choice A the only answer that is false. So choice A is the final answer
Both 4 – 3 = 2 and 6 · 3 = 9 parts are false, so overall the entire disjunction is false.
What is a disjunction?A logical relation called a disjunction states that either one or more of the stated choices are correct.
A. 4 – 3 = 2, is false
6 · 3 = 9, is false
Both parts are false, so overall the entire disjunction is false
B. 5 · 6 = 30, is true
3 + 4 = 7, is true
Neither part is false, so overall the entire thing is true
C. 8 + 3 = 11, is true
5 · 4 = 23, is false
While second piece is false, the overall disjunction is true. The first part (true) makes the whole thing true.
D. 7 + 6 = 13, is true
5 · 2 = 10, is true
Neither part is false, so overall the entire thing is true
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There are 20 counters in a box. A counter is chosen and replaced 100 times, the results are 32 blue and 68 red. How many of each color do you think there are in each box ?
Answers
45x = 2160
x - 2160/45 = 48 people
2)
n = (n - 1) - 5
3)
7x - 11 = 19 - 3x
add 3x to both sides:
10x - 11 = 19
add 11 to both sides:
10x = 30
divide both sides by 10:
x = 30/10 = 3
4)
4(8)(11) - 64 = 288
5)
(5, 0)
6)
-4x -3 + 2x - 6 = -2x - 9
7)
1.8(-20) + 32 = -4F
8)
Exterior angle add to 360
360/6 = 60 degrees
10)
2x/9 = 12
2x = 108
x = 108/2 = 54
11)
x = 0
12)
8 + 3 + 1 = 12
240/12 = 20
8(20) = 160
3(20) = 60
1(20) = 20
160 pounds, 60 pounds, 20 pounds
Factor out the greatest common factor. 2s4 - 4s2
Answers
The average rate of change of the function f(x)=4x^3 + 4 over the interval [66,88] is
Answers
Interval [66,88] which is x₁=66, x₂=88
f (x)=4x³+4
f (x₁)=f (66)=4 (66)³+4=1149988
f (x₂)=f (88)=4 (88)³+4=2725892
Average rate of change =2725892-1149988/88-66
=1575904/22
=71632
Krista is planning to mow her grandparents lawn the rectangular yard is 10 yards by 12 yards but there is a square patio that has 12 foot sides in the middle of Krista kenmo 15 square feet per minute about how long will it take to finish the yard
Answers
Which graph describes the open sentence –1 ≤ n + 2 ≤ 6?
A. Number line showing range from negative four to four. There are two rays on the graph. The first has a right end point with a closed dot at negative two with a ray pointing left past negative four. The second has a left end point with an open circle at three with a ray pointing right past four.
B. Number line -5 to +5 in single-integer increments - assessment graphic
C. Number line showing range from negative three to three The left end point is an open circle halfway between negative one and zero. There is a closed dot at three, and a ray points past three.
D. Number line showing range from negative eight to eight. There are two rays on the graph. The first has a right end point with an open circle halfway between negative six and negative four with a ray pointing left past negative eight. The second has a left end point with an open circle at four with a ray pointing right past eight.
Answers
The value of n≥-3 and n≤4 describes the open sentence -1≤n+2≤6
What will be the range of n for -1 ≤ n+2 ≤ 6 ?If we follow the above condition for the different values of n
At value of n=-3 we will get n+2=-3+2=-1
similarly at n=-2 we will get n+2=-2+2=0
and at n=-1 we will get n+2=-1+2=1
all three (-1,0,1) follow the condition -1 ≤ n+2
Similarly at n=(0,1,2,3,4) condition n+2 ≤ 6 is followed
Hence value of n≥-3 and n≤4 describes the open sentence -1≤n+2≤6
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The correct graph is option C.
Sure, let's break down the steps to understand why option C is the correct graph for the open sentence [tex]\(-1 \leq n + 2 \leq 6\)[/tex]:
1. Identify the Middle Term: The middle term in the open sentence is [tex]\(n + 2\)[/tex]. This means our focus is on the expression [tex]\(n + 2\)[/tex].
2. Understand the Inequality: The inequality [tex]\( -1 \leq n + 2 \leq 6\)[/tex] can be understood as "n + 2 is greater than or equal to -1 and less than or equal to 6".
3. Subtract 2 from Each Part: To isolate [tex]\(n\)[/tex], subtract 2 from each part of the inequality:
[tex]\[ -1 - 2 \leq n + 2 - 2 \leq 6 - 2 \][/tex]
Which simplifies to:
[tex]\[ -3 \leq n \leq 4 \][/tex]
4. Draw the Number Line: Draw a number line ranging from -3 to 4, inclusive.
5. Plot the Endpoints: On the number line, mark endpoints at -3 and 4.
6. Determine the Endpoints: Since the inequality includes "equal to" signs, the endpoints should be marked with closed dots (indicating inclusion).
7. Determine the Direction of the Ray: Since the inequality does not include strict inequality signs (< or >), the rays should extend in both directions from the endpoints.
8. Indicate the Rays: Draw rays to the left of -3 and to the right of 4, indicating the range extends indefinitely in both directions.
9. Mark the Open Circle: Since the inequality involves strict inequality at -1 and 6, mark an open circle at the points halfway between -1 and -3, and 6 and 4, respectively.
10. Verify the Result: The resulting graph should have closed dots at -3 and 4, indicating the range includes those values, and open circles at -1 and 6, indicating exclusion.
Option C correctly represents these steps, making it the correct graph.
The graph is given below:
How to prove system of nonlinear equations has finite solutions?
Answers
Please help me with 3 math questions!!! I will give 30 points and brainliest to whoever answers the best!
1. Write the inverse function for the function, ƒ(x) = 1/2x + 4. Then, find the value of ƒ -1(4). Type your answers in the box.
ƒ -1(x) = (answer) x (answer)(answer)
ƒ -1(4) = (answer)
2. Match each function with the expression representing its inverse function. Match one of the numbers with the correct letter.
1. y = x - 4
2. g(x) = -0.5x
3. k(x) = x
4. p(x) = x + 4
5. h(x) = 4x
6. ƒ(x) = x/2
a. 2x
b. x + 4
c. x - 4
d. -2x
e. 0.25x
f. x
3. The graph of a function g is shown below.
Find its inverse.
(picture below, my answer is NOT correct)
Answers
original function: f(x)=(1/2)x+4
switch: x=(1/2)f(x)+4
f(x)=2x-8, this is the answer for question 1
answer for question 2: 1-b, 2-d, 3-f, 4-c, 5-e, 6-a
question 3
From the given graph, we know the slope is 2/5, the y intercept is -2, so the original function is f(x)=(2/5)x-2
switch x and f(x): x=(2/5)f(x)-2
solve for f(x): (2/5)f(x)=x+2
multiply both side by 5/2: f(x)=(5/2)x+5,
so the second choice is the correct answer.
From long experience, it is known that the time it takes to do an oil change and lubrication job on a vehicle has a normal distribution with a mean of 17.8 minutes and a standard deviation of 5.2 minutes. An auto service shop will give a free lube and oil change service to any customer who must wait beyond the guaranteed time to complete the work. If the shop does not want to give more than 1% of its customers a free lube and oil change service, how long should the guarantee be? Round appropriately to the minute.
Answers
To find the guarantee time for an oil change and lubrication job, calculate the z-score for the 1% percentile of a standard normal distribution and use the formula z = (x - μ) / σ to solve for x. Round x to the nearest whole number.
Explanation:The question is asking for the guarantee time that an auto service shop should offer for an oil change and lubrication job. To find this, we need to calculate the z-score that corresponds to the 1% percentile of a standard normal distribution. The z-score can be found using a z-table or calculator, and then we can use the formula z = (x - μ) / σ to solve for x. Round x to the nearest whole number to get the guarantee time.
Assume that you pay $2,849.84 in state property taxes every year. If your property has an assessed value of $41,302, what is your state’s property tax rate? a. 0.077 b. 0.032 c. 0.014 d. 0.069
Answers
Answer:
Therefore, The correct option is D. 0.069
Step-by-step explanation:
Amount of the money paid in the state property taxes every year = $2849.84
The property owned has an assessed value.
Now, the assessed value of the property is $41302
We need to find the state's property tax rate.
[tex]\text{So, State's property tax rate = }\frac{\text{state's property tax}}{\text{assessed value}}\\\\\text{State's property tax rate = }\frac{2849.84}{41302}\approx 0.069[/tex]
Therefore, The correct option is D. 0.069
An article considered the use of a uniform distribution with A = 0.20 and B = 4.25 for the diameter X of a certain type of weld (mm).
Answers
Using the formula f(x) = 1/(b-a), where B is 4.25 and A is 0.20. Substituting these values to the formula, we get f(x) = 1/(4.25-0.2) = 0.24691358. Therefore, we get the answer f(x) = 0.24691358, 0.20<x<4.25. Otherwise, it is 0.
Using the formula f(x) =1/(b-a)
B is 4.25 and A is 0.20.
Put these values to the
We get f(x) = 1/(4.25-0.2) = 0.24691358.
f(x)= 0.24691358, 0.20<x<4.25.
Further Explanation:
uniform distribution:
A uniform distribution, some of the time otherwise called a rectangular circulation, is a dispersion that has steady likelihood. The likelihood thickness work and combined circulation work for a nonstop uniform appropriation on the interim are (1) (2).
we use uniform distribution:
The uniform circulation gets its name from the way that the probabilities for all results are the equivalent. Rather, every result is similarly prone to happen. Not at all like a chi-square dissemination, there is no skewness to a uniform dispersion. Accordingly, the mean and middle concur.
diameter:
In geometry, a breadth of a circle is any straight line portion that goes through the focal point of the circle and whose endpoints lie on the circle. It can likewise be characterized as the longest harmony of the circle. The two definitions are likewise substantial for the measurement of a circle.
formula of diameter:
In the event that you know the zone of the circle, separate the outcome by π and locate its square root to get the sweep; at that point increase by 2 to get the distance across. This returns to controlling the equation for finding the zone of a circle, A = πr2, to get the distance across. You can change this into r = √(A/π) cm.
Subject: mathematics
Level: High School
Keywords: uniform distribution, we use uniform distribution, diameter, formula of diameter.
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what is the answer to algebra with pizzazz page 100; what should you say if you see a tall, wrought-iron tower in paris, france?
there are 24 blanks
Answers
Given
[tex]3n^2-17n+24 \\ \\ \Rightarrow3n^2-9n-8n+24 \\ \\ \Rightarrow3n(n-3)-8(n-3) \\ \\ \Rightarrow(3n-8)(n-3)[/tex]
Part 2:
Given
[tex]4x^3y-49xy^3 \\ \\ \Rightarrow xy(4x^2-49y^2) \\ \\ \Rightarrow xy(2x-7y)(2x+7y)[/tex]
Part 3:
Given
[tex]5x^2+20xy-60y^2 \\ \\ \Rightarrow5x^2-10xy+30xy-60y^2 \\ \\
\Rightarrow5x(x-2y)+30y(x-2y) \\ \\ \Rightarrow(5x+30y)(x-2y) \\ \\ \Rightarrow5(x+6y)(x-2y)[/tex]
Part 4:
Given
[tex]3x^3-x^2y+12x-4y \\ \\ \Rightarrow3x^3+12x-x^2y-4y \\ \\ \Rightarrow3x(x^2+4)-y(x^2+4) \\ \\ \Rightarrow(3x-y)(x^2+4)[/tex]
Part 5:
Given
[tex]2x^4y-3x^3y-20x^2y \\ \\ \Rightarrow x^2y(2x^2-3x-20) \\ \\ \Rightarrow x^2y(2x^2-8x+5x-20) \\ \\ \Rightarrow x^2y[2x(x-4)+5(x-4)] \\ \\ \Rightarrow x^2y(2x+5)(x-4)[/tex]
Part 6:
Given
[tex]9x^3y+33x^2y^2+30xy^3 \\ \\ \Rightarrow3xy(3x^2+11xy+10y^2) \\ \\ \Rightarrow3xy(3x^2+6xy+5xy+10y^2) \\ \\ \Rightarrow3xy[3x(x+2y)+5y(x+2y)] \\ \\ \Rightarrow3xy(3x+5y)(x+2y)[/tex]
Part 7:
Given
[tex]16a^3b^4+40a^2b^5+8ab^3 \\ \\ \Rightarrow8ab^3(2a^2b+5ab^2+1)[/tex]
Part 8:
Given
[tex]t^4-37t^2+36 \\ \\ \Rightarrow(t-1)(t-36)[/tex]
Part 9:
Given
[tex]2a^7b^3-288ab \\ \\ \Rightarrow2ab(a^6b^2-144) \\ \\ \Rightarrow2ab(a^3b-12)(a^3b+12)[/tex]
Part 10
Given
[tex]35a^2b-5a-7ab^2+b \\ \\ \Rightarrow35a^2b-7ab^2-5a+b \\ \\ \Rightarrow7ab(5a-b)-(5a-b) \\ \\ \Rightarrow(7ab-1)(5a-b)[/tex]
Part 11:
[tex]6a^4b^2-11a^3b^3+4a^2b^4 \\ \\ \Rightarrow a^2b^2(6a^2-11ab+4b^2) \\ \\ \Rightarrow a^2b^2(6a^2-3ab-8ab+4b^2) \\ \\ \Rightarrow a^2b^2[3a(2a-b)-4b(2a-b)] \\ \\ \Rightarrow a^2b^2(3a-4b)(2a-b)[/tex]
Part 12:
Given
[tex]t^2(t+3)+6t(t+3)+9(t+3) \\ \\ \Rightarrow(t^2+6t+9)(t+3) \\ \\ \Rightarrow(t+3)(t+3)(t+3) \\ \\ \Rightarrow(t+3)^3[/tex]
Answer: That’s really quite an eyeful
Step-by-step explanation:
The bottom answer to all of it is
That’s really quite an eyeful.
Solve x2 + 4x − 4 = 0.
Answers
The solution to the given quadratic equation is: x = - 2 ± 2√2
What is the solution to the quadratic equation?The general form of a quadratic equation is expressed as;
y = ax ² + bx + c
The quadratic equation is given as;
x² + 4x - 4 = 0
We can solve either by quadratic formula or by factorization
We will use quadratic formula as;
x = [-b ± √(b² - 4ac)]/2a
Thus:
x = [-4 ± √(4² - 4(1 * - 4))]/2(1)
x = (-4 ± √32)/2
x = - 2 ± 2√2
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To solve the quadratic equation x^2 + 4x - 4 = 0, identify the coefficients, apply the quadratic formula, and find the solutions.
To solve the quadratic equation x2 + 4x - 4 = 0:
Identify the coefficients a = 1, b = 4, and c = -4.Substitute the values into the quadratic formula: x = (-b ± √(b2 - 4ac)) / 2a.Solve for x to find the two possible solutions.Write the complete balanced equation for the reaction between barium oxide (BaO) and water (H2O). You do not need to make the subscripts smaller; just write them out as regular numbers. For example: H2O.
Answers
Answer:
The balanced chemical equation is ;
[tex]BaO(s)+H_2O(l)\rightarrow Ba(OH)_2(aq)[/tex]
Step-by-step explanation:
When barium hydroxide react with water it gives an alkaline solution of barium hydroxide.
The balanced chemical equation is given as:
[tex]BaO(s)+H_2O(l)\rightarrow Ba(OH)_2(aq)[/tex]
according to stoichiometry,when 1 mole of barium oxide reacts with 1 mole of water it gives 1 mole of barium hydroxide.
The cost c ( x ) c(x), where x x is the number of miles driven, of renting a car for a day is $49 plus $0.55 per mile.
Answers
To calculate the cost c(x) of renting a car for a day based on the number of miles driven, use the formula c(x) = $49 + $0.55 imes x, where x represents miles driven.
Explanation:The student's question involves calculating the cost of renting a car for a day based on the number of miles driven. The function c(x) represents the total cost, which includes a fixed charge and a variable charge per mile. The fixed charge is $49, and the variable charge is $0.55 per mile. The total cost can be expressed as c(x) = $49 + $0.55 imes x, where x is the number of miles driven.
To calculate the cost for a given number of miles, simply multiply the number of miles by $0.55 and add the base charge of $49. For example, if a student drives 20 miles, the cost would be calculated as follows: c(20) = $49 + ($0.55 imes 20) = $49 + $11 = $60.
The gasoline prices in seven states are $1.96, $2.09, $1.79, $1.61, $1.75, 2.11, and $1.84 what is the median gas price and the difference of the first and third quartiles
Answers
1.61, [1.75], 1.79, (1.84), 1.96, [2.09], 2.11
the median (the middle number) = 1.84 <=
the difference of the first and 3rd quartiles (the IQR) =
2.09 - 1.75 = 0.34 <=
Answer:
Median = $1.84
The difference of the first and third quartiles = $0.34
Step-by-step explanation:
Median
How to calculate the median of a small data or ungrouped data;
1. Arrange the data in ascending or descending order.
2. Choose the middle value. The middle value can be a single value or two value. If the middle value is a single value, then, that value is the median but if the middle values are two, the mean of the two middle values is evaluated to get the median.
Arranging the gasoline prices given in ascending order;
$1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11
The middle value is a single number $1.84 in bold. Therefore, the median is $1.84.
Median = $1.84
First (Lower) Quartile
To calculate for the First (Lower) quartile,
1. Arrange the data give in ascending order.
2. The First (Lower) quartile, Q1 is then calculated using;
[tex]Q1 =\frac{1}{4} (n + 1)^{th}[/tex] term
where n is the total number of terms of the data. In the given question, the total number of terms, n = 7
[tex]Q1 =\frac{1}{4} (7 + 1)^{th}[/tex] term
[tex]Q1 =\frac{8}{4}^{th}[/tex] term
Q1 = 2nd term
3. Select the 2nd term of the given data already arranged in ascending order.
$1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11
The First Quartile, Q1 = $1.75
Third (Upper) Quartile
To calculate for the third (upper) quartile,
1. Arrange the data give in ascending order.
2. The third (upper) quartile (Q3) is then calculated using;
[tex]Q3 =\frac{3}{4} (n + 1)^{th}[/tex] term
where n is the total number of terms. In the given question, the total number of terms, n = 7
[tex]Q3 =\frac{3}{4} (7 + 1)^{th}[/tex] term
[tex]Q3 =\frac{24}{4}^{th}[/tex] term
[tex]Q3 = 6^{th} term[/tex]
3. Select the [tex]6^{th} term[/tex] of the given data already arranged in ascending order.
$1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11
The third (upper) quartile Q3 = $2.09
The difference between the first and third quartiles is called interquartile range.
Now, calculating the difference of the first and third quartiles
Interquartile Range = Q3 - Q1
$2.09 - $1.75 = $0.34
The difference of the first and third quartiles, Interquartile Range = $0.34
The perimeter of a rectangle is 78 cm and the basis measures 27 cm. Calculates the perimeter of the square equivalent to the rectangle.
Answers
27*12=324 cm² (A rectangle)
4*√324=
4*18=
72 cm (perimeter of the square)
SOMEONE PLEASE HELP ME ASAP!!!
1. In recent years, there has been considerable discussion about the appropriateness of the body shapes and proportions of the Ken and Barbie dolls. These dolls are very popular, and there is some concern that the dolls may be viewed as having the "ideal body shape," potentially leading young children to risk anorexia in pursuit of that ideal. Researchers investigating the dolls' body shapes scaled Ken and Barbie up to a common height of 170.18 cm (5'7") and compared them to body measurements of active adults. Common measures of body shape are the chest (bust), waist, and hip circumferences. These measurements for Ken and Barbie and their reference groups are presented in the table below.
Ken Barbie
Chest Waist Hips | Chest Waist Hips
Doll: 75.0 56.5 72.0 | 82.3 40.7 72.7
Human x-bar: 91.2 80.9 93.7 | 90.3 69.8 97.9
Human S: 4.8 9.8 6.8 | 5.5 4.7 5.4
Suppose that the researchers' scaled-up dolls suddenly found themselves in the human world of actual men and women.
Convert Ken's chest, waist, and hips measurements to z-scores. Which of those measures appears to be the most different from Ken's reference group (human males)? Justify your response with an appropriate statistical argument.
2. In recent years, there has been considerable discussion about the appropriateness of the body shapes and proportions of the Ken and Barbie dolls. These dolls are very popular, and there is some concern that the dolls may be viewed as having the "ideal body shape," potentially leading young children to risk anorexia in pursuit of that ideal. Researchers investigating the dolls' body shapes scaled Ken and Barbie up to a common height of 170.18 cm (5'7") and compared them to body measurements of active adults. Common measures of body shape are the chest (bust), waist, and hip circumferences. These measurements for Ken and Barbie and their reference groups are presented in the table below.
Ken Barbie
Chest Waist Hips | Chest Waist Hips
Doll: 75.0 56.5 72.0 | 82.3 40.7 72.7
Human x-bar: 91.2 80.9 93.7 | 90.3 69.8 97.9
Human S: 4.8 9.8 6.8 | 5.5 4.7 5.4
Suppose that the researchers' scaled-up dolls suddenly found themselves in the human world of actual men and women.
Convert Barbie's chest, waist, and hips measurements to z-scores. Do these z-scores provide evidence to justify the claim that the Barbie doll is too thin of a representation of adult women? Justify your response with an appropriate statistical argument.
3. Jill scores 680 on the mathematics part of the SAT. The distribution of SAT scores in a reference population is normally distributed with the mean 500 and standard deviation 100. Jack takes the ACT mathematics test and scores 27. ACT scores are normally distributed with mean 18 and standard deviation 6.
Find the standardized scores for both students.
4. Jill scores 680 on the mathematics part of the SAT. The distribution of SAT scores in a reference population is normally distributed with the mean 500 and standard deviation 100. Jack takes the ACT mathematics test and scores 27. ACT scores are normally distributed with mean 18 and standard deviation 6.
Assuming that both tests measure the same kind of ability, who has the higher score, and why?
5. A lunch stand in the business district has a mean daily gross income of $420 with a standard deviation of $50. Assume that the daily gross income is normally distributed.
If a randomly selected dat has a gross income of $520, then how many standard deviations away from the mean is that day's gross income?
Answers
zChest -> (91.2-75)/4.8=-3.4zWaist -> (80.9-56.5)/9.8≈-2.5zHips -> (93.7-72)/6.8≈-3.2It would be Ken's chest because the difference between the doll and an averaged human male is the greatest
2.)
zChest -> (82.3-90.3)/4.7≈-1.45zWaist -> (40.7-69.8)/4.7≈-6.19zHips -> (72.7-97.9)/5.4≈-4.7
Yes because the waist is far too thin compared to an averaged human woman
3.)
zJill -> (680-500)/100=1.8zJack -> (27-18)/6=1.5
4.)
It would be Jill because she has the higher z-score
5.)
$520-420=80$50=SDs$80(1 SD/50)=1.6 SD
Use lagrange multiplier techniques to find the local extreme values of f(x, y) = x2 − y2 − 2 subject to the constraint x2 + y2 = 16
Answers
The local extreme values of [tex]\( f(x, y) = x^2 - y^2 - 2 \)[/tex] subject to the constraint [tex]\( x^2 + y^2 = 16 \)[/tex] are -18 at points (0, 4) and (0, -4).
To find the local extreme values of [tex]\( f(x, y) = x^2 - y^2 - 2 \)[/tex] subject to the constraint [tex]\( x^2 + y^2 = 16 \)[/tex] using Lagrange multiplier techniques, we need to set up the Lagrangian function:
[tex]\[ L(x, y, \lambda) = f(x, y) - \lambda(g(x, y) - c) \][/tex]
where [tex]\( g(x, y) \)[/tex] is the constraint, c is a constant, and [tex]\( \lambda \)[/tex] is the Lagrange multiplier.
In this case, [tex]\( g(x, y) = x^2 + y^2 \)[/tex] is the constraint, and c = 16 .
So, the Lagrangian function is:
[tex]\[ L(x, y, \lambda) = x^2 - y^2 - 2 - \lambda(x^2 + y^2 - 16) \][/tex]
Now, find the partial derivatives of L with respect to ( x, y, ) and[tex]\( \lambda \)[/tex] and set them equal to zero to find critical points:
[tex]\[ \frac{\partial L}{\partial x} = 2x - 2\lambda x = 0 \]\[ \frac{\partial L}{\partial y} = -2y - 2\lambda y = 0 \]\[ \frac{\partial L}{\partial \lambda} = x^2 + y^2 - 16 = 0 \][/tex]
Solving the system of equations, we get two critical points:
1. When [tex]\( x = 0, y = 4, \lambda = -\frac{1}{4} \)[/tex]
2. When [tex]\( x = 0, y = -4, \lambda = -\frac{1}{4} \)[/tex]
Now, evaluate f(x, y) at these critical points:
1. f(0, 4) = 0 - 16 - 2 = -18
2. f(0, -4) = 0 - 16 - 2 = -18
Therefore, the local extreme values of [tex]\( f(x, y) = x^2 - y^2 - 2 \)[/tex] subject to the constraint [tex]\( x^2 + y^2 = 16 \)[/tex] are -18 at points (0, 4) and (0, -4).
A card is drawn from a standard deck of 52 cards. find p(drawing an ace and 9)
Answers
possibility of drawing any one card would be proportion
52(cards in deck) : 100%(full deck has 100%)=1(this is any one card in deck) : X(possibility you are looking for)
X=100/52=about 1.9% of geting Ace 9
Write an equation of the circle with center , −45 and radius 6 .
Answers
How do we modify this equation to shift the circle and change its radius, then? Well, if we want to change the radius, we simply have to change the hypotenuse of the triangle that's sweeping out the circle in the first place. The default for a circle is 1, but we're looking for a radius of 6, so our equation, in line with Pythagorus's, would look like [tex]x^2+y^2=6^2[/tex], or [tex] x^{2} +y^2=36[/tex].
Shifting the center of the circle is a bit of a longer story, but - at first counterintuitively - you can move a circle's center to the point (a,b) by altering the x and y portions of the equation to read:
[tex](x-a)^2+(y-b)^2[/tex]
Choose the correct answer.
You are offered an item for $22.85. If the seller states he normally sells the same item for $29.95, what percentage discount is he offering you
A. 24.22
B.23.96
C.23.71
Answers
29.95 - 22.85 = 7.10
7.10 / 29.95 = 0.23706 = 23.71 percent
Answer is C
Answer:
23.71%
Step-by-step explanation:
Given :You are offered an item for $22.85. If the seller states he normally sells the same item for $29.95,
To Find :what percentage discount is he offering you
Solution :
The original price is $29.95
The offered price is $22.85
So the discount percentage = [tex]\frac{\text{original price-offered price}}{\text{original price}}*100[/tex]
= [tex]\frac{29.95-22.85}{29.95}*100[/tex]
= [tex]\frac{7.1}{29.95}*100[/tex]
= 23.71%
Thus the percentage of discount is 23.71%
Given equal probabilities of the birth of a boy or girl, what is the probability that a group of four siblings includes all boys? all girls? all boys or all girls?
Answers
The probability of a group of four siblings being all boys or all girls is 1/8, with each individual probability being 1/16.
Probability of All Boys:
Probability of a boy birth: 1/2
Probability of all boys among 4 siblings:
(1/2) × (1/2) × (1/2) × (1/2) = 1/16
Probability of All Girls:
Probability of a girl birth: 1/2
Probability of all girls among 4 siblings:
(1/2) × (1/2) × (1/2) × (1/2) = 1/16
Probability of All Boys or All Girls: Since these are mutually exclusive events, add their probabilities:
1/16 (all boys) + 1/16 (all girls) = 1/8