The relationship between women’s whole-number shoe sizes and foot length forms an arithmetic sequence, where an is the foot length in inches that corresponds to a shoe size of n. A women’s size 3 fits a foot 8 inches long and women’s size 7 fits a foot 91 3 inches long. What is the common difference of the arithmetic sequence?
Answer:
part 1- 1/3
part 2- a.n = 22/3+(n-1)1/3
part 3- size 12
Step-by-step explanation:
The common difference of the arithmetic sequence is 0.5 inches.
To find the common difference of the arithmetic sequence, we can use the given information about the shoe sizes and corresponding foot lengths.
Let's denote the common difference by [tex]\( d \)[/tex]. In an arithmetic sequence, the[tex]\( n \)-th[/tex] term is given by [tex]\( a_n = a_1 + (n - 1)d \)[/tex], where [tex]\( a_1 \)[/tex] is the first term.
Given that a women's size 3 fits a foot 8 inches long, we can consider this as the first term of the arithmetic sequence:
[tex]\[ a_1 = 8 \][/tex]
We are also given that a women's size 7 fits a foot[tex]\( 9\frac{1}{3} \)[/tex] inches long. Since this corresponds to the 5th term in the sequence (because [tex]\( 7 - 3 = 4 \)[/tex] and we start counting from 0), we can write:
[tex]\[ a_5 = a_1 + 4d \][/tex]
[tex]\[ a_5 = 8 + 4d \][/tex]
We know[tex]\( a_5 = 9\frac{1}{3} \),[/tex]which is [tex]\( 9 + \frac{1}{3} \) or \( \frac{28}{3} \)[/tex] inches. Now we can set up the equation:
[tex]\[ 8 + 4d = \frac{28}{3} \][/tex]
To solve for [tex]\( d \)[/tex], we first convert[tex]\( \frac{28}{3} \)[/tex] to a decimal or a fraction with a denominator of 1 to match the units of the other terms:
[tex]\[ 8 + 4d = \frac{28}{3} \times \frac{1}{1} \][/tex]
[tex]\[ 8 + 4d = \frac{28}{3} \][/tex]
[tex]\[ 8 + 4d = 9\frac{1}{3} \][/tex]
[tex]\[ 8 + 4d = 9.333... \][/tex]
Now, we solve for[tex]\( d \)[/tex]:
[tex]\[ 4d = 9.333... - 8 \][/tex]
[tex]\[ 4d = 1.333... \][/tex]
[tex]\[ d = \frac{1.333...}{4} \][/tex]
[tex]\[ d = 0.333... \][/tex]
However, we need to express[tex]\( d \)[/tex] in inches, and since [tex]\( \frac{1}{3} \)[/tex] of an inch is [tex]\( 0.333... \)[/tex]inches, we convert it to a fraction that has a denominator of 2 to match the format of the options given:
[tex]\[ d = \frac{1}{3} \times \frac{2}{2} \][/tex]
[tex]\[ d = \frac{2}{6} \][/tex]
[tex]\[ d = \frac{1}{3} \][/tex]
[tex]\[ d = 0.5 \][/tex]
Therefore, the common difference of the arithmetic sequence is[tex]\( 0.5 \)[/tex]inches."
Katie wants to buy some popcorn for her family at the theater. Each small tub of popcorn costs $3 and each large tub of popcorn costs $4. She needs to buy at least 7 tubs of popcorn, but she only has $24 in her wallet.
If the solution region represents the number of small and large tubs of popcorn that Katie can buy, determine which graph represents the solution set to the system of inequalities representing this situation.
The correct solution is shown in the graph (D)
Given that the budget is $24 and the minimum is 7 tubs, the fourth graph shows the area in which both constraints are satisfied: triangular area between the points
7 small tubs
8 small tubs
3 large and 4 small tubs
Lets x = # of small tub of popcorn and y = # of large tub of popcorn
She needs to buy at least 7 tubs of popcorn: x + y >= 7
Each small tub of popcorn costs $3 and each large tub of popcorn costs $4 but she only has $24 in her wallet.
3x + 4y <= 24
So now you have the system of inequalities
x + y >= 7
3x + 4y <= 24
Find x and y intercepts of blue line
x + y = 7
x = 0 then y = 7
y = 0 then x = 7
The inequality sign is >= so it's above.
The blue line, B and D are matching the results
Find x and y intercepts of red line
3x + 4y = 24
x = 0 then 4y = 24; y = 6
y = 0 then 3x = 24; x = 8
The inequality sign is <= so it's below.
The red line, Only B is matching
Answer
D is the solution of the system of inequalities.
Which inequality represents the values of that ensure triangle exists? a triangle with these side lengths: AC = 18 units, BC = 6x units, and AB = 2x + 4 units
Answer:
7/4 < x < 11/2
Step-by-step explanation:
PLATO
Inequality which ensure triangle exists is 22 > 4x > 7.
What is inequality ?
" Inequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."
Theorem used
In ΔABC,
AB + BC >AC
AC+ BC >AB
AC + AB > BC
According to the question,
In triangle ABC.
AC = 18units
BC = 6x units,
AB = 2x + 4 units
Substitute the value in the inequality to ensure triangle exists we get,
[tex]AB + BC > AC[/tex]
⇒[tex]2x + 4 + 6x > 18[/tex]
⇒[tex]8x > 18 - 4[/tex]
⇒ [tex]8x > 14[/tex]
⇒ [tex]4x > 7[/tex] ___(1)
[tex]AC + AB > BC[/tex]
⇒ [tex]18 + 2x + 4 > 6x[/tex]
⇒ [tex]22 > 6x-2x[/tex]
⇒[tex]22 > 4x[/tex] ____(2)
From (1) and (2) inequality of triangle we get,
[tex]22 > 4x > 7[/tex]
Hence, Inequality which ensure triangle exists is 22 > 4x > 7.
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For this item, any answers that are not whole numbers should be entered as a decimal, rounded to the hundredths place. Nicole started the day with $63.44 in her bank account. Later in the day, Nicole's bank processed a check that Nicole mailed last week to pay her electric bill. When this happened, the bank deducted $186.56 from Nicole's balance which caused her account to be overdrawn. Before the bank closed, Nicole made a deposit equal to the amount her account was overdrawn. What was Nicole's bank balance at the end of the day? At the end of the day, Nicole's bank balance was how many dollars?
-92.34 is the answer
Final answer:
After Nicole's check for her electric bill was processed, her account was overdrawn. She then made a deposit equal to the overdraft amount, bringing her end-of-day balance to $0.00.
Explanation:
To determine the bank balance that Nicole had at the end of the day, we need to consider the transactions that affected her account. She started with $63.44. After her electric bill check of $186.56 was processed, her account would have been overdrawn by $186.56 - $63.44 = $123.12. To cover this overdraft, Nicole made a deposit equal to the amount her account was overdrawn. Therefore, she deposited $123.12, which brought her balance back to $0.
At the end of the day, Nicole's bank balance was $0.00.
She found that the area of the garden will be 127 1/2 square feet by using the equation Area=bh. I'd the height, h, of the parallelogram-shaped garden is 8 1/2 feet, what is the base, b, in feet?
To solve this problem yo must apply the proccedure shown below:
1. You must use the formula applied to calculate the area of the garden.
[tex]A=bh[/tex]
2. You know the value of the area ([tex]127^{\frac{1}{2}}ft^{2}=127.5ft^{2}[/tex] and the value of the heigth ([tex]8^{\frac{1}{2}}ft=8.5ft[/tex] , therefore, you only need to solve for the base:
[tex]b=\frac{A}{h}\\b=\frac{127.5ft}{8.5ft}\\b=15ft[/tex]
The answer is: 15 feet.
Please help!! Trying to understand these. Which of the following inequalities is shown in the graph?
y(line under) <-1/2x+4
y (line under) <4x-1/2
y (line under) > -1/2x+4
y (line under) < 1/2x+4
Answer:
y< -1/2x +4
Step-by-step explanation:
The line crosses the y-axis at +4 and has a slope of -1/2. The shaded area below means that all answers below that line are correct (this is not part of the test answer but it is good information to know)
Hope this helped :)
A supervisor finds the mean number of miles that the employees in a department live from work. He finds x=29 and s=3.6 . Which statement must be true?
z37 is within 1 standard deviation of the mean.
z37 is between 1 and 2 standard deviations of the mean.
z37 is between 2 and 3 standard deviations of the mean.
z37 is more than 3 standard deviations of the mean.
Answer:
Option 3 is right
z37 is between 2 and 3 standard deviations of the mean.
Step-by-step explanation:
Let X be a random variable which represents the mean number of miles that the employees in a department live from work
X is normal (N(29,3.6)
WE have to find Z score for X
Z =[tex]\frac{x-29}{3.6}[/tex]
=2.22
i.e. 37 is 2.22 std deviations from the mean.
In other words, z37 is between 2 and 3 standard deviations of the mean.
The z-score for z37 is approximately 2.22. This indicates that it lies between 2 and 3 standard deviations of the mean. Hence, the correct statement is: z37 is between 2 and 3 standard deviations of the mean.
To determine which statement is true regarding the z-score for the value z37, we need to calculate the z-score using the given mean and standard deviation.
We know the mean ( ext{x}) = 29 and the standard deviation (s) = 3.6.The z-score formula is z = (X - mean) / standard deviation. Here, X = 37.This means that z37 is approximately 2.22 standard deviations away from the mean. Therefore, the correct statement is:
z37 is between 2 and 3 standard deviations of the mean.
In a normal distribution, about 95 percent of the x values lie within two standard deviations, and about 99.7 percent lie within three standard deviations of the mean.
I need the answer for 16 and 17
What is the solution set of the following equation? 3x^2 - 6x = 0
Certain clouds form when temperatures fall below -62c. What is the temperature in degrees Fahrenheit? Temperature is_ Greece Fahrenheit.
Solution: The value of temperature is -79.6 degree fahrenheit.
Explanation:
The temperature is given in degree celsius and we have find the temperature in degree fahrenheit. The formula to convert the degree celcius in degree fahrenheit is given below,
[tex]F=32+\frac{9}{5} C[/tex]
Where, F is temperature in degree fahrenheit and C is temperature in degree celsius.
Since it is given that the temperature is -62 degree celsius. So put [tex]c=-62[/tex] in the above formula.
[tex]F=32+\frac{9}{5} (-62)[/tex]
[tex]F=32+\frac{(-558)}{5}\\F=32-111.6\\F=79.6[/tex]
Hence the value of temperature is -79.6 degree fahrenheit.
Jimmy’s age is one year less than the sum of the ages of his siblings Serena and Tyler. Which equation represents Jimmy’s age? Jimmy’s age is one year less than the sum of the ages of his siblings Serena and Tyler. Which equation represents Jimmy’s age?
The equation that represents Jimmy's age is J = S + T - 1.
Explanation:To represent Jimmy's age, we can use the equation:
J = S + T - 1
where J is Jimmy's age, S is Serena's age, and T is Tyler's age. By subtracting 1 from the sum of Serena and Tyler's ages, we account for Jimmy's age being one year less than theirs. This equation accurately represents Jimmy's age.
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At the dog show there are 4 times as many boxes as spaniels. if there are a total of 30 dogs how many dogs are spaniels
What is another way to show 3+3+3+3+3+3?
3 x 6 is the simplest way of saying it
Answer: 3x6 because there are 6 3's so it's 3x6
Two number that are equivalent to 0.20 and 0.30
Son proporciones.
cual es el resultado de :x/2,5=y/5 si x+y=6
Respuesta: x/2,5=y/5=4/5=0,8
x/2,5=y/5
Multiplicando ambos lados de la ecuación por 5:
5(x/2,5)=5(y/5)→2x=y→y=2x
Sustituyendo y por 2x en la ecuación x+y=6:
x+2x=6
Resolviendo para x: Sumando términos semejantes:
3x=6
Dividiendo ambos lados de la ecuación entre 3:
3x/3=6/3
x=2
Sustituyendo x por 2 en la formula y=2x
y=2(2)→y=4
Determinando la proporción:
x/2,5. Sustituyendo x por 2:
2/2,5
Multiplicando numerador y denominador por 2:
2*2/(2,5*2)=4/5
La proporción es 4/5=0,8
Si lo hacemos con y:
y/5
Reemplazando y por 4:
4/5=0,8 (la misma proporción)
a store advertises a sale as "get 30 percent off your highest priced item when you buy a 2 or more items ". Someone buys items with prices of $30 and $20. Find the percent of discount on the total purchase. Show work
.3 times 30= $9
20 plus 30 is $50 minus $9 which equals $41
find three consecutive integers whose sum is -93
The three consecutive integers will be negative 30, negative 31, and negative 32.
What is Algebra?Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.
Let the three consecutive integers will be (x - 1), x, and (x + 1).
Then the sum of three consecutive integers whose sum is -93. Then we have
x - 1 + x + x + 1 = - 93
3x = - 93
x = -31
Then the three consecutive integers will be negative 30, negative 31, and negative 32.
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the length of a rectangle is 5 less than twice its width. if the perimeter is 26 meters, find the dimensions of the rectangle
The width of the rectangle is 6 meters and the length is 7 meters.
Explanation:To solve this problem, let's assume that the width of the rectangle is represented by w. The length of the rectangle can be written as 2w - 5. The perimeter of a rectangle is given by the formula P = 2l + 2w, where P represents the perimeter, l represents the length, and w represents the width. We are given that the perimeter is 26 meters, so we can set up the equation:
26 = 2(2w - 5) + 2w
Simplifying this equation gives:
26 = 4w - 10 + 2w
Combining like terms:
26 = 6w - 10
Adding 10 to both sides:
36 = 6w
Dividing both sides by 6:
w = 6
Therefore, the width of the rectangle is 6 meters. To find the length, substitute the value of w back into the expression for the length:
l = 2w - 5
l = 2(6) - 5
l = 7
So the dimensions of the rectangle are width = 6 meters and length = 7 meters.
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The problem is solved by setting up an algebraic equation based on the given pointers about the rectangle's width, length, and perimeter. After solving it, we find that the rectangle's dimensions are: width=6 meters and length=7 meters.
Explanation:
This is a problem of algebra within the subject of Mathematics. The width and length of the rectangle are the unknowns we need to find.
Given in the problem, the length is '5 less than twice its width'. If we denote the width as 'x', the length can be expressed as '2x - 5'. The equation for the perimeter of a rectangle is '2(length + width)', which equals 26 in this case. So we can set up our equation as follows: 2(x + 2x - 5) = 26.Solving this equation step-by-step:
Firstly, unfold the parentheses - 2x + 4x - 10 = 26, Then combine like terms to simplify it into 6x - 10 = 26. Add 10 to both sides of the equation to isolate the term with 'x', which results in 6x = 36. Finally, divide by 6 on both sides to find the value of 'x', so x=6. Substituting x=6 into the expression for the length, we find the length to be 2*6 - 5 = 7.Therefore, the dimensions of the rectangle are width=6 meters and length=7 meters.
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What is the slope of the line passing through the points (2, −5) and (4, 1)?
A. 3
B. 2
C. -4/5
D. 5/4
Answer:
The slope is 3 (answer choice A).
Step-by-step explanation:
Take a look at the two given points, (2, -5) and (4, 1). As we move from the first point to the second, x increases by 2 and y increases by 6, so that the slope is m = 6/2, or 3.
Name all of the angles in these polygones (info in picture) FAST!!
First of all this is a very poor question, and you should question it a bit. What are these figures? Are they regular? (first 2). Is the last one a parallelogram. I'm going to assume that the yellow one is a rectangle and the middle one is a pentagon and the last one is a parallelogram.
Yellow
A has 4 right angles (That's the property of a rectangle).
Green
B has 5 angles that are equal to 108 degrees. If you draw a 2 lines from any vertex you get 3 triangles. The size of the interior angles totals 3 triangles * 180 degrees = 540 degrees.
540/3 = 108.
Each angle in the interior is 108 degrees.
B has 5 angles all equal 108 degrees. All 5 are obtuse.
Red
Just by sight and assumption C has 2 obtuse angles, and 2 acute angles.
A magazine can layout 1/16 of an issue in 3 days.How many days dies it take to layout one issue?
To determine the time needed to layout a full magazine issue, multiply the time taken to layout 1/16 of an issue (3 days) by 16, resulting in 48 days total.
If a magazine can layout 1/16 of an issue in 3 days, then to calculate how many days it takes to layout one entire issue, we simply multiply the number of days it takes to layout 1/16 of the issue by 16.
This is because if 1/16 takes 3 days, then 1/8 (which is twice the amount of 1/16) would take twice as long
(3 days * 2 = 6 days),
and similarly, we can scale up to the full issue (1/1) by multiplying 3 days by 16.
The calculation would be:
Identify the portion of the issue completed: 1/16.
Identify the time taken for this portion: 3 days.
Calculate the time for the whole issue: 3 days * 16 = 48 days.
So, it would take 48 days to layout one full issue.
How to work out 189,232÷8
The answer would be 23,654.
Use long divison to figure it out or a calcualtor.
Hi I need help solving these two questions?
Let's say that 1/3 of the eggs become cracked. What is the ratio of the number of eggs that have cracked to the number of eggs that haven't?
We can say we have 2 cracked egss and 4 uncracked eggs for a 6 egg total.
The ratio of cracked to uncracked eggs is 2:4 which reduces to 1 to 2.
Half of the product of two consecutive numbers is 105. which equation can be used to solve for n, the smaller of the two numbers
Givens
The numbers are n and n + 1
Average = Av = 105
Equation
Av = (n)(n + 1)/2
Solution
Av = 105
n(n +1)/2 = 105 Multiply both sides by 2
n(n + 1) = 105 * 2
n(n + 1) = 210 Remove the brackets.
n^2 + n = 210 Subtract 210 from both sides
n^2 + n - 210 = 0
factor
(n+15)(n - 14)
n + 15 = 0
n = - 15
n = - 15 which is the smallest of the two answers.
n + 1 = - 14
Check
(-15)*(-14)/2 =
210/2
105 It does check.
Answer:
The numbers are n and n + 1
Average = Av = 105
Step-by-step explanation:
Calculate the principal from the given interest, rate, and time.
I = $256, r = 8%, t = 1 year
A) $20.48
B) $32
C) $320
D) $3200
__________A) $20.48______
Describe the dilation needed to map each pre-image onto each image.
Answer:
(1)- 1/3 (2)- 2 (3)- 1/2 (4)- 4.
Step-by-step explanation:
We have been given four images and their pre-images and we are asked to find out the factor of dilation.
(1) We have been given a triangle ABC, whose center of dilation is A. In order to find out factor of dilation we will see lengths of two corresponding sides. AB is 6 units long and A'B' is two units long. To map triangle ABC on triangle A'B'C' we have to dilate triangle ABC by a factor of 1/3 as 2 is 1/3 of 6.
Therefore, factor of dilation is 1/3.
(2) Let us find the lengths of two corresponding sides of our image and pre-image. Side ST is 6 units long and S'T' is 12 units long. To map our image of quadrilateral on pre-image we have to dilate our image by a factor of 2 as S'T' is 2 times of ST.
Therefore, factor of dilation is 2.
(3) Side QR is 6 units long and its corresponding side Q'R' is 3 units long. We can see that Q'R' is 1/2 of QR so in order to map our triangle QRS on triangle Q'R'S' we have to dilate our pre-image by a factor of 1/2.
Therefore, our factor of dilation is 1/2.
(4) Length of side AB of our image is 2 units and A'B' is 8 units long. 8 is 4 times 2. To map our pre-image ABC on our image A'B'C' we have to dilate our mage by a factor of 4.
Therefore, factor of dilation is 4.
Need help on this kinda lost on it
A translation moves the image up, down and/or right, left. It does not change its size or shape.
Try this: Move your pencil up and to the right. Did its size or shape change? no
Answer: D
The Fall Festival charges $0.75 per ticket for the rides. Kendall bought 18 tickets for rides and spent a total of $33.50 at the festival. She only spent her money on ride tickets and admission into the festival. The price of admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Define your variables.
(b) Write a linear equation to calculate the cost for anyone who only pays for festival admission and rides
(c) Explain your answer to Part B.
Step-by-step explanation:
The Fall Festival charges $0.75 per ticket for the rides. Kendall bought 18 tickets for rides and spent a total of $33.50 at the festival
0.75 per ticket. So cost of 18 tickets= 0.75 * 18 = $13.5
Kendall spent $13.50 for tickets . Total spent = $33.50
Total spent = ticket cost + admission cost
33.50 = 13.50 + admission
Admission cost = 33.50 - 13.50 = $20
(a) y to represent the total cost , x to represent the number of ride tickets.
'b' represents the admission cost
(b) General form of linear equation is y=mx+b
m = 0.75 and b = admission cost = 20
So equation becomes y = 0.75x + 20
(c) Initially, she has to pay the admission price $20. then 0.75 per ticket.
The value of x changes depends on the number of tickets she wants to buy.
y is the total cost she has to pay for x tickets with admission price
Zoe had a board 5 1/4 feet long she cut off a piece now the board is 3 5/6 feet long how long was the piece she cut off
Least common denominator is 24