Upper fence of the statistics below provide a summary of the distribution of heights of 200 randomly selected elementary students from across Pennsylvania (in inches) is 115.5.
Define upper fence.The Upper Fence serves as the "upper limit" of the data, and any data that lies outside these restrictions is likely to be an anomaly. Q3 + 1.5 IQR, where Q3 is your third quartile and IQR is your interquartile range, can be used to compute the upper fence. An outlier is any value in your dataset that is higher than the upper fence.
Given Data
Min = 39
Q1 = 43
Median(IQR) = 45
Q3 = 48
Max = 56
Upper fence = Q₃ + (1.5(1QR)
Upper fence = 48 + 1.5(45)
Upper fence = 48 + 67.5
Upper fence = 115.5
Upper fence of the statistics below provide a summary of the distribution of heights of 200 randomly selected elementary students from across Pennsylvania (in inches) is 115.5.
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y = 1/2x + 8y = cx + 10In the system of equations above, c is a constant. Ifthe system has no solution, what is the value of c?
y = 1/2x + 8
y = cx + 10
In the system of equations above, c is a constant. If
the system has no solution, what is the value of c?
so, y=y
[tex]\begin{gathered} \frac{x}{2}+8=cx+10 \\ solve\text{ for x} \\ \\ \frac{x}{2}-cx=10-8 \\ x(\frac{1}{2}-c)=2 \\ x(\frac{1}{2}-c)=2 \\ \end{gathered}[/tex]this equation is indefinde when 1/2 - c= 0, there is not value for x that makes the equation true
[tex]\begin{gathered} \frac{1}{2}-c=0 \\ \frac{1}{2}=c \end{gathered}[/tex]so, the value of c =0.5
Which function Best represents the graph shown?
Y=4x+2
Y=2x+4
Y=2x-4
Y=4x-2
In the picture, there is a graph. The equation of the line y=2x+4. Option-B is correct.
Given that,
In the picture, there is a graph.
We have to find the equation of the line.
From the graph we can see there are points.
The point are (1,6) and (-2,0)
So,
The formula for equation of the line is y-y₁=m(x-x₁)
We have to find the m value
The slope of the line m=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m=(0-6)/(-2-1)
m=-6/-3
m=2
Now,
Take a point (-2,0)
y-0=2(x+2)
y=2x+4
Therefore, the option-B is correct, the equation of the line is y=2x+4.
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A debra is stuck in trac driving her kids to the park, 18km away from her home . She can only drive at a speed of 20km how long will it take debra to reach the park
It would take 54 minutes for Debra to reach park which is 18 km away from the house at speed of 20km/h.
What is speed?Speed is the rate at which an object moves along a path in time, whereas velocity is the rate and direction of an object's movement. In other words, speed is a scalar value, whereas velocity is a vector.
For example, 50 km/hr (31 mph) describes the speed at which a car travels along a road, whereas 50 km/hr west describes the velocity at which it travels.
We have given the speed 20km/h
the distance to cover is 18km
The formula for time is
t = D/S
where,
t is time
D is distance
S is speed
Substituting the values we get
t = 0.9 hours
t = 54 minutes
Thus, it would take 54 minutes for Debra to reach park which is 18 km away from the house at speed of 20km/h.
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Cost price = £360: Selling price = £144 Percentage loss?
Help me out!! Click the pic to see the question
You have to plug 30 in for x
13.00 + 0.10(30)
13 + 3
$16
Mary’s credit card company charges 16% interest on her outstanding credit card balance each month. Her minimum payment is $20 each month. Mary’s credit card bill is $70 in January.
Mary only pays the minimum amount each month, and she does not spend any additional money on her credit card. How long, in months, will it take her to pay off her bill from January?
It will take Mary 3.6 months (The period will occur in April.) from January to pay off her bill of $70 if she continues to pay $20 per month.
How is the period determined?The period Mary will take to pay off her credit card balance is determined using an online finance calculator.
The input data required includes the interest rate, the present value of the bill, and the periodic payments.
I/Y (Interest per year) = 16%
PV (Present Value) = $70
PMT (Periodic Payment) = $-20
FV (Future Value) = $0
Results:
N = 3.608
Sum of all periodic payments = $-72.16
Total Interest = $2.16
Thus, Mary requires 3.6 months to pay off her credit card balance, which will occur in period 4 from January.
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when dividing 560.9 by 100, how should the decimal point be moved?
Data were collected on the distance a golf ball will travel when hit by a golf club at a certain speed. the speed, s, is measured in miles per hour, and distance, y, is measured in yards. the regression line is given by Å· = 5.32 46.73s. identify the slope and y-intercept of the regression line. interpret each value in context. the slope, b = 5.32, indicates that the distance increases by 5.32 yards for every one mile per hour of speed. the y-intercept, a = 46.73, is the distance estimated by this model if the speed is zero miles per hour. the slope, b = 5.32, indicates that the distance decreases by 5.32 yards for every one mile per hour of speed. the y-intercept, a = 46.73, is the distance estimated by this model if the speed is one mile per hour. the slope, b = 46.73, indicates that the distance increases by 46.73 yards for every one mile per hour of speed. the y-intercept, a = 5.32, is the distance estimated by this model if the speed is zero miles per hour. the slope, b = 46.73, indicates that the distance decreases by 46.73 yards for every one mile per hour of speed. the y-intercept, a = 4.17, is the distance estimated by this model if the speed is one mile per hour.
The slope, b = 5.32, indicates that the distance increases by 5.32 yards for every one mile per hour of speed. The y-intercept, a = 46.73, is the distance estimated by this model if the speed is zero miles per hour.
Based on the given conditions, formulate,
The speed, s, is measured in miles per hour, and distance, y, is measured in yards.
The regression line is given by,
Å = 5.32 + 46.73s (Equation-1)
Then find,
The slope and y-intercept of the regression line.
The general form of linear regression line is
A linear regression line has an equation of the form Y = a + b x, where x is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0).
y = a + b x (Equation-2)
where x is variable. In the given equation the variable is denoted by s.
On comparing Equation-1 and Equation-2,
We can write,
a = 46.73
b = 5.32
It means slope is 5.32 and y-intercept is 46.73.
The slope, b = 5.32, indicates that the distance increases by 5.32 yards for every one mile per hour of speed.
The y-intercept, a = 46.73, is the distance estimated by this model if the speed is zero miles per hour.
Therefore,
The slope, b = 5.32, indicates that the distance increases by 5.32 yards for every one mile per hour of speed. The y-intercept, a = 46.73, is the distance estimated by this model if the speed is zero miles per hour.
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Last month, Ronald sold 52 packages of home-made brownies, earning a total profit of $195.00. He plans to make 125 brownie packages for a bake sale. If he sells all 125 brownie packages, how much profit can Ronald expect to earn?
If he sells all 125 brownie packages, Ronald can expect to earn a profit of $468.75
Ronald sold 52 packages of home-made brownies.
He earns a total profit of $195.00
Profit from 52 packages = 195
Profit from 1 brownie package = 195/52 = 3.75
If he sells all 125 brownie packages
Total profit he can expect = profit from one brownie x 125 brownie packages
= 3.75 x 125
= 468.75
Therefore, If he sells all 125 brownie packages, Ronald can expect to earn a profit of $468.75
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A square piece of tin of side length 20 cm has four squares of side length x cm removed from each corner. the sides are folded up to form a tray. the centre square forms the tray base a write an expression for the side length of the base of the tray. b write an expression for the area of the base of the tray. expand your answer. c find the area of the tray base if x = 3. d find the volume of the tray if x = 3
Analyzing the square and finding expressions for length, area, and volume.
A. Expression for length = (20-2x)cm
B. Expression for area = [tex](20-2x)^{2}[/tex]
C. Expression for the area of tray base if x=3 : 196 cm^2
D. Volume of the tray if x=3: 2744 cm^3
A square piece of a tin of side length 20 cm has four squares of side length x cm removed from each corner. the sides are folded up to form a tray.
Since the side of x has been removed from each corner, that means, 2x length has been removed from 20 cm.[tex](20-2*3)^{2} =(20-6)^{2} = 14^{2} = 196[/tex]
So, the length of the tray base will be ( 20 - 2x ) cm.
The area of the square is given by [tex](side)^{2}[/tex]
So, the area of the base of the tray = [tex](20-2x)^{2}[/tex]
Expanding the expression, [tex](a+b)^{2} =a^{2} + b^{2} + 2ab[/tex]
Now, [tex](20-2x)^{2} = 400 + 4x^{2} -80x[/tex]
Area of the tray base if x=3, Area (x=3) =[tex]400 + 4(3)^{2} -80*3 = 400 +36- 240 = 196 cm^{2}[/tex]
Now, Volume = [tex](side)^{3}[/tex]
Volume = [tex](20-2x)^{3}[/tex]
Volume (when x = 3) = [tex](20-2x)^{3}= (20-2*3)^{3}=(20-6)^{3} = 14^{3} =2744 cm^{3}[/tex]
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A tulip is 2 inches tall after 1 week, 5 inches after 2 weeks, and 8 inches after 3 weeks. Which functions shown below can be used to determine the height, f(n), of the tulip in n weeks. 1. f(n) = 3n-1 2. f(n) = 3+2(n-1) 3. f(n) = f(n-1) + 3 where f(1) = 2
The height of tulip can be expressed by expression f(n)=3n-1
What do you mean by expression?A mathematical expression is made up of a statement, at least one arithmetic operation, and at least two integers or variables.
Mathematical expression components:
a) Constant: a fixed numerical value
b Variables: They don't accept any predetermined values. Values are assigned based on the criteria.
c)Terms: Constants, variables, or constants multiplied by variables are all acceptable terms (s).
d) Operators:The four operations of addition (+), subtraction (-), multiplication (-), and division (-) are referred to as operators because they are employed to combine the components in an equation.
Given:
1. f(n)=3n-1
after 1 week (n=1)
f(1) = 3*1-1
f(1) = 2 in
After 2 week (n=2)
f(2) = 3*2-1
f(2) = 5in
After 3 week (n=3)
f(3) = 3 *3-1
f(3) = 8in
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2 A store sells sugar for $5 per bag. If a bag
contains 1.5 lbs., how many pound of sugar can
you buy with $8.
F 2.0 lbs.
G 26.7 lbs.
H 0.9 lbs.
J 2.4 lbs.
REALLY SIMPLE 7TH GRADE MATH, WILL GIVE A THANKS AND VOTE BRAINLIEST
A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for
every 30 miles.
a. What is the actual area of the park?
___ square miles
b. The map needs to be reproduced at a different scale so that it has an area of 6 square inches and can fit in a brochure. At what scale should the map be reproduced so that it fits on the brochure?
1 inch for every ___ miles
Answer:
a) 21,600 square miles
b) the map will be reduced to 50% of its original size. 1 in = 60 miles
Step-by-step explanation:
You have a 4-in by 6-in map of a park with a scale of 1 in : 30 miles, and you want to know the actual area of the park, the reproduction factor to fit the map in 6 square inches, and the new scale of the map at that size.
a) Park sizeThe 4-inch dimension of the map corresponds to an actual length of ...
(4 in)(30 mi)/(1 in) = 120 mi
Similarly, the 6-inch dimension represents ...
(6 in)(30 mi)/(1 in) = 180 mi
The area of the park is the product of its dimensions:
(120 mi)(180 mi) = 21,600 mi²
The area of the park is 21,600 square miles.
b) ReductionThe area of the current map is (4 in)(6 in) = 24 in². The ratio of the reduced area to this original area is the square of the reduction scale factor:
k² = (6 in²)/(24 in²) = 1/4
k = √(1/4) = 1/2
The map must be reproduced at 1/2 its original size.
At this scale, the scale of the map is ...
(1/2 in) : (30 mi) = (1 in) : (60 mi)
It will be 1 inch for every 60 miles.
<95141404393>
In every box of bubble gum there are 18 pieces, which describes a proportional relationship between the number of packages, x, and the number of pieces, y. Choose the equation that expresses this relationship.
Answer:
Thats nice
Step-by-step explanation:
Oscar wants to both spend and save the money he earns.
For every $7 he puts in his wallet, he puts $3 in savings
2. If Oscar puts $70` in his wallet, how much will he put
in savings?
If Oscar earns $70 in total, how much will he put in
savin
Step-by-step explanation:
answer is explained in my working. hope it helps
The amount of savings Oscar will save is $30.00
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Oscar wants to spend and save money he earns
For every $ 7 , The amount of money Oscar saves = $ 3
So ,
For every $ 70 , the amount of money Oscar saves =
For every $ 7 , The amount of money Oscar saves x 10
And ,
For every $ 70 , the amount of money Oscar saves = $ 3 x 10
= $ 30
Hence , for every $ 70 Oscar puts in his wallet he saves $ 30
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( will mark brainliest )
∠A and ∠B are vertical angles with m∠A = x and m∠B = 4x − 24.
m∠A = ____ degrees
Answer:
8
Step-by-step explanation:
Vertical angles are congruent. That means that they have the same measurement. Set them equal to each other and solve for x
x = 4x - 24 Subtract x from both sides of the equation
o = 3x - 24 Add 24 to both sides
24 = 3x Divide both sides by 3
8 = x
m<A is 8
What is the value of |238| + |−28| − |−14|?
A 224
B 196
C 280
D 252
Answer:
D
Step-by-step explanation:
av= absolute value
av of 238 = 238
av of -28 = 28
av of -14 = 14
238 (+) 28 (-) 14 = 252
238 + 28 = 266
266 - 14 = 252
therefore 252 is the correct answer
hope this helped ^^
The following equations define a system.
-2x - y = 10
x - 2y = 5
Which graph represents the system?
The system represents a straight graph.
How is straight lines and a linear equation related ?The graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation. If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points.
Graphing a system of linear equations is as simple as graphing two straight lines. When the lines are graphed, the solution will be the (x,y) ordered pair where the two lines intersect (cross). * Before you begin, rearrange the equations so they will read "y =".
The given system of equations indicate a linear equation .
This means that after solving this we will get a straight line slope whose value can be calculated by the formula tan theta = height / base
Thus the system represents a straight graph .
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Answer:
B
Step-by-step explanation:
Find the measure of FG.
Thank you ;)
Mike had $36 dollars. He spent 1/3 of his money for a moive and 2/9 for a sandwich and drink. How many dollars did Mike spend for the sandwich and drink?Does he have enough money left to buy a book for $18?
We are given that Mike has $36, if he spends 1/3 of this amount, the amount spent is the product of 36 and 1/3, that is:
[tex]\begin{gathered} A_1=36\times\frac{1}{3} \\ A_1=12 \end{gathered}[/tex]Therefore, he spends $12 on the movie.
Now we are told that he spends 2/9 of the money, therefore, he spent:
[tex]\begin{gathered} A_2=36\times\frac{2}{9} \\ A_2=8 \end{gathered}[/tex]In total, he spent $8 on the sandwich.
The money he has left is:
[tex]36-12-8=16[/tex]Therefore, he can't buy an $18 dollars book.
(a) find a combination of step functions that is equal to 4 when 2 ≤t ≤3 and equal to 0 otherwise. (b) write the following function in one line (i.e. without cases) using step functions: f(t)
(a) Recall the definition of the step function,
[tex]\theta(t) = \begin{cases} 1 & \text{if } t \ge 0 \\ 0 & \text{if } t < 0 \end{cases}[/tex]
Then we have
• [tex]\theta(t-2) = 1[/tex] if [tex]t-2\ge0[/tex], or [tex]t\ge2[/tex]
• [tex]\theta(t-3) = 1[/tex] if [tex]t-3\ge0[/tex], or [tex]t\ge3[/tex]
and we can combine these to get
[tex]\theta(t-2) - \theta(t-3) = \begin{cases} 1 & \text{if }2\le t < 3 \\ 0 & \text{if }t<2 \text{ or } t\ge3 \end{cases}[/tex]
then scale up by 4 to get the value we want over [2, 3].
[tex]f(t) = \boxed{4\bigg(\theta(t-2) - \theta(t-3)\bigg)}[/tex]
At least that's what I get using the aforementioned definition of "step function". I don't see a way to have both [tex]f(2)=4[/tex] and [tex]f(3)=4[/tex] with this definition...
(b) No function was given...
can someone please please solve 13y>9 or 2y-6>2 for me? please show work too!
The inequalities are solved below
What is an inequality?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. The notation a b indicates that an is less than b, while a > b indicates that an is more than b, among other distinct notations used to denote various types of inequalities. The notation a b indicates that a and b are not equal; this inequality is occasionally referred to as a type of stringent inequality. It doesn't even specify that a and b must be members of an ordered set, nor does it state that one is superior to the other.
The inequalities are
13y>9
or, y>9/13
and
2y-6>2
or, 2y>2+6
or, y>8/2
or, y>4
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Dog weighs 80 pounds a year ago now he weighs 92 pounds what is the percentage increase in weight
A year ago: 80 pounds
This year: 92 pounds
Yearly increase: 92 - 80 = 12 pounds
The percentage increase in weight will be taken with respect to 80 pounds. Then:
[tex]\frac{12\text{ lbs}}{80\text{ lbs}}\cdot100\text{\% }=15\text{\%}[/tex]Mariana receives a $20 gift card for downloading music and wants to determine how many songs she can purchase. Each downloaded song costs $1.29. If m represents the number of songs downloaded, which inequality represents the given situation?
20 m greater-than-or-equal-to 1.29
20 m less-than-or-equal-to 1.29
1.29 m less-than-or-equal-to 20
1.29 m greater-than-or-equal-to 20
I need help pleaseeeeeee
Compare the slopes and y-intercepts for the equations in this system of equations. How many solutions does this system of equations have? 2 x + 6 y Ž +6 y = 3 A) One solution B) No solution Infinitely many solutions
Infinitely many solutions
1) Given the equations, y =2/3x +6 and 2/3x +6
y=2/3x +6
y= 2/3x +6
2) As we have the same equation, then there will be infinitely many solutions since each and every point of line I belongs to line (II)
3) Hence, the answer is Infinitely many solutions
the sum of the 2 numbers is 92 the the product of the 2 nrumbers is 2107 what is the age of audras oldest parent is the youngest dugters age
By the concept of quadratic equation the oldest parent has 49 years and the other is 43 years.
What are quadratic equations?Any equation that can be written in standard form as where x stands for an unknown, a, b, and c are known values, and a 0 is an algebraic term is known as a quadratic equation. A quadratic equation is a second-order polynomial equation in one variable that goes like this: x ax2 + bx + c=0, where a 0. Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible. A quadratic function is one that has the formula f(x) = ax2 + bx + c, where a, b, and c are all integers with a not equal to zero. A curve known as a parabola makes up the quadratic function graph.
Let's define x = age of parent 1, and y = age of parent 2, and suppose that y is the oldest one.
We know that:
x + y = 92
x × y = 2107
Now we have a system of equations that we need to solve:
The first step is isolate one of the variables in one of the equation, let's isolate x in the first equation:
x = 92 - y
Now we can replace it in the second equation and find the value of y.
x × y = 2107
y × (92 - y) = 2107
92y - y² = 2107
Now we need to solve a quadratic equation!
-y² + 92y - 2107 = 0
so we have two solutions:
y = (-92 + 6)/(-3) = 43
y = (-92 - 6)/(-2) = 49
Because y is the oldest one, we need to take the biggest solution, this is y = 49.
So the oldest parent has 49 years.
If you want to find the age of the other parent, replace this in the first equation:
y + x = 92
49 + x = 92
x = 92 - 49
= 43
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22 points for doing this
Answer:
The correct answer is D. -8<535
Step-by-step explanation:
In a math perspective, -8 < 535. Done
Otherwise, the elevations of the lowest and highest points start from below sea levels up to land and so on. Since negative numbers here are feet below the sea level, we went from New Orleans up. So D.
calcular el valor de la constante razon
6/12 32/10 225/150
The value of the ratio (6/12) is 0.5, of (32/10) is 3.2 and that of (225/150) is 1.5.
As per the question statement, we are provided with three ratios, (6/12), (32/10) and (225/15).
We are required to calculate the values of the above mentioned ratios.
To solve this question, we need to simplify the ratios, and then divide their numerators by their denominators, to obtain our desired answers.
Therefore, (6/12) = [6/(6 * 2)] = (1/2) = 0.5
Similarly, (32/10) = [(16 * 2)/(5 * 2)] = (16/5) = 3.2
And finally, (225/150) = [(75 * 3)/(75 * 2)] = (3/2) = 1.5
Ratio: In Mathematics, Ratio is a term that is used to compare two or more numbers, typically to indicate how big or small a quantity is when compared to another, and is either expressed in the form of(a : b), or as a fraction of (a/b) both of which are equivalent.
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An electrician charges $50 for a service call plus $25 an hour. The last service call cost $125. If n= hours worked, write an equation to describe this situation.
Answer:
125=50+25n
Step-by-step explanation:
to figure how many hours worked you want to subtract 50 from both sides [tex]\frac{125}{-50}=\frac{50+25n}{-50}[/tex]you get 75=25nthen you want to divide 25 from both sides[tex]\frac{75}{/25} =\frac{25n}{/25}[/tex]then you get3=n