Answer:
Quartile 1 (Q1) = 24
Quartile 2 (Q2) = 47
IQR = 23
Step-by-step explanation:
Given:
The set of data are:
13, 23, 24, 25, 26, 26, 37, 47, 47, 48, 50
The data are in increasing order. The number terms are, [tex]n = 11[/tex].
Therefore, the middle term = [tex]\frac{n+1}{2}=\frac{11+1}{2}=6^{th}\ term[/tex]
So, the median = 26
Now, the median divides the set of data into two parts. The median of first part is the quartile 1 and the median of second part is quartile 2.
So, the first part has the following terms:
13, 23, 24, 25, 26
Here also, [tex]n=5[/tex]. So, the third term is the median.
∴ Q1 = 24
The second part has the following terms:
37, 47, 47, 48, 50
Here also, [tex]n=5[/tex]. So, the third term is the median.
∴ Q2 = 47.
Now, IQR = Q2 - Q1 = 47 - 24 = 23.
A book on the clearance rack was marked down 65% from $21.95. Approximately, how much was the book discounted?
Answer:
$7.6825
Step-by-step explanation:
65%=0.65
0.65*21.95=14.2675
21.95-14.2675=7.6825
Answer:
7.6825
Step-by-step explanation:
solve and explain how you got your answer
-3(c-1) = 33
Answer:
Step-by-step explanation:
-3(c-1) = 33
c - 1 = 33/ -3
c -1 = -11
c = -11 +1
c = -10
Answer:
-10
Step-by-step explanation:
-3 (c-1 ) = 33
Divide both sides by -3
c-1 = -11
Add 1 to both sides
c = -10
Ted likes to run long distances. He can run
20 km start text, space, k, m, end text in
95 minutes. He wants to know how many kilometers
(k)left parenthesis, k, right parenthesis he will go if he runs at the same pace for
285 minutes
Answer:
Step-by-step explanation:
20 km to 95 minutes = x km to 285 minutes
20 / 95 = x / 285.....cross multiply
(95)(x) = (20)(285)
95x = 5700
x = 5700/95
x = 60 km <======
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
X + 10y = 29
x - y = 7
Answer:
x = 9, y = 2
Step-by-step explanation:
Given the 2 equations
x + 10y = 29 → (1)
x - y = 7 → (2)
Subtracting (2) from (1) term by term will eliminate the term in x
(x - x) + (10y - (- y)) = (29 - 7), that is
11y = 22 ( divide both sides by 11 )
y = 2
Substitute y = 2 in either of the 2 equations
Substituting in (2)
x - 2 = 7 ( add 2 to both sides )
x = 9
What's 286 divided by 20??
Thanks if you help! :)
Answer:
14.3
Step-by-step explanation:
percent: 14.3%
decimal: 14.3
fraction: 14 3/10
Answer:
I got 143/10 ;-;
But as a decimal it's 143.0 and percent is 14.3%
When adding negative and positive numbers, you can use the associative and commutative properties to group all of the positive addends and then group all the negative addends. Which expression shows the second step of this method?
5 + (-1) + (-5) + (-2) + 11 + (-7) + 2
Answer:
The second step of this method is
[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=(5+11+2)-(1+5+2+7)[/tex]
The value of the given expression is
[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=3[/tex]
Step-by-step explanation:
Given expression is [tex]5+(-1)+(-5)+(-2)+11+(-7)+2[/tex]
To find the value of the given expression [tex]5+(-1)+(-5)+(-2)+11+(-7)+2[/tex]:
Arranging positive and negative addends by using the associative and commutative properties of the given expression as below:
[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=5+11+2+(-1)+(-5)+(-2)+(-7)[/tex]
[tex]=(5+11+2)-(1+5+2+7)[/tex]
[tex]=18-15[/tex]
[tex]=3[/tex]
[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=3[/tex]
The second step of this method is
[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=(5+11+2)-(1+5+2+7)[/tex]
The value of the given expression is
[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=3[/tex]
?? “solve the missing elements for each problem. use 3.14 for area
Answer:
Problem 4:
Radius = 11 cm.
Circumference = 69.08 cm.
Problem 5:
Radius = 14 mm.
Circumference = 87.92 mm.
Problem 6:
Radius = 9 inches.
Circumference = 56.52 inches.
Problem 7:
Diameter = 32 ft.
Circumference = 100.48 ft.
Problem 8:
Diameter = 26 yards.
Circumference = 81.64 yards.
Problem 9:
Diameter = 12 cm.
Circumference = 37.68 cm.
Step-by-step explanation:
Problem 4:
Given:
Diameter GH = 22 cm
We need to find the radius EF and Circumference of the circle.
Now radius is given by half of the diameter
Also Circumference is given by π times diameter.
Radius EF = [tex]\frac{1}{2}\times Diameter = \frac{1}{2}\times 22 = 11 \ cm[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 22 = 69.08\ cm[/tex]
Hence Radius = 11 cm
Circumference = 69.08 cm.
Problem 5:
Given:
Diameter OP = 28 mm
We need to find the radius MN and Circumference of the circle.
Now radius is given by half of the diameter
Also Circumference is given by π times diameter.
Radius MN = [tex]\frac{1}{2}\times Diameter = \frac{1}{2}\times 28 = 14 \ mm[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 28 = 87.92\ mm[/tex]
Hence Radius = 14 mm
Circumference = 87.92 mm.
Problem 6:
Given:
Diameter EF = 18 inches
We need to find the radius CD and Circumference of the circle.
Now radius is given by half of the diameter
Also Circumference is given by π times diameter.
Radius CD = [tex]\frac{1}{2}\times Diameter = \frac{1}{2}\times 18 = 9 \ in[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 18 = 56.52\ in[/tex]
Hence Radius = 9 inches.
Circumference = 56.52 inches.
Problem 7:
Given:
Radius GH = 16 ft
We need to find the Diameter CD and Circumference of the circle.
Now Diameter is given by twice the radius.
Also Circumference is given by π times diameter.
Diameter KJ = [tex]2 \times radius = 2 \times 16 = 32 \ ft[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 32 = 100.48\ ft[/tex]
Hence Diameter = 32 ft.
Circumference = 100.48 ft.
Problem 8:
Given:
Radius LM = 13 yards
We need to find the Diameter CD and Circumference of the circle.
Now Diameter is given by twice the radius.
Also Circumference is given by π times diameter.
Diameter NO = [tex]2 \times radius = 2 \times 13 = 26 \ yards[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 26 = 81.64\ yards[/tex]
Hence Diameter = 26 yards.
Circumference = 81.64 yards.
Problem 9:
Given:
Radius NO = 6 cm
We need to find the Diameter CD and Circumference of the circle.
Now Diameter is given by twice the radius.
Also Circumference is given by π times diameter.
Diameter PQ = [tex]2 \times radius = 2 \times 6 = 12 \ cm[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 12 = 37.68\ cm[/tex]
Hence Diameter = 12 cm.
Circumference = 37.68 cm.
A force of 200 N is exerted on
an object of mass 40 kg that is
located on a sheet of perfectly
smooth ice. Calculate the
acceleration of the object.
The acceleration of the object is 5 m/s^2
Step-by-step explanation:
Given
Mass of object = m = 40 kg
Force = F = 200 N
Newton's 2nd law states that:
[tex]F = ma[/tex]
As we have to find the acceleration
[tex]a = \frac{F}{m}[/tex]
Putting the values
[tex]a = \frac{200}{40}\\a = 5\ ms^{-2}[/tex]
The acceleration of the object is 5 m/s^2
Keywords: Force, acceleration
Learn more about force at:
brainly.com/question/8811218brainly.com/question/853574#LearnwithBrainly
To calculate the acceleration of the object, we can use Newton's second law of motion which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. Using the given force of 200 N and mass of 40 kg, we can determine that the acceleration of the object is 5 m/s^2.
Explanation:To calculate the acceleration of the object, we can use Newton's second law of motion which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
First, we need to determine the net force acting on the object. In this case, it is given as 200 N.Next, we need to determine the mass of the object, which is given as 40 kg.Using the formula: acceleration = net force / mass, we can substitute the given values to find the acceleration.Substituting the values, we get: acceleration = 200 N / 40 kg = 5 m/s^2.Therefore, the acceleration of the object is 5 m/s^2.
Learn more about Calculating acceleration here:https://brainly.com/question/32817533
#SPJ11
Does somebody know how to do this?
Answer:
Total length of running track is 371.24 m .
Step-by-step explanation:
Total running track = Running track around straight region + running track around curved region.
Running track around straight region = 2 × length of straight region
= 2×82 m
= 164 m
Running track around curved region = 2 × length of curved region
= 2 × π × radius of curved region
= 2 × 3.14 × 33 m
= 207.24 m
Therefore , total length of running track = 164 + 207.24 m
= 371.24 m
If a pair of jeans cost 45 dollars before the sale and the sale is taking 9 dollars off of the original price what was the percent taken off?
Answer:
20%
Step-by-step explanation:
A pair of jeans cost $45 before the sale.
The sale is taking $9 off of the original price.
Then
$45 - 100%
$9 - x%
Write a proportion:
[tex]\dfrac{45}{9}=\dfrac{100}{x}[/tex]
Cross multiply:
[tex]45\cdot x=9\cdot 100\\ \\45x=900\\ \\x=\dfrac{900}{45}\\ \\x=20\%[/tex]
Answer:
The sale price is $46.75
Step-by-step explanation:
For similar triangles, the side lengths are proportional. So, you can write a proportion relating the two pairs of vertical and horizontal side lengths. For the line y = 2x, a triangle can be drawn 2 units up and 1 unit right from the origin.
Write a proportion relating the side lengths of the triangle to any other triangle that has the line as a hypotenuse, a horizontal length of x units, and a vertical length of y units.
Answer:
[tex]\frac{y}{2}=\frac{x}{1}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
The corresponding vertical sides are y and 2
The corresponding horizontal lines are x and 1
so
The proportion is equal to
[tex]\frac{y}{2}=\frac{x}{1}[/tex]
What's x for 12x+1=4x+9
Nevermind someone already answered it.
Ramona spend 8 hours making picture frames if each picture frame takes her 1/4 of hour to make how many picture frame does Ramona have?
Which expression represents 8 less than two times X?
OA) 2x - 8
OB) 8 - 2x
OC) 8x - 2
OD) 2-8x
Answer:
Therefore the expression is option A)
[tex]2x-8[/tex]
Step-by-step explanation:
Given:
Statement as ' 8 less than two times X'
To Find :
Expression for the statement
'8 less than two times X'
Solution:
[tex]Two\ times\ 'x'\ means=2\times x[/tex]
Now 8 less than two times X means Subtract 8 from '2x'
[tex]2x-8[/tex]
Therefore the expression is option A)
[tex]2x-8[/tex]
Tony makes a phone call at a pay phone. The charge is 25 cents for the first four minutes,and 19 cents for each additional minute. Tony has $2.10 in change in his pocket. Write an inequality that can be used to find m, the maximum number of whole minutes he can talk on the phone
Cindy worked 4 hours each day for 12 days. She earned a total of $240. How much did Cindy earn per hour?
Answer:
$5 per hour
Step-by-step explanation:
12*4=48 hours
240/48=5
yyyeeeeeeeee
1-2k-2k=5
Answer:
k=-1
Step-by-step explanation:
1-2k-2k=5
1-4k=5
4k=1-5
4k=-4
k=-4/4
k=-1
Home city bank pays 5% interest compounded quarterly on regular savings accounts. Miguel cardosa deposited 1000 for 1 year. He made no other deposits or withdrawals. How much interest did he earn during the year.
Answer:
The interest earned was $50.95
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=1\ year\\ P=\$1,000\\ r=5\%=5/100=0.05\\n=4[/tex]
substitute in the formula above
[tex]A=1,000(1+\frac{0.05}{4})^{4*1}[/tex]
[tex]A=1,000(1.0125)^{4}[/tex]
[tex]A=\$1,050.95[/tex]
Find the interest earned I
we know that
[tex]I=A-P[/tex]
substitute the values
[tex]I=\$1,050.95-\$1,000=\$50.95[/tex]
For what value of R does the equation have a solution of X = 9.5?
7 (5x - R) + 3r = 173.5
Show how you got your answer step-by-step.
Answer:
r=39.75
Step-by-step explanation:
7(5*9.5-R)+3r=173.5
7(47.5-R)+3r=173.5
332.5-7R+3r=173.5
332.5-4r=173.5
4r=332.5-173.5
4r=159
r=159/4
r=39.75
Step-by-step explanation:
7 (5x - R) + 3r = 173.5
let x = 9.5 as given
solve for R
substitute the value of x=9.5 into the equation:
7 (5 * 9.5 - R) + 3R = 173.5
7 (47.5 - R) + 3R = 173.5 expand
332.5 - 7R + 3R = 173.5 combine similar terms
332.5 - 173.5 = 7R - 3R simplify
159 = 4R divide 4 on each side
R = 159/4 simplify
R = 39.75
WILL GIVE BRAINLIEST IF CORRECT! 25 PTS
Which statement is true about the graph of this equation?
y + 4 = 4(x + 1)
A.
The graph is a line that goes through the points (1,-4) and (0,0).
B.
The graph is a line that goes through the points (1,4) and (2,8).
C.
The graph is a line that goes through the points (-4,-1) and (-3,-3).
D.
The graph is a line that goes through the points (4,1) and (5,5).
Answer:45x-5 is the answer
Step-by-step explanation:
(4,1) and 5,5 add them both
Answer:
B.) The graph is a line that goes through the points (1,4) and (2,8).
Step-by-step explanation:
1.) (4) + 4 = 4((1) +1)
2.) 8 = 4 + 4
3.) 8 = 8 --> Correct
4.) (8) + 4 = 4((2) + 1)
5.) 12 = 8 + 4
6.) 12 = 12 --> Correct
1. Which equation shows a non-proportional
relationship?
A y=-2x
By= 2X
x
Cy=2x+ 0
Dy=2x + 2
Answer:
Option D. [tex]y=2x+2[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Verify each case
case A) we have
[tex]y=-2x[/tex]
Is a equation of the form [tex]y=kx[/tex]
The value of k=-2
This equation represent a proportional relationship
case B) we have
[tex]y=2x[/tex]
Is a equation of the form [tex]y=kx[/tex]
The value of k=2
This equation represent a proportional relationship
case C) we have
[tex]y=-2x+0[/tex]
The line passes through the origin, because the y-intercept is b=0
This equation represent a proportional relationship
case D) we have
[tex]y=2x+2[/tex]
The line not passes through the origin, because the y-intercept is not equal to zero (b=2)
This equation not represent a proportional relationship
The length of a rectangle is 5 centimeters less than its width What are the dimensions of the rectangle if its area is 66 square centimeters?
The length of the rectangle is
The width of the rectangle is
Answer:
length of rectangle=6cm
width of rectangle=11cm
Step-by-step explanation:
let, width of rectangle=x
length of rectangle=x-5
area of rectangle=[tex]length\times(width)[/tex]
given area of rectangle=66
so 66=[tex]x\times(x-5)[/tex]
66=x^2-5x
x^2-11x+6x-66=0
x(x-11)+6(x-11)=0
(x+6)(x-11)=0
x=-6,11
here x=11 is acceptable
length of rectangle=x-5=11-5=6cm
length of rectangle=6cm
width of rectangle=11cm answer
What is the slope of the line represented by the equation y= -1/2x+1/4
Answer:
-1/2
Step-by-step explanation:
The format your equation in is called slope-intercept form:
y=mx+b
m stands for slope, the slope basically determines how much the line is tilted. b stands for the y intercept, the y intercept is when the line intercepts with the y axis.
Your equation is:
y= -1/2x+1/4
y= m x+ b
Solve the following system of equations using the substitution method. x=2y2x+5y=9
Answer:
x=2, y=1. (2, 1).
Step-by-step explanation:
x=2y
2x+5y=9
-------------
2(2y)+5y=9
4y+5y=9
9y=9
y=9/9
y=1
x=2(1)=2
A publishing industry report predicts that magazine subscriptions will drop
by 10% each year. If this prediction is correct, then how many subscribers
will a magazine with 51,000 subscribers have in 7 years?
If necessary, round your answer to the nearest whole number.
Answer:
24,393 subscribers
Step-by-step explanation:
This is exponential decay problem. The formula for exponential decay is:
[tex]F=P(1-r)^t[/tex]
Where
F is the future value (what we are looking for, in 7 years)
P is the present amount (that is 51,000)
r is the rate of decrease per year (r = 10% = 10/100 = 0.1)
t is the time, in years (t = 7)
Now substituting, we get:
[tex]F=P(1-r)^t\\F=51,000(1-0.1)^7\\F=51,000(0.9)^7\\F=24,393.14[/tex]
Rounding to nearest whole number,
Number of subscribers after 7 years = 24,393 subscribers
Using the exponential decay formula, a magazine with an initial 51,000 subscribers will have approximately 24,393 subscribers left in 7 years if subscriptions decline by 10% annually.
Explanation:The question is asking to predict the number of magazine subscribers after a period of 7 years, assuming a 10% annual decline. To calculate this, we can use the formula for exponential decay, which is A = P(1 - r)^t, where A is the amount after time t, P is the initial principal amount (51,000 subscribers), r is the rate of decline (10% or 0.10), and t is the time in years (7 years). Calculating this, we get:
Initial subscribers: 51,000Annual decline rate: 10%Number of years: 7Subscribers after 7 years: A = 51,000(1 - 0.10)^7Now, calculate the value of A:
A = 51,000(1 - 0.10)^7
A = 51,000(0.90)^7
A = 51,000(0.4782969)
A ≈ 24,393 subscribers (after rounding to the nearest whole number).
Therefore, if the magazine subscriptions continue to decline at a rate of 10% per year, the magazine is predicted to have approximately 24,393 subscribers in 7 years.
The Ferris wheel has a radius of 70 feet. The distance between the wheel and the ground is 4 feet. The rectangular coordinate system shown has its origin on the ground directly below the center of the wheel. Write the equation of the circular wheel. (JUSTIFY)
Show your work. i will give brainliest.
Answer:
The equation of the circular wheel is [tex]x^2+(y-74)^2=(70)^2[/tex].
Step-by-step explanation:
Given :
Radius of Ferris wheel r = 70 feet.
The distance between the wheel and the ground = 4 feet.
Also, the rectangular coordinate system shown has its origin on the ground directly below the center of the wheel.
So the x coordinate of center of wheel must be 0 , and y coordinate = 70 + 4 = 74
Thus, Coordinates of center = (0,74)
The equation of circle is given by :-
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Now center (h,k) = (0,74) and r = 70 , we get
[tex]x^2+(y-74)^2=(70)^2[/tex]
Hence, the equation of the circular wheel is [tex]x^2+(y-74)^2=(70)^2[/tex].
MNOP is a parallelogram. U is any point on side OP. Show that ar( MUN)= ar ( Δ △ PUM)+ar( UNO) △
Answer:
The Proof is below.
Step-by-step explanation:
Given:
[]MNOP is a Parallelogram
U is any point on side OP
To Show:
ar(Δ MUN)= ar ( Δ PUM)+ar (Δ UNO)
Proof:
Theorem:
If a triangle and parallelogram are on the same base and have the same altitude, the area of the triangle will be half that of the parallelogram.
If they have same altitude, they will lie between the same parallels.
Hence the area of the triangle will be equal to half that of the parallelogram.
Area of Parallelogram will be twice of Area of Triangle
∴ [tex]\textrm{Area of Parallelogram MNOP}=2\times (area\ of\ Triangle\ MUN)[/tex].............( 1 )
Also,
[tex]\textrm{Area of Parallelogram MNOP}=Ar(MUN) + Ar(PUM)+ Ar(UNO)[/tex]
Substituting equation 1 we get
[tex]2\times Ar(MUN)=Ar(MUN) + Ar(PUM)+ Ar(UNO)[/tex]
[tex]2\times Ar(MUN)-Ar(MUN) = Ar(PUM)+ Ar(UNO)[/tex]
[tex]Ar(MUN) = Ar(PUM)+ Ar(UNO)[/tex]...........Proved
how many times can 7 go into 50
Answer:
7 without going over
Step-by-step explanation:
The number 7 can go into 50 a total of 7 times with 1 remainder.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
The number 7 can go into 50 a total of 7 times because 50 / 7 = 7 with 1 remainder.
To understand this, consider that when you divide 50 by 7, you are trying to find out how many groups of 7 can be created from 50. Since 50 is a multiple of 7 (50 is divisible by 7 with 1 remainder), there will be an integer number of groups. In this case, that integer is 7, so 7 groups of 7 can be created from 50.
Learn more about the number system here:
brainly.com/question/21751836
#SPJ2
x^2-5x=14 solve for x
Answer:
x=7, -2.
Step-by-step explanation:
x^2-5x=14
x^2-5x-14=0
factor out the trinomial,
(x-7)(x+2)=0
zero property,
x-7=0, x+2=0,
x=0+7=7,
x=0-2=-2
Answer:
x = - 2, x = 7
Step-by-step explanation:
Given
x² - 5x = 14 ( subtract 14 from both sides )
x² - 5x - 14 = 0 ← in standard form
Consider the factors of the constant term (- 14) which sum to give the coefficient of the x- term (- 5)
The factors are - 7 and + 2, since
- 7 × 2 = - 14 and - 7 + 2 = - 5, thus
(x - 7)(x + 2) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 7 = 0 ⇒ x = 7
Use the following figure to answer the question.
∠ 1 and ∠ 2 are supplementary angles.
True
False
Answer:
True
Step-by-step explanation:
Because angles on a straight line are supplementary and these anglea <1 and <2 are supplementary angles
Answer: True
Step-by-step explanation: