Answer:
interquartile range=21.05
Step-by-step explanation:
3.5, 12, 19.1, 25.8, 31.8
median is 19.1
Quartile 1= (3.5+12)/2=7.75
Quartile 3=(25.8+31.8)/2=28.8
interquartile range=Q3-Q1=28.8-7.75= 21.05
Tapiwa raked %5, percent more leaves than Adam raked. Tapiwa raked 357 liters of leaves. How many liters of leaves did Adam rake?
HELP!! DUE SOON
Answer:
340 liters
Step-by-step explanation:
357/1.05=340
The number of bacteria in a petri dish on the first day was 113 cells. If the number of bacteria increase at a rate of 82% per day, how many bacteria cells will there be after 7 days?
Answer:
4107 cells
Step-by-step explanation:
From the question, we have the following values:
Day 1 : 113 cells
Number of cells increases by day by 82%
Hence,
Day 2
113 × 82% = 92.66cells
Hence, Total number of bacteria cells for Day 2 = 113 + 92.66 = 205.66cells
Day 3
205.66 × 82% = 168.6412 cells
Hence, Total number of bacteria cells for Day 3 = 168.6412 + 205.66 = 374.3012 cells
Day 4
374.3012 × 82% = 306.926984 cells
Hence, Total number of bacteria cells for Day 4 = 306.926984 + 374.3012 = 681.228184 cells
Day 5
681.228184 × 82% = 558.60711088 cells
Hence, Total number of bacteria cells for Day 5 = 558.60711088 + 681.228184 = 1239.8352949 cells
Day 6
1239.8352949 × 82% = 1016.6649418 cells
Hence, Total number of bacteria cells for Day 5 = 1016.6649418 + 1239.8352949 = 2256.5002367 cells
Day 7
2256.5002367 × 82% = 1850.3301941 cells
Hence, Total number of bacteria cells for Day 7 = 1850.3301941 + 2256.5002367 = 4106.8304308 cells
Approximately to nearest whole number, the total number of bacteria cells that would be present after 7 days = 4107 cells
SOMEONE PLSSSS HELPPPP. When under equal tension, the frequency of a vibrating string in a piano varies inversely with the string length. If a string that is 410 millimeters in length vibrates at a frequency of 515 cycles a second, at about what frequency will a 705-millimeter string vibrate?
Answer: 299.5 cycles per second.
Step-by-step explanation:
An inverse variation can be written as:
y = k/x
Where, in this case:
y = frequency
x = length of the string
k = constant.
We know that 410 mm correspond to 515 cps.
then:
515cps = k/410mm
k = 515cps*410mm = 211,150 cps*mm
now, if we use x = 705mm we can find the frequency as:
y = ( 211,150 cps*mm)/705mm = 299.5 cycles per second.
MATH HELP ME ASAP!!!!
Answer:
You get 12$ per B and 15$ per A. Thus, the answer is A) $282
Step-by-step explanation:
4A+4B=108
Divide by 4
A+B=27
Subtract B
A = 27 - B
3A+5B=105
Substitution
3(27-B)+5B = 105
Distribute
81-3B+5B=105
Combine like terms
81+2B=105
Subtract 81
2B=24
Divide by 2
B = 12
A = 15
14(15)+6(12)=x
210+72=x
282=x
Hope it helps <3
Which expression is equivalent to log Subscript 2 Baseline 9 x cubed? log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x log Subscript 2 Baseline x + 3 log Subscript 2 Baseline 9 3 log Subscript 2 Baseline x minus log Subscript 2 Baseline 9 3 log Subscript 2 Baseline 9 minus log Subscript 2 Baseline x
Answer:
log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x.
Log₂ 9 + 3Log₂ x
Step-by-step explanation:
Log subscript 2 baseline 9 x cubed can be written as:
Log₂ 9x³
Now, let us simply Log₂ 9x³.
This is illustrated below:
Log₂ 9x³
Recall: LogMN = Log M + Log N
Log₂ 9x³ = Log₂ 9 + Log₂ x³
Recall: Log Mⁿ = nLog M
Log₂ 9x³ = Log₂ 9 + 3Log₂ x
Therefore, the answer is log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x.
The equivalent expression of [tex]\log_2(9x^3)[/tex] is [tex]\log_2(9) + 3\log_2(x)[/tex]
The logarithmic expression is given as:
[tex]\log_2(9x^3)[/tex]
Apply the quotient law of logarithm
[tex]\log_2(9x^3) = \log_2(9) + \log_2(x^3)[/tex]
Apply the power rule of logarithm
[tex]\log_2(9x^3) = \log_2(9) + 3\log_2(x)[/tex]
Hence, the equivalent expression of [tex]\log_2(9x^3)[/tex] is [tex]\log_2(9) + 3\log_2(x)[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/2972832
In a standard normal distribution, what is the probability of a z-score being less than 2.55?
Answer:
The probability is 0.0053861
Step-by-step explanation:
To answer this question, the best thing to do is to put the wordings in a mathematical expression.
Thus what we have is;
P(z < 2.55)
Now since we have the mathematical expression, the next thing to do here is to use the standard normal distribution table.
From the standard normal distribution table, we can get the probability value that equals the given z-score value
Mathematically this is;
P(z<2.55) = 0.0053861
John has 9 boxes of apples. Each box holds 16 apples. If 7 boxes are full, and 2 of the boxes are half full, how many apples does john have?
Answer:
128 Apples
Step-by-step explanation:
Answer:
128 apples
Elaborated:
Your first multiple 16 and 7 which is 112. Your than multiply 2 and 8 since the remaining boxes are half full which is 16. 112+16 is 128. Hope this helps!
Pls hellppp
Jennifer wants to visit 4 different cities A,B,C and D on her vacation. If she will visit them one at a time, and completly random, what is thr probabitly that she will visit them in the exact order ABCD or DCBA?
Answer: The probability that she will visit them in the exact order ABCD or DCBA = [tex]\dfrac{1}{12}[/tex]
Step-by-step explanation:
Given: Jennifer wants to visit 4 different cities A,B,C and D on her vacation.
If she visits in an order , total such orders will be [tex]4![/tex] = 4 x 2 x 3 x 1 =24.
Since probability = [tex]\dfrac{\text{Favourable outcomes}}{\text{total outcomes}}[/tex]
In this case favorable outcomes ( ABCD , DCBA)= 2
Total outcomes = 24
Required probability = [tex]\dfrac{2}{24}=\dfrac{1}{12}[/tex]
Hence, the probability that she will visit them in the exact order ABCD or DCBA = [tex]\dfrac{1}{12}[/tex]
What is the slope of the line?
O slope = 1/3
O slope = -3
O slope = 3
Answer:
Slope = 3
Step-by-step explanation:
Slope is rise (vertical distance) over run (horizontal distance).
Our rise is equal to 3
Our run is equal to 1
So, slope = 3/1 = 3
How do you solve this? Please provide a step-by-step explanation
The residual value is the distance between where the line is and the dot is.
At x = 2, the line crosses at y = 2, and the dot is at y = 1
The difference is: 2-1 = 1
BeUse the dot is below the line it becomes a negative value.
The answer would be -1
A waffle cone has a height of 7 inches and a diameter of 3 inches. What is the volume of ice cream that can be contained within the cone? Use 3.14 to for pi. Round your answer to the nearest hundredth.
15.43 in^3
16.49 in^3
17.86 in^3
18.89 in^3
Hey there! I'm happy to help!
To find the volume of a cone, we multiply the base by the height and then divide by three.
First, we find the area of the base, which is a circle. To find a circle, you square the radius and then multiply by pi (or 3.14 in our case).
Radius is half of the diameter.
3/2=1.5
We square this.
1.5²=2.25
We multiply by 3.14
2.25×3.14=7.065
Now, we multiply this base area by the height.
7.065×7=49.455
We divide by 3.
49.455/3=16.485
Therefore, if we round this, our answer is 16.49 in³.
Now you can find the volume of a cone! Have a wonderful day! :D
Answer:
16.49
Step-by-step explanation:
What is the weight (in grams) of a liquid that exactly fills a 202 milliliter container if the density of the liquid is 0.685g/mL? Round to the nearest hundredth
Answer:
138.37 gram
Step-by-step explanation:
Formula of density
density = mass/ volume
given
volume = 202 mL
density = 0.685g/mL
using these values in Formula of density
0.685g/mL = mass/ 202 mL
mass = 0.685g/mL * 202 mL = 138.37 gram
Thus, weight of liquid is 138.37 gram to the nearest hundredth.
Answer:
138.37 grams
Step-by-step explanation:
I'm taking the exam. Good luck on yours!
Instructions: Find the missing length indicated.
225
144
X=
Answer:
108
Step-by-step explanation:
To find x, you need the geometric mean. First, find the second part of 225 by doing 225 - 144 = 81. Now, to find geometric mean, do 81 x 144 = 11,664; [tex]\sqrt{11,664} = 108[/tex].
The missing length in the right triangle as given in the task content is; 108.
What is the missing length indicated?It follows from the complete question that the triangle given is a right triangle and the missing length can be calculated as;
First, find the second part of 225 by
225 - 144 = 81.
Now, to find geometric mean,
81 × 144 = x²
11,664 = x²
x = 108
Thus, The missing length in the right triangle as given in the task content is; 108.
Read more on missing length;
https://brainly.com/question/28040679
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A rectangle has a height of 2 and a width of 5x^2-2x+3x
Express the area of the entire rectangle.
Expression should be expanded.
how would I do this?^^ if you can break down the steps for me that'd be amazing!
Answer:
[tex] area = 10x^2 - 4x + 6 [/tex]
Step-by-step explanation:
Given that the rectangle has a height = 2, and width of [tex] 5x^2 - 2x + 3 [/tex]
Area of the whole rectangle can be calculated as:
[tex] area = 2(5x^2 - 2x + 3) [/tex]
Use the distributive property of multiplication by using 2 to multiply each term in the expression, [tex] (5x^2 - 2x + 3) [/tex]
[tex]area =2(5x^2) +2 (-2x) + 2(3)[/tex]
[tex] area = 10x^2 - 4x + 6 [/tex]
Find the equation of the line.
Answer:
y = 2x + 4
Step-by-step explanation:
y = mx + b
b = y-intercept = 4
m = slope = rise/run = 4/2 = 2
y = 2x + 4
The factory quality control department discovers that the conditional probability of making a manufacturing mistake in its precision ball bearing production is 4 % 4\% 4% on Tuesday, 4 % 4\% 4% on Wednesday, 4 % 4\% 4% on Thursday, 8 % 8\% 8% on Monday, and 12 % 12\% 12% on Friday. The Company manufactures an equal amount of ball bearings ( 20 % 20\% 20%) on each weekday. What is the probability that a defective ball bearing was manufactured on a Friday?
Answer:
The probability that a defective ball bearing was manufactured on a Friday is 0.375.
Step-by-step explanation:
The conditional probability of an events X given that another event A has already occurred is:
[tex]P(X|A)=\frac{P(A|X)P(X)}{P(A)}[/tex]
The information provided is as follows:
P (D|M) = 0.08
P (D|Tu) = 0.04
P (D|W) = 0.04
P (D|Th) = 0.04
P (D|F) = 0.12
It is provided that the Company manufactures an equal amount of ball bearings, 20% on each weekday, i.e.
P (M) = P (Tu) = P (W) = P (Th) = P (F) = 0.20
Compute the probability of manufacturing a defective ball bearing on any given day as follows:
[tex]P(D)=P(D|M)P(M)+P(D|Tu)P(Tu)+P(D|W)P(W)\\+P(D|Th)P(Th)+P(D|F)P(F)[/tex]
[tex]=(0.08\times 0.20)+(0.04\times 0.20)+(0.04\times 0.20)+(0.04\times 0.20)+(0.12\times 0.20)\\\\=0.064[/tex]
Compute the probability that a defective ball bearing was manufactured on a Friday as follows:
[tex]P(F|D)=\frac{(D|F)P(F)}{P(D)}[/tex]
[tex]=\frac{0.12\times 0.20}{0.064}\\\\=0.375[/tex]
Thus, the probability that a defective ball bearing was manufactured on a Friday is 0.375.
Select the correct answer.
Which table shows a proportional relationship between x and y?
x y
1
5
2
6
3
7
x y
2
3
4
6
6
9
x y
4
16
8
64
12
144
x y
1
3
2
9
3
27
Answer:
I think
x y
2
3
4
6
6
9
Step-by-step explanation:
but i don't see any table
30 - 7p = -7 (p+6) -5
Answer:
I think it doesnt have solution.
What is the product of the complex numbers below? (3-9i) (6-i)
[tex](3-9i)(6-i)=18-3i-54i+9i^2=18-57i-9=\boxed{9-57i}[/tex].
Hope this helps.
Using this data, what is the population proportion of semesters for which the number of student applications is less than 200,000?
Complete question :
The table shows the total number of student applications to universities in a particular state over a period of 12 semesters. States base their decisions on data like this. Suppose they decide that if fewer than 200,000 students apply during 6 or more semesters, the state will make a special effort to promote university education. Using this data, what is the population proportion of semesters for which the number of student applications is less than 200,000?
Semester Student Applications (in thousands)
1 106
2 137
3 285
4 120
5 202
6 195
7 327
8 139
9 307
10 318
11 212
12 217
Answer:
42%
Step-by-step explanation:
Given the above data in thousand :
Proportion of students
1 - - - - 106, 000
2 - - - -137, 000
3 - - - - 285, 000
4 - - - 120, 000
5 - - - 202, 000
6 - - - 195, 000
7 - - - 327, 000
8 - - - 139, 000
9 - - - 307, 000
10 - - - 318, 000
11 - - -212, 000
12 - - - 217, 000
Therefore, proportion of semesters with student application below 200,000
= (Number of semesters below 200,000 / total number of semesters)
Semesters below 200,000 :
(106000, 137000, 120000, 195000, 139000) = 5
(5 / 12) = 0.416666
= 0.42
In terms of percentage :
0.42 * 100 = 42%
which step should be completed first in the following problem 4(27÷3²)
Answer:
3²
Step-by-step explanation:
We have to use BPEMDAS Order of Operations:
B - Brackets
P - Parenthesis
E - Exponents
M - Multiply
D - Divide
A - Addition
S - Subtraction
We use this order left to right. Since we have parenthesis, we look at that first. Inside, we have division and exponents. Since exponents come first, we have to evaluate 3² first.
Answer:
square the 3
Step-by-step explanation:
In the order of operations, you must do the exponent inside the parentheses first, so the first step is:
4(27 ÷ 3²) =
= 4(27 ÷ 9)
Answer: square the 3
It is 64º F at the 5000-foot level of a mountain, and 48º F at the 10,000-foot level of the mountain. Write a linear equation, in slope-intercept form, to find the temperature T at an elevation e on the mountain, where e is in thousands of feet.
Answer:
T = - 3.2e + 80
Step-by-step explanation:
Given the following :
e = elevation in thousands of feets
T = temperature (°F)
e1 = 5 ; e2 = 10 (in thousands of feet)
T1 = 64° ; T2 = 48°
y = mx + c ; T = me + c
y = ; m = slope, c = intercept
64 = m5 + c - - - - (1)
48 = m10 + c - - - - (2)
From (1)
c = 64 - m5
Substitute c = 64 - m5 into (2)
48 = m10 + c - - - - (2)
48 = m10 + 64 - m5
48 - 64 = 10m - 5m
-16 = 5m
m = - 16 / 5
m = - 3.2
Substitute the value of m into c = 64 - m5
c = 64 - 5(-3.2)
c = 64 - (-16)
c = 64 + 16
c = 80
Inserting our c and m values into T = me + c
T = - 3.2e + 80
Where e is in thousands of feet
T is in °F
Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that
costs $3.25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most $30
before tax. The restaurant only sells pancakes in stacks of 4 pancakes for $5.50.
Let S represent the number of stacks of pancakes that Benjamin buys.
1) Which inequality describes this scenario?
Answer:
[tex]\bold {3.25+5.50S \le 30}[/tex] is the correct answer.
Step-by-step explanation:
Given that
Chocolate milk already ordered for the cost of $3.25.
Maximum bill that Benjamin wants = $30
Cost of a stack pancake = $5.50
Number of stacks of pancakes bought = S
It is given that all the money available is to be spent on 1 chocolate milk and S number of stacks of pancakes.
Cost of 1 pancake = $5.50
Cost of S number of stacks of pancakes = [tex]\text{Number of stacks of pancakes} \times \text{Cost of each pancake}[/tex]
i.e. [tex]S \times 5.50 = 5.50S[/tex]
So, total money spent = $3.25+5.50S
Now, this money should be lesser than or equal to $30 because maximum bill that Benjamin wants is $30.
So, the inequality can be written as:
[tex]\bold{3.25+5.50S \le 30}[/tex]
Given $m\geq 2$, denote by $b^{-1}$ the inverse of $b\pmod{m}$. That is, $b^{-1}$ is the residue for which $bb^{-1}\equiv 1\pmod{m}$. Sadie wonders if $(a+b)^{-1}$ is always congruent to $a^{-1}+b^{-1}$ (modulo $m$). She tries the example $a=2$, $b=3$, and $m=7$. Let $L$ be the residue of $(2+3)^{-1}\pmod{7}$, and let $R$ be the residue of $2^{-1}+3^{-1}\pmod{7}$, where $L$ and $R$ are integers from $0$ to $6$ (inclusive). Find $L-R$.
[tex](2+3)^{-1}\equiv5^{-1}\pmod7[/tex] is the number L such that
[tex]5L\equiv1\pmod7[/tex]
Consider the first 7 multiples of 5:
5, 10, 15, 20, 25, 30, 35
Taken mod 7, these are equivalent to
5, 3, 1, 6, 4, 2, 0
This tells us that 3 is the inverse of 5 mod 7, so L = 3.
Similarly, compute the inverses modulo 7 of 2 and 3:
[tex]2a\equiv1\pmod7\implies a\equiv4\pmod7[/tex]
since 2*4 = 8, whose residue is 1 mod 7;
[tex]3b\equiv1\pmod7\implies b\equiv5\pmod7[/tex]
which we got for free by finding the inverse of 5 earlier. So
[tex]2^{-1}+3^{-1}\equiv4+5\equiv9\equiv2\pmod7[/tex]
and so R = 2.
Then L - R = 1.
need help nadding and subtracting functions
Answer:
2x² + [tex]\frac{3}{2}[/tex] x - 5
Step-by-step explanation:
(f + g)(x) = f(x) + g(x), thus
f(x) + g(x)
= [tex]\frac{x}{2}[/tex] - 2 + 2x² + x - 3 ← collect like terms
= 2x² + [tex]\frac{3}{2}[/tex] x - 5
Can someone please help me?
Answer:
B
Step-by-step explanation:
When you plug it in, another form could be y=-3x+2
Answer:
y=-3x+2
Step-by-step explanation:
y=-3x+7
parallel lines have the same slope but different y intercept which is b in the equation y=mx+b
since it passes through (2,-4) then x=2 and y=-4, m(slope)=-3
y=mx+b
-4=-3(2)+b
b=-4+6
b=2
y=-3x+2
A square has diagonals of length 10 cm. Find the sides of the square
Answer:
5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
The diagonal divides the square into 2 right triangles.
let s be the side of the square with the diagonal being the hypotenuse.
Applying Pythagoras' identity to one right triangle, gives
s² + s² = 10² , that is
2s² = 100 ( divide both sides by 2 )
s² = 50 ( take the square root of both sides )
s = [tex]\sqrt{50}[/tex] = [tex]\sqrt{25(2)}[/tex] = [tex]\sqrt{25}[/tex] × [tex]\sqrt{2}[/tex] = 5[tex]\sqrt{2}[/tex]
Determine the perimeter and area of the red portion of the 2 dimensional figure below, given the circle diameter of 7 cm and the perimeter of the entire figure is 42 cm. Round if necessary
Answer:
Perimeter = 20cm ; area = 59.5cm
Step-by-step explanation:
Given the following :
Perimeter of entire figure = 42cm
Diameter of circle (d) = 7cm
Find the perimeter of the circle :
The perimeter (p) of a circle equals :
2πr
Where r = radius of circle
r = diameter /2 = 7/2 = 3.5cm
Therefore,
P = 2 * (22/7) * 3.5
P = 22 cm
Looking at the figure, we only take the semicircle :
Therefore perimeter of each semicircle =
22cm / 2 = 11cm
Therefore, perimeter of the red shaded region =
(42 - 22)cm = 20cm
Area of Circle = πr^2
(22/7) * 3.5^2 = 38.5 cm
Area of each semicircle = 38.5/2 = 19.25cm
Total area of semicircle = (19.25 +19.25) = 38.50cm
To find sides of rectangle :
Perimeter of the rectangle :
width = diameter of circle = 7cm
2(l + w) = 42
2(l + 7) = 42
2l + 14 = 42
2l = 42 - 14
2l = 28
l = 28/2
length (l) = 14cm
Therefore, area of rectangle :
Length * width
14 * 7 = 98cm
Area of red portion:
Area of rectangle - (area of the 2 semicircles)
98cm - 38.50cm
= 59.50cm
Natasha and her two dogs were walking on a perfectly straight road when her two dogs ran away from her in opposite directions. Her beagle is now \dfrac{25}{4} 4 25 start fraction, 25, divided by, 4, end fraction meters directly to her right, and her labrador is \dfrac{51}{20} 20 51 start fraction, 51, divided by, 20, end fraction meters directly to her left. Which of the following expressions represents how far apart the two dogs are?
Answer:
[tex]\dfrac{74}{20}=3.7 meters[/tex]
Step-by-step explanation:
Hello!
1) Since no other data has been given. Suppose Natasha is in the center and the beagle is to the right.
[tex]\dfrac{25}{4} \:meters[/tex]
2) The labrador is [tex]\dfrac{51}{20}\: to\: the\: left.[/tex]
[tex]\dfrac{25}{4} -\dfrac{51}{20} =\dfrac{(5*25)-51}{20} \\\dfrac{(125-51}{20} =\dfrac{74}{20}[/tex]
Answer:
The answer is B :D hope this helps
Step-by-step explanation:
Find the measure of b.
Please help
Answer:
125 degrees
Step-by-step explanation:
Using a theorem, you know that angle a is half of 110. Also, in all quadrilaterals inscribed in a circle, the opposite angles are supplimentary. So then, knowing that angle a is 55 degrees, you can come to the conclusion that b is 125 degrees.
Hope this is helpful! :)