Answer:
The five number summary are;
The minimum is 198
The 1st quartile, Q₁, is 205
The 2nd quartile, Q₂, or median is 214
The 3rd quartile, Q₃, is 228
The Maximum is 237
Step-by-step explanation:
The numbers are;
232, 198, 214, 205, 222, 228, 208, 237, 217, 199, 213, 208, 228, 224, 203
Which can be rearranged in increasing order as follows;
198, 199, 203, 205, 208, 208, 213, 214, 217, 222, 224, 228, 228, 232, 237
The five number summary are;
The minimum = The lowest number in the list = 198
The 1st quartile, Q₁, is the (n + 1)/4 th term which is (15 + 1)/4 = 4th term = 205
The 2nd quartile, Q₂, or median is the (n + 1)/2 th term which is (15 + 1)/2 = 8th term = 214
The 3rd quartile, Q₃, is the 3×(n + 1)/4 th term which is 3×(15 + 1)/4 = 12th term = 228
The Maximum = The highest number in the list = 237.
Micah solves a linear equation and concludes that x = 0 is the solution. His work is shown below. (1 – 3x) = 4(– + 2) 4 lines of math. The first line is, StartFraction 5 Over 6 EndFraction left-parenthesis 1 minus 3 x right-parenthesis equals 4 left-parenthesis negative StartFraction 5 x Over EndFraction plus 2 right-parenthesis. The second line is, StartFraction 5 Over 6 EndFraction minus StartFraction 5x Over 2 EndFraction equals StartFraction 5x Over 2 EndFraction plus 8. The third line in plus StartFraction 5x Over 2 EndFraction and StartFraction 5x Over 2 EndFraction on both sides of the equal sign. The fourth line is 0 equals x. 0 = x
Answer:
Micah's solution is wrong
Step-by-step explanation:
Micah solves a linear equation and concludes that x = 0 is the solution. His work is shown below.
(1 – 3x) = 4(– + 2)
0 = x
Which statement is true about Micah’s solution?
Micah’s solution is wrong.
There are no values of x that make the statement true.
Micah’s solution is correct, and the value of x that makes the statement true is 0.
Micah should have divided by .
Micah should have subtracted
Solution
First solve for the value of x
Given
(1 – 3x) = 4(– + 2)
It could mean; (1 – 3x) = 4(+ 2)
or
(1 – 3x) = 4(-2)
In the first option (1 – 3x) = 4(+ 2)
1 – 3x = 4(+ 2)
1-3x= 8
-3x=8-1
-3x=7
x= -7/3
In the second option
(1 – 3x) = 4(-2)
1-3x= -8
-3x= -8-1
-3x = -9
x= 3
x= 3 0r -7/3
The values of x that make the statement true are 3 and -7/3
Micah's solution of x=0 is wrong
Answer:
A. Micah’s solution is wrong. There are no values of x that make the statement true.
Step-by-step explanation:
The length of a garden is 2 feet more than its height. Write an equation for the area of the rectangles in terms of height, h. Area = ? sq. ft.
Answer:
h^2+2h
Step-by-step explanation:
Let h be the heigth of this garden
The length of this garden is 2 feet more than the heigth.
So the length can be expressed as h+2
The area of this triangle is the product of the heigth and the length.
A = h*(h+2)
A= h^2 +2h
To which set or sets below does the number -7/8 belongs to ?
Answer:
-7/8
Step-by-step explanation:
Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a
$7.50 delivery fee and $14 per pizza. She wants to buy as many pizzas as she can, and she also needs to
keep the delivery fee plus the cost of the pizzas under $60.
Each pizza is cut into 8 slices, and she wonders how many total slices she can afford.
Let P represent the number of pizzas that Jacque buys.
1) Which inequality describes this scenario?
Choose 1 answer:
7.50 +14P < 60
B
7.50+ 14P > 60
14 + 7.50P < 60
D
14+ 7.50P > 60
Answer: A. 7.50 +14P < 60
Step-by-step explanation:
Let P represent the number of pizzas that Jacque buys.
Given, delivery fee =$7.50
Per pizza cost = $14
She wants to buy as many pizzas as she can, and she also needs to
keep the delivery fee plus the cost of the pizzas under $60.
i.e. (delivery fee) + (Number of pizzas) x (Per pizza cost) < $60
i.e. 7.50 +14P<60
Required inequality : 7.50 +14P<60
Answer:
A. 7.50 +14P < 60 Answer: Jacque can only afford 24 slices of pizza
Step-by-step explanation:
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]
In a bag containing 3 red balls,and 2 blue balls,one of which is drawn at random.
Find the probability that its a red ball
Step-by-step explanation:
Given:
Successful outcome
Red=3
Blue=2
Possible outcome
Total=5 balls
Required:
The probability of drawing red ball
Formula:
Probability= Successful outcome ÷ Possible outcome
Solution:
Probability= Successful outcome ÷ Possible outcome
Probability=3÷5
Probability=3/5 or 0.6
Hope this helps ;) ❤❤❤
N students joined the radio control club. Some had boats, some had airplanes, and some had cars. They divided into 3 equal groups according to what model each one had. Ten more students joined the radio-controlled airplane group. There are 15 students in this group now. How many students joined the radio control club in the beginning?
Answer:
36 people joined the radio control club.
Step-by-step explanation:
15-3= 12
12*3=36
What is the slope of the following graph? M=
Answer:
-2/3
Step-by-step explanation:
We have two points ( 0,3) and ( 3,1)
We can use the slope formula
m = (y2-y1)/(x2-x1)
= (1-3) /(3-0)
= -2/3
Answer:
-2/3
Step-by-step explanation:
Two points are given on the graph:
(0, 3) and (3, 1)
Use slope formula.
m = rise/run
m = (y₂ - y₁)/(x₂ - x₁)
x₁ = 0
y₁ = 3
x₂ = 3
y₂ = 1
m = (1 - 3)/(3 - 0)
m = -2/3
The slope of the line is -2/3.
By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 16 in. long and 6 in. wide, find the dimensions (in inches) of the box that will yield the maximum volume. (Round your answers to two decimal places if necessary.)
Answer:
x=3.00 or x= 8.00
Explanation:
Let us denote side of the cut-out square as x inches
Then base of box = 16-2x by 6-2x
The volume = V = (16-2x)(6-2x)
= 96-3x-12x+4x
dV/dx = 96-44x+4x^2
= 0 for a max V
divide by 4
X^2 -11x +24=0
Using quadratic formula to solve the equation
X= (11± √11^2-(4×1×24)/2
(11± √25)/2
x= 3 or 8inches
From the equation of volume = V = x(16-2x)(6-2x)
Substitute
let x = 3 , V = 3(16-6)(6-6) = 0
let x = 8 , V = 8(16-16)(6-16) = 0
Therefore, the maximum volume exist at both point x=3 or x= 8
Paige launched a ball using a catapult she built. The
height of the ball (in meters above the ground) t seconds
after launch is modeled by
h(t) = -5t2 + 40t
Paige wants to know when the ball will hit the ground.
1) Rewrite the function in a different form (factored
or vertex) where the answer appears as a number in
the equation.
h(t) =
2) How many seconds after launch does the ball hit
the ground?
seconds
Answer:
5 seconds ma boii
Step-by-step explanation:
i just took tha test
Answer:
1) h(t) = -5t(t - 8)
t - 8 = 0, so
2) t = 8 seconds
Step-by-step explanation:
Using the linear combination method, what is the solution to the system of linear equations 5 x + 3 y = negative 10 and Negative 20 x minus 7 y = 15? (–5, 1) (–1, 5) (1, –5) (5, –1)
Answer:
work is shown and pictured
Answer:
The answer is C
Step-by-step explanation:
An integer minus 5 times its reciprocal is
76
9
What is the integer?
Can anyone help me with this question? Which reason justifies the conclusion that ∆PST ≅ ∆RST?
Answer:
A) SAS postulate
Step-by-step explanation:
Answer:
SAS
Step-by-step explanation:
you know that ST is equal and you also know two equal angles and one other equal side
3. The ratio of the number of male and female teachers in a school is 2 : 11. If the
number of male teachers is 112, find the number of female teachers.
Answer:
the number of female teachers is 616
Step-by-step explanation:
male 2: 112
Female 11 : x
now you want to find x which is the number of female teachers
multiply 11 with 112 and 2 with x
11 x 112= 2x
divide 2
1 232 = 2x/2
616 = x
Hope that help :)
Can someone help me with this plz? Will give brainliest
Answer:
∆ABC=∆DBC
Step-by-step explanation:
The angle of ABC, which is 90° is the same as the angle DBC which is also 90°
would someone please help me thank you very much * no fake answer *
Answer:
a = 1500
b = 0.97
Step-by-step explanation:
The equation we are modeling is ;
F(x) = ab^x
Now we have two parameters to fix.
These are the density and the annual percentage increase
We can substitute the value of 1500 for a and also make a corresponding substitution for b.
Now for b, the value to substitute is quite dicey.
3% = 3/100 = 0.03
To make any substitution, we need to subtract this value from 1 and that would be 0.97
So it is this 0.97 that we now raise x to for each of the number of years
What is the area of the button? Use 3.14 for π and round to the nearest tenth. The circumference of a button is 40.8 millimeters. What is the radius of the button? Use 3.14 for π and round to the nearest tenth. i need this answered quick
Answer: radius = 6.5millimeters; Area = 132.7m²
Step-by-step explanation:
The circumference of a circle = 2πr
The area of a circle = πr²
The circumference of a button is 40.8 millimeters. Then we can get the radius, thus will be:
Circumference = 2πr
40.8 = 2 × 3.14 × r
40.8 = 6.28r
r = 40.8/6.28
r = 6.5
Radius is 6.5 millimeters
Area = πr²
Area = 3.14 × 6.5 × 6.5
Area = 132.7m²
!!!!!!WILL GIVE BRAINLEIST !!!!!!
Answer:
[tex]\boxed{Median = 152}[/tex]
Step-by-step explanation:
Observation = 568 , 254 , 152 , 101 , 100
In ascending order:
=> 100 , 101 , 152 , 254 , 568
Median is the middlemost no. So here:
Median = 152
Answer:
152
Step-by-step explanation:
If you set the data in an ascending order, you will find 152 to be the middle value, thus being the median
PLS HELP ME !!! A community garden is divided into 10 equal parts. Carrots are planted in 5/10 of the garden and peas are planted in 1/10 of the garden. The rest of the garden is planted with corn. What fraction of the garden is corn? Show a model and solve.
Answer:
The fraction of corn is 4/10 of the garden.
Step-by-step explanation:
5/10 + 1/10 = 6/10
10/10 - 6/10 = 4/10 or 2/5
The following set of ordered pairs represents a power inverse variation. Find the value of r given that k = 5.
Answer:
r=2
Step-by-step explanation:
y = k x^r is the formula for a direct variation
y = k x^ -r is the formula for a indirect variation
20= 5 (1/2)^ -r
Divide each side by 5
4 = (1/2) ^ -r
Rewriting
2^2 = 2^ -1 ^ -r
2^2 = 2 ^ r
The bases are the same so
2 =r
Answer:
r=-2
Step-by-step explanation:
because i had this questiion and i got it right
WILL MARK BRAINLIEST!!!!
Answer:
See below.
Step-by-step explanation:
SQUARE:
The area of the square is:
[tex]9x^2-12x+4[/tex]
Factor it:
[tex]=9x^2-6x-6x+4\\=3x(3x-2)-2(3x-2)\\=(3x-2)(3x-2)\\=(3x-2)^2[/tex]
Remember that all four sides of a square is equal. The area is simply the side squared. Therefore, all four sides of the square measure (3x-2).
RECTANGLE:
[tex]25x^2-16y^2\\[/tex]
Factor it. This resembles the difference of two squares, where:
[tex](x-a)(x+a)=x^2-a^2[/tex]
[tex]25x^2-16y^2\\=(5x)^2-(4y)^2\\=(5x-4y)(5x+4y)[/tex]
This cannot be simplified further. Note that the sides of rectangles doesn't necessarily have to be the same.
The dimensions of the rectangle is:
(5x-4y) by (5x+4y)
Answer:
Step-by-step explanation:
1. the area of square is 9x^2-12x+4 square units
shortcut: (a-b)^2= a^2-2ab+b^2
then simplify 9x^2-12x+4 to (3x-2)^2
area of square = s^2
then side equals sqrt((3x-2)^2)
s = (3x-2) units
2. the area of rectangle is (25x^2-16y^2) square units
shortcut: (a^2-b^2) = (a-b)(a+b)
then simplify (25x^2-16y^2) to (5x-4y)(5x+4y) square units
one side is: (5x-4y) units
one side is (5x+4y) units
7th grade-Post-test Summer Sc...
Show all steps
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Which of the following pairs are like terms? Select all that apply.
11a and 13a power of 2
18k and 18b
7x and 16x
17yz and 12y
9pq and 8qp
Answer:
9pq, 8qp, and 7x, 16y
Step-by-step explanation:
these pairs have the same variable and exponent. To be a like term, you have to have same variables and same exponents, so therefore 11a and 13a^2 can't be like terms.
Please help me with this question!!!
Answer:
tan (40°) = [tex]\frac{x}{100}[/tex]
Step-by-step explanation:
tan [tex]\theta[/tex] = [tex]\frac{opposite}{adjacent}[/tex]
The opposite side to angle B is x. The adjacent side to angle B is 100 ft.
tan (40°) = [tex]\frac{x}{100}[/tex]
Answer:
tan 40° = x/100
Step-by-step explanation:
As, AC is perpendicular and BC is the with respect to angle ABC. So, tan 40° will be use to determine the distance in feet from point C to point A.
tan ABC = perpendicular/base
tan 40° = AC/BC
tan 40° = x/100 feet
Find the value of x
A. 5.5
B. 6.6
C. 1.1
D. 8.8
Answer:
b
Step-by-step explanation:
PLEASE HELP the formula m=12,000+12,000rt/12t gives keri's monthly loan payment where t is the annual interest rate and t is the length of the loan, in years. Keri decideds that she can afoord at most a $275
Answer:
The answer is below
Step-by-step explanation:
The formula m = (12,000 + 12,000rt)/12t gives Keri's monthly loan payment, where r is the annual interest rate and t is the length of the loan, in years. Keri decides that she can afford, at most, a $275 monthly car payment. Give an example of an interest rate greater than 0% and a loan length that would result in a car payment Keri could afford. Provide support for your answer.
Answer: Let us assume an annual interest rate (r) = 10% = 0.1. The maximum monthly payment (m) Keri can afford is $275. i.e. m ≤ $275. Using the monthly loan payment formula, we can calculate a loan length that would result in a car payment Keri could afford.
[tex]m=\frac{12000+12000rt}{12t}\\ but\ m\leq275, \ and \ r=10\%=0.1\\275= \frac{12000+12000(0.1)t}{12t}\\275= \frac{12000}{12t} +\frac{12000(0.1)}{12t}\\275= \frac{1000}{t} + 100\\275-100= \frac{1000}{t} \\175= \frac{1000}{t} \\175t = 1000\\t= \frac{1000}{175}\\ t=5.72\ years[/tex]
The loan must be at least for 5.72 years for an annual interest rate (r) of 10%
Here's the keywords you need! :)
example of an interest rate and a loan length that costs under $275/month (example: 4-year loan at 2% interest)
monthly payment for the loan you described (example: 4-year loan at 2% interest is $270/month)
statement that the monthly payment for the loan you described is less than or equal to $275 (example: $270/month payment is less than $275)
Just got it right on edge 2020, hope this helps!! :)
Dmitri needs 6 liters of a 16% solution of sulfuric acid for a research project in molecular biology. He has two supplies of sulfuric acid solution: one is an unlimited supply of the 12% solution and the other an unlimited supply of the 24% solution. How many liters of each solution should Dmitri use?
Answer:
4 litres of 12% solution
2 litre of 24% solution
Step-by-step explanation:
Let the 12% solution = l
Let the 24% solution = h
Dimitri needs a total of 6 litres of both :
l + h = 6 - - - - - - - - (1)
He needs a mixture of both volumes of both to give a 16% volume
12%l + 24%h = 16% * 6
0.12l + 0.24h = 0.96 ----(2)
From (1)
l + h = 6;
l = 6 - h
Substitute l =6-h into (2)
0.12(6 - h) + 0.24h = 0.96
0.72 - 0.12h + 0.24h = 0.96
0.72 + 0.12h = 0.96
0.12h = 0.96 - 0.72
0.12h = 0.24
h = 0.24 / 0.12
h = 2
From ;
l = 6 - h
l = 6 - 2
l = 4
Someone pls help me I put numbers so it will be more easier
Answer:
1.road 1
2. scooter
3. walk
Answer:
1. road 1
2. scooter
3. walk
Step-by-step explanation:
1. in the corresponding point on the tree, you have road 2. therefore, the most logical answer would be road 1.
2. you are given three options of travel. as "walk" and "bike" are already provided, they cannot be the answer to fill in for box 2. therefore, you are left with "scooter."
3. similarly, you are given three options of travel. as "bike" and "scooter" are already provided, they cannot be the answer to fill in for box 3. therefore, you are left with "walk."
Last week Lisa had a gross earning of $1441.30. Cathy receives a base salary of $375 and a commission on sales exceeding her quota of $5000. What is her rate of commission if her sales were $6560?
Answer:
4.25%
Step-by-step explanation:
Commision = 441.30 - 375 = 66.30
Commision is based on = 6560-5000 = 1560
Rate of Commision = (in decimal) 66.30/1560 = 0.0425
Rate of Commision = 0.0425 * 100 = 4.25 %
A tissue sample is three cells thick. Each cell has a thickness of 0.000004m. What is the thickness of the tissue sample in mm. Give your answer in standard form. PLZ SHOW WORKING NOT IN NANO METERS. IN STANDARD FORM
Answer:
0.012 millimeters
Step-by-step explanation:
First, we solve for 0.000004 m to mm = 0.004 mm x 3 = 0.012 millimeters
Find the values of k so that the area of the triangle with vertices (1, -1), (-4,2k) and (-k, – 5) is 24 sq. units
Step-by-step explanation:
We need to find the value of k so that the triangle with vertices (1, -1), (-4,2k) and (-k, – 5) is 24 sq. units.
The area of triangle is given by :
[tex]A=\dfrac{1}{2}\times [x_1(y_2-y_3)-x_2(y_3-y_1)+x_3(y_1-y_2)][/tex]
Here,
x₁ = 1, y₁ = -1, x₂ = -4, y₂ = 2k, x₃ = -k and y₃ = -5
So,
[tex]24=\dfrac{1}{2}\times [1(2k-(-5))-(-4)((-5)-(-1))+(-k)((-1)-(2k))][/tex]
We need to solve the above equation,
[tex]48=[1(2k-(-5))-(-4)((-5)-(-1))+(-k)((-1)-(2k))][/tex]
On solving the above equation we get the value of k as :
k = 4.7