The Approximate values of the five number summary are ;
(i) the Minimum is 10 ,
(ii) the First quartile is 30 ,
(iii) the Third Quartile is 80 ,
(iv) the Median is 55 ,
(v) the Maximum is 100 .
The values of the data set are : {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 ,55 ,60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;
The Five number summary consists of the minimum , maximum , first quartile , third quartile and the median .
(i) the Minimum of the data set is = 10 ;
(ii) we split the data set into , 2 halves ;
that means ; {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 } and {60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;
the first quartile lies in the lower half : {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 } ;
So , first quartile (Q₁) = 30 ;
(iii) the third quartile (Q₃) lies in the upper half : {60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;
So , Q₃ = 80 ;
(iv) the total number of terms in the set is = 19 ;
So , the median is = tenth term = 55 ;
(v) the maximum of the data set is = 100 .
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Pls help me fast fast fast
The value of ∠E = 31 degrees and the value of ∠G = 149 degrees for the given triangle.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "."
The two triangles are similar thus the measure of its angle are also equal.
Using the similar triangle we have:
Angle D = Angle A = 82 degrees.
Angle F = 67 degrees
Using the sum of interior angles of triangle we have:
∠D + ∠F + ∠E = 180
82 + 67 + ∠E = 180
∠E = 31
From the figure we observe that,
∠E + ∠G = 180 (straight line)
31 + ∠G = 180
∠G = 149
Hence, the value of ∠E = 31 degrees and the value of ∠G = 149 degrees for the given triangle.
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Ryan purchased 3 ties and 4 shirts for $500 Earl purchased 6 ties and 7 shirts at the same store for $920.00. What is the total cost of 1 tie and 1 shirt .? Show working
Ryan purchased 3 ties and 4 shirts for $500 Earl purchased 6 ties and 7 shirts at the same store for $920.00 then the total cost of 1 tie and 1 shirt is $153.33.
What is system of equations?
A system of equations is a set of two or more equations that are solved simultaneously to find the values of the variables that satisfy all the equations in the system. The solution of the system is the set of values of the variables that satisfy all the equations. There are different methods to solve a system of equations, such as substitution, elimination, and matrix methods.
Let x be the cost of 1 tie and y be the cost of 1 shirt.
From the problem, we can set up a system of equations:
3x + 4y = 500 (equation 1)
6x + 7y = 920 (equation 2)
To solve for x and y, we can use elimination method. Multiply equation 1 by 2 and subtract it from equation 2:
6x + 7y = 920
(6x + 8y = 1000)
-y = -80
Therefore, y = 80. We can substitute y = 80 into equation 1:
3x + 4(80) = 500
Simplifying the equation, we get:
3x = 220
So, x = 220/3 = 73.33 (rounded to two decimal places).
Therefore, the total cost of 1 tie and 1 shirt is $73.33 + $80 = $153.33.
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Help answer this
Two functions are represented below.
Function 1:
Function 2:
x y
-1 3
0 1
1 -1
2 -3
Which statement is true about the y-intercepts of the functions?
A. At least one of the functions does not have a y-intercept.
B. Function 1 and Function 2 have y-intercepts that are equal.
C. Function 1 has a y-intercept that is less than the y-intercept of
Function 2.
D. Function 1 has a y-intercept that is greater than the y-intercept of
Function 2.
Function 1 and Function 2 have y-intercepts that are equal. The solution has been obtained by using slope-intercept form.
What is slope-intercept form?
The line that represents the graph of the equation y = mx + b has a slope of m and a y-intercept of b. The m and b values are real integers, and the slope-intercept form of the linear equation is used.
We are given two functions.
Now, we will represent the functions in the slope-intercept form to find the y-intercept.
Function 1
⇒4x - 2y = -2
⇒2x - y = -1 (Dividing both sides by 2)
⇒ -y = -1 - 2x
⇒y = 2x + 1
So, the y-intercept is 1.
Function 2
We are given two points as (-1,3) and (0,1)
The slope comes out to be = -2
So, b = 3 - (-2)(-1) = 1
So, the y-intercept is 1.
Hence, function 1 and function 2 have y-intercepts that are equal.
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Lena says that 42y% and -5.%y are like terms. Is she correct? Why or why not?
Answer:
why and why not why .I have no idea wish I did
at most, how many references in this line could be null and might cause the nullpointerexception to be thrown?
None. There are no references in this line. This line does not contain any references, so no references can be null. Therefore, no NullPointerException can be thrown.
This line does not contain any references, so no references can be null. Therefore, no NullPointerException can be thrown.
This line of code does not contain any references at all. Therefore, it is not possible for any references to be null, and it is impossible for a NullPointerException to be thrown in response to this line. NullPointerExceptions are only thrown when a program attempts to use a reference that is null, but this line does not contain any references, so such an exception is not possible. Consequently, no references can be null in this line and no NullPointerException can be thrown.
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15.
Mrs Dixon puts 230 eggs into boxes.
Each box holds 12 eggs.
How many egg boxes does Mrs Dixon need to put all the eggs into boxes?
Answer:
20 boxes
Step-by-step explanation:
Each box ca hold 12 eggs
There are 230 eggs
So you will need 230/12 = 19 1/6 boxes = 19.167 boxes
Since you cannot get less than 1 box, round up to 20 boxes. There will be some empty spaces in one of the boxes
Graph the line that represents this equation:
3x - 4y = 8
Drawing Tools
Select
Point
Line
X
Click on a tool to begin drawing.
-10
-8
-6
-4
-2
10-
4
8
2
S
A
2
2
Delete
++
Answer:
Step-by-step explanation:
Mari bought 6 packets of tomato seeds. Each packet contained 24 seeds. She planted 1 packet of the seeds, and 15 seeds sprouted.Which statement about the seeds in the remaining packets is best supported by this information?
Answer:
Mari bought 6 packages of tomato seeds and each package contains 24 seeds then
Seeds = (6) * (24) = 144.
Mari has a total of 144 seeds.
Mari planted a pack of seeds and has 15 germinated seeds.
144-24-15 = 105
Mari then has 105 seeds left.
Answer
C At least 100 but no more than 120 seeds will sprout
The statement about the seeds in the remaining packets is best supported by this information is option C: At least 100 but no more than 120 seeds will sprout
What is the seeds about?Mari bought 6 packages of tomato seeds and each package contains 24 seeds so:
Seeds = 6 x 24 = 144.
Note that Mari has a total of 144 seeds. In the question, Mari planted a pack of seeds and has 15 germinated seeds.
Hence:
144-24-15 = 105
Mari then has 105 seeds left.
Hence option c: At least 100 but no more than 120 seeds will sprout, is correct.
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See full text below
Mari bought 6 packets of tomato seeds. Each
packet contained 24 seeds. She planted 1 packet
of the seeds, and 15 seeds sprouted.
Which statement about the seeds in the remaining
packets is best supported by this information?
A No more than 50 sees will sprout
B Between 50 and 100 seeds will sprout
C At least 100 but no more than 120 seeds will
sprout
D All 120 seeds will sprout
Question 13:
Christine had 0.8 times the amount of money Sarah had. They went shopping and spent
$684 altogether. Christine spent 0.25 of her money and had thrice as much money left
as Sarah. How much money did Sarah spend?
Answer: Let's call Sarah's original amount of money as x. Then, Christine had 0.8x.
After they spent $684 altogether, Christine had 0.8x - 0.25(0.8x) = 0.8x - 0.2x = 0.6x left.
Sarah had x - 684.
Since Christine had thrice as much money left as Sarah, we can write an equation:
0.6x = 3(x - 684)
Expanding the right side of the equation:
0.6x = 3x - 2052
Solving for x:
2.6x = 2052
x = 787.69
So Sarah originally had 787.69 dollars and spent 787.69 - 684 = 103.69 dollars.
Step-by-step explanation:
whats the middle product of (-2x+1)(-3x-5)
Answer:
7x
Step-by-step explanation:
That would be ( -2x )(-5) + -3x(1) = 10x - 3x = 7x
the perimeter of the shaded part of a square is 28 inches. find the area of the square
Answer:
Step-by-step explanation:
A square has 4 equal sides therefore to find the side of one we would divide the perimeter by 4. Doing that we get 7 inches.
Now seeing as it has four equal sides in order for us to find the area we would do:
Area = side x side = 7x7 = 49 squared inches
Henry has 30 coins. He has 1 fewer pennies than dimes. he has 2 fewer nickels than dimes. how many dimes does Henry have?
A : 3
B: 9
C: 11
D: 27
Answer:
C 11
Step-by-step explanation:
you have 1 less penny than dimes which is 10 pennies
you have 2 less nickels than dimes which is 9
11+10+9=30
at noon, a ship leaves a harbor and sails south at 20 knots. four hours later, a second ship leaves the harbor and sails east at 15 knots. when will the ships be 100 nautical miles apart? round to the nearest minute. note that 1 knot = 1 nautical mile per hour.
Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.
What is Pythagorean theorem?
The Pythagorean theorem is a fundamental concept in geometry that relates to the three sides of a right-angled triangle. It states that the square of the length of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, it can be expressed as:
[tex]a^2 + b^2 = c^2[/tex]
We can use the Pythagorean theorem to find the distance between the two ships at any given time:
d² = (20t)² + (15(t-4))²
Simplifying this equation, we get:
d² = 400t² + 225(t² - 8t + 16)
d² = 625t² - 1800t + 3600
d = √(625t²- 1800t + 3600)
We want to find the value of t when d = 100 nautical miles, so we can set up the following equation:
100 = √(625t² - 1800t + 3600)
Squaring both sides, we get:
10000 = 625t² - 1800t + 3600
Rearranging, we get:
625t² - 1800t - 6400 = 0
Using the quadratic formula, we get:
t = (1800 ± √(1800² + 46256400)) / (2*625)
t = (1800 ± 3900) / 1250
t = 3.84 or t = 8.16
So the time elapsed for the second ship is:
t2 = t + 4
t2 = 7.84 or t2 = 12.16
We can see that the only solution that works is when t = 8.16 and t2 = 12.16. At that time, the first ship will have sailed for 8.16 hours at 20 knots, or 163.2 nautical miles, and the second ship will have sailed for 8.16 - 4 = 4.16 hours at 15 knots, or 62.4 nautical miles. The distance between the two ships will be:
d = √((163.2)² + (62.4)²) = 174.9 nautical miles
Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.
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I NEED HELP ON THIS ASAP!!!!
Answer: Look below :)
Step-by-step explanation:
Hello again Sarah!
a. the dashed line indicated our answer will use > or <
furthermore, we can see two points, (0,2) and (1,6) on the graph.
So the slope is: 4/1 = 4
and the y intercept can be visually seen as 2
Since the shaded part is to the right, we will use <
The final equation is: y < 4x + 2
I wont show working for the others, but its pretty similar:
b. [tex]y \geq 0.5x - 3[/tex]
c. y < 0.75x - 2
if you generate multiple datasets from a distribution with a given mean and variance, the mean and variance that you calculate from the generated data will always be the exact same as the original?
If we generate the multiple datasets from a distribution with a given mean and variance , then mean and variance of from generated data will not be same .
The sample mean and the variance are random variables that vary from sample to sample, even if the samples are drawn from the same population.
When we generate a sample from a distribution with a known mean and variance, the sample mean and variance will be estimates of the population mean and variance ;
So , because of sampling variability, the estimates obtained from different samples may differ from one another and from the true population parameters.
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Pls help thank you will mark the Brainliest
The exponential function from the decay function given is y = 30.5(0.7)ˣ
What is an exponential functionAn exponential function is a mathematical function that models the growth of a quantity as a power of another quantity, typically as the exponent of a constant called the base. The general form of an exponential function is given by:
f(x) = a^x
where "a" is the base and "x" is the input. The value of "a" must be positive and greater than zero. When "a" is greater than 1, the exponential function grows very quickly, and when "a" is between 0 and 1, the exponential function decreases very quickly.
In this problem, we can find the exponential function by;
when x = 0
f(0) = 30.5
The function can be written as;
f(x) = 30.5(b)ˣ
To find the value of b,
We can take another point and solve;
f(0) = 30.5
f(1) = (21.35)
Looking at the graph, this is a decay function and we can easily find the value as 0.7.
The function is given as y = 30.5(0.7)ˣ
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Find the sum of each infinite geo sequence
Answer:
0.15 repeating
Step-by-step explanation:
solve the equation x^3-x^2-18=0 given that x-3 is a factor of x^3-x^2-18
The solutions to the equation x³ - x² - 18 = 0 are given as follows:
x = 3, x = -1 ± 2.236i.
How to obtain the solutions to the equation?The equation for this problem is defined as follows:
x³ - x² - 18 = 0
x - 3 is a factor, hence one solution is given as follows:
x - 3 = 0
x = 3.
Also considering that x - 3 is a factor, and x - 3 is of the first degree while the equation is of the third degree, we have that:
(x - 3)(ax² + bx + c) = x³ - x² - 18
ax³ + (b - 3a)x² + (c - 3b)x - 3c = x³ - x² - 18
Hence the coefficients are given as follows:
a = 1.b - 3 = -1 -> b = 2.-3c = -18 -> c = 6.Hence the remaining solutions are given as follows:
x² + 2x + 6 = 0.
Using a quadratic function calculator:
x = -1 ± 2.236i.
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graphing systems of equations
graph equation and state the solution (the point where they intersect)
pls pls pls help i’m ripping my hair off trying to solve this
The system of linear equations represented in the graph have (b) ne solution at (-3, 1)
How to determine the number of solutionsFrom the question, we have the following parameters that can be used in our computation:
0 = y - x - 4
3y + 9 = -4x
The above system represents two linear functions
The point of intersection of the linear functions represent the solution
In this case, the linear functions intersect at (-3, 1)
See attachment for graph
Hence, it has one solution at (-3, 1)
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12-8 +4+ [(6+2) -3] 2х3
240
Step-by-step explanation:
12-8+4+[(6+2)-3]2×3
= 4+4[(6+2)-3]2×3
= 8[(6+2)-3]2×3
= 8[(8)-3]2×3
= 8[5]2×3
= 8[5]6
= 40(6)
= 240
not yet answered points out of 5.00 not flaggedflag question question text what is the radius of a right circular cylinder with a volume of 12 in3 if it has a minimum surface area?
The height of the cylinder is 18 cm and its volume is 450π cubic centimeters, given that the radius of its base is 5 cm and its total surface area is 165πcm².
A right circular cylinder is a three-dimensional geometric shape with a circular base and a curved surface that extends upward in a cylindrical fashion.
Let's begin by identifying the formula for the total surface area of a cylinder. It is given by:
Total surface area = 2πr(h + r)
Where r is the radius of the base, h is the height, and π is a mathematical constant (approximately 3.14). We are given that the total surface area of the cylinder is 165πcm², and the radius of its base is 5 cm. Substituting these values in the formula, we get:
165π = 2π(5 + h)5 + 2π(5)²
Simplifying this equation, we get:
165π = 10πh + 150π
Dividing both sides by 10π, we get:
h + 15 = 33
Therefore, the height of the cylinder is 18 cm (33 - 15).
Now, let's find the volume of the cylinder. The volume of a cylinder is given by:
Volume = πr²h
Substituting the values of r and h, we get:
Volume = π(5)²(18)
Simplifying this equation, we get:
Volume = 450π
Therefore, the volume of the cylinder is 450π cubic centimeters.
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Complete Question:
The total surface area of a right circular cylinder is 165πcm². If the radius of its base is 5 cm; find its height and volume.
Tiffany is taking a 42-question test worth 100 points. The test includes two-point and four-point questions. How many of each type of question are on the test?
Which equations represent the scenario, where t represents the number of two-point questions and f represents the number of four-point questions? Check all that apply.
A. t + f = 42
B. t + f = 100
C. 2t + 4f = 42
D. 2t + 4f = 100
E. 4t + 2f = 100
it's A and D good luck
Answer:
A., D.
Step-by-step explanation:
Let t = number of two-point questions.
Let f = number of four-point question.
First we deal with the number of questions.
There are 42 questions. All the questions are either 2-point questions or 4-point questions.
t + f = 42
Now we deal with the number of points.
t two-point questions are worth 2t points.
f four-point questions are worth 4f points.
Altogether, they are worth 2t + 4f points.
The total number of points is 100, so
2t + 4f = 100
The system of equations has the equations:
t + f = 42
2t + 4f = 100
Answer: A., D.
Please help! I don't understand how my teacher does the work, so therefore, I don't understand how to do these word problems. 100-point jackpot for answering.
Answer: 1) 4 $3 and 4 $2; 2) 4 candles; 3) 4 adults and 6 students; 4) Small is 11.67 and Large is 83.75
Step-by-step explanation: 1. Total of $20 and needs 9 donuts. One is $3 and one is $2. Start with 3 $3 that 9 and let's do 3 for $2 which is 6. 9+6 is $15. 20-15 is 5. We have $5 left so we can buy in total 4 $3 donuts and 4 $2 donuts.
2. She has to make at least 4 candles. Booth is $40. And $2 per candle. 4*2 is $8. 40+8 = 48 and 48/12 is 4 candles.
3. They have a total of 120 sold. So let's start with adult tickets: $15 each. So let's start with 4 sold. 15*4 = 60. Students: $10 each. 10*4 is $40. 60+40 is 100 sold! So let's do 2 more student tickets to get 120 sold. 4 adults sold and 6 students sold.
4. Let's work with 6 and 8 you set up the equation 6x+8y=670 you get x = 11.67 and y is 83.75. So the large price is $83.75 and the Small is $11.67
Keiko was working with a new function, g(x). He wrote down the following steps for g(x):
• Add 5.
• Divide by 2.
• Cube it. (Find the third power.)
Multiply by 6.
a. What is the equation for g(x)? What is the output when 3 is put in?
b. Help Keiko write down the steps (in words) of the inverse machine, g¹(a), and then write its equation.
c. Verify that your equation in part (b) correctly "undoes" the output of g(x) in part (a).
a.) The equation for g(x) is g(x) = 6((x+5)/2)³and output is 384.
b.) The inverse machine, g¹(a), we need to undo each of the four steps in reverse order is g¹(a) = [tex]((a/6)^{(1/3)})*[/tex]2 - 5
c.) To verify that g¹(a) correctly "undoes" the output of g(x), we can plug in the output of g(3) (384) into g¹(a) and see if we get 3 as the result is 3.
What is Function?
A function is a mathematical rule that takes one or more inputs (also called independent variables or arguments) and produces a single output (also called a dependent variable or function value). In other words, a function is a relationship between the inputs and the output, where each input produces a unique output.
Functions can take many different forms and can be used to describe a wide variety of mathematical and real-world phenomena.
a. The equation for g(x) is:
g(x) = 6((x+5)/2)³
When 3 is put in for x, the output is:
g(3) = 6((3+5)/2)³= 6(4)³ = 384
b. To find the inverse machine, g¹(a), we need to undo each of the four steps in reverse order:
Undo step 4: Divide a by 6.Undo step 3: Take the cube root of the result from step 1.Undo step 2: Multiply the result from step 2 by 2.Undo step 1: Subtract 5 from the result from step 3.Putting this in equation form, we get:
g¹(a) = [tex]((a/6)^{(1/3)})[/tex]*2 - 5
c. To verify that g¹(a) correctly "undoes" the output of g(x), we can plug in the output of g(3) (384) into g¹(a) and see if we get 3 as the result:
g¹(384) =[tex]((384/6)^{(1/3)})[/tex]*2 - 5 =[tex](64^{(1/3)})[/tex]2 - 5 = 42 - 5 = 3
Since the output of g¹(a) is 3 when we input the output of g(x), we can conclude that g¹(a) correctly undoes the output of g(x).
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How many 4-letter words with at least one vowel can be constructed from the
letters A, B, C, D, and E? (Note that A and E are vowels.)
Answer: that would be 5^4 = 625
Step-by-step explanation:
Answer:
544
Step-by-step explanation:
How many 4 letter words can be constructed from ABCDE that would be 5^4 = 625
How many 4 letter words can be constructed using BCD that would be 3^4 = 81
So the number of words that use at least one vowel would be 5^4 - 3^4 = 625-81 = 544
What is 2x times 2x in algebra
Answer: 4x2
Step-by-step explanation:
Answer:
[tex]4x^2[/tex]
Step-by-step explanation:
[tex](2x)(2x)=(2*2)(x*x)=4x^2[/tex]
a plane ticket to baecelona is £175 the price decreased by 6%
how much is it now?
The plane ticket to Barcelona is now £164.50. This is because 6% of £175 is £10.50 and if you subtract £10.50 from £175, it equals £164.50.
PLEASE HELPPP me ASAP and show your work. If I get 2 questions I will mark one person BRAINLIEST. So PLEAASEEEEEEEEEEE Help on #4, #7, and #8 DUE TONIGHT
QUESTION 4: m∠A = 53 degrees
QUESTION 7: Area of triangle PQR is 23.6 unit²
QUESTION 8: Using cosine law, JK = 3.1 units
How to find the angle and area of triangle?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
QUESTION 4
tan A = 9.6/7.2
A = arctan(9.6/7.2)
A = 53 degrees
QUESTION 7
Area of ΔPQR = 1/2 * 6 * 8 * sin 80
Area of ΔPQR = 23.6 unit²
QUESTION 8
JK = √(6² + 8² - 2*6*8*cos 20°) (cosine law)
JK = 3.1 units
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QUESTION FOR FOR LIH04
Select the correct answer.
Which graph shows the solution region of this system of inequalities?
y ≥3(0.8)^x
y ≥ x² - 5
The solution to the inequality are the region in the shaded area and the graph is attached
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
y ≥3(0.8)^x
y ≥ x² - 5
Represent properly
y ≥ 3(0.8)^x
y ≥ x² - 5
Next, we make a plot of the system to determine the solution
The shaded area in the plot represent the solution to the inequality
In this case, one of the coordinates in the shaded area has a coordinate of (0, 5)
None of the options represent the shaded area (see attachment)
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