Answer:
width = 1.8 in
length = 3.6 in
height =[tex]8-3w =8-3(1.8)= 2.6 in[/tex]
Step-by-step explanation:
A designer is making a rectangular prism box with maximum volume, with the sum of its length, width, and height 8 in
Let l , w and h are the length , width and height
[tex]l +w+h=8\\l=2w[/tex]
Plug it in the first equation
[tex]2w+w+h=8\\3w+h=8\\h=8-3w[/tex]
volume the box is length times width times height
[tex]volume = (2w)(w)(8-3w)\\16w^2-6w^3[/tex]
To get maximum volume we take derivatived
[tex]v'=32w-18w^2[/tex]
set the derivative =0 and solve for w
[tex]0=32w-18w^2\\0=-2w(9w-16)\\w=0 , w= \frac{16}{9}[/tex]
width = 1.8 in
length = 2w= 3.6 in
height =[tex]8-3w =8-3(1.8)= 2.6 in[/tex]
If the probability that a student is on-time to class is 0.1 and the probability he is on-time or marked tardy on the attendance roster is 0.9, what is the probability he will be marked tardy if the events on-time and marked tardy are mutually exclusive? If A and B are independent?
Answer:
.10 %
Step-by-step explanation:
Final answer:
The probability of being marked tardy when events are mutually exclusive is 0.8, and when they are independent, the probability is 0.09.
Explanation:
The probability that a student will be marked tardy if the events on-time and marked tardy are mutually exclusive is 0.9 - 0.1 = 0.8. When events A and B are independent, the probability of both events occurring is the product of their individual probabilities: P(A and B) = P(A) * P(B). In this case, P(on-time) * P(tardy) = 0.1 * 0.9 = 0.09.
Help me please. 10 pts.
3.)
Variables:
New tablet cost (575),
Money already saved, (56),
Money saved per week(14w)
Write an Equation:
The amount of weekly money you need to earn must cover the leftover cost needed to buy the tablet, therefore:
money_needed - money_you_have = money_earned_per_week
575 - 56 = 14w
Solving:
575 - 56 = 14w
519 = 14w
37.071428 = w
37 weeks needed
You solve the other two on your own.
Order these numbers from least to greatest
151/20, 7 6/11, 7.32, 7.546
Answer:
76/11 ; 7.32 ; 7.546 ; 151/20
Step-by-step explanation:
Given data:
The numbers are listed as below
151/20 ; 76/11 ; 7.32 ;7.546
The numbers are written in the same format that is in decimal form
7.55 ; 6.90901 ; 7.32 ; 7.546
Arranging the numbers starting with the least number
6.90901 ; 7.32 ; 7.546 ; 7.55
76/11 ; 7.32 ; 7.546 ; 151/20
Please note the value of 151/20 is exactly 7.550 which makes it larger than 7.546.
Suppose that f(x) = x2 and g(x) = 2/5 x2 Which statement best compares the
graph of g(x) with the graph of f(x)?
O
A. The graph of g(x) is the graph of f(x) compressed vertically.
O
B. The graph of g(x) is the graph of f(x) compressed vertically and
flipped over the x-axis.
O
C. The graph of g(x) is the graph of f(x) stretched vertically and
flipped over the x-axis.
O
D. The graph of g(x) is the graph of f(x) stretched vertically.
The function g(x) is the function f(x) scaled down by a factor of 2/5, resulting in a vertical compression of the graph. Thus, the correct answer is A. The graph of g(x) is f(x)'s graph vertically compressed.
Explanation:The function g(x) = 2/5 x2 is f(x) = x2 multiplied by a scalar factor of 2/5. This means that every y-coordinate in the graph of f(x) is scaled down by a factor of 2/5 to produce the corresponding y-coordinate in the graph of g(x). It does not flip the graph over the x-axis. Therefore, the graph of g(x) is simply the graph of f(x) compressed vertically. So, the correct answer is A. The graph of g(x) is the graph of f(x) compressed vertically.
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Which statement is best supported by the dot plot? Choose ONE and explain your
answer.
I. The range of the number of miles Amanda skated in August is less than the range
of the number of miles she skated in July.
II. The distribution of data is approximately symmetrical in both sets of data.
III.The mode of the number of miles Amanda skated in July is equal to the mode of
the number of miles skated in August.
Answer:
The first statement.
Step-by-step explanation:
Because when you look at the July graph you can see that the highest number of miles is 15 and the lowest number of miles is 1 so the range is 15 - 1 = 14.
When you look at the August graph you can see that the highest number of miles is 13 and the lowest number of miles is 5 so the range is 13 - 5 = 8
So the range of the July month is greater than the range of the August month
Determine the quadrant(s) in which (x,y) is located so that the condition is satisfied. (Select all that apply.)
xy < 0
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
The quadrants II and IV in which (x,y) are located so that the condition xy < 0 is satisfied.
What is the quadrant?A quadrant is defined as an area contained by the x and y axes, which there are four quadrants in a graph.
For Quadrant I : the value of x and y both are positive ( +,+ )
For Quadrant II : the value of x is negative and y is positive ( -,+ )
For Quadrant III : the value of x is negative and y is negative ( -, - )
For Quadrant IV : the value of x is positive and y is negative ( +, - )
To determine the quadrant(s) in which (x,y) is located so that the condition is satisfied.
⇒ xy < 0
When the value of x is negative and y is positive in Quadrant II
So that the condition xy < 0 is satisfied
When the value of x is positive and y is negative in Quadrant IV
So that the condition xy < 0 is satisfied
Hence, the quadrants II and IV in which (x,y) are located so that the condition xy < 0 is satisfied.
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The sum of two numbers is 60. If twice the smaller number is subtracted from the large number, the result is 9. Find the two numbers
Answer:Therefore the two numbers are -20 and -40
Step-by-step explanation:
Let the two numbers be a and b,
It is given that their sum is 60, so a + b = -60,
It is also given that their difference is 20, so a - b = 20,
Since we don’t know yet which one out of a and b is greater, assume any one of them to be larger than the other (a in my case),
Add the above two equations, you get,
2a = -40 or a = -20,
Substitute this value of a in any of the formed equations,
a + b = -60,
-20 + b = -60 or b = -40,
Let the two numbers be a and b,
It is given that their sum is 60, so a + b = -60,
It is also given that their difference is 20, so a - b = 20,
Since we don’t know yet which one out of a and b is greater, assume any one of them to be larger than the other (a in my case),
Add the above two equations, you get,
2a = -40 or a = -20,
Substitute this value of a in any of the formed equations,
a + b = -60,
-20 + b = -60 or b = -40,
Therefore the two numbers are -20 and -40
The smaller number is 17, and the larger number is 43. The two equations formed from the given information are solved simultaneously to find these numbers.
To solve this problem, we need to set up two equations based on the given information. Let's denote the smaller number by s and the larger number by l.
The sum of the two numbers is 60: s + l = 60.
If twice the smaller number is subtracted from the large number, the result is 9: l - 2s = 9.
We can solve these equations simultaneously. First, rearrange the second equation to express l in terms of s: l = 2s + 9. Next, substitute this expression into the first equation:
s + (2s + 9) = 60
3s + 9 = 60
3s = 51
s = 17
Now we have found the smaller number is 17. To find the larger number, we substitute s back into the equation for l:
l = 2(17) + 9
l = 34 + 9
l = 43
So the two numbers are 17 and 43
how many times more is 21.25 than 1.7 answers?
Answer:
19.55
Step-by-step explanation:
21.25
- 1.7
_____
19.55
Please help! Give the answer and how you got it
The distance between the points C(-3,1) and D(5,6) is 10.3 units.
Step-by-step explanation:
Let us consider CD is a line segment.
The point C is (-3,1) and D is (5,6).
The Cartesian formula for line is used to find the length between the CD.
Distance between two points = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
The points are (-3,1) and (5,6).
=[tex]\sqrt{(6-(-3))^2+(6-1)^2}[/tex].
=[tex]\sqrt{(6+3)^2+(6-1)^2}[/tex]
=[tex]\sqrt{9^2+5^2}[/tex].
=[tex]\sqrt{81+25}[/tex].
=[tex]\sqrt{106}[/tex].
=10.295 ≈ 10.3.
Distance between two points 10.3 units.
Payton plays 15 games of fortnight in 15 minutes. If he maintains this rate, how many games will he play in 3 hours
Payton will play 180 games in 3 hours.
Step-by-step explanation:
Given,
Games played in 15 minutes = 15 games
We will find unit rate;
15 minutes = 15 games
Dividing both sides by 15
[tex]\frac{15}{15}\ minutes=\frac{15}{15}\ games\\\\1\ minute = 1\ game[/tex]
Time = 3 hours = 3*60 = 180 minutes
180 minutes = 180*games per minute
180 minutes = 180*1 games
180 minutes = 180 games
Payton will play 180 games in 3 hours.
Keywords: unit rate, multiplication
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The centroid of a triangle is at (8, 7). One vertex of the triangle is at (0, 1). What is the midpoint of the side opposite this vertex?
Answer:
(12,10)
Step-by-step explanation:
Let the midpoint of the side opposite this vertex have coordinates B(a,b)
We have the centroid at C(8,7) and the vertex of the triangle at A(0,1).
The centroid divides AB internally in the ratio 2:1
We use the formula:
[tex](\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]
where m:n=2:1 is the ratio of internal division.
We substitute the coordinates of A and B and the ratio to get:
[tex](\frac{2a+1*0}{2+1},\frac{2b+1*1}{2+1})[/tex]
This should simplify and give us the centroid.
[tex](\frac{2a}{3},\frac{2b+1}{3})=(8,7)[/tex]
This implies that:
[tex]\frac{2a}{3}=8,\frac{2b+1}{3}=7[/tex]
We solve for a and b
[tex]2a=24,2b+1=21[/tex]
[tex]a=12,b=10[/tex]
Therefore the midpoint of the side opposite this vertex is (12,10)
A family on vacation drove the first 200 miles in 4 hours and the second 200 miles in 5 hours. Which expression below gives their average speed for the entire trip?
A.200+2004+5
B.(2004+2005)÷2
C.2004+2005
D.4004+4005
Answer:
(2004+2005) divided by 2
Step-by-step explanation:
How do I simplify 3x (2y + 8)
Answer:
Step-by-step explanation:
one third plus one half
Answer:5/6
Step-by-step explanation:
So 1/3 + 1/2 turn them to equivalent denominators so 1/3 = 2/6
1/2 equals 3/6 . 3/6+2/6 is 5/6
Write a function rule that relates y to x
The function rule that relates y (circumference) to x (diameter) is y = π x [pi × x]
Explanation:Since x represents the diameter of the circle and y represents the circumference.
For a circle with radius r, circumference of the circle (y)equals,
y = 2πr ................................(1)
Diameter of a circle is twice the radius of the circle.
Assuming x as the diameter
[tex]x = 2\times r = 2r[/tex] ...........................(2)
Substituting (2) in (1), we get
y = π(2r) = πx ..............................................(3)
A function rule is an equation that determines the relation between a dependent variable and an independent variable. The relation between diameter of a circle and its circumference can be given as
Circumference = Pi × Diameter of circle
y = π × x
where π = 3.142
the function f(x)=5x+12 models the amount of money in dollars, makes when cutting loans for x hours. How many dollars will alex for 3 hours of loan-cutting work?
Answer:
$27
Step-by-step explanation:
f(x) = 5x + 12
= 5(3) + 12
= 15 + 12
= 27
Alex will earn $27 for 3 hours of lawn-cutting work, as calculated using the function f(x) = 5x + 12.
Explanation:The function f(x) = 5x + 12 models the amount of money, in dollars, Alex makes when cutting lawns for x hours. To calculate the amount Alex will make for 3 hours of lawn-cutting work, we simply substitute x with 3 in the equation:
f(3) = 5(3) + 12
For instance, events G and H (taking a math class and taking a science class, respectively) from Example 3.9 were shown to be independent by verifying that P(G AND H) = P(G) * P(H). Similarly, events A and B from 'Try It Σ' 3.8, learning Spanish and German, were tested for independence by checking if P(A AND B) = P(A) * P(B).
Thus, f(3) = 15 + 12 which equals $27. Therefore, for 3 hours of work, Alex will earn $27.
Find the value of 49/50 divided by 7/6
Drag each equation to the correct location on the table.
Match the inequalities with the value of a for which they hold true.
4 + 3a + 8 < 16
5a − 4a + 6 < 8
2a + 3 < 9 − 3a
14 + 5a < 12a + 1
2a + 3 > 10 − 3a
3a − 2a + 1 > 2
Answer:
a=1
-2a + 3 < 9 − 3a
5a − 4a + 6 < 8
2a + 3 > 10 − 3a
a=2
-4 + 3a + 8 < 16
14 + 5a < 12a + 1
3a − 2a + 1 > 2
Step-by-step explanation:
i did the test
Answer:
a=1
-2a + 3 < 9 − 3a
5a − 4a + 6 < 8
2a + 3 > 10 − 3a
a=2
-4 + 3a + 8 < 16
14 + 5a < 12a + 1
3a − 2a + 1 > 2
Step-by-step explanation:
i just did the test
Patty spent 3.5 times as much as Sandy
on their shopping trip. If Sandy spent
$20.50, how much did Patty spend?
Answer:
Patty spent $71.75
Step-by-step explanation:
20.50 x 3.5 = 71.75
Answer: 71.75
3.5* 20.50
The solid shown has a volume of 9 units3. Determine the surface area of the solid.
A) 29 units2
B) 36 units2
C) 38 units2
D) 41 units2
Answer:
C) 38 units2
Step-by-step explanation:
we know that
The surface area of the composite figure is equal to the area of all its square faces
Each face area is one square unit
so
[tex]SA=2(9)+2(4)+2(6)=38\ units^2[/tex]
points a b and c are collinear point b is between A and C solve for x AB = 3x BC = 2x -2 and AC =18
=====================================
Work Shown:
AB + BC = AC .... see diagram below
(3x)+(2x-2) = 18 ... plug in given expressions
5x-2 = 18
5x-2+2 = 18+2 ... add 2 to both sides
5x = 20
5x/5 = 20/5 ... divide both sides by 5
x = 4
Given points A, B and C are collinear, with B between A and C, and the distances between them expressed in terms of 'x'. We use the fact that AB + BC = AC to form an equation, solve it to find 'x' = 4.
Explanation:To solve for 'x' in this problem, we need to utilize the fact that points A, B, and C are collinear and that point B is between A and C.
Given AB = 3x, BC = 2x - 2, and AC = 18.
When points are collinear and one is between the other two, the sum of the distances between the points equals the total distance. So, we know that AB + BC = AC.
Substitute the known values into this equation to get 3x + 2x - 2 = 18.
Combine like terms to give 5x -2 = 18. Rearrange this to make 'x' the subject, you get 5x = 20, then x = 4.
So the value of 'x' that satisfies the given conditions is 4.
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Find the solution of the system of equations -6x+3y=-15 4x-3y=13
In Science Class, Sara needed 8 test tubes for 3 different experiments. The first experiment required 2 test tubes and the other two experiments required the same number of test tubes. How many test tubes were need for each of the other two experiments l?
Answer:
[tex]Each\ of\ other\ two\ experiments\ required\ 3\ test\ tubes.[/tex]
Step-by-step explanation:
[tex]Let\ each\ of\ other\ experiment\ requires\ x\ test\ tube\\\\Total\ number\ of\ test\ tubes\ needed=8\\\\Test\ tubes\ used\ in\ the\ experiments=sum\ of\ number\ of\ test\ tubes\ in\ each\ experiment\\\\Test\ tubes\ used\ in\ the\ experiments=2+x+x\\\\2+x+x=8\\\\2+2x=8\\\\Subtract\ 2\ from\ both\ sides\\\\2+2x-2=8-2\\\\2x=6\\\\divide\ both\ sides\ by\ 2.\\\\x=3[/tex]
[tex]Each\ of\ other\ two\ experiments\ required\ 3\ test\ tubes.[/tex]
Hans runs 3 miles in 25 minutes. At the same rate, how many miles would he run in 20 minutes?
Answer:
2.4 miles
Step-by-step explanation:
If Hans ran 3 miles in 25 minutes, that would mean he ran 0.6 miles every five minutes. So, 0.6*4=2.4, as 4/5*25=20.
846 is tens or not why?
The number 846 does have a component in the tens place, which is the digit 4, representing 40 when viewed in terms of place value. Understanding the concept of place value, including the tens place, is fundamental in mathematics for efficient calculation and comprehension of numbers.
Explanation:The question seems to be asking whether the number 846 can be classified in terms of its placement in the tens place value or not. To understand this, let's break down the number 846 in terms of place value. The number 846 is comprised of three digits, each representing a different place value in the base-10 numbering system. Starting from the right, the first digit (6) represents the ones place, the second digit (4) represents the tens place, and the third digit (8) represents the hundreds place.
Therefore, yes, 846 does have a component in the tens place, which is the digit 4. This means that the number 846 has 4 tens or 40 when breaking it down by place value. Understanding place value is crucial in mathematics as it helps in doing calculations, understanding the value of numbers, and in various operations such as addition, subtraction, multiplication, and division. The tens place specifically is important when dealing with numbers ranging from 10 to 99 and beyond, as it helps in grouping numbers in units of ten, simplifying calculations, and enhancing comprehension of numbers' sizes.
5. Find the midpoint of AB given A(-7, 4) and B(3,-4).
Answer:
The answer is (-2,0)
Step-by-step explanation:
When you put both points on the graph. Draw a line through them.
See where the line hits a point from in between the points.
3400 dollars is placed in an account with an annual interest rate of 7.5%. How much will be in the account after 17 years, to the nearest cent?
Answer: 11625.8
Step-by-step explanation:
The total amount in the account after 17 years, with an annual interest rate of 7.5%, is approximately $7420.50.
Explanation:To calculate the amount in the account after 17 years, we use the formula for simple interest: Total future amount (with simple interest) = Principal + (Principal × Interest Rate × Time). In this case, the principal is $3400, the interest rate is 7.5%, and the time is 17 years. Plugging in these values, we get:
Total future amount = 3400 + (3400 × 0.075 × 17)
Calculating this, the total future amount in the account will be approximately $7420.50.
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Steps to solve 4.3x+19.35=8.11+4.0x
Answer:
x = -37 7/15
Step-by-step explanation:
1. Find the terms with the variable. They are 4.3x on the left and 4.0x on the right.
2. Identify the term with the least coefficient*. It is 4.0x on the right.
3. Subtract that term from both sides of the equation.
4.3x -4.0x +19.35 = 8.11 +4.0x -4.0x
0.3x +19.35 = 8.11 . . . . . . simplify
4. Identify any constant term on the side of the equation with the variable. It is 19.35 on the left.
5. Subtract that constant from both sides of the equation.
0.3x +19.35 -19.35 = 8.11 -19.35
0.3x = -11.24 . . . . . . . simplify
6. Divide both sides of the equation by the coefficient of the variable. That coefficient is 0.3 in this equation.
(0.3x)/0.3 = (-11.24)/0.3
x = -37.466666... (repeating decimal)
__
If you like, you can express the solution as a mixed number:
x = -11.24/0.30 = -1124/30 = -562/15
x = -37 7/15
_____
You are expected to be able to do the math using the numbers in any form they might appear: integers, mixed numbers, fractions, decimals, scientific notation. You can convert the problem here to an integer problem by multiplying both sides by 100:
430x +1935 = 811 +400x
The answer still has a fraction in it: x= -1124/30 = -37 7/15.
_____
* You subtract the term with the least coefficient so the variable term in the result has a positive coefficient. That may be desirable, but is not necessary. You can subtract either variable term to get the variable on one side of the equal sign. You have to pay attention to the resulting sign when you divide by the variable's coefficient.
Heres an easy question...
What's 2+2+6+7+9???
Whoever answers it first gets 76pts!!!! :)
Answer: 26
Step-by-step explanation: I think so...
Answer:
26
Step-by-step explanation:
What is the perimeter, P, of a rectangle that has a length of x + 5 and a width of y - 1?
Answer:
P = 2x + 2y + 8, Answer is A
Step-by-step explanation:
I got it right on the test so yea.