The maximum no. of small boxes that can fit is 27 boxes.
What is a cuboid?A cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
The total surface area of a cuboid is 2( lw + wh + wl) and the lateral surface area is 2(l + w)×h.
Given, A crate is 24cm by 18cm by 15cm and it has to be packed with boxes that are 8cm by 6cm by 5cm.
Now, the maximum no of small boxes that can fit is the volume of the larger box divided by the volume of the sampler box which is,
= (24×18×15)/(8×6×5).
= 3×3×3.
= 27 boxes.
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AT&T is having a sale on all cell phones. They will give you a loan to pay for the phone. Your phone costs $899 How much will you pay for the phone if they charge you 4.5% interest, and it will take you 24 months to pay it off.
-How do you do this equation?
Answer:
Its a scam AT&T has no such sale going on right now.
Step-by-step explanation:
Andy, Bobby, and Cathy each went for a walk yesterday afternoon. Andy walked 1 3/4 mi at a constant speed of 1 1/4 mi/h. Bobby walked 2 3/4 mi at a constant speed of 2 1/2 mi/h. Cathy walked for 1 h and 22 min at a constant speed of 1 1/4 mi/h. List the three people in order of the times they spent walking from least time to greatest time.
Answer:
In order of the times they spent walking from the least to the greatest time, we have:
Cathy
Andy
Bobby
Explanation:
Given the following:
Andy walked 1 3/4 min at a constant speed of 1 1/4 mi/h
Bobby walked 2 3/4 mi at a constant speed of 2 1/2 mi/h
Cathy walked for 1 h and 22 min at a constant speed of 1 1/4 mi/h
We are required to list the three people in order of the times they spent walking from least to the greatest time,
This is the same thing as listing the following numbers:
1 3/4, 2 3/4, and 1h 22min from least to greatest.
Andy: 1 3/4 = 7/4 = 1.75 = 2 hours, 15 minutes
Bobby: 2 3/4 = 11/4 = 2.75 = 3 hours, 15 minutes
Therefore, from the least to the greatest time, we have:
Cathy
Andy
Bobby
graph the function f(x)=3-(x)
The given function is
[tex]f(x)=3-x[/tex]To graph this linear function we have to complete a table of values. We replace each x-value in the function to get each y-values to form coordinated pairs.
x f(x)
-2 5
-1 4
0 3
1 2
Let's do the calculations for each f(x) value.
[tex]\begin{gathered} f(-2)=3-(-2)=3+2=5 \\ f(-1)=3-(-1)=3+1=4 \\ f(0)=3-0=3 \\ f(1)=3-1=2 \end{gathered}[/tex]At last, we have to graph each point and draw a straight line. The graph below shows the graph for the function.
what is 9/7 ÷ 2/3 ?
we have the expression
[tex]\frac{9}{7}\div\frac{2}{3}=\frac{9*3}{2*7}=\frac{27}{14}[/tex]The answer is 27/14Traci needs to change $300 US Dollars into Euros. the exchange rate is 1 euro for 1.25 dollars. how many euros does Traci get for her dollars?
Let's begin by identifying key information given to us:
Amount = $300
Amount (after changing) = ?
Exchange rate: €1 = $1.25
We will calculate how much Euros Traci gets for her dollar using simple proportion:
[tex]\begin{gathered} x=\text{\$}300 \\ \euro1=\text{\$}1.25 \\ \text{Cross multiply, we have:} \\ 1.25(x)=300\cdot1 \\ x=\frac{300}{1.25}=240 \\ x=\euro240 \end{gathered}[/tex]Therefore, Traci gets €240 for her dollars
[tex] \frac{1}{5} [/tex]convert into a prercentage
Answer:
20%
Explanation:
To convert a fraction into a percentage, multiply the fraction by 100.
Thus, the fraction 1/5 as a percentage is:
[tex]\begin{gathered} =\frac{1}{5}\times100 \\ =\frac{100}{5} \\ =20\% \end{gathered}[/tex]The percentage equivalent of 1/5 is 20%.
-4x-5-2x+3 simplify
Starting with the expression:
[tex]-4x-5-2x+3[/tex]Use the commutative property to bring like terms together:
[tex]-4x-5-2x+3=-4x-2x-5+3[/tex]Add like terms:
[tex]-4x-2x-5+3=-6x-2[/tex]Therefore:
[tex]-4x-5-2x+3=-6x-2[/tex]to rent a booth at a County Fair cost $42 per day plus a one-time equipment fee of $85 find the number of days mr. Jones rented a booth if he paid a total of $337
Solve the following equation for x. Please show all your solution steps. 2x - 5 + 3x = x - 41
Solve the system of equations x + 2y = 0 Solve the equation for x.
Given the equation :
[tex]x+2y=0[/tex]Solve the equation for x:
[tex]x=-2y[/tex]Final Answer:
x = -2yIn-depth explanation:
Hi! The question is asking us to solve the equation x + 2y = 0 for x.
________________________
To Solve
Rearrange the equation for x.
________________________
All we need to do is subtract '2y' from both sides.
[tex]\implies\sf{x+2y=0}[/tex]
[tex]\implies\sf{x=0-2y}[/tex]
[tex]\implies\sf{x=-2y}[/tex]
∴ Equation: x = -2y
_______________________
If the population of a small town satisfies the exponential model A = Aoe^0.015t, where is measured in years, how long will it take for the town's population to increasefrom 5,450 to 10,355? Round your answer to two decimal placesAnswer
ANSWER :
The answer is 42.79 years
EXPLANATION :
From the problem, we have the function :
[tex]A=A_oe^{0.015t}[/tex]Solve for the value of t when A = 10,355 and Ao = 5,450
That will be :
[tex]\begin{gathered} 10355=5450e^{0.015t} \\ \frac{10355}{5450}=e^{0.015t} \\ 1.9=e^{0.015t} \\ \text{ Take the ln of both sides :} \\ \ln(1.9)=\ln(e^{0.015t}) \\ \ln(1.9)=0.015t \\ t=\frac{\ln(1.9)}{0.15} \\ t=42.79 \end{gathered}[/tex]Find the Value of X, round your answer to the nearest 10th
The value of x is 13.31 units.
What is trigonometric ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled.
Given a right angle with perpendicular = 8 units and base = x units and one acute angle = 59°
tangent of an angle = perpendicular/base
Therefore,
tan59° = x/8
x = tan59°*8
x = 13.31
Hence, the value of x is 13.31 units.
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Use graph to find the slope and y-intercept of the line. Compare the values to the equation y= -x+5
As given by the question
There are given that the graph of the line.
Now,
To find the slope and y-intercept of the line, first select two intersect point from the graph.
Then,
The points are:
[tex](0,\text{ 5) and (5, 0)}[/tex]Then,
First find the slope,
So,
From the formula of slope,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=0,y_1=5,x_2=5,y_2=0[/tex]Then,
Put all the value into the given formula.
So,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0_{}-5_{}}{5_{}-0_{}} \\ m=-\frac{5}{5} \\ m=-1 \end{gathered}[/tex]Now,
From the standard form of the line,
[tex]y=mx+b[/tex]Then,
Put y is 5, x is 0 and m is -5 into the above equation to find the y-intercept
So,
[tex]\begin{gathered} y=mx+b \\ 5=-1(0)+b \\ b=5 \end{gathered}[/tex]Hence, the value of the y-intercept is 5.
Now,
The line equation is shown below:
[tex]\begin{gathered} y=mx+b \\ y=-1x+b \\ y=-x+5 \end{gathered}[/tex]Hence, the slope of the line is -1, y-intercept of the line is 5 and the equation of line is y = -x + 5.
Unit 4 What is the rate of return when 20 shares of Stock A, purchased for $20/share, are sold for $490? The commission on the sale is $6. Rate of Return = [?] % Give your answer as a percent rounded to the nearest tenth.
Answer:
21%
Step-by-step explanation:
You want the rate of return on 20 shares of stock bought for $20 per share and sold for $490 with a commission on the sale of $6.
Rate of returnThe rate of return is the percentage change between the sale proceeds and the cost of the stock.
rate of return = (proceeds/cost -1) × 100%
= ((490 -6)/(20·20) -1) × 100% = 21%
The rate of return is 21%.
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Diane opened a savings account 3 years ago the account earns 9% interest compounded monthly if the current balance is 100.00 how much did she despoit initially
Answer:
The amount she deposited initially is $76.41.
[tex]\text{ \$76.41}[/tex]Explanation:
We want to find the amount of Principal she deposited initially.
Recall that the formula for calculating the Principal of a compound interest is;
[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]Where;
P = Principal / initial amount
A = Future/ final amount
r = Interest rate (decimal)
n = number of times the interest is compounded per year.
t = Time in years
From the question, we were given the following;
A = $100.00
r = 9% = 0.09
n = monthly (12 months in a year) = 12 times
t = 3 years
Substituting the given values into the formula, we have;
[tex]\begin{gathered} P=\frac{100.00}{(1+\frac{0.09}{12})^{12(3)}} \\ P=\frac{100.00}{(1+0.0075)^{36}} \\ P=\frac{100.00}{(1.0075)^{36}} \\ P=76.41 \\ P=\text{ \$76.41} \end{gathered}[/tex]Therefore, the amount she deposited initially is $76.41.
[tex]\text{ \$76.41}[/tex]5. The shadow of a tree extends 25 feet from the top of the tree to the ground. Sarah measures thatthe distance from the base of the tree to the tip of its shadow is 15 feet. How tall is the tree?A. 20 feetB. 25 feetC. 29.2 feetD. 40 feetO
Given :
The shadow of the tree = 25 feet from the top of the tree to the ground
the distance from the base of the tree to tip of its shadow is 15 feet
Let the height of the tree = x
So, 25 , 15 and x are forming a right angle triangle
25 is the hypotenuse of the triangle ,
x and 15 are the legs of the triangle
WE will find x using Pythagorean theorem
So,
[tex]\begin{gathered} x^2+15^2=25^2 \\ x^2=25^2-15^2=625-225=400 \\ x=\sqrt[]{400}=20 \end{gathered}[/tex]So, the height of the tree = 20 feet
The answer is option A. 20 feet
9. If two lines are cut by a transversal so that (alternate interior, alternate exterior, corresponding, consecutive interior) angles are congruent, then the lines are parallel.
Answer:
If two lines are cut by a transversal so that (alternate interior, alternate exterior, corresponding, consecutive interior) angles are congruent, then the lines are parallel
Explanation:
When two lines are cut by a transversal so that alternate interiors, alternate exterior or corresponding, are congruent, then the line must be parallel
If;
[tex]\begin{gathered} \measuredangle a=\measuredangle b\text{ (alternate interior)} \\ \measuredangle x=\measuredangle y\text{ (alternate exterior)} \\ \measuredangle x=\measuredangle b\text{ (corresponding angles)} \end{gathered}[/tex]then the lines are parallel.
Two more than the cube root of a number
We have
[tex]undefined[/tex]Name the rotation that maps the black triangle onto the red triangle. Explain how you know(See picture below)
We would compare the coordinates of corresponding vertices on the red and black triangles. The vertex at the top of the black triangle and the vertex at the bottom of the red triangle correspond to each other. We would compare them.
For black triangle, coordinate is (1, - 3)
For red triangle, coordinate is (- 1, 3)
If a vertex with coordinate, (x, y) is rotated 180 degrees counterclockwise about the origin, the new coordinate is (- x, - y). By rotating (1, - 3) 180 degrees counterclockwise, it becomes (- 1, - - 3) = (- 1, 3). This corresponds to the coordinate of the corresponding vertex of the red triangle. Thus, the rotation that maps the black triangle onto the red triangle is 180 degrees counterclockwise rotation about the origin
how do I find the length of x and y?
I need help with my practice questions. I don’t know where i’m supposed to plot the points on the graph and I need an explanation please.
Use the following two points to answer parts a - c. (2, 9), (4, - 7) a . Find the slope of the line passing through the two points. b . Write an equation of a line passing through the two points in point-slope form. c Rewrite the equation of the line in slope-intercept form.
slope= m =y2-y1/x2-x1, then
[tex]\begin{gathered} m=\frac{-7-9}{4-2} \\ m=-\frac{16}{2} \\ m=-8 \end{gathered}[/tex]a. slope = -8
9. Leyla has 18 50-cent and 20-cent coins altogether. She has a total of $6.90. How many 20-cent coins does she have?
According to the information given in the exercise:
- Leyla has 18 coins of 50 cents and 20 cents.
. She has a total of $6.90.
Let be "f" the number 50-cent coins and "t" the number 20-cent coins.
Since 1 dollar is equal to 100 cents, you know that:
[tex]6.90dollars=690cents[/tex]Then, knowing the above, you can set up the following System of Equations:
[tex]\begin{cases}f+t=18 \\ \\ 50f+20t=690\end{cases}[/tex]To find the value of "t", you can apply the Substitution Method:
1. Take the first equation and solve for "f":
[tex]f=18-t[/tex]2. Substitute this equation into the second equation and solve for "t":
[tex]\begin{gathered} 50f+20t=690 \\ \\ 50(18-t)+20t=690 \end{gathered}[/tex][tex]\begin{gathered} 50(18-t)+20t=690 \\ \\ 900-50t+20t=690 \end{gathered}[/tex][tex]\begin{gathered} 900-30t=690 \\ \\ -30t=690-900 \\ \\ -30t=-210 \end{gathered}[/tex][tex]\begin{gathered} t=\frac{-210}{-30} \\ \\ t=7 \end{gathered}[/tex]Therefore, the answer is: She has 7 coins of 20 cents.
On January 1, 2012 Hector put his life savings of $17,229 into a savings account at Barclays, which was pain 0.9 interest at the time. Over the next year, the inflation rate averaged 1.7%. Now consider the following propositions
Answer:
what propositions?
Step-by-step explanation:
The left and the right page of numbers of an open book are two consecutive integers whose sum is 381 . Whats are the page numbers
In order to determine the number of page numbers, let x the number of one page and x + 1 the number of the other page.
The sum of both numbers is 381, then:
x + (x + 1) = 381
Solve the previous equation for x, as follow:
x + x + 1 = 381 simplify like terms
2x + 1 = 381 subtract 1 both sides
2x = 381 - 1
2x = 380 divide by 2 both sides
x = 380/2
x = 190
Then, the numbers are 190 + 191
Trey made $2000 in taxable income last year. suppose the income tax rate is 10% for the first $9500 plus 14% for the amount over $9500. How much must trey pay in income tax for last year?
SInce he made $2000 , and this is less than the limit for the first bracket, Trey will need to pay just 10% on his gain:
10% of $2000 = 0.1 * 2000 = $200.
His tax is $200.
guess this i am less than 10 i am not a multiple of 2 i am a composite number
Composite numbers have a smaller divisor, other than 1 and itself. Hence, the required number is 9.
What is composite number?Any positive integer that may be created by multiplying two other positive integers is referred to as a composite number. It is, in other words, a positive integer that has at least one divisor besides itself and the number 1.
Numbers with more than two elements are known as composite numbers in mathematics. Composite numbers are non-prime numbers that can be divided by more than two other numbers.
Composite numbers below 10 :
4, 6, 8, 9
From the composite numbers given, the value which is not a multiple of 2 is 9.
The values 4, 6, and 8 are multiples of 2.
Hence, the required is 9.
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Consider the following quadratic equation - x ^ 2 + 3x - 7 = 0 Step 1 of 2 Find the values of a , b, and that should be used in the quadratic formula to determine the solution of the quadratic equation
Recall that the quadratic formula states that the solution to the quadratic equation:
[tex]ax^2+bx+c=0[/tex]are:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]Notice that a is the coefficient of the quadratic part, b is the coefficient of the linear part and c is a constant.
We can rewrite the given equation as follows:
[tex](-1)x^2+3x+(-7)=0.[/tex]Therefore, the values a, b, and c that should be used in the quadratic formula to compute the solutions to the quadratic equation:
[tex]-x^2+3x-7=0[/tex]are:
[tex]\begin{gathered} a=-1, \\ b=3, \\ c=-7. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} a=-1, \\ b=3, \\ c=-7. \end{gathered}[/tex]PLEASE HELP ME.Match the shape with its area formula Column A Column B 1: Triangle a. A= LW2: Parallegram. b: A=(TTr^2)/23: Semi- circle. c:(bh)/2 or 1/2(bh)4:Trapizoid. D. A= (b1+b2)(h)2
1. Triangle: the area of the triangle is C. (bh)/2
2:Parallegram: the area is a. LW
3. Semi-circle: the area is b. (pi r^2)/2
4. Trapezoid: the area will be D. (b1+b2)(h)2
Lily has 30 Marvel Funko Pops. The number of Marvel Funky Pops in her collection is only 60% of hes total Funko Pops. How many total Funko Pops are in her collection?
Lily has 30 Marvel Pops, they are 60% of the total Pops
How many in total ?
We can say that the realation between 30 an the total is the same relation between 60% and 100%, so we can write:
30/x = 60/100
[tex]\frac{30}{x}=\frac{60}{100}[/tex]Where x is the total number of Pops
Solving this for x:
x = 30(100)/60 = 3000/60 = 50
[tex]x\text{ = }\frac{\text{30(100)}}{60}=\frac{3000}{60}=50[/tex]Answer:
Number of total Funlo Pops in her collection: 50