The dimensions of the box are = 4 feet (length); 3 feet(width); 2 feet(height)
So, volume of the box is = [tex]4\times3\times2=24[/tex] cubic feet
The dimensions of the storage locker are = 12 feet(length); 6 feet(width) ; 9 feet(height)
So, volume of the storage locker is = [tex]12\times6\times9=648[/tex]
So, the greatest number of boxes that can be stored are =
[tex]\frac{648}{24}= 27[/tex] boxes
Hence, a maximum of 27 boxes are stored.
Jayden's storage locker has a volume of 648 cubic feet, and each of his boxes has a volume of 24 cubic feet. By dividing the locker's volume by the volume of a single box, we find that Jayden can store a maximum of 27 boxes in the locker.
Explanation:To determine the greatest number of boxes Jayden can store in the storage locker, we need to calculate the volume of the storage locker and the volume of one box. The storage locker is 12 feet long, 6 feet wide, and 9 feet high, so its volume is calculated as follows:
Storage Locker Volume = length × width × height = 12 ft × 6 ft × 9 ft = 648 cubic feet.
The box has dimensions of 4 feet long, 3 feet wide, and 2 feet high. Thus, its volume is:
Box Volume = length × width × height = 4 ft × 3 ft × 2 ft = 24 cubic feet.
Now, to find the greatest number of boxes that can fit into the locker, we divide the volume of the storage locker by the volume of one box:
Number of Boxes = Storage Locker Volume / Box Volume = 648 cubic feet / 24 cubic feet.
When we perform the division, we get:
Number of Boxes = 27.
Hence, Jayden can store a maximum of 27 boxes in the storage locker when placed upright with a 4-foot by 3-foot side on top.
What is the product?
Answer:
The correct answer is,
| -8|
| 4 |
Step-by-step explanation:
It is given two matrices,
1)Let Matrix A = 5 -2
-6 2
2) Matrix B = -1
-1
Matrix A is 2 x 2 matrix and matrix B is 2 x 1 matrix
To find the product of two matrices
A x B = 5 -2 x -1 = -10+2 = -8
-6 2 -1 6 -2 4
Therefore the correct answer is
| -8|
| 4 |
Which equations could be used to find the length of a side in a right triangle with legs a and b and hypotenuse of c?
The Pythagorean Theorem says for a right triangle with legs a,b and hypotenuse c,
[tex]c^2 = a^2+b^2[/tex]
Solving for each in turn,
[tex] c= \sqrt{a^2+b^2}[/tex]
[tex]a^2=c^2 - b^2[/tex]
[tex]a = \sqrt{c^2-b^2}[/tex]
[tex]b = \sqrt{c^2-a^2}[/tex]
Looking at our choices, we select the third and fourth.
The pythagorean theorem states that, in every right triangle, the following formula holds:
[tex]a^2+b^2=c^2[/tex]
where a and b are the legs, and c is the hypotenuse.
We can deduce the following expressions for a,b and c:
[tex]a = \sqrt{c^2-b^2},\quad b=\sqrt{c^2-a^2},\quad c=\sqrt{a^2+b^2}[/tex]
Brock exercises every day. The function E = 15m + 5 represents the number of sit-ups he can do in m minutes. After drinking a new sports drink to stay hydrated, he finds that he can increase the number of sit-ups per minute by a factor of 3, represented by the function S = 3E. Which function represents the number of sit-ups he can do after drinking the sports drink?
Answer:
S = 45m + 15
Answer:
[tex]S=45m+15[/tex]
Step-by-step explanation:
we have
E------>the number of sit-ups
m----> the time in minutes
S----> the number of sit-ups after drinking the sports drink
[tex]E=15m+5[/tex] ----> equation A
[tex]S=3E[/tex] ----> equation B
substitute the equation A in the equation B
[tex]S=3(15m+5)[/tex]
[tex]S=45m+15[/tex]
Answer: Its the Second one!
Step-by-step explanation: Ur welcome <3
Sean uses the point (10, 8) to represent the location of his house and uses the point (1, 3) to represent the
location of the gym. Each unit on the graph represents 1 mi. How far is the gym from Sean’s house? Round to
the nearest tenth. Show your work.
Answer:
[tex]10.3\ mi[/tex]
Step-by-step explanation:
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]A(10,8)\\B(1,3)[/tex]
substitute the values
[tex]d=\sqrt{(3-8)^{2}+(1-10)^{2}}[/tex]
[tex]d=\sqrt{(-5)^{2}+(-9)^{2}}[/tex]
[tex]d=\sqrt{25+81}[/tex]
[tex]d=\sqrt{106}[/tex]
[tex]d=10.3\ mi[/tex]
A rectangle prism has a length of 3 1/2 inches a width of 5 inches and height of 1 1/2 inches what is the volume
Answer:
Step-by-step explanation: I hope that helps you.
The decimal equivalent of 3/7 rounded to the nearest hundredth is
0.43
0.428
0.429
0.40
The decimal equivalent of 3/7 rounded to the nearest hundreds is 0.428
Answer: 0.43 cause hundredths place is the 3 and its rounded
Step-by-step explanation:
I need help with 9 please
Answer:
12
Step-by-step explanation:
Treat the less than or equal too sign as you would a normal equal sign.
Add 27 to -15 so that x is less than or equal to 12
In 2000 the population of a district was 750,000. With a continuously compounding growth rate of approximately 4%, what will the population be in 2025?
Answer:
2,038,711
Step-by-step explanation:
For a continuously compounding rate r, the growth is modeled by ...
P = P0·e^(rt)
where P0 is the initial population, r is the annual growth rate (compounded continuously) and t is the number of years.
Putting your values into this formula, you have
P = 750000·e^(0.04·25) ≈ 2,038,711
Using the formula for continuous compound growth, the population of the district in 2025 is projected to be approximately 1,226,030.
Explanation:The question is asking about the future population of a district based on continuous compound growth. In this case, the compound interest formula, which includes the principle amount, the rate of growth (interest), and time. The formula often looks as follows: A = P * e^(rt), where A is the amount in the future, P is the principle amount (initial population), r is the rate of growth (interest), and t is the time.
In your case, the calculation would be: A = 750,000 * e^(0.04 * 25). Here, 'e' represents Euler's number (approximately equal to 2.71828), 0.04 is the growth rate, and 25 is the time (years from 2000 to 2025).
Using this formula, we can calculate that the population of the district in 2025 will be approximately 1,226,030 people, assuming a steady growth rate of 4% annually.
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twelve more than the quotient of a number and eight
Answer:
12+x/8
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
i hope it helps if not 17 then it is ..................... 12+x/8
what is 4 radical sign 5 equivalent to
Answer:
1.31950791
Step-by-step explanation:
I don't actually know if this is correct
Solve 2(y – 3) = 1.2 – y.
Answer:
y = 2.4
Step-by-step explanation:
first distribute into the parenthesis' -
2(y-3) = 1.2 -y
2y - 6 = 1.2 - y
+y +y
3y -6 = 1.2
+6 +6
3y = 7.2
/3 /3
y = 2.4
hope this helps!!
Answer: y=2.4
Step-by-step explanation:
The work is below Hopefully this helps:)
* Mark me the brainliest:)!!
Help Me Please!!!!
Find the Mean from the line plot. , , .
Analyze the sequence 243, 162, 108, 72,…
Answer: You multiply 1.5 each time.
Step-by-step explanation:
72*1.5=108
108*1.5=162
162*1.5=243
And so on and so forth.... Hope it helped!
243 = 3x3x3x3x3
162 = 3x3x3x3x2
108 = 3x3x3x2x2
72 = 3x3x2x2x2
The next two numbers in the sequence would be
48 = 3x2x2x2x2
32 = 2x2x2x2x2
A parking lot in a shape of a trapezoid has an area of 12,052.1 square meters.the lean the of one base is 82.4 meters and the length of the other base is 108.6 meters.what is the height of the parking lot?
Answer:
126.2 meters
Step-by-step explanation:
A trapezoid's area is found using the formula A = 1/2 (a+b)h where a and b are the two bases. Substitute A = 12,052.1, a = 82.4 and b=108.6. Then solve for h.
A = 0.5(a+b)h
12,052.1 = 0.5(82.4 + 108.6)*h
12,052.1 = 0.5(191)h
12,052.1 = 95.5h
126.2 = h
help me !!!!!!please im begging u all for help i really need it please help me im begging u find the zero's of the function
[tex]y = - 2(x - 2)(x - 10)[/tex]
[tex]0 = - 2(x - 2)(x - 10)[/tex]
[tex]x - 2 = 0 \\ x = 2[/tex]
[tex]x - 10 = 0 \\ x = 10[/tex]
Answer:
The zero's are x=2 and x=10
Step-by-step explanation:
y = -2(x-2) (x-10)
We want to find the zero's so we set y=0
0 = -2(x-2) (x-10)
Using the zero product property
x-2 = 0 and x-10 =0
x-2+2 =0+2 x-10+10 =0+10
x =2 x=10
The zero's are x=2 and x=10
what is the mode of 6.0, 6.5,6.2,5.5,6.8,6.3,6.4,6.7,6.5,6.2
Answer:6.2 and 6.5
Step-by-step explanation:
First, make a plotline from least to greatest and organize your list of numbers from least to Greatest.
Next, go through your list of organized numbers and add a dot to that number on the plotline. Repeat until done with list of numbers.
Then, go through your plotline and find the number(s) with the most dots and you have your mode.
Definition of mode: The number which appears most often in a set of numbers.
Answer provided in the image attached.
What is the mode of the data set?
Fifth Grade Jump Distance
2|0
3|2 4 6
4|0 2 4 8
5|5
6|5
2|0 = 20 inches
The data set is
20
32, 34, 36
40, 42, 44, 48
55
65
We can see that each value only shows up one time. Therefore there is no mode. To have a mode, we need to have a value show up more than once, and it must be the most frequent value. For example, the set {1,2,3,3,4} has a mode of 3 since it shows up twice, the most of any value in that set. However we don't have that occur for the data set your teacher gave you.
Final Answer: There is no mode for this data setAnswer:
no mode i just got it right
Step-by-step explanation:
Hey guys please help, thanks so much
12) D'(3, 1) E'(1, -2) F'(5, 0)
13) Vertex E
14) D'(3, 1)
15) D'(1, 3) E'(3, 0) F'(-1, -2)
16) D'(-11, 11) E'(13, 8) F'(-9, 6)
P'(-9, 10) Q'(-7, 12) R'(-5, 10)
17) Translate 4 units down; (x, y) ---- (x, y - 4)
18) P'(-1, 2) Q'(-3, 4) R'(-5, 2)
19) P'(-2, 1) Q'(-4, 3) R'(-2, 5)
20) P'(-1, -2) Q'(-3, -4) R'(-5, -2); Rotated 180° about the origin
21) P'(3, 6) Q'(9, 12) R'(15, 6)
22) A'(-9, 0) B'(0, 12) C'(9, 0) D'(0, -12)
23) Image (yes, the answer is actually Image)
24) (x, y) → (1.5x, 1.5y)
This took me 45 mins to do, lol.
You're welcome? :) <3
Match the functions with their inverse functions.
The answers are:
[tex]f(x)=\frac{5x+3}{2}[/tex]
[tex]f(x)=2x-8[/tex]
[tex]f(x)=7x-2[/tex]
[tex]f(x)=\frac{1}{x+2}[/tex]
Why?To find the inverse function of a function, we need to replace the variable (x for this case) for the function itself (f(x)), where we see "x" we must rewrite with "y" or "f(x) and then, isolate "y" or "f(x). If we have the inverse function and we want to find the function, we need to reverse the process.
Let's find each function of the given inverse functions in order to match each one with its inverse.
First inverse function,
[tex]f^{-1}(x)=\frac{2x-3}{5}[/tex]
Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:
[tex]x=\frac{2f(x)-3}{5}\\\\5x=2f(x)-3\\\\5x+3=2f(x)\\\\f(x)=\frac{5x+3}{2}[/tex]
Therefore, the function that matches with the first inverse function is:
[tex]f(x)=\frac{5x+3}{2}[/tex]
Second inverse function,
[tex]f^{-1}(x)=\frac{x+8}{2}[/tex]
Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:
[tex]x=\frac{f(x)+8}{2}\\\\2x=f(x)+8\\\\2x-8=f(x)\\\\f(x)=2x-8[/tex]
Hence, the function that matches with the second inverse function is:
[tex]f(x)=2x-8[/tex]
Third inverse function,
[tex]f^{-1}(x)=\frac{x+2}{7}[/tex]
Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:
[tex]x=\frac{f(x)+2}{7}\\\\7x=f(x)+2\\\\7x-2=f(x)\\\\f(x)=7x-2[/tex]
So, the function that matches with the third inverse function is:
[tex]f(x)=7x-2[/tex]
Fourth inverse function,
[tex]f^{-1}(x)=\frac{1-2x}{x}[/tex]
Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:
[tex]x=\frac{1-2f(x)}{f(x)}\\\\xf(x)=1-2f(x)\\\\f(x)x+2f(x)=1\\\\f(x)(x+2)=1\\\\f(x)=\frac{1}{x+2}[/tex]
So, the function that matches with the fourth inverse function is:
[tex]f(x)=\frac{1}{x+2}[/tex]
Have a nice day!
Solve the following equation for d:b=cd
Answer:
d = b/c.
Step-by-step explanation:
Just divide both sides by c:
b = cd
b / c = cd/ c
b/c = d.
Answer:
[tex] d = \frac { b } { c } [/tex]
Step-by-step explanation:
We are given the following equation and we are to solve it for d:
[tex] b = c d [/tex]
Since we are asked to solve this equation for d and it contains all variables, it means that we need to make the variable 'd' the subject of the equation by keeping all other variables at the other side of the equation.
[tex] b = c d [/tex]
[tex]d=\frac{b}{c}[/tex]
Plz help
simplify (2x+1) (3x+4)
[tex](2x + 1)(3x + 4) \\ = 2x(3x + 4) + 1(3x + 4) \\ = 6 {x}^{2} + 8x + 3x + 4 \\ = 6 {x }^{2} + 11x + 4[/tex]
evaluate i^31 please help
ANSWER
[tex] {i}^{31} = - i[/tex]
EXPLANATION
We want to evaluate
[tex] {i}^{31} [/tex]
Use indices to rewrite the expression as:
[tex] = {i}^{30} \times i[/tex]
We know that
[tex] {i}^{2} = - 1[/tex]
So we rewrite the expression to obtain;
[tex] = ({ {i}^{2}) }^{15} \times i[/tex]
This gives us;
[tex]= {( - 1) }^{15} \times i[/tex]
This simplifies to
[tex] = - 1 \times i[/tex]
[tex] = - i[/tex]
two step Equations ... problem :
-6n - 5=31
plz explain the answer ....thank u have a great day !
Answer:
n = - 6Step-by-step explanation:
[tex]-6n-5=31\qquad\text{First step: add 5 to both sides}\\\\-6n-5+5=31+5\\\\-6n=36\qquad\text\qquad\text{Second step: divide both sides by (-6)}\\\\-6n:(-6)=36:(-6)\\\\n=-6[/tex]
The product of 17 and 1.27
Answer:
1.27 x 17 = 21.59 Product means multiply
Step-by-step explanation:
Answer:
21.59
Step-by-step explanation:
17 x 1.27 = 21.59
21.59/17=1.27
Which day was the weather forecast most accurate?
Answer:
Thursday
Step-by-step explanation:
Since the forecast being completely accurate would be 0, you would have to choose the closest number to 0, and if you look -2 or Thursday is the closest number the 0,
if f={(2,3),(5,7),(3,3),(5,4),(9,1)} what is the range
[tex]\bf \stackrel{\textit{range is always the set of y-coordinates}}{f=\{(2,\stackrel{\downarrow }{3}),(5,\stackrel{\downarrow }{7}),(3,\stackrel{\downarrow }{3}),(5,\stackrel{\downarrow }{4}),(9,\stackrel{\downarrow }{1})\}}\qquad \qquad \{3,7,3,4,1\}\implies \{3,7,4,1\}[/tex]
Answer:
{3, 7, 3, 4, 1}
Step-by-step explanation:
Help me with number 2 plss people
Answer:
3/8
Step-by-step explanation:
1/2 of a yard is 4/8 of a yard, so you can subtract 7-4 to get 3/8 of a yard.
What is the length of bd?
The length of the bd in the given triangle is 12 cm. This is obtained by applying the Pythagoras theorem.
What is the Pythagoras theorem state?The Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse. I.e., [tex]a^2+b^2=c^2[/tex].
Given data from the diagram:The triangle is perpendicularly divided into two halves looking like right-angled triangles.
The side lengths for the given triangle are bc=13 cm and ac=10 cm
Finding the length of the arm bd:The line segment bd divides the triangle into two right-angled triangles symmetrically.
So, the base ac of the given triangle is divided at the mid-point d.
Thus,
ac = ad + dc
here, d is the mid point, ad = dc
So, ad=dc=5 cm
Now, the triangle forms a right-angled triangle with sides bd, dc, and bc. Where bc is the hypotenuse.
To find the length of bd, applying the Pythagoras theorem
[tex](bc)^2=(bd)^2+(dc)^2[/tex]
⇒ [tex](13)^2 = (bd)^2 + (5)^2[/tex]
⇒ [tex]169 = (bd)^2 +25[/tex]
⇒ [tex](bd)^2 = 169 - 25[/tex]
⇒ [tex](bd)^2 = 144[/tex]
∴ bd = 12 cm
Therefore, the length of the bd is 12 cm.
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How do Federal Reserve banks and the federal government typically calculate simple interest?
Interest (I) = Principal (P) X Rate (R) X Time (T)
They tend to use 'Exact Interest' in which Interest calculated using a 365-day year. Time that counts exact number of days in the month that the borrower has the loan
Hope this helps :)
Answer:
Interest (I) = Principal (P) X Rate (R) X Time (T)
Hope this helps you:)
5INGH
Step-by-step explanation:
What is the reciprocal of -b/3
Answer:
-3/b
Step-by-step explanation:
The reciprocal of -b/3 is -3/b