Evan enjoys eating fresh fruits and vegetables. This
year, he decided to grow his own garden. The diagram
shows the dimensions of his garden
He fills his garden with enriched topsoil at a height of 2
inches. How much topsoil does Evan use?
48 in
cubic inches
24 in
Answers
Answer:
[tex]2304 \ in^3[/tex]
Step-by-step explanation:
Given the surface dimensions of the garden as 24 inches by 48 inches:
#Calculate surface area of the garden's top:
[tex]A=lw\\\\=48\times 24\\\\=1152 in^2[/tex]
Given the soil's thickness is 2 Inches, we multiply this thickness by the garden's surface area to get volume of soil used:
[tex]V=tA, t-thickness, A=Area=1152 \ in^2\\\\=2 \ in \times 1152\ in^2\\\\=2304 \ in^3[/tex]
Hence, the amount of soil used is 2304 cubic inches.
Answer: those are right!
Hope this helps ❤️
Related Questions
In the isosceles triangle ABC, we have AB=AC=4. The altitude from B meets AC at H. If AH=3(HC) then determine BC.
Answers
In isosceles triangle ABC with AB=AC=4, and AH=3HC, the length of BC is [tex]\( \frac{4\sqrt{5}}{5} \)[/tex] units, determined using the Pythagorean Theorem and the given relationship between AH and HC.
In isosceles triangle ABC, let BH be the altitude from B to side AC. Given AB = AC = 4 and AH = [tex]3 \cdot[/tex] HC, we can use the Pythagorean Theorem in right triangle ABH:
[tex]\[ BH^2 + AH^2 = AB^2 \][/tex]
Substitute the given values:
[tex]\[ BH^2 + (3HC)^2 = 4^2 \][/tex]
Simplify:
[tex]\[ BH^2 + 9HC^2 = 16 \][/tex]
Since BH = HC in an isosceles triangle, substitute BH with HC:
[tex]\[ HC^2 + 9HC^2 = 16 \][/tex]
Combine like terms:
[tex]\[ 10HC^2 = 16 \][/tex]
Solve for HC :
[tex]\[ HC^2 = \frac{8}{5} \][/tex]
Now, use the Pythagorean Theorem in right triangle BHC:
[tex]\[ BC^2 = BH^2 + HC^2 \][/tex]
Substitute the known values:
[tex]\[ BC^2 = HC^2 + HC^2 \]\[ BC^2 = 2HC^2 \]\[ BC^2 = 2 \cdot \frac{8}{5} \]\[ BC^2 = \frac{16}{5} \][/tex]
Therefore, BC is the square root of [tex]\( \frac{16}{5} \)[/tex], which simplifies to [tex]\( \frac{4}{\sqrt{5}} \)[/tex] or [tex]\( \frac{4\sqrt{5}}{5} \)[/tex].
The length of BC in an isosceles triangle with sides AB=AC=4 and altitude BH, where AH=3(HC), is 2√2 units.
Explanation:To determine the length of BC in an isosceles triangle ABC with sides AB=AC=4 and altitude BH, where AH=3(HC), we can use the properties of similar triangles and the Pythagorean theorem.
Since the triangle is isosceles, the altitude BH will bisect the base AC at H, creating two right triangles ABH and CBH. We know that AH=3(HC), which can be expressed as AH=3x and HC=x for some value x. Therefore, AC = AH + HC = 3x + x = 4x.
Using the Pythagorean theorem (a² + b² = c²), in triangle ABH, we get:
AH² + BH² = AB²(3x)² + BH² = 4²9x² + BH² = 16And in triangle HBC, we have:
HC² + BH² = BC²x² + BH² = BC²Since we want to find BC, we first solve for BH from the first right triangle:
BH² = 16 - 9x²Substitute BH² into the second equation:
x² + (16 - 9x²) = BC²-8x² + 16 = BC²To find x, we use AC = 4x = 4, thus x = 1. Substituting x into the equation for BC, we get:
-8(1)² + 16 = BC²-8 + 16 = BC²BC² = 8BC = √8BC = 2√2 unitsExplain how to write the equations of vertical lines, and why they are written this way
Answers
1. Recall the vertical line equation.
2. Plug in the x that we know.
3. Write down the final equation
Pls mark me brainiest :)
find the recursive formula.
-28, -35, -42, -49, ...
Answers
Answer:
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] - 7
Step-by-step explanation:
Note the common difference d between consecutive terms in the sequence, that is
d = - 35 - (- 28) = - 42 - (- 35) = - 49 - (- 42) = - 7
Thus to obtain a term in the sequence subtract 7 from the previous term
[tex]a_{n+1[/tex] = [tex]a_{n}[/tex] - 7 with a₁ = - 28
Brainliest Giveaway!! Also gives all of my points.!!
Answers
Answer:
wf
axStep-by-step explanation:
Answer:
Her ride is about 15.1 miles long.
Step-by-step explanation:
40.03 = 6.75 + 3.20m
33.28 = 3.20m
ISOLATE M
m = 15.1272
m = 15.1
I NEED HELP ASAP WITH THE QUESTION
Answers
Equivalent expression for x + x + x + x + x is 5x and that of 18y - 12 are 6·3y - 6·2 and 6(3y - 2)
Step-by-step explanation:
Step 1: Find equivalent expression for x + x + x + x + x. It is 5x. Step 2: Find equivalent expressions for 18y - 12Equivalent expressions are 6·3y - 6·2 and 6(3y - 2)
A new car is Purchased for 16200 dollars. The value of the car depreciates at 14.25% per year. What will the value of the car be, to the nearest cent,after 6 years?
Answers
Answer:
6,440.5
Step-by-step explanation:
So the car starts at 16,200. For the first part of the equation it's 16,200 × x raised to the y. X in this equation would be 1-.1425 = 0.8575. 16,200×(.8575)^y. Y is the number of years after you purchased the car. So, 16,200×(.8575)^6 and that equals 6,440.5
Answer:
$6440.5
Step-by-step explanation:
I hope this helps!
Write a verbal expression for 2n+7
Answers
Because when it says “twice the number” it doesn’t give you what the number is so it has to be a variable which in “n” in this situation. And 7 more is obviously adding 7, so it is 7 more than twice a number
Why do you think George Washington wanted the us to avoid entangling alliances
Answers
Norma has 9 pies to divide among 4 friends. How many pies will each friend receive if all of the pies must be used and can be divided into smaller parts?
Answers
Answer:
2 1/4
Step-by-step explanation:
Solve 3x + k = cfor x.
Answers
The width of a rectangle is 2m less than the length. The area is 48m squared. Find the dimensions.
Answers
Length of the rectangle is 8m and width is 6m
Step-by-step explanation:
Step 1: Given area of the rectangle = 48m². Let the length be x, then the width is x - 2. Find the dimensions using the area of the rectangle = length × breadth48 = x (x - 2)
48 = x² - 2x
x² - 2x - 48 = 0
x² - 8x + 6x - 48 = 0
x(x - 8) + 6(x - 8) = 0
(x + 6)(x - 8) = 0
x = -6, 8 (neglecting the negative value)
∴ Length of the rectangle = 8m
∴ Width of the rectangle = 8 - 2 = 6m
What is the greatest area that you can make with a rectangle that has a perimeter of 24.
Answers
Answer:
Step-by-step explanation:
The greatest area of the rectangle with a perimeter of 24 units is in fact a square. So we take 24 units and divide by 4 to get a square of 6 units to a side. the area of that square is 6 units x 6 units = 36 square units
help! need asap! brainiest if right
Answers
Step-by-step explanation:
After the translation, rotation and reflection position of the image may differ but the side lengths, angle, orientation remains the same, so that the congruence is maintained, but in dilation the size of the image may get enlarged or reduced, so that congruence is not there.
Parallelograms are congruent when
Reflect across the y- axis and then translate 1 unit left.
Reflect across the y- axis then rotate 45° counterclockwise.
Translate 4 units up then rotate 180° counterclockwise
Parallelograms are non-congruent when
Translate 5 units right then dilate by a factor of 2
Rotate 90° clockwise then dilate by a factor of 6
Dilate by a factor of 3 then reflect across the x- axis
A directed line segment on a gridded map shows the path of a hot air balloon from 1(0,0) to B(8,4). Each grid unit represents 1 mile. The balloon traveled at a constant speed of 20 miles per hour Point V divides line segment AB in the ratio 6 to 2.
a) What are the coordinates of point V? Round to the nearest tenth if necessary
b) Mary states that the distance from point A to point Vis 6 miles. What is Mary's mistake? What is the
correct distance? (Check)
Answers
Answer:
Step-by-step explanation:
There is a point V with ration 6 to 2, therefore we must find the coordinates of point V and the distance from A to V
According to the graph
[tex]c^{2}=x^{2}+y^{2}\\c^{2}=8^{2}+4^{2}\\c=\sqrt{64+16}=8.9.4\\sin\alpha =\frac{4}{8.94}[/tex]
α≅27°
V=2*8.94/6 (ratio 6:2)
V=2.98mile
[tex]sin27=\frac{y}{2.98}\\y=sin27*2.98=1.35\\cos27=\frac{x}{2.98}\\x=cos27*2.98=2.65[/tex]
coordinates of V = (2,65;1.35)
Distance from A to V
[tex]d_{AV}=2.98 miles[/tex]
finally
Mary's mistake is to take the 6 to 2 ratio as the distance traveled from the globe only in the x direction
Choose the equation that represents this situation. Use p to represent the
price of an item and tto represent its total cost with gift wrapping.
A store adds a $5 fee to the price of each item that a customer wants to have
gift-wrapped
O A. p=t+5
O B. t= 5p
OC. t= p +5
O D. t+p=5
Answers
Answer:
(c)t=p+5
Step-by-step explanation:
total price= item price + gift wrapping cost (given)
gift wrapping cost is constant/unchanged= 5
total price= t
item price=p
therefore by derivation t=p+5 (option c)
Final answer:
The correct equation to represent the store's $5 gift wrapping fee added to the price of an item is C. t = p + 5, where p is the price of the item and t is the total cost with gift wrapping.
Explanation:
The question is asking to find an equation that shows the relationship between the price of an item, represented by p, and its total cost with gift wrapping, represented by t. Given that the store adds a $5 fee for gift wrapping, the correct equation needs to include the original price of the item and the additional gift wrapping fee. Therefore, the total cost t is equal to the price of the item p plus the $5 wrapping fee.
The correct equation representing this situation is C. t = p + 5.
This is because when you start with the initial price of an item p and add a fixed gift wrapping fee of $5, you get the total cost t. It is the sum of the two values: the price of the item plus the additional fixed fee for gift wrapping.
How do I find vertex
Answers
Answer:
Get the equation in the form y = ax2 + bx + c.
Calculate -b / 2a. This is the x-coordinate of the vertex.
To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y.
Step-by-step explanation:
Create a chart to show how to use the distributive property to simplify the expression: 7 (5x +
10) – 10x.
Answers
Answer:
25x + 70
Step-by-step explanation:
Step 1: Distribute
7 (5x + 10) - 10x
7*5x + 7*10 - 10x
35x + 70 - 10x
25x + 70
Answer: 25x + 70
$800 is deposited in an account
that pays 9% annual interest,
compounded annually. Find the
balance after four years.
Answers
Answer:
The balance after four years is $1129.27
Step-by-step explanation:
The formula for compound interest, including principal sum, is [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
A = the future value of the investment/loan, including interestP = the principal investment amount (the initial deposit or loan amount)r = the annual interest rate (decimal)n = the number of times that interest is compounded per unit tt = the time the money is invested or borrowed for∵ $800 is deposited in an account
∴ P = 800
∵ The account pays 9% annual interest
∴ r = 9% = 9 ÷ 100 = 0.09
∵ The interest is compounded annually
∴ n = 1
∵ The time is 4 years
∴ t = 4
- Substitute the values of P, r, n, and t in the formula above
∵ [tex]A=800(1+\frac{0.09}{1})^{(1)(4)}[/tex]
∴ [tex]A=800(1.09)^{4}[/tex]
∴ A = 1129.265
∴ The balance after four years is $1129.27
I WILL MARK BRINLIEST FOR CORRECT ANSWER, PLEASE HELP.
Answers
Answer:
f(-2) = 4
f(0.5)= 0
f(1)=1
Step-by-step explanation:
Find the product.
4(−12)(−3)
Answers
Answer:
144
Step-by-step explanation:
Answer:
-12/3
Step-by-step explanation:
a regular hexagon is to be cut out of a circular sheet of metal that has a radius of 6 inches.
Approximately how many square centimeters of sheet will be left over a scraps?
A:32.9
B:93.5
C:113.1
D:126.2
Answers
Answer:
[tex]\large \boxed{\text{D. 126.2 cm}^{2}}[/tex]
Step-by-step explanation:
The area left over for scrap is the area of the circle minus the area of the hexagon.
1. Area of circle
The formula for the area of a circle is
A = πr²
A = π(6)² = 36π = 113.1 in²
2. Area of hexagon
A hexagon consists of six equilateral triangles, each of side a, and we can divide each of them into two right triangles.
So, we can calculate the area of one right triangle and multiply by 12.
The formula for the area of one triangle is
A = ½bh
(a) Height of a small triangle
Per the Pythagorean Theorem,
[tex]\begin{array}{rcr}h^{2} + 3^{2} & = & 6^{2}\\h^{2} + 9 & = & 36\\h^{2} & = & 27\\& = & 3\sqrt{3}\\\end{array}\\[/tex]
(b) Area of a small triangle
A = ½ bh = ½ × 3 × 3√3 = 4.5√3 in²
(c) Area of the hexagon
The hexagon contains 12 small triangles.
A = 12 × 4.5√ 3 = 54√3 ≈ 93.53 in²
3. Area of scrap
A ≈ 113.1 in² - 93.53 in² = 19.6 in²
[tex]A = \text{19.6 in}^{2} \times \left(\dfrac{\text{2.54 cm}}{\text{1 in}}\right )^{2} = \text{126.2 cm}^{2}\\\\\text{The area of the scrap is $\large \boxed{\textbf{126.2 cm}^{\mathbf{2}}}$}[/tex]
Elle earned $45 last month babysitting. This month she earned $35. What is the percent decrease?
Answers
Answer:
10percent
Step-by-step explanation:
I think
Elle experienced a 22.22% decrease in earnings from babysitting, from $45 to $35. This is calculated by finding the difference between the two amounts, dividing by the original amount, and then multiplying by 100 to convert to a percentage.
Explanation:Elle's decrease in earnings can be calculated using the formula for calculating the percentage decrease, which is [(Original value - New value)/(Original value)] * 100.
In Elle's case, the original value is $45 (the amount she earned last month), and the new value is $35 (the amount she earned this month). So, follow the formula:
Subtract the new value from the original value: $45 - $35 = $10Divide the decrease by the original value: $10/$45 = 0.2222Multiply the result by 100 to convert it to a percentage: 0.2222 * 100 = 22.22%So, Elle experienced a 22.22% decrease in her earnings from babysitting.
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Two linear equations are shown.
What is the solution to the system of equations?
(7,4)
• (31)
• (s. *)
(9,7)
y=
1/3x + 2
4
5
6
x
y = 4/3x - 5
Answers
The solution to the system of equations is (7, 13/3).
We have Equations,
y= 1/3x + 2,
y= 4/3 x - 5
Solving above two equations we get
1/3 x + 2 = 4/ 3 x - 5
1/3 x - 4/3 x = -5 - 2
-3/3 x = -7
-x = -7
x = 7
and, y = 4/3(7) - 5 = 28/3-5 = 13/3
Thus, the solution of equation is (7, 13/3).
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What is (-7a^4bc^3)(5ab^4c^2)
Answers
Answer:=-35a^5b^5c^5
Step-by-step explanation:
Answer:
-35a^5b^5c^7
Step-by-step explanation:
Step 1: Distribute
(-7a^4bc^3)(5ab^4c^4)
(-7 * 5) * (a^4 * a) * (b * b^4) * (c^3 * c^4)
(-35) * (a^5) * (b^5) * (c^7)
-35a^5b^5c^7
Answer: -35a^5b^5c^7
The lifespans of meerkats in a particular zoo are normally distributed. The average meerkat lives 13.1 years; the
standard deviation is 1.5 years.
Use the empirical rule (68 – 95 - 99.7%) to estimate the probability of a meerkat living less than 14.6
years.
Answers
Using the Empirical Rule, it is found that there is a 84% probability of a meerkat living less than 14.6.
----------------------
The Empirical Rule states that in a normal distribution, 68% of the measures are within 1 standard deviation of the mean, 95% are within 2 standard deviations and 99.7% are within 3 standard deviations.----------------------
The mean is of 13.1 years, while the standard deviation is of 1.5 years.We have also consider that the normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.14.6 = 13.1 + 1.5, thus, one standard deviation above the mean.Of the 50% of the measures below the mean, all are below 14.6, while of the 50% above, 68% are below 14.6, thus:[tex]P = 50 + 0.68(50) = 50 + 34 = 84[/tex]
84% probability of a meerkat living less than 14.6.
A similar problem is given at https://brainly.com/question/13503878
To estimate the probability of a meerkat living less than 14.6 years, we can use the empirical rule which states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Explanation:To estimate the probability of a meerkat living less than 14.6 years, we can use the empirical rule which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Given that the average lifespan is 13.1 years and the standard deviation is 1.5 years, we can calculate the z-score for 14.6 years using the formula:
z = (x - μ) / σ
where x is the value we want to find the probability for (14.6 years), μ is the mean (13.1 years), and σ is the standard deviation (1.5 years).
Substituting the values, we get:
z = (14.6 - 13.1) / 1.5 = 1.0
Now we can look up the probability corresponding to a z-score of 1.0 in a standard normal distribution table, which is approximately 0.8413. This means that the probability of a meerkat living less than 14.6 years is about 0.8413 or 84.13%.
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Write an inequality to describe the relationship between -1 2/3 and -1/4.
Answers
Answer:
-14>-1 2/3
Step-by-step explanation:
Answer:
-14>-1 2/3
Step-by-step explanation:
Write an equation for the nth term of the geometric sequences-3,6,-12,......
Answers
Answer:
Write an equation for the nth term of the geometric sequences-3,6,-12,....
an= ar∩-1
a= first term
r= common ratio
an= nth term
an= -3 x (-2) (-12-1)
an= -3 x (-2) (-13)
an= -3 x (-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)
an= -3 x -16384
nth term= 49152
Step-by-step explanation:
What is the value of x in the figure?
Enter your answer in the box.
x =
Answers
Answer:
X = 29
fyfufubivih8g8hih
Answer: X = 29
X + 61 = 90
x+61−61=90−61
x=29
(I NEED THIS ANSWERED QUICKLY! I WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER!)
The coordinates of the vertices of quadrilateral ABCD are (7, -7), (4, -10), (1.5, -2.5), and (6, -3), respectively. If quadrilateral ABCD is rotated 180° counterclockwise about the origin, what are the coordinates of D’?
A. (6, 3)
B. (3, -6)
C. (-6, 3)
D. (-3, 6)
Answers
Answer:
D
Step-by-step explanation:
literlay just count
Answer:
i believe the answer is c
Step-by-step explanation:
The theoretical probability of landing on blue on a single spin of a spinner with 1 purple, 1 blue , 1 red , and 1 orange section is?
Answers
Hey there!
[tex]\large\boxed{25\%}[/tex]
Assuming that all the sections are the same size, there are four sections of equal size.
Blue would be one out of those four sections, so the probability is 1/4. In decimal form this is .25, and as a percent this is 25%.
Hope this helps!
The theoretical probability of landing on blue on a single spin of a spinner with 1 purple, 1 blue , 1 red , and 1 orange section is 1/4.
The theoretical probability of landing on blue on a single spin of a spinner with 1 purple, 1 blue, 1 red, and 1 orange section is 1/4 or 25%.
Total = 1+1+1+1 = 4
Number of blue =1
Therefore, probability =1/4