The length of the missing side is 9.92 ft given that the base of the following pyramid is a square, base side length(s) is 11 ft and the volume of the square pyramid is 400 ft³. This can be obtained using the formula of finding the volume of the pyramid with base as square.
Calculate the length of the missing side:The formula of finding the volume of the pyramid with base as square is,
⇒ V = s²h/3
where V is the volume of the square pyramid, s is the side length of the base and h is the height of the square pyramid.
Here in the question it is given that,
it is a pyramid with base as squarethe side length of the base is 11 ftvolume of the square pyramid is 400 ft³that is, s = 11 ft, V = 400 ft³
By using the formula of finding the volume of the pyramid with base as square we get,
V = s²h/3
400 = (11)²h/3
By rearranging the equation we get,
h = 400 × 3/11²
h = 9.92 ft
Hence the length of the missing side is 9.92 ft given that the base of the following pyramid is a square, base side length(s) is 11 ft and the volume of the square pyramid is 400 ft³.
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please solve this question asap
Step-by-step explanation:
[tex]y = \sqrt{4x + 6} [/tex]
[tex] {y}^{2} = 4x + 6[/tex]
[tex] {y}^{2} - 6 = 4x[/tex]
[tex] \frac{1}{4} ( {y}^{2} - 6) = x[/tex]
Swap x and y
[tex] \frac{ {x}^{2} - 6 }{4} = y[/tex]
If f(x)=√x^3 and (fog)(x)=√√x, then g(64) =
The value of g(x) is (x^3+5) and g(64) = 262149.
According to the statement
we have given that the
f(x)=√x^3 and (fog)(x)=√(x^3+5) and we have to find the value of the g(64).
So, For find the value of g(64), Firstly we have to find the g(x).
So,
We given that
f(x)=√x^3 and (fog)(x)=√(x^3+5)
And here the formula used is
(f o g)(x) = f (g(x))
here (fog)(x)=√(x^3+5) and f(x)=√x^3
From this we get g(x) is (x^3+5)
So,
g(x) = (x^3+5) and
g(64) = ((64)^3+5)
g(64) = 262149.
So, The value of g(x) is (x^3+5) and g(64) = 262149.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
If f(x)=√x^3 and (fog)(x)=√(x^3+5). Then find the value of g(64).
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I take this to mean [tex]f(x) = \sqrt{x^3}[/tex] and [tex](f\circ g)(x) = \sqrt x[/tex].
Let's first find the inverse of [tex]f[/tex].
[tex]f\left(f^{-1}(x)\right) = \sqrt{\left(f^{-1}(x)\right)^3} = x \\\\ \implies \left(f^{-1}(x)\right)^3 = x^2 \\\\ \implies f^{-1}(x) = x^{2/3}[/tex]
(Note that [tex]f[/tex] is defined only if [tex]x^3\ge0[/tex], or [tex]x\ge0[/tex].)
Apply the inverse of [tex]f[/tex] to [tex]f\circ g[/tex].
[tex](f\circ g)(x) = f(g(x)) = \sqrt x \\\\ \implies f^{-1}\left(f(g(x))\right) = f^{-1}(\sqrt x) \\\\ \implies g(x) = \left(\sqrt x\right)^{2/3} = \left(x^{1/2}\right)^{2/3} = x^{1/3} = \sqrt[3]{x}[/tex]
Then
[tex]g(64) = \sqrt[3]{64} = \sqrt[3]{4^3} = \boxed{4}[/tex]
Which of the following statements is equivalent to 10x – 30? 10(x – 30) 10(x – 3) 10 + (x – 20) 10(x – 20)
Answer:
10(x-3) is equivalent to 10x – 30
Step-by-step explanation:
First you have to take everything of out the parentheses and then simplify if needed.
10(x – 30) is not equivalent to 10x – 30 because, 10 times x is 10x, but 10 times 30 is 300. So, 10(x – 30) is not equivalent to 10x – 30.10(x – 3) is equivalent to 10x – 30 because, 10 times x is 10x, and 10 times 3 is 30. So, 10(x – 3) is equivalent to 10x – 30.10 + (x – 20) is not equivalent to 10x – 30 because, 10 minis 20 plus x are -10 + x. So, 10+(x – 20) is not equivalent to 10x – 30.10(x – 20) is not equivalent to 10x – 30 because, 10 times x is 10x, but 10 times 20 is 200. So, 10(x – 20) is not equivalent to 10x – 30.Answer: 10(x-3) is equivalent to 10x – 30
Calculate the following, and place the calculated solution on the appropriate line. In all cases, assume the companies that are the subject of the question are US companies using US GAAP.
a. Berful sells one product. It had one item in beginning inventory that cost $10,000, and purchased 4 more items during the accounting period. The cost changed with each purchase, as shown below:
Item Cost of Item
First $12,000
Second 14,000
Third 15,000
Fourth 16,000
If 3 items were sold during the year, calculate the cost of ending inventory using the following cost flow assumptions (Remember beginning inventory in your calculations!):
FIFO $_____________
LIFO $_____________
Weighted Average $_____________
b. Berful purchased a machine on the first day of the accounting period at a cost of $22,000. The machine is expected to have a life of 5 years or 20,000 units, and a salvage value of $2,000. Calculate the second year depreciation expense using the following depreciation methods (6,000 units produced in year 2):
Straight-line $_____________
Double-declining Balance $_____________
Units-of-production $_____________
c. Calculate the correct balance of cash to be included in the Cash account on the firm’s balance sheet by preparing a bank reconciliation of its checking account from the data given below:
Item Amount
Balance per Bank Statement $16,655.44
Balance per Books $12,091.94
Deposits in Transit $ 2,234.81
Outstanding Checks $ 6,808.16
Bank Service Charge $ 9.85
Correct balance of cash in this account $__________
d. Show the accounting entry required as a result of the above bank reconciliation in the space below:
e. If Berful uses the Allowance Method to determine its bad debt expenses, establishing its estimate as 1% of Net Sales, and Net Sales total $600,000, show the adjusting journal entry required if the Allowance for Bad Debts account has a debit balance of $2,000?
a) The calculation of the cost of ending inventory using the following cost flow assumptions are as follows:
FIFO $31,000 ($15,000 + $16,000)
LIFO $22,000 ($10,000 + $12,000)
Weighted Average $26,800 ($13,400 x 2)
b) The calculation of the second-year depreciation expense using these depreciation methods is as follows:
Straight-line $4,000
Double-declining Balance $5,280
Units-of-production $6,000.
c) The correct balance of cash to be included in the Cash account on the firm’s balance sheet based on the bank reconciliation is $12,082.09.
d) The accounting entry required for the bank reconciliation is as follows:
Debit Bank Service Charges $9.85
Credit Cash Account $9.85
To record the bank service charge for the period.e) The adjusting journal entry required is as follows:
Debit Bad Debt Expense $8,000
Credit Allowance for Bad Debts $8,000
To record the bad debt expense for the period.Data and Calculations:a) Berful Company:
Beginning inventory = $10,000
Purchases:
First $12,000
Second 14,000
Third 15,000
Fourth 16,000
The total cost of goods available for sale = $67,000
Weighted average cost = $13,400 ($67,000/5)
Total items available for sale = 5 items (1 + 4)
Sales = 3 items
Ending inventory = 2 items (5 - 3)
b) Cost of machine = $22,000
Estimated useful life = 5 years or 20,000 units
Salvage value = $2,000
Depreciable amount = $20,000 ($22,000 - $2,000)
Straight-line Method:Annual depreciation for second year = $4,000 ($20,000/5)
Double-declining balance:Depreciation rate = 40% (100/5 x 2)
For the first year = $8,800 ($22,000 x 40%)
Declined balance = $13,200 ($22,000 - $8,800)
For the second year = $5,280 ($13,200 x 40%)
Units-of-production Method:Depreciation per unit = $1 ($20,000/20,000)
For the second year, Depreciation = $6,000 ($1 x 6,000)
c) Bank Reconciliation Statement:Balance per Bank Statement $16,655.44
Add: Deposits in Transit $ 2,234.81
Less: Outstanding Checks $ 6,808.16
Balance as per Cash Book $12,082.09
Cash Book Adjustment:Balance per book $12,091.94
Bank Service Charge ($ 9.85)
The correct balance of cash in this account $12,082.09.
Bank Service Charges $9.85 Cash Account $9.85
e) Data and Calculations:Allowance for Bad Debts = $2,000 Debit
Net Sales = $600,000
Estimated allowance for bad debt expenses = 1% of Net Sales
= $6,000 ($600,000 x 1%)
Bad Debt Expense $8,000 Allowance for Bad Debts $8,000 ($2,000 + $6,000)
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Find the equation of the line that passes through point (6, 1) with the x-intercept of 2.
Answer:
○ [tex]y = \frac{1}{4}x - \frac{1}{2}[/tex]
Step-by-step explanation:
To find the equation of the line, let's first consider the points whose coordinates we have been given:
• (6, 1)
• (2, 0).
The point (2, 0) is what is called the x-intercept, which is the point where the line crosses the x-axis. This means that at this point, the y-coordinate of the line is 0.
Next, let's calculate the slope (gradient) of the line using the formula:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
where:
m = gradient,
[tex](x_2, y_2)[/tex] and [tex](x_1, x_2)[/tex] = points on the line.
Using the formula:
[tex]m = \frac{1 - 0}{6 - 2}[/tex]
⇒ [tex]m =\bf \frac{1}{4}[/tex]
Finally, now that we have two points on the line as well as the line's slope, we can use the following formula to find the equation of the line:
[tex]\boxed{y - y_1 = m(x - x_1)}[/tex]
You can use any of the points on the line as [tex]y_1[/tex] and [tex]x_1[/tex].
Using (2, 0):
[tex]y - 0 = \frac{1}{4}( x - 2)[/tex]
⇒ [tex]y = \frac{1}{4}x - \frac{1}{2}[/tex]
Therefore the equation of the line is [tex]y = \frac{1}{4}x - \frac{1}{2}[/tex].
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Set W consists of the even whole numbers from 2 to 20, inclusive. If a number is selected at random from set W, then what is the probability that the number is a
multiple of 4 and also a multiple of 6?
Answer:
1/19
Step-by-step explanation:
The number in the set that are a multiple of both 4 and 6 is 12.
This is one number out of the 19 numbers in the set, so the probability is 1/19.
(GIVING BRAINLYST)Which expression represents the following statement? Multiply 7 by the sum of 6 and 3, and then subtract the quotient of 4 and 2. 07x (6+3)-4+2 07+6 (3+4) x 2 - 07+6+3 (4+2) 7x (6+3)+4-2
The expression representing the given statement is 7×(6+3)-(4÷2). Option A is correct.
Given the statement is Multiply 7 by the sum of 6 and 3, and then subtract the quotient of 4 and 2.
Firstly, we will break the statement in two parts that is Multiply 7 by the sum of 6 and 3 and second part is subtract the quotient of 4 and 2.
Multiply 7 by the sum of 6 and 3 means there is addition sign between 6 and 3 and the addition of 6 and 3 is multiply with 7, we get
7×(6+3) ......(1)
subtract the quotient of 4 and 2 means 4 is divisible by 2 and this is subtract means there is a minus sign, we get
-(4÷2) .....(2)
Combine equation (1) and (2), we get
7×(6+3)-(4÷2)
Hence, the expression which represents the given statement Multiply 7 by the sum of 6 and 3, and then subtract the quotient of 4 and 2 is 7×(6+3)-(4÷2).
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PLEASE HELPPPPP PLEASE so confused
Answer:
105°
Step-by-step explanation:
EFGH is an isosceles trapezoid (a trapezoid with congruent legs is an isosceles trapezoid)
∠G=75° (base angles of an isosceles trapezoid are congruent)
∠F=105° (same-side interior angles theorem)
Find the measures of x and y
Answer:
x = 159; y = 140
Step-by-step explanation:
a = 40
a + y = 180
y = 180 - 40
y = 140
b = 61
b = (180 - x) + a
61 = 180 - x + 40
x = 159
Answer:
m∠x = 159°
m∠y = 140°
Step-by-step explanation:
PART I: Find the measure of yGiven information
∠a = 40°
Given formula
∠a + ∠y = 180° (Supplementary angles)
Substitute values into the formula
40 + ∠y = 180
∠y = 180 - 40
[tex]\Large\boxed{\angle y=140^\circ}[/tex]
PART II: Find the measure of xGiven information
∠b = 61°
∠c = Supplementary angle of ∠b
Given formula
∠b + ∠c = 180°
Substitute values into the formula
61 + ∠c = 180
∠c = 180 - 61
∠c = 119°
Determine the value of ∠x
∠x = ∠a + ∠c (Exterior angle theorem)
∠x = (40) + (119)
[tex]\Large\boxed{\angle x=159^\circ}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Claim: Fewer than 94% of adults have a cell phone. In a reputable poll of 1057 adults, 89% said that they have a cell phone. Find the value of the test statistic. The value of the test statistic is nothing. (Round to two decimal places as needed.)
Answer:
suma todos los decimales
Step-by-step explanation:
empieza sumando 1059-94%eso te da 993,58 luego le sumas 89% lo que te da 884,2862 espero haberte ayudado
find the square roots by division method of 151,321
Answer: 389 is the square root.
Answer:
389 is the square root
Step-by-step explanation:
BRAINIEST PLS
Which function has the greatest y-intercept?
Answer:
Second one from the left
Answer:
b
Step-by-step explanation:
edg 22'
hey can anyone give me the answers to the questions that are blank
The value of the rate of change of the function is 14a + 7h
Rate of change of functionThe rate of change of function is also known as the slope expressed according to the equation shown below;
f'(x) = f(a+h)-f(a)/h
Given the function below expressed as:
f(x) =1 + 7x^2
Determine the function f(a)
To determine the function, simply replace x with 'a" to have:
f(a) =1 + 7a^2
Determine the function f(a+h)
f(a+h) = 1 + 7(a+h)^2
f(a + h) = 1 + 7(a^2+2ah+h^2)
f(a + h) = 1 + 7a^2 + 14ah + 7h^2
To determine the rate of change
f'(x) = f(a+h)-f(a)/h
f'(x) = 1 + 7a^2 + 14ah + 7h^2 - 1 - 7a^2/h
f'(x) = + 14ah + 7h^2/h
f'(x) = 14a + 7h
Hence the value of the rate of change of the function is 14a + 7h
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