Answer:
Step-by-step explanation:
in similar triangles
sides are proportional.
4 kilometer from house to the nearest mailbox. how far is it in meter?
Answer:
4 kilometers is equal to 4000 meters.
Step-by-step explanation:
1 kilometer is equal to 1000 meters, so 4 kilometers is equal to 4 x 1000 = 4000 meters. This is because the prefix "kilo" means 1000, so 1 kilometer is equivalent to 1000 meters.
leg-leg (ll) congruence theorem if the legs of a right triangle are congruent to the legs of a second right triangle, then the triangles are congruent.
The leg-leg (LL) theorem of congruency states that if the legs of a right triangle are equal to the legs of a second right triangle, then the two triangles are congruent.
We know that two triangles are congruent if and only if they have three pairs of equal sides.
In the case of the LL congruence theorem,
the two triangles have two pairs of equal sides (the legs) and one pair of equal angles (the right angles).
Therefore by the Side-Angle-Side (SAS) congruence criterion, the 2 triangles are congruent.
Alternatively
If the legs are of equal length then
Their squares would be equal to
Hence, the sum of these squares too would be equal.
Now taking a root over these would give us the hypotenuse for these triangles, which in turn should be equal.
Hence, by SSS congruence criteria
the triangles would be congruent.
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use lagrange multipliers to find the maximum or minimum values of the function subject to the given constraint. (if an answer does not exist, enter dne.) f(x, y, z)
The minimum and the maximum values are 0 and 1/27, respectively.
The extreme values of a function are the minimum and the maximum values of the function.
The function is given as:
f(x, y, z) = x²y²z²
x² + y² + z² = 1
Subtract 1 from both sides of x² + y² + z² – 1
x² + y² + z²-1=0
Using Lagrange multiplies, we have:
L(xy.z. λ) f(x. y.z) + λ(0)
Substitute f(x.y. z) = x³y²z² and x² + y² + z² − 1 = 0
L(x, y, λ) = x²y²z² + λ(x² + y² + 2² – 1)
Differentiate
Lx = 2xy²z² + 2λx
Ly = 2x²yz² + 2λy
Lz = 2x²y³z + 2λz
Lλ = x² + y² + z²
Equate to 0
2xy²z² + 2λx = 0
2x²yz² + 2λy = 0
2x²y²z+ 2λz = 0
x² + y² + z²-1=0
Factorize the above expressions
2xy²z²+2λx = 0
2x(y²z² + λ) = 0
2x = 0 or y²z²+λ=0
x=0 or y²z² = -λ
2x²yz² + 2λy = 0
2y(x²z² + λ) = 0
2y=0 or x²z²+λ=0
y = 0 or x²z² = -λ
2x²y²z+λz = 0
2z(x²y² + λ) = 0
2z = 0 or x²y² +λ=0
z = 0 or x²y² = -λ
So, we have:
x = 0 or y²z² = -λ
y=0 or x²z² = -λ
z = 0 or x²y² = -λ
Because
-λ= -λ
The above expressions become:
x=y=z=0
x²z² = y²z²
x² = y²
x = ±y
Also, we have:
x²y² = x²z²
y² = z²
y = tz
Also:
y²z² = x²y²
z² = x²
z = ±x
So, we have:
x = ±y
y = ±z
z = ±x
This means that:
x=y=z
Recall that: x² + y² + z² = 1
So, we have:
x² + x² + x² = 1
3x² = 1
Divide through by 3
x² = 1/3
Take square roots of both sides
x=±[tex]\frac{1} \sqrt{3}[/tex]
So, we have:
x=y=z=±[tex]\frac{1} \sqrt{3}[/tex]
So, the critical points are:
x=y=z=0
x=y=z=±[tex]\frac{1} \sqrt{3}[/tex]
Substitute the above values in f(x, y, z)=x²y²z²
f(0,0,0) = 0² × 0² × 0² = 0
f(±[tex]\frac{1} \sqrt{3}[/tex],±[tex]\frac{1} \sqrt{3}[/tex],±[tex]\frac{1} \sqrt{3}[/tex]) = (±±[tex]\frac{1} \sqrt{3}[/tex])² × (±±[tex]\frac{1} \sqrt{3}[/tex])² × (±±[tex]\frac{1} \sqrt{3}[/tex])² =[tex]\frac{1}{27}[/tex]
Considering the above values, we have:
Minimum 0
Maximum = 1/27
Hence, the minimum and the maximum values are 0 and 1/27, respectively.
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The ABC Corporation is considering opening an office in a new market area that
would allow it to increase its annual sales by $2.6 million. The cost of goods sold is
estimated to be 40 percent of sales, and corporate overhead would increase by
$306,500, not including the cost of either acquiring or leasing office space. The
corporation will have to invest $2.6 million in office furniture, office equipment, and
other up-front costs associated with opening the new office before considering the
costs of owning or leasing the office space.
A small office building could be purchased for sole use by the corporation at a total
price of $5.8 million, of which $900,000 of the purchase price would represent land
value, and $4.9 million would represent building value. The cost of the building would
be depreciated over 39 years. The corporation is in a 21 percent tax bracket. An
investor is willing to purchase the same building and lease it to the corporation for
$645,000 per year for a term of 15 years, with the corporation paying all real estate
operating expenses (absolute net lease). Real estate operating expenses are
estimated to be 50 percent of the lease payments. Estimates are that the property
value will increase over the 15-year lease term for a sale price of $6.3 million at the
end of the 15 years. the property is purchased, it would be financed with an interest-
only mortgage for $3,280,000 at an interest rate of 4.5 percent with a balloon
payment due after 15 years.
Required:
a. What is the return from opening the office building under the assumption that it is
leased?
b. What is the return from opening the office building under the assumption that it is
owned?
c. What is the return on the incremental cash flow from owning versus leasing?
A:
The return from opening the office building under the assumption that it is leased would be the difference between the net income generated by the increase in sales and the expenses associated with opening the new office, including the cost of leasing the office space.
To calculate the net income generated by the increase in sales, we first need to calculate the total cost of goods sold. Since the cost of goods sold is estimated to be 40 percent of sales, the cost of goods sold for the new office would be 40 percent x $2.6 million = $<<40*.01*2.6=1.04>>1.04 million.
Subtracting the cost of goods sold from the increase in sales, we find that the net income generated by the increase in sales would be $2.6 million - $1.04 million = $<<2.6-1.04=1.56>>1.56 million.
Next, we need to calculate the expenses associated with opening the new office, including the cost of leasing the office space. Since the corporate overhead would increase by $306,500, the total up-front costs associated with opening the new office would be $306,500 + $2.6 million = $<<306.5+2.6=2.906>>2.906 million.
To calculate the cost of leasing the office space, we need to multiply the annual lease payment by the number of years in the lease term. Since the annual lease payment is $645,000 and the lease term is 15 years, the total cost of leasing the office space would be $645,000 x 15 years = $<<645000*15=9675000>>9.675 million.
Subtracting the total up-front costs and the cost of leasing the office space from the net income generated by the increase in sales, we find that the return from opening the office building under the assumption that it is leased would be $1.56 million - $2.906 million - $9.675 million = $<<1.56-2.906-9.675=-9.020>>-9.020 million. This means that the corporation would incur a loss of $9.020 million by opening the new office and leasing the office space.
B:
C:
To calculate the return on the incremental cash flow from owning versus leasing, we need to subtract the cash flow from leasing the office space from the cash flow from owning the office space.
First, let's calculate the cash flow from leasing the office space. We already know that the total cost of leasing the office space would be $9.675 million. To calculate the cash flow from leasing the office space, we need to subtract the real estate operating expenses from the total cost of leasing the office space. Since the real estate operating expenses are estimated to be 50 percent of the lease payments, the real estate operating expenses would be 50 percent x $645,000 = $<<50*.01645=322500>>322,500 per year. Since the lease term is 15 years, the total real estate operating expenses would be $322,500 x 15 years = $<<322.515=4837.5>>4,837,500. Subtracting the real estate operating expenses from the total cost of leasing the office space, we find that the cash flow from leasing the office space would be $9.675 million - $4.837.5 million = $<<9.675-4.837.5=4.837.5>>4,837,500.
Next, let's calculate the cash flow from owning the office space. We already know that the total up-front costs associated with opening the new office would be $2.906 million. To calculate the cash flow from owning the office space, we need to subtract the total annual operating expenses from the net income generated by the increase in sales. Since the net income generated by the increase in sales is $1.56 million and the total annual operating expenses are $217,774.36, the cash flow from owning the office space would be $1.56 million - $217,774.36 = $<<1.56-217774.36=1.34222564>>1,342,225.64.
Finally, to calculate the return on the incremental cash flow from owning versus leasing, we need to subtract the cash flow from leasing the office space from the cash flow from owning the office space. Therefore, the return on the incremental cash flow from owning versus leasing would be $1,342,225.64 - $4,837,500 = $<<1.34222564-4.837.5=-3.495.5>>-3,495,500. This means that the corporation would incur a loss of $3.495.5 million by choosing to own the office space instead of leasing it.
Round 13.689 to the nearest hundredth
In triangle, HIJ, N is the centroid. If
HK = 10, find KI.
Answer:
4k because is right is the best answer
let sn be the number of successes in n independent bernoulli trials, where the probability of success for each trial is 1/2. evaluate the following limits.
(a) n→[infinity]lim P( 2n− 3n ≤S n ≤ 2n + 3n)
(b)n→[infinity] lim P( 2n− 4n ≤S n ≤ 2n+ 4n)
(c) n→[infinity]lim P(2n−20≤Sn ≤ 2n+20)
Let sn be the number of successes in n independent bernoulli trials, the probability of success for each trial is 1/2.
(a) 1 , (b) 0 ,(c) 0
(a) As n approaches infinity, the probability of having 2n - 3n successes in n trials is equal to the probability of having 2n + 3n successes in n trials. Since the probability of success for each trial is 1/2, the probability of having 2n - 3n successes is the same as the probability of having 2n + 3n successes. Therefore, the limit is 1.
(b) As n approaches infinity, the probability of having 2n - 4n successes in n trials is equal to 0, since the probability of success for each trial is 1/2. Similarly, the probability of having 2n + 4n successes in n trials is also equal to 0. Therefore, the limit is 0.
(c) As n approaches infinity, the probability of having 2n - 20 successes in n trials is equal to 0, since the probability of success for each trial is 1/2. Similarly, the probability of having 2n + 20 successes in n trials is also equal to 0. Therefore, the limit is 0.
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You are currently getting 26 sales opportunities per day and closing 64% of them.”I am closing ____ sales opportunities per day!”
I am closing 17 sales opportunities per day.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The total number of sales = 26.
64% of sales are closing.
This means,
The number of closing sales.
= 64% of 26
= 64/100 x 26
= 0.64 x 26
= 16.64
Thus,
The number of closing sales is 17.
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give the component from the following vectors shown
Find the missing values of the ratio table
The missing values for the equivalent ratios in the order that they appear in this table include the following;
3/23/210What is a proportion?In Mathematics, a proportion can be defined as an expression which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
From column 1, we have:
Let the missing value be represented by x.
1/4/(1/2) = 3/4/x
2/4 = 3/4x
8x = 12
x = 12/8
x = 3/2
From column 2, we have:
Let the first missing value be represented by y.
1/4/(1/2) = y/3
2/4 = y/3
4y = 6
y = 6/4
y = 3/2.
From column 2, we have:
Let the second missing value be represented by z.
1/4/(1/2) = 5/z
2/4 = 5/z
2z = 20
z = 20/2
z = 10.
In conclusion, we can logically deduce that t 10/2, 5/(11/20), and 5/4.
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an assembly consists of two mechanical components. suppose that the probabilities that the firt and second components meet specfications are 0.81 and 0.84 respectfully. assume that the components are independent. x denotes the number of components in the assembly that meet specifications. obtain the cumulative distribution function (cdf)
The probability of the cumulative distribution function to meet the specification of the components is given by P( X = 0 ) = 0.0304 ,
P( X = 1 ) = 0.2892 , P( X = 2) = 0.6804.
As given in the question,
Let probability of the first component to meet the specification be P (M)
= 0.81
And probability of the second component to meet the specification be P (N)
= 0.84
Probability of the first component do not meet the specification be P ( M' )
= 1 - 0.81
= 0.19
Probability of second component do not meet the specification be P(N' )
= 1 - 0.84
= 0.16
X defined the number of components to the meet the specifications
Here X = 0, 1, 2
P( X = 0 ) represents components do not meet any specifications
= P( M' ∩ N' )
= P(M') P(N') ( Independent )
= 0.19 × 0.16
= 0.0304
P( X= 1) represents components meet only one specification
= P( M∩N') ∪ P( M'∩N)
= P( M∩N') + P( M'∩N)
= P(M) P(N') + P(M') P(N)
= 0.81(0.16) + (0.19)(0.84)
= 0.1296 + 0.1596
= 0.2892
P( X=2) represents components meet both the specification
= P( M ∩ N )
= P(M) P(N)
= 0.81(0.84)
= 0.6804
Therefore, the probability of the cumulative distribution function is given by P( X = 0 ) = 0.0304 , P( X = 1 ) = 0.2892 , P( X = 2) = 0.6804.
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If w is FALSE, x is TRUE, and y is FALSE, what is ((w OR Y') AND (x' AND y')) OR ((w OR y') AND (x OR Y)') ? A) TRUE B) Not enough information.C) FALSE D) NULL
After solving the logical operations it can be determined that the correct answer is C) FALSE.
What are logical operations?Logical operations are phrases that connect expressions to test if they are true or not.
What does the complement sign mean?The complement (') sign means that the opposite value of the variable is needed. For example if y is false, y' means true.
Let False = 0 and True = 1
= ((0 OR 0') AND (1' AND 0')) OR ((0 OR 0') AND (1 OR 0)')
= ((0 OR 1) AND (0 AND 1)) OR ((0 OR 1) AND (1)')
= (1 AND 0) OR (1 AND 0)
= 0 OR 0
= 0
Hence, the answer is C) FALSE
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Cast Iron Grills, Incorporated, manufactures premium gas barbecue grills. The
company reports inventory and cost of goods sold based on calculations from a LIFO
periodic inventory system. Cast Iron's December 31, 2024, fiscal year-end inventory
consisted of the following (listed in chronological order of acquisition):
Units. Unit cost
6,800. 600
4,900. 700
7,800. 800
The replacement cost of the grills throughout 2025 was $900. Cast Iron sold 36,000
grills during 2025. The company's selling price is set at 200% of the current
replacement cost.
Required:
1. & 2. Compute the gross profit (sales minus cost of goods sold) and the gross profit
ratio for 2025 under two different assumptions. First, that Cast Iron purchased 37,000
units and, second, that Cast Iron purchased 19,500 units during the year.
4. Compute the gross profit (sales minus cost of goods sold) and the gross profit ratio
for 2025 assuming that Cast Iron purchased 37,000 units (as per the first assumption)
and 19,500 units (as per the second assumption) during the year and uses the FIFO
inventory cost method rather than the LIFO method.
Answer:
a) ending inventory: 11,850,000
cost of goods sold: 25,200,000
gross profit 25,200,000
b)
ending inventory: 1,800,000
cost of goods sold: 23,100,000
gross profit 50,400,000 - 23,100,000 = 27,300,000
5,200 at $600
4,100 at $700
6,200 at $800
purchase 29,000 at $900
-sold 28,000 grills
As we use LIFO we sale from the last purchase thus, 29,000 - 28,000 = 1,000 of this units are added as another layer for the inventory account
ending inventory
5,200 at $ 600
4,100 at $ 700
6,200 at $ 800
1,000 at $ 900
Total $ 11,850,000
cost of good sold:
28,000 x $900 = $25,200,000
sales revenue
28,000 x 900 x 200% = $50,400,000
gross profit sales revenue less COGS
b) 5,200 at $600
4,100 at $700
6,200 at $800
purchase 15,500 at $900
-sold 28,000 grills
we check how many layer deep we go:
28,000 - 15,500 at 900= 12,500
12,500 - 6,200 at 800= 6,300
6,300 - 4,100 at 700 = 2,200 at 600
Ending Inventory
3,000 at $600 = $ 1,800,000
COGS:
15,500 x 900 + 6,200 x 800 + 4,100 x 700 + 2,200 x 600 = 23,100,000
Step-by-step explanation:
Ariel earns $8.00 per hour. Her benefits package is equal to 15% of her hourly wages.
Ariel works 40 hours each work week. How much does Ariel earn in a week WITH
benefits?
Answer:
$368 per week
Step-by-step explanation:
[tex]8 \times 40 \times 1.15 = 368[/tex]
evaluate the integral below by interpreting it in terms of areas in the figure. the areas of the labeled regions are a1
The integral can be evaluated by interpreting it in terms of the area of the labeled regions in the figure. The integral is equal to the sum of the areas of the labeled regions, which is equal to a1.
1. The integral is given as an area under a graph.
2. The graph has labeled regions.
3. The integral can be evaluated by interpreting it in terms of the area of the labeled regions in the figure.
4. The integral is equal to the sum of the areas of the labeled regions, which is equal to a1.
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we have the number of rinks resurfaced by zzz zambonis is equal to the rate for zzz zambonis times the time. we want the time for 1\,\text{rink}1rink1, start text, r, i, n, k, end text , and we want that time to be less than or equal to 5\,\text{minutes}5minutes5, start text, m, i, n, u, t, e, s, end text. therefore: 1\,\text{rink}
we want that time to be less than equation or equal to 5 minutes start text, m, i, n, u, t, e, s, end text. therefore: 1[tex]5minutes[/tex]
Rate for ZZZ Zambonis × Time ≤ 5 minutes
Time ≤ 5 minutes/Rate for ZZZ Zambonis
To solve for the time needed to resurface one rink, we first need to set up an equation. We know that the number of rinks resurfaced by ZZZ Zambonis is equal to the rate for ZZZ Zambonis multiplied by the time. We want the time for 1 rink to be less than or equal to 5 minutes, so we need to solve for time in the equation. We can do this by dividing both sides of the equation by the rate for ZZZ Zambonis, resulting in the equation Time ≤ 5 minutes/Rate for ZZZ Zambonis. This equation gives us the maximum time needed to resurface one rink.
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Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.
a. y= ?
b. y=?
The equation of line that passes through the given point and is (a) parallel to given line is 4x + y - 16 =0
(b) perpendicular to given line is 4x - y -8 =0
According to the question,
The required line is passing through given points and is
(a) parallel (b) perpendicular to given line
Let the equation of required line be (y - y') = m'(x - x')
(a) Parallel
If two lines are parallel to each other then their slopes are equal
Slope of given line : m = y2 - y1 / x2-x1
This line passes through (2,2) and (1,6)
=> m = 6 - 2 / 1 - 2
=> m = -4
Therefore , the slope of required line will be -4 also,
Required line passes through (4,3)
Equation of required line = (y - 4) = -4(x - 3)
=> y - 4 = -4x + 12
=> 4x + y - 16 =0
(b) Perpendicular
If two lines are perpendicular to each other then the product of their slope is -1
So, m × m' = -1
=> -4 × m' = -1
Dividing by -4
=> m' = 4
Therefore , equation of required line => (y - 4) = 4(x - 3)
=> y - 4 = 4x - 12
=> 4x - y -8 =0
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Which of the following sets of numbers could not represent the three sides of a right
triangle?
O {48, 55, 73}
O {39, 80, 89}
O {42, 56, 70}
O {10, 23, 26}
Submit Answer
{48, 55, 73} and {10, 23, 26} do not represent a right angle triangle.
What is the way of classifying a triangle?If a² + b² < c² then it is an acute angle triangle.
If a² + b² = c² then it is a right-angle triangle.
If a² + b² ≥ c² then it is an obtuse angle triangle.
Now,
48² + 53² = 73².
2304 + 2809 = 5329.
5113 ≠ 5329 so do not represents a right-angle triangle.
Similarly,
39² + 80² = 89² represents a right-angle triangle.
42² + 56² = 70² represents a right-angle triangle.
10² + 23² ≠ 26²so do not represent a right-angle triangle.
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At a time t hours after taking a tablet, the rate at which a drug is being eliminated is r(t) = 50(e^-0.1 t - e^-0.20 t) mg/hr. Assuming that all the drug is eventually eliminated, calculate the original dose. Enter the exact answer. The original dose was _______mg
At a time t hours after taking a tablet, the rate at which a drug is being eliminated is r(t) = 50(e^-0.1 t - e^-0.20 t) mg/hr. Assuming that all the drug is eventually eliminated, calculate the original dose. Enter the exact answer. The original dose was 0 mg.
A limit is a value that a function or sequence approaches as the input or index approaches a certain value. Limits are a fundamental concept in calculus, and they are used to define important ideas such as derivatives and integrals. They are also used in other areas of mathematics, such as real analysis and mathematical analysis.
The rate at which the drug is being eliminated is the derivative of the amount of drug present at time t. We can write this as:
r(t) = dA(t)/dt = 50(e^-0.1 t - e^-0.20 t) mg/hr
If we integrate both sides of this equation with respect to t, we get:
A(t) = ∫r(t) dt = ∫50(e^-0.1 t - e^-0.20 t) dt
This integral can be evaluated using integration by parts. Let u = e^-0.1 t and dv = e^-0.20 t. Then du = -0.1 e^-0.1 t and v = -1/(0.2) * e^-0.20 t = -5e^-0.20 t. We can then write:
A(t) = -5 ∫e^-0.1 t * e^-0.20 t dt + (1/0.2) ∫e^-0.1 t dt
The first integral on the right-hand side can be evaluated using the substitution y = -0.3t, which gives:
A(t) = -5 ∫e^y dy + (1/0.2) ∫e^-0.1 t dt
The first integral is simply -5e^y, and the second integral is -5e^-0.1 t. Substituting these results back into the expression for A(t) gives:
A(t) = -5(-5e^-0.3 t) + (1/0.2)(-5e^-0.1 t)
Combining constants and simplifying gives:
A(t) = 25e^-0.1 t - 25e^-0.3 t
We are told that all the drug is eventually eliminated, so A(t) approaches 0 as t approaches infinity. This means that the original dose A(0) must be equal to the limit of A(t) as t approaches 0.
Taking the limit as t approaches 0 gives:
A(0) = lim t → 0 [25e^-0.1 t - 25e^-0.3 t]
This limit is equal to 25 - 25 = 0, so the original dose was 0 mg.
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Water is steadily dripping from a faucet into a bowl. You want to write an equation that represents the number of milliliters y of water in the bowl after . What is the constant of proportionality for the relationship between the number of milliliters y of water in the bowl and the time in seconds x? What is the equation?
Answer:
Read below
Step-by-step explanation:
The equation for the volume of water in the bowl after a certain amount of time can be represented by the formula: y = k * x, where k is the constant of proportionality. This constant represents the rate at which water is dripping into the bowl, in milliliters per second.
To find the constant of proportionality, you need to know the rate at which the water is dripping into the bowl. If you know the rate, you can plug it into the formula above to find the equation that represents the volume of water in the bowl over time. For example, if the water is dripping into the bowl at a rate of 1 milliliter per second, the equation would be: y = 1 * x. This means that after 1 second, the bowl would contain 1 milliliter of water, after 2 seconds it would contain 2 milliliters of water, and so on.
It's important to note that the constant of proportionality will change if the rate at which the water is dripping into the bowl changes. For example, if the water is dripping into the bowl at a rate of 2 milliliters per second, the equation would be: y = 2 * x. This means that after 1 second, the bowl would contain 2 milliliters of water, after 2 seconds it would contain 4 milliliters of water, and so on.
In summary, the equation for the volume of water in the bowl after a certain amount of time can be represented by the formula: y = k * x, where k is the constant of proportionality, which represents the rate at which water is dripping into the bowl. To find the equation, you need to know the rate at which the water is dripping into the bowl, and plug that value into the formula as the value of k.
Use the given information to prove that ΔRST ≅ ΔVUT.
Given: ST ≅ UT
∠SRT ≅ ∠UVT
Prove: ΔRST ≅ ΔVUT
Based on the given information , the proof of triangle RST ≅ triangle VUT is shown below .
In the question ,
two triangles are given where ;
it is given that side ST ≅ UT
and ∠SRT ≅ ∠UVT .
we have to prove that ΔRST congruent ΔVUT .
In triangle RST and triangle VUT .
side ST = side UT .....given that ST ≅ UT ;
angle SRT = angle UVT ....given that ∠SRT ≅ ∠UVT ;
angle RTS = angle VTU .....because they are vertically opposite angles .
Hence by ASA congruence , triangle RST ≅ triangle VUT .
Therefore , it is proved that triangle RST ≅ triangle VUT .
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a clothing business finds there is a linear relationship between the number of shirts, n ,it can sell and the price, p , it can charge per shirt. in particular, historical data shows that 6000 shirts can be sold at a price of $55, while 8000 shirts can be sold at a price of $47. give a linear equation in the form p
The linear relationship between the number of shirts, n ,it can sell and the price, p is p = (-1/250)x + 79
The linear equation is
y = mx + b
Where m is the slope of the line
b is the y intercept
Here p is the total price
n is the number of shirts
The equation will be
p = mn + b
The price of 6000 shirts = $55
The price of 8000 shirts = $47
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line
The slope of the line = (47-55) / (8000-6000)
= -8/2000
= - 1/250
Substitute the point (6000, 55) in the equation
55 = (-1/250)(6000) + b
55 = -24 + b
b = 55 + 24
b = 79
Substitute the values in the equation
p = (-1/250)x + 79
Therefore, the linear relation in the form of p is p = (-1/250)x + 79
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differentiate of the following w.r.t.x
i mark u branlist if u give me right answer
The differentiation of y = logx - cosecx + 5ˣ + 3/(x^(3/2)) with respect to x is cotx.cosecx + log(5).5ˣ + 1/x - 9/(2x^(5/2))
How to differentiate y = logx - cosecx + 5ˣ + 3/(x^(3/2)) with respect to x?In mathematics, differentiation is the process of finding the derivative of a function. The derivative of a function is a measure of how the function changes as its input (or independent variable) change
Given: y = logx - cosecx + 5ˣ + 3/(x^(3/2))
Thus, the derivative will be:
d/dx [logx - cosecx + 5ˣ + 3/(x^(3/2))]
= d/dx [logx] - d/dx [logx] + d/dx [5ˣ] + 3d/dx[(x^(3/2))]
= 1/x - (-cotx)cosecx + log(5).5ˣ + 3(-3/2)x^((3/2) -1)
= cotx.cosecx + log(5).5ˣ + 1/x - 9/(2x^(5/2))
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(easy) Jinsoul had 2 apples and Chaeyoung had 3 apples. Chaeyoung suggest they share, Jinsoul agrees. Together it makes 5 apples. BUT The apple tree they picked from has 20? 5+20=?
Answer:
Step-by-step explanation:
5+ 20= 25
Because when you set them up and add them properly you get 25
(Not sure if that was the question you wanted us to answer..)
What improvement can we make?
In general, the improvements that we can make refer to optimizations that can be applied in a context.
¿What are the improvements?In a particular process or context, the best are optimizations that are done to make something more efficient or to improve the quality of an element.
For example, some improvements that we could make in our community are:
Establish more efficient containers to better collect garbage.Optimize public lighting. Improve solid waste management.¡Hope this helped!
Score on last attempt: 2.5 out of 3 Score in gradebook 2.5 out of 3 For each of the following accounts, determine the growth factor and percent change for the account value over one compounding period a Account A has a 5% APR compounded monthly (12 times per year). Determine the account value's growth factor and percent change per compounding period Preview 1. Monthly Growth Factor: 1.0041667 ii. Monthly Percent Change: (1.0041667-1)-100 % Preview b. Account B has a 6.9% APR compounded quarterly (4 times per year). Determine the account value's growth factor and percent change per compounding period. i. Quarterly Growth Factor: 14(0.069/4) Preview 11. Quarterly Percent Change: (1.01725-1)*100 % Preview c. Account Chas a 3.4% APR compounded daily (365 times per year). Determine the account value's growth factor and percent change per compounding period i. Daily Growth Factor: 1+(0.034/100) Preview 11. Daily Percent Change: (1.00034.1) 100 N% Preview Submit
given rate r = 5% compounded monthly r = 0.05/12 = 0.0041667
(1) monthly growth factor = 1.0041667 (2) monthly percent change = (1.0041667-1)*100%= 0.0041667*100% monthly percent change = 0.41667%
(B) given rate r = 6.9% compounded quarterly
r = 0.069/4 = 0.01725
(1) Quarterly growth factor = 1.01725
(2) Quarterly percent change = (1.01725-1)*100%= 0.01725*100% monthly percent change =1.725%
(C) given rate r = 3.4% compounded quarterly
r = 0.034/365 = 9.315 * 10 ^ - 5
(1) daily growth factor = 1 + 9.315 * 10 ^ - 5 = 1.00009315
(2) daily percent change = (1.00009315-1)*100%= 0.00009315*100% monthly percent change =0.009315%
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The table shows values for a quadratic function.
A. 32
X
0
1
2
3
4
5
6
B. 10
y.
0
What is the average rate of change for this function for the interval from x = 3
to x = 5?
2
8
18
32
50
72
Answer:
c
Step-by-step explanation:
Gretchen spends 5.1 hours on Monday, 3/3/5 hours on Tuesday, and 5/3/10 hours on Wednesday studying for her final exams. If she spends 3/1/2 hours studying for each exam, how many exams does she have to take?
The number of exams that Gretchen has to take is 4 exams.
How many exams does Gretchen have to take?From the information illustrated, Gretchen spends 5.1 hours on Monday, 3/3/5 hours on Tuesday, and 5/3/10 hours on Wednesday studying for her final exams. The total hours that she used will be:
= 5.1 + 3 3/5 + 5 3/10
= 5.1 + 3.6 + 5.3
= 14 hours.
Since she spends 3/1/2 hours studying for each exam, the number of exams that she has to take will be:
= Number of hours / Hours used for each exam
= 14 / 3 1/2
= 4 exams
The number of exams are 4.
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Please help will mark Brainly
The number of the adult will be 77
The number of the child will be 160.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
237 peoples used the public swimming pool.
And, The daily prices are $1.75 for children and $2 for adult.
Now,
Let The number of the adult = x
The number of the child = y
So, We can formulate;
237 peoples used the public swimming pool.
⇒ x + y = 237 ..(i)
And, The daily prices are $1.75 for children and $2 for adult.
⇒ 2x + 1.75y = 444 ..(ii)
From (i);
⇒ x + y = 237
⇒ x = 237 - y
Substitute above value in (ii), we get;
⇒ 2x + 1.75y = 444
⇒ 2 (237 - y) + 1.75y = 444
⇒ 474 - 2y + 1.75y = 444
⇒ 474 - 444 = 0.25y
⇒ 40 = 0.25y
⇒ y = 160
And, from (i),
⇒ x + y = 237
⇒ x + 160 = 237
⇒ x = 77
Thus, The number of the adult = 77
The number of the child = 160.
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If a line is tangent to a circle, then it is ___________ to the radius drawn to the point of tangency.
If a radius is drawn to the point of tangency of a tangent line, then the radius is basically perpendicular to the tangent line.
Given that the radius is drawn to the point of tangency of a tangent line.
We are required to fill the blank with the appropriate word.
Radius is basically the line segment which joins the center to any point on the circumference of the circle.
Tangent line is basically a line which is drawn from an outside point on the circumference of the circle.
When the radius is drawn to the point of tangency of a tangent line, then the radius is perpendicular to the tangent line.
Hence if a radius is drawn to the point of tangency of a tangent line, then the radius is perpendicular to the tangent line.
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