Using the confidence interval formula for the mean of normally-distributed data, the amount that a typical parent would spend on their child's birthday gift at a 98% confidence level is between $31.6 and $44.4.
What is the confidence interval formula?The confidence interval formula is given as follows:
Formula
CI = xˉ ± z √(σ/ₙ)
Where
CI = confidence interval
xˉ = sample mean
z = confidence level value
σ = sample standard deviation
{n} = sample size
The number of survey participants, n = 19
The sample mean, xˉ = $38
Standard deviation, σ = $12
Confidence level = 98% = 2.33
Confidence Interval = 38 ± 2.33 √12/19
= 38 ± 6.42
= (31.58, 44.42)
= 31.6, 44.4
Thus, at 98% confidence level, we can conclude that a typical parent would spend between $31.6 and $44.4 on their child's birthday gift.
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A 50lbs melon is 90% water. How much water must be drained so that the melon is 25% water? Show your work.
43.33 lbs of water must be drained from the melon so that the melon is 25% water.
First, we find out how much water is in the melon when it is 90% water.
The melon weighs = 50 lbs, and
so the weight of the water in the melon is:
0.9 x 50 lbs = 45 lbs
This means there are 45 lbs of water in the melon, and the remaining 5 lbs is the weight of the melon's solid components.
Now, we want to drain some of the water so that the melon is 25% water. Let's call the water weight we need to drain "x" (in lbs).
After draining x lbs of water, the weight of the remaining solid components of the melon will still be 5 lbs, but the total weight of the melon will be:
= (50 - x) lbs
The weight of the water that remains in the melon after draining x lbs is:
(45 - x) lbs
According to the problem, this remaining water must be 25% of the total weight of the melon:
(45 - x) lbs = 0.25 x (50 - x) lbs
Now we solve for x:
45 - x = 0.25 x (50 - x)
45 - x = 12.5 - 0.25x
0.75x = 32.5
x = 43.33 lbs
Therefore, we must drain 43.33 pounds of water from the melon for 25%.
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helppp so my teacher said the Nearpod lesson is based on accuracy
meaning that i gotta get them right but lets say on the first try i just guess then on the second one i get them right would he be able to see that i RETAKEN IT AGAIN? or like does anyone know how flashcards nearpod lesson works for grading like if u go back to the slide and do them again wouldhe BE ABLE TO TELL U DID IT AGAIN OR WOULD IT SAY 1 TRY ?(EVEN THO I DID IT AGAIN?)
Answer:
They would see that you redid it yes
Step-by-step explanation:
10. Category:Returning a Polygon to its Original Position
Select the correct answer.
O
Which transformation will always map a parallelogram onto itself?
a 90° rotation about its center
O a 180° rotation about its center
O a reflection across a line joining the midpoints of opposite sides
O a reflection across one of its diagonals
00:16:55
The solution is: a 180° rotation about its center, this transformation will always map a parallelogram onto itself.
Here, we have,
A parallelogram has rotational symmetry of order 2.
Thus, rotation transformation maps a parallelogram onto itself 2 times during a rotation of 360 about its center.
And that is at 180 and 360 about its center.
Therefore, a 180° rotation about its center will always map a parallelogram onto itself .
A figure has rotational symmetry when it can be rotated and it still appears exactly the same.
The order of rotational symmetry of a shape is the number of times it can be rotated around 360 and still appear the same.
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complete question:
Which transformation will always map a parallelogram onto itself?
a 90° rotation about its center
a reflection across one of its diagonals
a 180° rotation about its center
a reflection across a line joining the midpoints of opposite sides
graph g(x)= 2^x mark 5 plots
Answer:
(0,1),(1,2),(-10, .001),( 3.804,13.997), (5,32)
Consumers surplus and producers surplus
The consumer surplus is $254.67.
The producer surplus is $108.33.
We have,
To find the consumer surplus, we need to find the area between the demand curve and the equilibrium price line.
The equilibrium price is given as $25(1/3)$, which is the same as the equilibrium point on the demand curve.
At the equilibrium point, we have:
D(x) = S(x)
48 - 2x = 14 + x
3x = 34
x = 11(1/3)
So, the equilibrium point is (11(1/3), 25(1/3)).
To find the consumer surplus, we need to integrate the demand curve from 0 to 11(1/3) and subtract the area of the triangle formed by the equilibrium point, the y-axis, and the point (0, 48).
Consumer Surplus
= ∫[0 to 11(1/3)] D(x) dx - (1/2)(11(1/3))(48 - 25(1/3))
= ∫[0 to 11(1/3)] (48 - 2x) dx - (1/2)(34)(23(2/3))
= [48x - x²] from 0 to 11(1/3) - 391(1/3)
= 254(2/3)
To find the producer surplus, we need to integrate the supply curve from 0 to 11(1/3) and subtract the area of the triangle formed by the equilibrium point, the y-axis, and the point (0, 14).
Producer Surplus
= (1/2)(11(1/3))(25(1/3) - 14) - ∫[0 to 11(1/3)] S(x) dx
= 91(2/3) - ∫[0 to 11(1/3)] (14 + x) dx
= 91(2/3) - [14x + (1/2)x²] from 0 to 11(1/3)
= 108(1/3)
Therefore,
The consumer surplus is $254.67.
The producer surplus is $108.33.
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In triangle ABC below, (which is not drawn to scale, do not trust the picture, the following is true about the given trigonometric raitos.
sin(x) = cos(y)
what must be the measure of angle ABC, explain.
Answer:
Since sin(x) = cos(y), we can write this as sin(x) = sin(90° - y), using the identity that cos(y) = sin(90° - y).
This means that angle x and angle (90° - y) have the same sine ratio, which implies that they must be equal or supplementary.
If angle x and angle (90° - y) are equal, then x = 90° - y, and angle BAC would be (x + y) = (90° - y + y) = 90°.
If angle x and angle (90° - y) are supplementary, then x + (90° - y) = 180°, which implies that angle BAC is equal to (x + y) = [(180° - (90° - y)) + y] = 90° + y.
Therefore, the measure of angle ABC cannot be determined uniquely based on the given information.
A party rental company has chairs and tables for rent the total cost to rent a chairs and four tables is $53 the total cost to rent three chairs and two tables is $25 what is the cost to rent each chair and each table
The cost of each chair is $6.2 and the cost of each table is $1.34.
Let's solve this problem by assuming the cost of each chair as ‘c’ and the cost of each table as ‘t.’ We can create two equations from the information given we can obtain the values of ‘c’ and ‘t.’
From the given information, the first equation is ‘c + 4t = 53’ because the cost to rent one chair and four tables is $53. The second equation is ‘3c + 2t = 25’ because the cost to rent three chairs and two tables is $25.
We can solve this by either substitution or elimination, but the method we used earlier works - multiplying the first equation by 3 and subtracting the second equation from it, to obtain:
3c + 12t = 159
- (3c + 2t =25)
------------------
10t = 134
Therefore, the cost of each table is $13.4.
We can plug this value back into equation 1 and solve for c
c + 4(13.4) = 53
c + 53.6 = 53
c = -0.6
This isn't a possible solution as the cost of the chair cannot be negative.
Thus, we need to check if an error was made earlier. We can plug the value of t in the second equation:
3c + 2t = 25
3c + 2(13.4) = 25
3c + 26.8 = 25
This equation is contradictory, indicating that there is no solution. We need to revise the problem statement, a possible typo can be a misplaced decimal point for example, if the cost of each table is instead $1.34, all equations will hold, and the final answer will be:$6.2 and $1.34 respectively according to the question.
This is a possible solution and makes sense.
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The mean height of a Hobbit is 42 inches with a standard deviation of 3 inches and there are currently 325 Hobbits in the Shire. SELECION 188 CHEE 1516822 527-4-5- # 15000 10 Assume the data is normally following questions. a) How many Hobbits are over 42 inches tall? Round to the nearest Hobbit. distributed and use the 68-95-99.7 Rule to answer the Hobbits Preview 188 Hobbits b) How many Hobbits are between 39 and 45 inches tall? Round to the nearest Hobbit. c) How many Hobbits are between 39 and 48 inches tall? Round to the nearest Hobbit.
Approximately 325 Hobbits will be between 39 inches and 48 inches tall.
a) How many Hobbits are over 42 inches tall? Round to the nearest Hobbit.
Using the 68-95-99.7 Rule, we can determine that roughly 16% of the Hobbits will be over 42 inches tall. 16% of 325 Hobbits is 51.6, which would round up to 52 Hobbits. So there are 52 Hobbits over 42 inches tall.
b) How many Hobbits are between 39 and 45 inches tall? Round to the nearest Hobbit.
Using the 68-95-99.7 Rule, we can determine that roughly 68% of the Hobbits will be between 39 and 45 inches tall. 68% of 325 Hobbits is 220.8, which would round up to 221 Hobbits. So there are 221 Hobbits between 39 and 45 inches tall.
c) How many Hobbits are between 39 and 48 inches tall? Round to the nearest Hobbit.
Using the 68-95-99.7 Rule, we can determine that roughly 95% of the Hobbits will be between 39 and 48 inches tall. 95% of 325 Hobbits is 308.75, which would round up to 309 Hobbits. So there are 309 Hobbits between 39 and 48 inches tall.
Therefore, approximately 325 Hobbits will be between 39 inches and 48 inches tall.
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A slice of pie costs $2.50. How much do 4 slices of pie cost?
Answer:
4 slices of pie costs $10.
Step-by-step explanation:
If one slice costs $2.50 and you’re trying to find the cost of four slices, you must multiply 2.50 x 4 = 10.
A study was commissioned to find the mean weight of the residents in certain town.
The study found the mean weight to be 187 pounds with a margin of error of 3
pounds. Which of the following is not a reasonable value for the true mean weight of
the residents of the town?
The value that is not reasonable for the true mean weight of the residents of the town is 193 pounds
Given that the mean weight is 187 pounds with a margin of error of 3 pounds, we can construct the interval as follows:
Mean weight - Margin of error = 187 - 3 = 184 pounds
Mean weight + Margin of error = 187 + 3 = 190 pounds
So, the reasonable range for the true mean weight of the residents of the town is between 184 and 190 pounds.
Now, let's evaluate the options to identify the value that falls outside this reasonable range:
A. 170 pounds - This value falls below the lower limit of the reasonable range (184 pounds). Therefore, it is not a reasonable value for the true mean weight.
B. 188 pounds - This value falls within the reasonable range of 184 to 190 pounds. It is a reasonable value.
C. 193 pounds - This value falls above the upper limit of the reasonable range (190 pounds). Therefore, it is not a reasonable value for the true mean weight.
D. 186 pounds - This value falls within the reasonable range of 184 to 190 pounds. It is a reasonable value.
E. 182 pounds - This value falls below the lower limit of the reasonable range (184 pounds). Therefore, it is not a reasonable value for the true mean weight.
From the options provided, the value that is not reasonable for the true mean weight of the residents of the town is 193 pounds.
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Question 3(Multiple Choice Worth 3 points)
(01.04 LC)
Which of the following expressions is equivalent to 2x +4? (The x+4 is to the power of x)
A) 8(2) ^x
B) 2^x/8
C) 16(2)^x
D) 2^x/16
The expression that is equivalent to the expression 2ˣ⁺⁴ is 16(2ˣ)
Which expression is equivalent to the expressionFrom the question, we have the following parameters that can be used in our computation:
2ˣ⁺⁴
The above expression is an exponential expression with the following properties
Base = 2Exponent = x + 4When the above expression is expanded, we have
2ˣ⁺⁴ = 2ˣ * 2⁴
Evaluate the expression 2 exponent 4
So, we have the following representation
2ˣ⁺⁴ = 2ˣ * 16
Rewrite as follows
2ˣ⁺⁴ = 16 * 2ˣ
This gives
2ˣ⁺⁴ = 16(2ˣ)
Hence, the expression that is equivalent to the expression is 16(2ˣ)
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Part A: Maci made $170 grooming dogs one day with her mobile dog grooming business. She charges $60 per appointment and earned $50 in tips. Write an equation to represent this situation and solve the equation to determine how many appointments Maci had.
Part B: Logan made a profit of $235 as a mobile groomer. He charged $75 per appointment and received $40 in tips, but also had to pay a rental fee for the truck of $10 per appointment. Write an equation to represent this situation and solve the equation to determine how many appointments Logan had.
Maci and 2 appointments and Logan had 3 appointments.
How many appointments did Maci and Logan have?The linear equation that represents the total amount earned by Maci is:
Total amount earned = (amount per appointment x number of appointments) + tips
$170 = ($60 x a) + $50
$170 = $60a + $50
$170 - $50 = $60a
$120 = $60a
a = $120 / $60
a = 2
The linear equation that represents the total amount earned by Logan is:
Profit = total revenue - total cost
Profit = (fee per appointment x number of appointments) + amount received in tips - (rental fee x number of appointments)
$235 = ($75 x a) + $40 - ($10 x a)
$235 = $75a + $40 - $10a
$235 = $65a + $40
$235 - $40 = $65a
$195 = $65a
a = $195 / 65
a = 3
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Natalie borrowed money from her parents to pay for a trip.
Natalie will pay her parents in equal amounts every week until she pays back the entire amount she borrowed.
The table below shows the amount of money Natalie still owes her parents at the end of every two weeks for the first eight weeks.
Number of Weeks Natalie Has Paid,
�
w
Amount Natalie Still Owes,
�
d
0
0
$
180
$180
2
2
$
162
$162
4
4
$
144
$144
6
6
$
126
$126
8
8
$
108
$108
Part A
How much does Natalie pay her parents each week?
$
per week
Part B
Write a function that shows the relationship between the amount Natalie still owes,
�
d, and the number of weeks she has paid,
�
w.
Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.
We can see that Natalie is reducing the amount she owes by $18 every two weeks.
Therefore, the amount she owes after 2 weeks is $180 - $18 = $162, after 4 weeks is $144, after 6 weeks is $126, and after 8 weeks is $108.
This means that after n weeks, the amount she still owes is:
$180 - $18n
Since she will pay the same amount each week, let's call the weekly payment P. After one week, she will owe:
$180 - P
After two weeks, she will owe:
($180 - P) - P = $180 - 2P
After four weeks, she will owe:
($180 - 2P) - P - P = $180 - 4P
After six weeks, she will owe:
($180 - 4P) - P - P = $180 - 6P
And after eight weeks, she will owe:
($180 - 6P) - P - P = $180 - 8P
We can set up an equation using the information we have:
$180 - 8P = $108
Solving for P, we get:
P = $9
Therefore, Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.
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The complete question:
Natalie borrowed money from her parents to pay for a trip. Natalie will pay her parents in equal amounts every week until she pays back the entire amount she borrowed. The table below shows the amount of money Natalie still owes her parents at the end of every two weeks for the first eight weeks. How much does Natalie pay her parents each week? What is the initial amount Natalie still owes?
Week 0 = $180
Week 2 = $162
Weeks 4 = $144
Week 6 = $126
Week 8 = $108
What is the volume of this rectangular prism?
Answer:
Step-by-step explanation:
385
what is cheaper for a 56 dollar item 5 dollars off or 15 % off
Answer: Cost of item with free shipping is cheaper than 15% coupon off
Step-by-step explanation:
Answer:
To determine which discount is cheaper for a $56 item, we need to calculate the actual discount amount of each option.
A discount of $5 off means the new price would be $56 - $5 = $51.
A discount of 15% off means the discount amount is: 15% x $56 = $8.40. Therefore, the new price would be $56 - $8.40 = $47.60.
So the discount of 15% off is cheaper for a $56 item compared to a $5.
In a survey of 259 professional athletes, it was found that 110 of them owned a convertible, 91 of
them owned a giant screen TV, and 120 owned a sporting goods store. 15 owned a convertible and a
store, 43 owned a TV and a store, and 44 owned a covertible and a TV. 9 owned all three items.
1. How many athletes did not own any of the three items?
2. How many owned a covertible and a TV, but not a store?
3. How many athletes owned a convertible or a TV?
4. How many athletes owned exactly one type of item in the survey?
5. How many athletes owned at least one type of item in the survey?
6. How many owned a TV or a store, but not a convertible?
1. Number of athletes did not own any of the three items = 259 - 228
= 31.
2. Number of athletes own a convertible and a TV but not a store = 44 - 9
= 35.
3. Number of athletes own a convertible or a TV = 110 + 91 - 44
= 157.
4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.
5. Number of athletes owned at least one type of item = 259 - 31
= 228
6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71
= 118.
The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.
Total number of athletes surveyed = 259
Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228
Number of athletes who did not own any of the three items = 259 - 228 = 31.
The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.
Number of athletes who own a convertible and a TV = 44
Number of athletes who own all three items = 9
Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35
The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.
Number of athletes who own a convertible or a TV = 110 + 91 - 44
= 157.
The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.
Number of athletes own a convertible only = 110 - 15 - 9 = 86
Number of athletes own a TV only = 91 - 44 - 9 = 38
Number of athletes own a store only = 120 - 15 - 43 - 9 = 53
Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.
The number of athletes who owned at least one type of item can use the result from part (1).
Number of athletes who owned at least one type of item = 259 - 31
= 228
The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.
Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159
Number of athletes own a TV or a store not a convertible = 13 + 34 +71
= 118.
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What is the chance of landing on an even number on two of two spins? (WILL GIVE BRAINLIEST! 30 POINTS)
1/2
1/4
2/9
1/3
The probability of landing on an even number on two of two spins is 1/6.
In the given spinner, there are 6 numbers.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
In two spins
Total number of outcomes = 12
Number of favorable outcomes = 2
Here, probability = 2/12
= 1/6
Therefore, the probability of landing on an even number on two of two spins is 1/6.
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What’s the difference between y=f(-x) and y=-f(x) ?
Answer:
The function y = f(-x) is the reflection of the function f(x) about the y-axis. In other words, it is obtained by replacing x with -x in the function f(x).
On the other hand, the function y = -f(x) is obtained by reversing the sign of the output values of the function f(x). This means that for any given value of x, the corresponding value of y for the function y = -f(x) will have the opposite sign of the corresponding value of y for the function f(x).
In other words, y = -f(x) will reflect the function f(x) about the x-axis.
A rectangular prism and a cylinder have the same height. The length of each side of the prism base is equal to the diameter of the cylinder. Which shape has a greater volume? Use the drop-down menus to explain your answer. The has the greater volume because the fits within the with extra space between the two figures.
The rectangular prism has a greater volume than the cylinder.
Volume of shapesThe rectangular prism has a greater volume than the cylinder. This is because the rectangular prism fully occupies the space within its boundaries, while the cylinder has empty space above and below it.
The cylinder's rounded shape leaves gaps between its curved surface and the boundaries of the rectangular prism.
Therefore, the rectangular prism can hold more volume than the cylinder as it utilizes the entire space within its shape efficiently.
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The length of each side of the prism base is equal to the diameter of the cylinder. Which shape has a greater volume? Drag and drop the labels to explain your answer. cylinder rectangular prism The has the greater volume because the fits within the with extra space between the two figures.
Sita started to walk from her office to home. She first walked a distance of 1 km towards North and after finishing her shopping she walked for another 4 km towards West to meet her friend. From there she took a left turn and walked for another 4 km to reach her home. What is the shortest distance between her office and home?
Answer:
5km
Step-by-step explanation:
A - her office
E - her home
AB = 1km; BC = CE = 4km
AE - the shortest disctance between her office and home.
ADE - right triangle, where AD = 4km, ED = 3 (EC - CD) =>
According to the Pythagorean theorem , we make up the equation:
AE = √ED^2 + AD^2 = √25 = 5km
What is the 30th term of the expansion (5r+s)^32?
The 30th term of the expansion[tex](5r+s)^{32[/tex] is[tex]12,400r^2 * s^{30.[/tex]
To find the 30th term of the expansion [tex](5r+s)^{32[/tex], we can use the binomial theorem. The binomial theorem allows us to expand expressions of the form[tex](a + b)^n[/tex], where "a" and "b" are constants and "n" is a positive integer.
The binomial theorem states that the coefficient of the kth term in the expansion is given by the formula:[tex]C(n, k) * a^{(n-k)} * b^k,[/tex] where C(n, k) represents the binomial coefficient, also known as "n choose k."
In this case, our expression is [tex](5r+s)^{32.}[/tex] We can identify "a" as 5r and "b" as s, so we need to find the coefficient of the 30th term in the expansion.
Using the formula mentioned above, the 30th term will have a binomial coefficient of C(32, 30), multiplied by [tex](5r)^{(32-30)[/tex]and[tex](s)^{30.}[/tex]
To calculate the binomial coefficient, we use the formula: C(n, k) = n! / (k! * (n-k)!), where "!" denotes factorial.
In this case, C(32, 30) = 32! / (30! * (32-30)!) = 32! / (30! * 2!) = (32 * 31) / (2 * 1) = 496.
Thus, the 30th term of the expansion [tex](5r+s)^{32[/tex] is given by: [tex]496 * (5r)^{(32-30)} * (s)^{30} = 496 * (5r)^2 * s^{30} = 496 * (25r^{2}) * s^{30}.[/tex]
Therefore, the 30th term of the expansion [tex](5r+s)^{32}[/tex] is [tex]12,400r^2 * s^{30.[/tex]
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On an 88 question test, Beth missed 11 questions. What percent did she get correct for that test? Round to the nearest tenths place.
A real estate company wanted to see the relationship
between home prices and square footage of homes for
sale. The regression line is 0-802,456 + 144x, where
x is the square footage of a home.
Complete the statement based on the information.
For every——-
square-foot increase, the
predicted home price is predicted to increase by
$——-
For every one square-foot increase, the predicted home price is predicted to increase by $144.
What is predicted increase in home price per sq-ft increase?In any graph, the regression line displays connection between scattered data points in any set. It shows relation between dependent y variable and independent x variables when there is a linear pattern.
Given the regression line y = -802,456 + 144x, where x is the square footage of a home, we can determine the predicted increase in home price per square-foot increase by looking at the coefficient of x, which is 144.
That gives us that for every one square-foot increase, the predicted home price is predicted to increase by $144.
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Complete the statement
For every ✔1-square-foot increase, the predicted home price is predicted to increase by $✔ 144
How many 300mL glasses can be filled from 1L bottle fresh milk?
Answer:
First you should know every Liter is 1000ml
so now we know we have a 1000ml bottle of milk
now you should divide 1000 by 300
and the answer is 3 glasses and one third glass
Step-by-step explanation:
mili = 10^-3
liter = dm³
deci = 10^-1
dm³ = (10^-1)³ =10^-3 m³
miliLiter = 10^-3 × 10^-3 = 10^-6m³
300 ml = 3×10² × 10^-6 = 3 × 10^-4
10^-3 ÷ (3× 10^-4)= 3.3333
Answer:
3 glasses (with the remainder of 0.3333 ml)
Step-by-step explanation:
How many 300mL glasses can be filled from 1L bottle fresh milk?convert liters to milliliters
1L = 1000 ml
divide the milliliters in the bottle by the milliliters of one glass1000 : 300 = 3.33
3 glasses (with the remainder of 0.3333 ml)
The rate of change of function f is the same from x = −2 to x = 1 as it is from x = 1 to x = 4.what function is this
The function that satisfies the situation is f(x) = 2x + 2.
There are infinitely many functions that satisfy this condition, but one possible example is:
f(x) = 2x + 2 for -2 <= x < 1
f(x) = 2x - 2 for 1 <= x <= 4
To see that this function has the same rate of change over both intervals, we can compute the derivative:
f'(x) = 2 for -2 < x < 1
f'(x) = 2 for 1 < x < 4
Note that the derivative is constant over both intervals, indicating that the rate of change is the same.
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1. Find the lateral and total surface area of a rectangular prism whose height is 8cm and base 4cm by 6cm.
The side face area of the blockish prism is 160 cm ², and the total Surface area is 208 cm ².
To find the side face area of a blockish prism, we need to add up the areas of all the faces that aren't the top or nethermost faces. For a blockish prism, this means adding up the areas of the four side faces.
The formula for the side face area of a blockish prism is Side face
Area = 2lh+2wh
where" l" represents the length of the base," w" represents the range of the base, and" h" represents the height of the prism. Plugging in the values given in the problem, we get
Side face Area = 2( 4 x 8) +2( 6 x 8) = 160 cm ²
To find the total face area, we need to add up the areas of all six faces of the prism. The formula for the total face area of a blockish prism is
Total Surface Area = 2lw +2lh +2wh Plugging in the values given in the problem, we get Total face Area = 2( 4 x 6)+ 2( 4 x 8) +2( 6 x 8) = 208 cm ²
thus, the side face area of the blockish prism is 160 cm ², and the total face area is 208 cm ².
To know more about Surface area.
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silicon dioxide in the sand has to be converted into
Answer:
Silicic acid
*Step by step*
You have to acidify the solution to produce Silicic Acid. I recommend using a strong acid to ensure full conversion to Silicic Acid
Enter the number that belongs in the green box
The number that belongs in the green box using sine rule is 13.96.
What is sine rule?The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.
To calculate the number that belongs in the green box, we use the formula below
Formula:
SinA/a = SinB/b.................. Equation 1From the diagram,
Given:
A = 70°B = 61°b = 15a = xSubstitute these values into equation 1
Sin70°/15 = sin61°/xSolve for x
x = (15×sin61°)/sin70°x = 13.96Learn more about sine rule here: https://brainly.com/question/28523617
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l want the solution
Answer:
6x-6
Step-by-step explanation:
Differentiate.
3x2+ddx[−3x2]+ddx[1]
Evaluate
ddx[−3x2].
3x2−6x+ddx[1]
Differentiate using the Constant Rule.
f'(x)=3x2−6x
Find the second derivative.
By the Sum Rule, the derivative of 3x2−6x
with respect to x would be
ddx[3x2]+ddx[−6x].ddx[3x2]+ddx[−6x]
Evaluate
ddx[3x2].
6x+ddx[−6x]
Evaluate dd
x[−6x].f''(x)=6x−6
The second derivative of f(x)with respect to x is 6x−6.6x−6
9. (a) (b) (c) (d) (e) Bako is twice as old as he was five years ago. His mother was then six times as old as he was. She is now 35 years old. How old is Bako? 10 How old was his mother when Bako was five? How old will Bako be when his mother is 50? How old was Bako's mother when he was born? What is the difference between Bako's age and his mother's?
Answer:
(a) Bako is 10 years old
(b) His mother was 30 years old when Bako was 5
(c) Bako will be 25 years old when his mother is 50
(d) Bako's mother was 25 years old when he was born
(e) The difference between Bako's age & his mother's is 25 years
Step-by-step explanation:
Let Bako's age five years ago be x years
Presently, Bako is 2x years old (according to the 1st statement)
Normal, Bako's present age should have been (x + 5) years; since he was x years old 5 years ago.
This simply means that Bako's present age is BOTH 2x years & (x + 5) years.
We have to equate them since they mean the same thing (Bako's present age)
x + 5 = 2x
2x - x = 5
Therefore x = 5 years
Remember that x signified Bako's age five years ago... This simply means that Bako's age five years ago was 5 years.
This simply means that Bako's age now is 10 years old.
His mother was then six times 5 years = 30 years old (from the 2nd statement).
If Bako was 5 years old five years ago and his mother was 30 years old... It simply means that Bako was born ten years ago when his mother was 25 years old.
This simply means that Bako's mother is older than him with 25 years.
Therefore, Bako will be 25 years old when his mother is 50 years old
