The sale price of a pillow originally priced at 12 dollars is given as follows:
$9.
How to obtain the sale price?The sale price of a pillow originally priced at 12 dollars is obtained applying the proportions in the context of the problem.
The original price is given as follows:
$12.
The markdown rate for this problem is given as follows:
25%.
Hence the sale price of a pillow originally priced at 12 dollars is given as follows:
0.75 x 12 = $9.
(markdown of 25% means that 75% of the price is paid).
Missing InformationThe complete problem is:
"A pillow was marked down at 25%. What is the sale price of a pillow originally priced at 12 dollars?"
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For the following exercises, use Figure 2 to approximate the values.
I'm lost on number 15 and 17
Answer:
15. f(-2) = 2
17. f(x) = 1 for x = ±1.7
Step-by-step explanation:
You want various values of the function and its inverse relation for f(x)=x²-2.
Reading the graphThe value of f(x) is found by locating the value x on the x-axis and following the vertical line until it intersects the graph. Find the y-coordinate of that point.
The value of x for f(x) = k is found by locating k on the y-axis and following the horizontal line to the points of intersection with the graph. The x-coordinates of the points are the values of interest. Interpolation is often required.
15. f(-2)The graph intersects the vertical line at x=-2 where y = 2.
f(-2) = 2
17. f(x) = 1The horizontal line at y=1 intersects the graph in two places, located symmetrically about the y-axis. The leftmost point is approximately (-1.7, 1). The rightmost point is approximately (1.7, 1).
x ≈ -1.7 or +1.7
__
Additional comment
The instructions are to use the figure to answer the question. We interpret that to mean that you are to read the answers from the graph.
You can also use the figure to determine the equation for the graph (part of our problem statement, above). Then you can find the solutions by using the equation.
f(x) = 1
x² -2 = 1
x² = 3
x = ±√3 ≈ ±1.732 . . . . the values for problem 17
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A store owner wishes to make a new tea with a unique flavor by mixing black tea and oolong tea. If he has 35 pounds of oolong tea that sells for $2.40 per pound, how much black tea worth $1.80 per pound must he mix with it so that he can sell the final mixture for $2.10 per pound?
Answer:
Step-by-step explanation:
To solve this problem, we can use the following formula:
(quantity of tea 1 x price of tea 1) + (quantity of tea 2 x price of tea 2) = total quantity x price of mixture
Let x be the number of pounds of black tea that the store owner needs to mix with the oolong tea.
We know that:
The store owner has 35 pounds of oolong tea that sells for $2.40 per pound.
The store owner wants to sell the final mixture for $2.10 per pound.
The black tea is worth $1.80 per pound.
Using the formula above, we can write:
(35 x 2.40) + (x x 1.80) = (35 + x) x 2.10
Simplifying this equation, we get:
84 + 1.8x = 73.5 + 2.1x
0.3x = 10.5
x = 35
Therefore, the store owner needs to mix 35 pounds of black tea with the oolong tea.
I hope this helps! Let me know if you have any other questions.
Answer:
Step-by-step explanation:
Let's assume the store owner needs to mix x pounds of black tea with the 35 pounds of oolong tea.
The cost of the oolong tea is $2.40 per pound, so the total cost of the oolong tea is:
Cost of oolong tea = 35 pounds × $2.40/pound = $84
The cost of the black tea is $1.80 per pound, and the final mixture needs to be sold for $2.10 per pound. To achieve an average price of $2.10 per pound, the total cost of the mixture should be:
Total cost of mixture = (35 + x) pounds × $2.10/pound = $73.5 + $2.10x
Since the cost of the mixture should equal the sum of the costs of the oolong and black teas, we can set up the equation:
$73.5 + $2.10x = $84
Now, let's solve for x to find the amount of black tea needed:
$2.10x = $84 - $73.5
$2.10x = $10.5
x = $10.5 / $2.10
x ≈ 5
Therefore, the store owner needs to mix approximately 5 pounds of black tea with the 35 pounds of oolong tea in order to sell the final mixture for $2.10 per pound.
Invent a data set with 7 values that has a mean of 10 and a median of 12. Draw a dot plot to represent your data set.
Data set: 6, 8, 10, 12, 14, 16, 18
To draw a dot plot representing this data set, we can place a dot above the corresponding value on a number line. Here's the dot plot:
Value |
---------------------------------
6 | o
---------------------------------
8 | o
---------------------------------
10 | o
---------------------------------
12 | o
---------------------------------
14 | o
---------------------------------
16 | o
---------------------------------
18 | o
---------------------------------
In the dot plot, each "o" represents a data point. The values are shown on the left side, and the dots are placed above their respective values on the number line.
Find the zeros of the function. Enter the solutions from least to greatest.
f(x) = (x-10)^2-49
Answer:f(x) = (x-10)^2-49
f(x) = (x-10+7)(x-10-7)
f(x) = (x-3)(x-17)
The zeros of the function are 3 and 17.
Step-by-step explanation:
Rita's school is 5 kilometers west of her house and 5 kilometers south of her friend Jayce's
house. Every day, Rita bicycles from her house to her school. After school, she bicycles from
her school to Jayce's house. Before dinner, she bicycles home on a bike path that goes
straight from Jayce's house to her own house. How far does Rita bicycle each day? If
necessary, round to the nearest tenth
A group of ten students recorded the number of minutes they spent on one math homework problem. The
mean amount of time was 9 minutes, but the MAD was 7 minutes.
Draw a dot plot to represent a data set that matches this description. Be sure to include a title and label
your axis.
1. Create a horizontal axis labeled "Time Spent on Homework Problem (Minutes)."
2. Choose an appropriate scale for the axis, such as labeling every other unit of time from 0 to 18.
3. Plot a dot for each student's data point along the horizontal axis.
4. Arrange the dots in order from smallest to largest time spent on the problem.
5. Title the dot plot to reflect the data set being represented, such as "Math Homework Problem Time Spent: Mean 9 Minutes, MAD 7 Minutes."
6. Include a legend or key if needed to clarify the meaning of the dot plot.(The dot plot is attached below)
To draw a dot plot representing a data set where the mean amount of time spent on one math homework problem is 9 minutes and the MAD is 7 minutes for a group of ten students, we can follow these steps:
The resulting dot plot may show a spread of data between 2 and 16 minutes, with more dots around the center or mean of 9 minutes and fewer dots at the tails. The MAD of 7 minutes suggests a relatively high degree of variability in the data, with some students spending significantly less or significantly more time on the math homework problem. The dot plot can help to visualize these differences and identify any potential outliers in the data.
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PLS HELP MARKING AS BRAINLIST!
Answer:
0.90
Step-by-step explanation:
You want the probability of either event A or event B given the Venn diagram shown.
ProbabilityThe probability of an event shown in the diagram is the ratio of counts for that event to the total of all counts in the diagram. That total is 50.
The number of counts that are not part of either event is shown as 5.
P(A or B) = 1 - P(not (A or B)) = 1 - 5/50
P(A or B) = 0.90
__
Additional comment
Using the given formula, ...
P(A or B) = (25+5)/50 +(15 +5)/50 -5/50 = (25 +15 +5)/50 = 45/50
P(A or B) = 0.90
<95141404393>
I need help with this!
The length AC in the kite is 8.7 cm.
How to find the side AC in the kite?A kite is a quadrilateral that has two pairs of consecutive equal sides and
perpendicular diagonals. Therefore, let's find the length AC in the kite.
Hence, using Pythagoras's theorem, let's find CE.
Therefore,
7² - 4² = CE²
CE = √49 - 16
CE = √33
CE = √33
Let's find AE as follows:
5²- 4² = AE²
AE = √25 - 16
AE = √9
AE = 3 units
Therefore,
AC = √33 + 3
AC = 5.74456264654 + 3
AC = 8.74456264654
AC = 8.7 units
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given f(x)=3x-5, solve for x when f(x)= (x-1)
Answer: Pretty sure it should be 2.
Step-by-step explanation:
maybe -2 but i dont think so
how many terms are in the following Expression 2x³-4x²+2x-x-3
In the given expression, 2x³-4x²+2x-x-3, there are five terms. An expression is a mathematical phrase that can be constructed using variables, constants, and operators.
It can include any mathematical operations such as addition, subtraction, multiplication, and division. Additionally, an expression can be made up of one or more terms.In the given expression, 2x³-4x²+2x-x-3, there are five terms. The terms are:2x³: This is the first term in the expression.
It is a cubic term, which means it has an exponent of 3.4x²: This is the second term in the expression. It is a quadratic term, which means it has an exponent of 2.2x: This is the third term in the expression. It is a linear term, which means it has an exponent of 1.-x:
This is the fourth term in the expression. It is also a linear term, but it has a negative coefficient.-3: This is the fifth term in the expression. It is a constant term since it does not have any variable attached to it.In summary, the given expression has five terms, which are 2x³, -4x², 2x, -x, and -3.
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I need help solving this please. Image is below.
The volume of the solid obtained by rotating the region enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0 about the y-axis is 288π cubic units.
To find the volume of the solid obtained by rotating the region enclosed by the given graphs about the y-axis, we can use the method of cylindrical shells.
First, let's sketch the region to visualize it better.
The region is enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0.
Let's find the intersection points of these curves by setting them equal to each other:
18 - x = 3x - 6
Simplifying the equation, we have:
4x = 24
x = 6
So, the intersection point is (6, 12).
Now, we can integrate to find the volume of the solid.
The radius of each cylindrical shell is the distance from the y-axis to the curve y = 18 - x.
This can be expressed as x.
The height of each cylindrical shell is the difference between the two curves, which is (18 - x) - (3x - 6).
The volume of each cylindrical shell is given by the formula:
V = 2πrhΔx, where r is the radius, h is the height, and Δx is the width of each shell.
Integrating from x = 0 to x = 6, we can find the total volume:
V = ∫[0,6] 2πx[(18 - x) - (3x - 6)] dx
V = ∫[0,6] 2πx(24 - 4x) dx
V = 2π ∫[0,6] (24x - 4x²) dx
V = 2π [12x² - (4/3)x³] | [0,6]
V = 2π [(12(6)² - (4/3)(6)³) - (12(0)^2 - (4/3)(0)^3)]
V = 2π [(12(36) - (4/3)(216)) - (0 - 0)]
V = 2π [(432 - 288) - (0 - 0)]
V = 2π (432 - 288)
V = 2π (144)
V = 288π
Therefore, the volume of the solid obtained by rotating the region enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0 about the y-axis is 288π cubic units.
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What is the answer pls
By translation, the images of the vertices Q and S are Q'(x, y) = (- 1, 4) and S'(x, y) = (- 3, 2).
How to find the image of a point by translation
In this problem we find the representation of a parallelogram, which is formed by four vertices. The images of the vertices can be found by means of translation, whose formula is introduced below:
C'(x, y) = C(x, y) + T(x, y)
Where:
C(x, y) - Original pointT(x, y) - Translation vector.C'(x, y) - ImageIf we know that Q(x, y) = (4, 1), S(x, y) = (2, - 1) and T(x, y) = (- 5, 3), then the images of the points are:
Q'(x, y) = (4, 1) + (- 5, 3)
Q'(x, y) = (- 1, 4)
S'(x, y) = (2, - 1) + (- 5, 3)
S'(x, y) = (- 3, 2)
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If the radius, r, of a sphere is
7
3.14 yd, what is the surface area? Use 3.14 for π. Use pencil and paper. Explain why you can use mental math.
The surface area of the sphere is about enter your response here yd2. =
The surface area of the sphere is 98 yd².
To find the surface area of a sphere, we can use the formula:
Surface Area = 4πr²
Given that the radius, r, of the sphere is 7/3.14 yd, we can substitute this value into the formula:
Surface Area = 4 x 3.14 x (7/3.14)²
= 4 x 3.14 x 49/9.86
= 4 x 49/2
= 98 yd²
Therefore, the surface area of the sphere is 98 yd².
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What is a cash cycle? explain. calculate using the following information. (assume 360 days in a year). opening balances raw material 1,00,000 wip 45,000 finishes goods 1,35,000 debtors 6,00,000 creditors 8,60,000 closing balances raw material 2,00,000 wip 65,000 finishes goods 1,25,000 debtors 5,45,000 creditors 9,75,000 costs incurred during the year manufacturing costs 11,60,000 excise duty 18,80,000 selling and distribution expenses 6,20,000 admin. overheads 2,00,000 total sales 2,01,96,800 total purchases 1,46,00,000 40% of sales are on credit and 70% of purchases are on credit
The cash cycle, also known as the operating cycle or cash conversion cycle, is a financial metric that measures the time it takes for a company to convert its investments in inventory and other resources into cash flow from sales. It provides insight into the efficiency of a company's working capital management.
The cash cycle can be calculated using the following formula:
Cash Cycle = Inventory Conversion Period + Receivables Conversion Period - Payables Conversion Period
1. Inventory Conversion Period (ICP):
ICP measures the average number of days it takes for the company to convert its raw materials into finished goods. It is calculated as:
ICP = (Average Inventory / Cost of Goods Sold) x Number of Days in a Year
Average Inventory = (Opening Inventory + Closing Inventory) / 2
Cost of Goods Sold = Total Sales - Closing Inventory
2. Receivables Conversion Period (RCP):
RCP measures the average number of days it takes for the company to collect payment from its customers. It is calculated as:
RCP = (Average Receivables / Total Sales) x Number of Days in a Year
Average Receivables = (Opening Receivables + Closing Receivables) / 2
Opening Receivables = Total Sales x Percentage of Sales on Credit
Closing Receivables = Total Sales x Percentage of Sales on Credit - Collections
3. Payables Conversion Period (PCP):
PCP measures the average number of days it takes for the company to pay its suppliers. It is calculated as:
PCP = (Average Payables / Total Purchases) x Number of Days in a Year
Average Payables = (Opening Payables + Closing Payables) / 2
Opening Payables = Total Purchases x Percentage of Purchases on Credit
Closing Payables = Total Purchases x Percentage of Purchases on Credit - Payments
Now, let's calculate the cash cycle using the provided information:
Given data:
Opening balances:
Raw material: ₹1,00,000
WIP: ₹45,000
Finished goods: ₹1,35,000
Debtors: ₹6,00,000
Creditors: ₹8,60,000
Closing balances:
Raw material: ₹2,00,000
WIP: ₹65,000
Finished goods: ₹1,25,000
Debtors: ₹5,45,000
Creditors: ₹9,75,000
Costs incurred during the year:
Manufacturing costs: ₹11,60,000
Excise duty: ₹18,80,000
Selling and distribution expenses: ₹6,20,000
Admin. overheads: ₹2,00,000
Total sales: ₹2,01,96,800
Total purchases: ₹1,46,00,000
Percentage of sales on credit: 40%
Percentage of purchases on credit: 70%
1. Calculate the Inventory Conversion Period (ICP):
Average Inventory = (Opening Inventory + Closing Inventory) / 2
Opening Inventory = Raw Material + WIP + Finished Goods
Closing Inventory = Raw Material + WIP + Finished Goods
Opening Inventory = ₹1,00,000 + ₹45,000 + ₹1,35,000 = ₹2,80,000
Closing Inventory = ₹2,00,000 + ₹65,000 + ₹1,25,000 = ₹3,90,000
Average Inventory = (₹2,80,000 + ₹3,90,000) / 2 = ₹3,35,000
Cost of Goods Sold = Total Sales - Closing Inventory
Cost of Goods Sold = ₹2,01,96,800 -
Area of a parallelogram
Find the area of this parallelogram. Be sure to include the correct unit in your answer.
16 yd
13 yd
K-12 yd →
Answer:
156yd²
Step-by-step explanation:
area of parallelogram = base X vertical height
= 12 X 13
= 156yd²
The mean rounded to the nearest 10th of the following data set is 15, 16, 17, 23, 11, 19, 20, 15, 18, 22, 15, 19
Answer:
17.5
Step-by-step explanation:
You can find the mean of a data set by adding all numbers in the data set together and dividing by the amount of numbers in the given data set.
In this case, your data set is:
15 , 16 , 17 , 23 , 11 , 19 , 20 , 15 , 18 , 22 , 15 , 19 (12 numbers).
Firstly, add all the numbers together: [tex]15 + 16 + 17 + 23 + 11 + 19 + 20 + 15 + 18 + 22 + 15 + 19 = 210[/tex]
Next, divide 210 (total sum) with the amount of terms in total (12):
[tex]\frac{(210)}{(12)} = 17.5[/tex]
17.5 is already in the tenth digit place value, and so you do not need to round.
17.5 is your answer.
~
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What complex number is represented by the polar coordinates (4, negative StartFraction pi Over 4 EndFraction).?
Answer:
The complex number represented by the polar coordinates (4, -π/4) is 4(cos(-π/4) + i*sin(-π/4)).
d) √√(x²y²) = i. xy ii. xy² iii. x²y iv. x4y4
The expression √(x²y²) when simplified is i. xy
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
√(x²y²)
When the expression is expanded, we have
√(x²y²) = √(x² * √(y²)
Evaluae the exponents in the expression
So, we have
√(x²y²) = x * y
Evaluae the products in the expression
So, we have
√(x²y²) = xy
Hence, the expression when simplified is i. xy
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9. Difference between the place values of "1" in 3116365 is
Isosceles trapezoid 3 The minor base, the height and oblique side of a trapezoid isosceles measure respectively 34 m. 20m and 29m. Calculate the perimeter and area of the trapezius.
The perimeter of the trapezoid is 106 meters.
The area of the trapezoid is 1360 square meters.
To calculate the perimeter and area of an isosceles trapezoid, we need to use the given measurements:
The length of the minor base (34 m), the height (20 m), and the length of the oblique side (29 m).
First, let's calculate the length of the major base (the other parallel side). In an isosceles trapezoid, the major base and minor base have the same length.
So, the length of the major base is also 34 m.
The perimeter of a trapezoid is the sum of all its sides. In this case, the perimeter can be calculated as follows:
Perimeter = length of minor base + length of major base + 2 × length of oblique side
Perimeter = 34 m + 34 m + 2 × 29 m
Perimeter = 34 m + 34 m + 58 m
Perimeter = 106 m
To calculate the area of the trapezoid, we can use the formula:
Area = (sum of the lengths of the bases) × height / 2
Area = (34 m + 34 m) × 20 m / 2
Area = 68 m × 20 m / 2
Area = 1360 m²
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HELP! Can someone please help with the picture question below?
The probability that either event A or B will occur is 11/17.
We have,
The Addition Rule for Probability:
P(A U B) = P(A) + P(B) - P(A ∩ B),
where P(A U B) represents the probability of the union of events A and B, P(A) represents the probability of event A, P(B) represents the probability of event B, and P(A ∩ B) represents the probability of the intersection of events A and B.
Now,
P(A) = 9/17
P(B) = 2/17
There is no intersection of Q and B so,
P(A ∩ B) = 0
Now,
P(A U B) = P(A) + P(B) - P(A ∩ B),
Substituting the values.
P(A U B) = The probability that either event A or B will occur.
So,
P(A U B)
= 9/17 + 2/17 - 0
= 11/17
Thus,
The probability that either event A or B will occur is 11/17.
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uck onto the tin has a height of 8 cm. 2.1 Calculate the area of sheet metal needed to make a soup tin. 2.2 Calculate the total surface area of the label. Use the formula: TSA = 2 × x radius x height where π = 3,142 2.3 Tins of butternut soup are tightly packed into boxes, with 4 tins fitting in the width of the box, and 5 tins fitting in the length of the box as shown in the diagrams. What are the dimensions (length and breadth) of the box? 7 4 1f thin box
The dimensions (length and breadth) of the box are 10r x 8r.
We are given that;
π = 3,142
Number of tins=4,5
Now,
To calculate the area of sheet metal needed to make a soup tin, we can use the formula for surface area of a cylinder which is given by:
Surface Area = 2πrh + 2πr^2
where r is the radius of the cylinder and h is the height of the cylinder.
Using the given values, we can calculate the surface area of the soup tin as follows:
Surface Area = 2π(4.5)(8) + 2π(4.5)^2 Surface Area = 226.08 cm^2
To calculate the total surface area of the label, we can use the formula for surface area of a cylinder which is given by:
Surface Area = 2πrh
where r is the radius of the cylinder and h is the height of the cylinder.
Using the given values, we can calculate the surface area of the label as follows:
Surface Area = 2π(4.5)(8) Surface Area = 226.08 cm^2
To find out the dimensions (length and breadth) of the box in which tins are packed, we can use the given information that 4 tins fit in the width of the box and 5 tins fit in the length of the box. Let’s assume that each tin has a diameter of d cm.
4d = width of box 5d = length of box
We know that diameter (d) = 2r where r is radius.
So, width of box = 4d = 8r length of box = 5d = 10r
Therefore, by the area the answer will be 10r x 8r.
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quadratic cccccccccccccccccccccccc
Answer: -3 and -17
Step-by-step explanation:
When completing the square we add and subtract [tex]\frac{b}{2} ^2[/tex] in the form ax² + bx + c.
[tex]\frac{b}{2} ^2 = \frac{-6}{2} ^2=(-3)^2=9[/tex]
x² - 6x - 8 = (x - __)² - __
(x² - 6x) - 8 = (x - __)² - __
(x² - 6x + 9) - 8 - 9 = (x - __)² - __
(x - 3)² - 17 = (x - __)² - __
The blanks are 3 and 17.
The following is a trapezoid. Find Angle XWZ, Angle XMY, and Angle YMZ
According to the figure of the trapezoid
angle XMZ = 115 degrees
angle XMY = 102 degrees
Angle YMZ = 78 degrees
How to find the missing anglesThe given figure is an isosceles trapezoid, hence
angle XMZ + angle XYZ = 180
angle XYZ = 39 + 26 = 65
angle XMZ + angle XYZ = 180
angle XMZ = 180 - 65
angle XMZ = 115 degrees
angle XMY
angle XMY = 180 - 39 - 39 = 180 - 78 = 102 degrees
Angle YMZ + angle XMY = 180 (angle on a straight line)
Angle YMZ = 180 - angle XMY = 180 - 102 = 78 degrees
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Solve the system with elimination.
-2x + 7y =10
x - 3y = -3
Answer:
x = 9 and y = 4
Step-by-step explanation:
-2x + 7y = 10 (call this equation '1')
x - 3y = -3 (call this '2')
multiply '2' by 2:
2x - 6y = -6 (call this '3')
add '1' and '3':
(-2x + 7y = 10) + (2x - 6y = -6)
0x + y = 4
y = 4
sub that back into '1':
-2x + 7y = 10
-2x + 7(4) = 10
-2x + 28 = 10
-2x = 10 - 28 = -18
x = -18/-2 = 9
sub both y = 4 and x =9 into '2' to check if everything adds up:
x - 3y = -3
9 - 3(4) = 9 - 12 = -3
so x = 9 and y = 4
Assume lines n and m are parallel. If μ(∠)1=147°
, find the following angle measures. (Type each answer as a number, in the corresponding blank below.)
The angle measures of the numbered angles from <1- 8 would be listed below as follows:
<1=147°
<2= 33°
<3= 147°
<4=33°
<5=33°
<6=147°
<7=33°
<8=147°
How to determine the measures of the missing angles?When two parallel lines a crossed by a transverse line then the following occurs:
the pair of corresponding angles is equal. That is <2=<4the pair of interior alternate angles is equal. That is; <6=<3 and <2=<7the pair of exterior alternate angles is equal. That is;<1=<8,<5=<4interior angles on the same side of transversal are supplementary.That is; <2+<3=180°Learn more about parallel lines here:
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For the following exercises, find (f x g)(x) and (g x f)(x) for each pair of functions.
f(x)=√x+2, g(x)=1/x
(f x g)(x) = √(1/x + 2)
(g x f)(x) = 1/(√(x + 2))
To find (f x g)(x), we need to evaluate the composition of functions f and g, which is denoted as f(g(x)).
Similarly, to find (g x f)(x), we need to evaluate the composition of functions g and f, which is denoted as g(f(x)).
Let's calculate (f x g)(x) and (g x f)(x) for the given pair of functions f(x) = √(x + 2) and g(x) = 1/x:
1. (f x g)(x):
We start by substituting g(x) into f(x) wherever we see an x in f(x):
(f x g)(x) = f(g(x)) = f(1/x)
Substitute 1/x into f(x):
(f x g)(x) = f(g(x)) = f(1/x) = √(1/x + 2)
2. (g x f)(x):
We start by substituting f(x) into g(x) wherever we see an x in g(x):
(g x f)(x) = g(f(x)) = g(√(x + 2))
Substitute √(x + 2) into g(x):
(g x f)(x) = g(f(x)) = g(√(x + 2)) = 1/(√(x + 2))
Therefore, we have:
(f x g)(x) = √(1/x + 2)
(g x f)(x) = 1/(√(x + 2))
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Given PR = RQ, find the measure of arc RQ and the Measure of arc PQ.
12. mRQ=
13. mPQ=
The measure of LABD = 11x - 3 and mZACD = 8x + 15. Find the following:
112
14. x=
15. mLABD =
17
16. m AD =
3/11
110'
(11x-3) B
E
(8x + 15)*
Please show work
Answer:
x = 8
Step-by-step explanation:
Intersecting tangent and secant theorem:
If a tangent and a secant are drawn to the circle from a point from outside, the square of the measure of the tangent is equal to the product of the measures of the secant segment and its external secant segment.
x² = (4+12)*4
x² = 16 * 4
x² = 64
x = √64
x = 8
Consider a hemisphere with a diameter of 12 mm. Find the volume of the hemisphere in terms of π.
Hello !
Answer:
[tex]\boxed{\sf V_{hemisphere}=144\pi\ mm^3}[/tex]
Step-by-step explanation:
The volume of a sphere is given by the following formula : [tex]\sf V_{sphere}=\frac{4}{3}\pi r^3[/tex] where r is the radius.
Moreover, we know that the volume of a hemisphere is half the volume of a sphere : [tex]\sf V_{hemisphere}=\frac{1}{2} V_{sphere}[/tex]
We obtain : [tex]\sf V_{hemisphere}=\frac{2}{3}\pi r^3[/tex]
Given :
d = 12mm[tex]\sf r=\frac{1}{2} d=\frac{12}{2} \\\underline{\sf r=6mm}[/tex]
Let's substitue r with it value in the previous formula :
[tex]\sf V_{hemisphere}=\frac{2}{3} \pi\times 6^3\\\boxed{\sf V_{hemisphere}=144\pi\ mm^3}[/tex]
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In the early stages of building the Hoover Dam diversion tunnels were built to divert the flow of water away from the main construction site. Each diversion tunnel was cylindrical with a radius of 56 feet and a length of 4,000 feet. Find the volume and surface area of a diversion tunnel.
Answer:
Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.
Step-by-step explanation:
To find the volume and surface area of a diversion tunnel, we can use the formulas for the volume and lateral surface area of a cylinder.
The volume of a cylinder is given by the formula:
V = πr^2h
Where:
V is the volume,
π is a mathematical constant approximately equal to 3.14159,
r is the radius of the cylinder, and
h is the height (or length) of the cylinder.
Substituting the given values:
r = 56 feet
h = 4,000 feet
V = π(56^2)(4,000)
V ≈ 3.14159 * 56^2 * 4,000
Calculating the volume:
V ≈ 9,839,916,800 cubic feet
The surface area of the lateral (curved) part of a cylinder is given by the formula:
A = 2πrh
Where:
A is the surface area,
π is a mathematical constant approximately equal to 3.14159,
r is the radius of the cylinder, and
h is the height (or length) of the cylinder.
Substituting the given values:
r = 56 feet
h = 4,000 feet
A = 2π(56)(4,000)
A ≈ 2 * 3.14159 * 56 * 4,000
Calculating the surface area:
A ≈ 1,000,530.9 square feet
Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.