88 is the measure of arc BC.
What is arc ?
In general, an arc is any smooth wind joining two points. The length of an arc is known as its arc length. In a graph, a graph arc is an ordered brace of conterminous vertices. In particular, an arc is any portion( other than the entire wind) of the circumference of a circle.
An arc is the term used to describe the convex area of a circle that curves away from an angle like this, between two line segments or rays. A circle's circumference, or outside border, is known as the arc's circumference, and it is this area that is measured when an arc is drawn along it.
DE ≅ BC
3x + 22 = 4x
4x - 3x = 22
x = 22
BC = 4X = 4 * 22
= 88
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Please help me quick
[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{V_{(cylinder) } = \pi\:r^2\:h \: cubic \:units }\\[/tex]
Where -
V= Volume of cylinder π = [tex]\sf\dfrac{22}{7} [/tex]= 3.1416..........r = Radius of cylinder. h = Height of cylinder.As per question, we are given that-
V= 1800 in³ r = 7 inchπ =3.14Now that, we are given all the required values, so we can put all the values into the formula and solve for the height -
[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{Volume _{(cylinder) } = \pi\:r^2\:h }\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf 1800= 3.14 \times \bigg(7\bigg)^2 \times h\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf 1800 = 3.14 \times 7\times 7\times h\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf 1800 =3.14 \times 49 \times h\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf 1800 =153.86\times h\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf 153.86\times h=1800\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf h = \dfrac{1800}{153.86}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf h = 11.69894...........\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{ h =11.69\: inch }\\[/tex]
Therefore, the length of height [tex] \sf \underline{ \pink{11.69\: inch }}\\[/tex]
Two forces of 8.6 newtons and 3.5 newtons act simultaneously on an object. The angle between the two forces is 58°. Find the magnitude of the resultant, to the nearest 10th of a newton.
Hence, the force that results has a magnitude of about 10.3 newtons (rounded to the nearest 10th of a newton).
What does magnitude imply?"How much of a quantity" is the definition of magnitude. For instance, the amount of data can be utilized for assessing the speeds of a car and a bicycle. In addition, it can be used to express how far an object has come or how much weight it carries relative to its size.
The law of cosines, which connects a triangle's sides and angles, can be used to calculate the size of the resulting force:
A2 + B2 - 2ab*cos = C2 (C)
We can define the 8.6 newtons in this case as side a, the 3.5 newtons as side b, and the angle between them as C:
a = 8.6 N b = 3.5 N
C = 58°
By applying the law of cosines, we may determine the length of the resultant force or side c.
c = sqrt(105.36)
c ≈ 10.3
Hence, the force that results has a magnitude of about 10.3 newtons (rounded to the nearest 10th of a newton).
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Would I be able to get some help with question 9
a. The direction vector of the line given by x=1/3+2t, y=3-2/3t is (2,-2/3).
The point on the line by setting t=0, gives us the point (1/3,3).
b. The direction vector of the line given by r=(1/3,1/2)+t(1/3-1/4) is
(1/12,0).
The a point on the line by setting t=0 gives us the point (1/3,1/2).
c. The direction vector of the line given by r=(1/2,3)+t(-1/2,5) is (-1/2,5).
The point on the line by setting t=0, which gives us the point (1/2,3).
What is a vector?A vector is described as a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.
The vector equation defines the placement of the line or a plane in the three-dimensional framework.
The vector equation of a line is r = a + λb, and the vector equation of a plane is r x n = d.
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URGENT PLEASE HELP!! I WILL MARK BRAINLIEST THE BEST ANSWER PLEASEE WORTH LOTS OF POINTS!!
Geometry: Circle Dilations
For problem 3, Noah created the following diagram: (image provided)
He then made the following measurements and calculations:
- He calculated the ratio OB/OA=2.25
- He measured the perimeter of triangle ARG, And found it to be 4.4 cm.
- he measured angle RAG =180゚
- He calculated the area of triangle ARG, and found it to be 0.8 cm squared
- He calculated the circumference of circle A, and found it to be approximately 8.13 cm.
He would now like to calculate corresponding values for the triangle in the larger circle, and he needs your help.
Calculate the following, using your knowledge that all circles are similar, along with the data already collected by Noah.
1. Find the perimeter of triangle BSH
2. Find the measure of angle SBH
3. Find the area of triangle BSH
4. Find the length of the circumference of circle B
1. Perimeter of AARG = 1.6 × 4.4 cm = 7.04 cm
2. The measure of SBH is 162°.
3. Area of AARG = 2.56 × 0.8 cm² = 2.048 cm²
4. The length of the circumference of circle B is approximately 13.01 cm.
What is perimeter ?The circumference of a this double shape's perimeter is its total length. In other terms, it is the total length of all a shape's sides. For instance, the circumference of a circle is equal to the distance around its outside, or circumference, whereas the perimeter of a rectangle may be computed by combining the measurements of all four sides.
To solve this problem, we can use the fact that all circles are similar. This means that corresponding lengths of the circles are proportional. In particular, if the ratio of the radii of two circles is k, then the ratio of their circumferences is also k, and the ratio of their areas is k².
Let's start with finding the radius of the larger circle. Since OB/OA = 2.25, we can write:
OA + AB = OB
OA + 1 = 2.25 OA
OA = 1 / 1.25 = 0.8
Therefore, the radius of the larger circle is 0.8 cm. Since the circles are similar, the ratio of the radii is 0.8/0.5 = 1.6.
1. The perimeter of ABSH is proportional to the radius of the circle, so we have:
Perimeter of ABSH = 1.6 × Perimeter of AARG = 1.6 × 4.4 cm = 7.04 cm
2. Let x be the measure of SBH. Then we have:
RAG + SBH + HBS = 360°
108° + x + 90° = 360°
x = 162°
Therefore, the measure of SBH is 162°.
3. The area of ABSH is proportional to the square of the radius of the circle, so we have:
Area of ABSH = 1.6² × Area of AARG = 2.56 × 0.8 cm² = 2.048 cm²
4. The circumference of circle B is proportional to the radius of the circle, so we have:
Circumference of circle B = 1.6 × Circumference of circle A ≈ 1.6 × 8.13 cm ≈ 13.01 cm
Therefore, the length of the circumference of circle B is approximately 13.01 cm.
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Percy's town had a recycling drive last weekend. 5,320 of the residents of the town participated and 1,680 did not. What percentage of the residents of Percy's town participated in the recycling drive?
Answer:
To find the percentage of residents who participated in the recycling drive, we need to divide the number of participants by the total number of residents and then multiply by 100 to get the percentage. Total number of residents in Percy's town = 5,320 + 1,680 = 7,000 Number of residents who participated = 5,320 Percentage of residents who participated = (Number of participants / Total number of residents) x 100 = (5,320 / 7,000) x 100 = 76% Therefore, 76% of the residents of Percy's town participated in the recycling drive.
Answer:
The correct answer is 76%.
Step-by-step explanation:
To find the percentage of Percy's town that participated in the recycling drive, we must divide the number of people that participated by the total number of residents.
To do this, we should first find the total number of residents. Since residents either participated or did not participate, the total number of residents is the sum of these two values. This is modeled below:
Total number of residents = 5,320 + 1,680 = 7,000 total residents
Now, we can continue with the percentage calculation.
% participation = # of participants/# of residents * 100
% participation = 5,320/7,000 * 100
% participation = 76%
Therefore, we can conclude that 76% of Percy's town participated in the recycling drive.
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the distance between single-family residences in the new desert vista subdivision in mesa is 30 feet. what is the distance known as in subdivision development terms?
The 30-foot distance between single-family residences in the Desert Vista subdivision is called a "setback" in development terms.
This setback ensures that the neighborhood maintains adequate spacing between homes for privacy, safety, and aesthetics.
The distance between single-family residences in the new Desert Vista subdivision in Mesa is known as the "setback" in subdivision development terms.
Setbacks are regulations that define the minimum distance a building, such as a single-family residence, must be located from property lines or other structures.
These regulations ensure adequate spacing between buildings for various reasons, including privacy, safety, and aesthetics.
1. The student question mentions that the distance between single-family residences in the new Desert Vista subdivision in Mesa is 30 feet.
2. In subdivision development terms, such a distance is referred to as a "setback."
3. Setbacks are important for maintaining privacy, safety, and aesthetics in a neighborhood.
4. These regulations ensure that there is enough space between buildings, preventing overcrowding and allowing for proper ventilation, sunlight, and access to emergency services.
5. Setbacks vary depending on the type of structure and local zoning laws, which determine the minimum distance required between buildings.
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What is the measure of AB?
Answer:
The answer is 22
Step-by-step explanation:
You would first start by solving for the x value. You would do 6x-7=2x+5, then start factoring out number and variable until the variable is on 1 side and the number are on the other, so it'd be 4x=12. After you would calculate for the x which is 3, which you did, then you would plug that back into the values. You'd plug 3 into 2(x)+5 which simplifies down to 6+5 which is 11 and since DB is half of AB you multiply by 2 to get 22.
the nebraska license plate has 6 characters, each one filled with a number (0-9) or a letter. how many license plates are possible?
The number of possible license plates is 2,176,782,336
To calculate the number of possible Nebraska license plates with 6 characters, we will use the counting principle.
Each character can either be a number (0-9) or a letter (A-Z). There are 10 possible numbers and 26 possible letters. So, for each character,
there are [tex]36 (10 + 26)[/tex]possibilities.
Now, we will apply the counting principle to find the total number of combinations. The counting principle states that if there are n ways to do one thing and m ways to do another, there are n * m ways to do both.
In our case, there are 6 characters on the license plate, and each character has 36 possible options.
Therefore, the number of possible license plates is:
[tex]36 * 36 * 36 * 36 * 36 * 36 = 36^6 = 2,176,782,336[/tex]
There are 2,176,782,336 possible Nebraska license plates with 6 characters, each filled with a number (0-9) or a letter (A-Z).
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On June 1, Marika’s Cards and Gifts had 117 birthday cards on hand. Over the month, Marika’s sold 208 of this type of card and received two orders from the distributor, each for 144 cards. The cost of birthday cards to Marika’s is $0.56 each. What is the value of the inventory at the end of the month?
Since the cost of each card is $ [tex]0.56[/tex], you can now multiply the total number of cards by the cost per card. the value of the inventory at the end of the month is $ [tex]343.28[/tex].
What is the value of the inventory?To find the value of the inventory at the end of the month, you need to start by calculating the total number of birthday cards that Marika's Cards and Gifts had at the end of the month.
First, you need to add the number of birthday cards that Marika's sold during the month (208) to the number of cards received from the distributor in two separate orders) [tex](144 \times 2) = 288[/tex]
[tex]117[/tex] (initial inventory) + [tex]208[/tex] (cards sold) + [tex]288[/tex] (cards received from distributor) = [tex]613[/tex] (total number of birthday cards at the end of the month)
Since the cost of each card is $0.56, you can now multiply the total number of cards by the cost per card to get the value of the inventory:
[tex]613 \times[/tex] $[tex]0.56 =[/tex] $[tex]343.28[/tex]
Therefore, the value of the inventory at the end of the month is $343.28.
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HELP!
Follow this link to view Jamie’s work. Critique Jamie’s work by explaining the reasonableness of the scenario and the accuracy of the two parts of the graph he described . For any portion of Jamie’s response in which he has made an error, provide and explain an alternative response.
To enhance Jamie’s explanation, describe both sections of the piecewise function using linear equations. Include any limits to the domain.
The given graph is an illustration of a piecewise linear equation.
Jamie correctly described what the graph could be used for (a relay race)
Jamie wrongly described the axes of the graph, in both sections
The piece-wise function is: [tex]y=\left \{ {{\frac{1}{12}x, 0 < = x < 12} \atop {\frac{1}{8}x+\frac{1}2},12 < x < =20}} \right.[/tex]
See the attachment for the graph and Jamie's work
From the graph, we have:
Time (minutes) = x
Distance (miles) = y
(a) When the runner begins the race
From the graph, we have:
x=[0,12]
y=[0,1]
This means that the runner runs a distance of 1 mile in 12 minutes
So; Jamie's description here is wrong because he misrepresented the axes.
The equation of this part is calculated as follows:
Start by calculating the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{1-0}{12-0}=\frac{1}{12}[/tex]
The equation is then calculated using:
[tex]y=m(x-x_1)+y_1\\\\y=\frac{1}{12}(x-0)+0\\\\y=\frac{1}{12}x[/tex]
(b) When his partner takes over
From the graph, we have:
x=(12,20]
y=(1,2]
This means that his partner runs a distance of 1 mile in 8 minutes
So; Jamie's description here is also wrong because he misrepresented the axes, again.
The equation of this part is calculated as follows:
Start by calculating the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{20-12}=\frac{1}{18}\\\\y=\frac{1}{8}(x-12}+1\\\\y=\frac{1}{8}x-\frac{1}{2}[/tex]
Hence, the piece-wise function can be represented as:
The piece-wise function is: [tex]y=\left \{ {{\frac{1}{12}x, 0 < = x < 12} \atop {\frac{1}{8}x+\frac{1}2},12 < x < =20}} \right.[/tex]
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find all unknown measures in the triangle
Therefore , the solution of the given problem of triangle comes out to be C is an 80-degree angle.
What precisely is a triangle?If a polygon has at least one additional segment, it is a hexagon. Its structure is a simple rectangle. Something like this can only be distinguished from a regular triangular form by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.
Here,
We can use the knowledge that a triangle's total angles equal 180 degrees to determine the missing angle measurements in the given triangle.
Angle A:
=> Angle A = 180 - (90 + 45) = 45 degrees
Angle B:
=> Angle B = 180 - (90 + 35) = 55 degrees
Angle C:
=> Angle C = 180 - (45 + 55) = 80 degrees
As a result, the triangle's sides' measurements are as follows:
=> A is a 45 degree angle.
=> B is a 55 degree angle.
=> C is an 80-degree angle.
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AB and CD are arcs of point 0. AB and CD intersect at point J. 17). If AJ = 9, BJ = 8, and CJ = 6, then CD = ____. 18). If AJ = x, BJ = x + 5, and CJ = DJ = x + 2, find the value of x. Please help I need it.
Using the intersecting chords theorem the value of x is 4.
What is chord?
It is the straight line segment that intersects the circle at two points, and it can be of any length or orientation, as long as it lies entirely within the circle.
According to question:17) Using the intersecting chords theorem, we have:AJ * BJ = CJ * DJ
Substituting the given values, we get:
9 * 8 = 6 * CD CD = (9 * 8) / 6CD = 12
Therefore, CD = 12.18)
Again, using the intersecting chords theorem, we have:
AJ * BJ = CJ * DJ
Substituting the given values, we get:
x * (x + 5) = (x + 2) * (x + 2)
Expanding the right-hand side, we get:
x² + 5x = x² + 4x + 4Subtracting x² and 4x from both sides
, we get:x = 4
Therefore, the value of x is 4.
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a hemispherical tank has a radius of 13ft . given that the water weighs is 62.5lb/ft3 , find the work required to pump the water out of the tank.
The work required to pump the water out of the hemispherical tank is 5,930,818.125 ft-lb.
To find the work required to pump the water out of the hemispherical tank, we need to consider the following steps:
Step 1: Determine the volume of the hemispherical tank.
The formula for the volume of a hemisphere is (2/3)πr³,
where r is the radius.
Given the radius is 13 ft, we can calculate the volume as follows:
Volume = (2/3)π(13³)
= (2/3)π(2197)
= 14603.86 ft³.
Step 2: Calculate the weight of the water in the tank.
Given the water weighs 62.5 lb/ft³, we can determine the weight of the water in the tank by multiplying the volume by the water weight:
Water weight = Volume × Weight/ft³
= 14603.86 ft³ × 62.5 lb/ft³
= 912741.25 lb.
Step 3: Determine the average height at which the water must be pumped out.
Since the tank is hemispherical, the average height for pumping the water is half the radius (13 ft).
So, the average height is:
Average height = 13 ft ÷ 2 = 6.5 ft.
Step 4: Calculate the work required to pump the water out of the tank.
Work = Weight × Distance × Force of gravity.
where Force of gravity = 1 (as we're working with pounds and feet, the force of gravity is already accounted for).
Work = 912741.25 lb × 6.5 ft × 1 = 5930818.125 ft-lb.
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if the median of a set of scores is greater than the mean, what can be said about the distribution? group of answer choices leptokurtic negatively skewed positively skewed platykurtic
If the median of a set of scores is greater than the mean, then the distribution will be option (c) It is positively skewed.
The relationship between the median and mean of a distribution can give an indication of the shape of the distribution. If the median is lower than the mean, it suggests that the distribution is positively skewed.
Option a) It is leptokurtic refers to the degree of peakedness of the distribution, which is not directly related to the relationship between the median and mean.
Option b) It is platykurtic refers to a distribution that has less peakedness than a normal distribution, which is also not directly related to the relationship between the median and mean.
Option d) It is negatively skewed is the opposite of the correct answer and suggests that the median is higher than the mean, indicating a negatively skewed distribution.
Therefore, the correct option is (c) It is positively skewed.
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The given question is incomplete, the complete question is:
If the median of a set of scores is lower than the mean, what does that suggest about the shape of the distribution?
Group of answer choices
a) It is leptokurtic
b) It is platykurtic
c) It is positively skewed
d) It is negatively skewed
Plssssss!!!! Help SOLVE FOR Y!!!!!!
Answer:
y = 23 degrees
Step-by-step explanation:
115° and 5y° are equal because they are alternate exterior angles
115 = 5y
Divide by 5 to isolate the y
23 = y
so y is 23°
A Cap is discounted at 25% off. The original price is $60.
What is the sales price?
O $40
O $50
O $45
O $30
Answer:
It's 45.
Step-by-step explanation:
Same as the last question :)
can someone help with question c and do step by step thank u
Therefore, the equation of the line passing through (0, -3) and (5, -3) is y = -3.
What is equation?An equation is a mathematical statement that shows the equality between two expressions. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equals sign (=) and can be manipulated in various ways to find the value of the variable(s) that satisfies the equation.
Here,
To find the equation of the line passing through two points (x₁, y₁) and (x₂, y₂), we can use the point-slope form of a linear equation, which is:
y - y₁ = m(x - x₁)
where m is the slope of the line.
In this case, the two points are (0, -3) and (5, -3), so we have:
x₁ = 0, y₁ = -3
x₂ = 5, y₂ = -3
The slope of the line can be found using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the values, we get:
m = (-3 - (-3)) / (5 - 0)
m = 0 / 5
m = 0
Since the slope m is zero, the line is a horizontal line.
To find the equation of the line, we can use the point-slope form with one of the points, say (0, -3). Substituting the values, we get:
y - y₁ = m(x - x₁)
y - (-3) = 0(x - 0)
y + 3 = 0
y = -3
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What is the area of a right triangle with a height of sixteen and three-fourths meters and a base of 45 meters?
The area of a right triangle is given by the formula:
Area = 1/2 * base * height
Substituting the values given in the problem:
Area = 1/2 * 45 meters * 16 and 3/4 meters
To simplify the computation, we convert the mixed fraction 16 and 3/4 to an improper fraction:
16 and 3/4 = (16 * 4 + 3) / 4 = 67/4 meters
Substituting this value, we get:
Area = 1/2 * 45 meters * 67/4 meters
Simplifying:
Area = 843.75 square meters
Therefore, the area of the right triangle is 843.75 square meters.
Answer: 376 7/8
Step-by-step explanation: if you multiply the base and the height you'll get 754 3/4 since this is a triangle we are talking about it would be halved which would make it 376 7/8.
and im doing the exam and its correct.
on a monday a friend says he will meet you again in 31 days. what day of the week will that be? sunday monday tuesday wednesday thursday friday saturday
If someone says they will meet you again in 31 days on a Monday, then that meeting would occur on a week day of Thursday. so, the correct answer is E).
To determine the day of the week that is 31 days from a Monday, we can use the fact that there are seven days in a week. Since 31 is not evenly divisible by 7, we cannot simply add or subtract a certain number of days to find the day of the week.
Instead, we must use modular arithmetic. Specifically, we can take the remainder of 31 divided by 7, which is 3. This means that after 31 days, we will be three days ahead of Monday, so the day will be Thursday. Therefore, the day of the week that is 31 days from a Monday is Thursday. So, the correct option is E).
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I NEED HELP ON THIS ASAP!!!!
Horace says that he determined the area of Rectangle ABCD by determining the product (CD) (CB). Bernice says that Horace is incorrect because he needs to use the base of the rectangle and that the base is AB, not CD. Horace responded by saying that CD is one of the bases. Who’s correct? Explain your reasoning.
Answer:
Horace
Step-by-step explanation:
You want to know if "base" refers to any particular side of a rectangle.
Area formulaThe formula for the area of a rectangle can be written ...
Area = base × height
It can also be written ...
Area = length × width
In each formula, the factors of the area refer to orthogonal dimensions of the rectangle. Any side of the rectangle can be considered to be the "base" or the "length" or the "width" or the "height". The other factor in the area formula is whatever dimension is orthogonal to that choice.
Properties of arithmeticThe commutative property of multiplication tells you that you get the same product if you reverse the order of the numbers.
So, you could have ...
Area = AB·BC
or
Area = BC·AB
If you insist that the fist of these numbers is the "base", then the base can be either AB or BC and the area will be the same.
The substitution property of equality tells you that you can substitute any equal values. Opposite sides of a rectangle are equal length, so either can be substituted for the other. In short, you can write the product for the area any of 8 ways:
Area = AB·BC = AB·AD = BC·AB = AD·AB
= CD·AD = CD·BC = AD·CD = BC·CD
If you want to distinguish between AB and BA, you can write this many more ways.
Horace seems to understand the fundamental interchangeability of the dimensions in the area formula. Horace has the right idea.
Bernice seems more attached to one particular understanding. We wonder what Bernice would call the "base" if the rectangle were drawn at a different angle to the grid.
COMPARING METHODS In Exercises 27-32, tell whether you would use the Law of Sines, the Law of Cosines, or the Pythagorean Theorem (Theorem 9.1) and trigonometric ratios to solve the triangle with the given information. Explain your reasoning. Then solve the triangle.
what is the value of 16^1/2?
A. 2
B. 4
C. 8
D. 32
Answer: 8
Step-by-step explanation:
YALLL I NEED HELP PLS
Volume of the award is 510.25 square centimeter.
Define volumeVolume is a measure of the amount of space that a three-dimensional object occupies. It is a physical quantity that is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³).
The volume of an object is calculated by multiplying its three dimensions together. For example, the volume of a rectangular prism can be calculated by multiplying its length, width, and height. The formula for the volume of a rectangular prism is V = l x w x h, where V is the volume, l is the length, w is the width, and h is the height.
Given;
Height of the conical part, h=12cm
Radius of the conical part, r=5cm
Height of the cylindrical part, H=2.5cm
Total volume of award=Volume of conical part+ Volume of cylindrical part
=πr²h/3+πr²H
=π×5²×12/3+π×5²×2.5
=314+196.25
=510.25cm²
Hence, volume of the award is 510.25 square centimeter.
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Ariel got a job at a restaurant and needed to purchase black dress pants and red shirts to work there. She found shirts she liked for $7.50 each and pants she liked for $18. She needs at least 2 shirts, at least 2 pairs of pants, and wants to spend no more than $150.
Ariel got a job at a restaurant and needed to purchase 2 shirts and 2 pairs of pants.
Let's use the variable "x" to represent the number of shirts Ariel buys and "y" to represent the number of pants she
buys.
Then, we can write the following system of inequalities:
2 ≤ x ≤ ∞ (Ariel needs at least 2 shirts)
2 ≤ y ≤ ∞ (Ariel needs at least 2 pairs of pants)
7.50x + 18y ≤ 150 (Ariel wants to spend no more than 150)
Now, we can graph the system of inequalities on a coordinate plane to find the feasible region, which represents all the possible combinations of shirts and pants that satisfy the given constraints.
The feasible region is shaded in the graph below:
graph {(150-7.5 × x)/18}
As you can see from the graph, the feasible region is a quadrilateral with vertices at (0, 8.33), (2, 7), (8, 3), and (25, 0).
This means that Ariel can buy any combination of shirts and pants within this region and still meet her requirements.
To find the optimal solution, we can simply check the corner points of the feasible region and see which combination gives us the most value for our money.
For example, if Ariel buys 2 shirts and 2 pants (i.e., the point (2, 2) on the graph), she will spend:
7.50(2) + 18(2) = 51
This is within her budget of 150 and meets her requirement of at least 2 shirts and 2 pants.
Therefore, the answer is: Ariel should buy 2 shirts and 2 pairs of pants.
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Arianna ate 0.45 of the grapes and Alex at 35% of them if there were 18 grapes left how many were in the container at first
There were 90 grapes in the container at first.
What is the percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
Let's assume that there were x grapes in the container at first.
Arianna ate 0.45 of the grapes, which means she ate 0.45x grapes.
Alex ate 35% of the grapes, which means he ate 0.35x grapes.
The total number of grapes eaten is the sum of what Arianna and Alex ate:
0.45x + 0.35x = 0.8x
This means that 0.8x grapes were eaten, and the number of grapes left is x - 0.8x = 0.2x.
We know that there were 18 grapes left, so we can set up an equation:
0.2x = 18
Solving for x, we get:
x = 90
Therefore, there were 90 grapes in the container at first.
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Keith will rent a car for the weekend. he can choose one of two plans. the first plan has an initial fee of $53.98 and cost an additional 0.13 per mile driven. the second plan has an initial fee of $67.98 and cost an additional 0.11 per mile driven. how many miles would Keith need to drive for the two plans to cost the same
(Using trig to find a side)
Solve for x. Round to the nearest tenth, if necessary.
Value of hypotenuse x in the triangle is 9.4.
Define trigonometric functionA trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of the sides of the triangle. The sine, cosine, and tangent functions—abbreviated as sin, cos, and tan, respectively—are the three most used trigonometric operations. Other trigonometric functions include the cosecant (csc), secant (sec), and cotangent (cot) functions. These functions are used extensively in mathematics, science, and engineering to model periodic phenomena, such as sound and light waves, and to solve problems related to geometry and trigonometry.
Given triangle is right angled triangle.
base of triangle=8
hypotenuse of triangle=x
Using trigonometric function,
Cosθ=base/Hypotenuse
For θ=30°,
Cos32°=b/h
cos32°=8/x
x=8/cos32°
x=8/0.84
x=9.4
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PLEASE HELP QUICKLY!!!
Answer:
tanx= -1 is the correct answer.
Determine if the following triangles are similar by AA, SAS, SSS or Not Similar. Then, complete the triangle similarity statement.
The triangles are similar by SAS similarity and the similarity statement is ΔABC ~ ΔPQR.
We can determine the similarity of the triangles by checking if they satisfy the conditions of AA, SAS, or SSS similarity.
AA Similarity: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Looking at the triangles, we can see that angle A is congruent to angle P, and angle B is congruent to angle Q. However, we cannot conclude that the triangles are similar by AA similarity because we do not know if the third pair of angles are congruent.
SAS Similarity: If two pairs of sides of one triangle are proportional to two pairs of sides of another triangle, and the included angles are congruent, then the triangles are similar.
Looking at the triangles, we can see that:
AB is proportional to PQ (since AB/PQ = 4/5)
BC is proportional to QR (since BC/QR = 3/4)
Angle BAC is congruent to angle QPS (since they are vertical angles)
Therefore, the triangles are similar by SAS similarity. The triangle similarity statement is:
ΔABC ~ ΔPQR (by SAS similarity)
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3. Celine is knitting a scarf. The finished length will be 1.2 meters. So far
she has knitted 0.8 meters. How many more meters does Celine
need to knit? Draw a number line to solve.
Celine has already knitted 0.8 meters. Her final result should be 1.2 meters.
To calculate how many meters Celine has to knit we should subtract the already knitted length of scarf from the entire length. This give the equation:
[tex]x=1.2m-0.8m[/tex]
x is the unknown
x = 0.4 meters