Area of sector = 161.1 square inches
Activity 1:
The radius of the pizza is half of its diameter, which is 16/2 = 8 inches.
The central angle of the sector is 80%, which is 0.8 times 360 degrees = 288 degrees.
To find the area of the sector, we use the formula:
Area of sector = (central angle / 360) x πr^2
Area of sector = (288 / 360) x π x 8^2
Area of sector = (0.8) x π x 64
Area of sector = 161.1 square inches (rounded to the nearest tenth)
Activity 2:
The unit of measurement for the area of the sector is square inches (in²).
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A pot contains 3/4 gallon of soup.A serving is 1/16 gallon.How many servings does the pot contain?
by taking the quotient between the volume in the pot and the volume of each serving, we conclude that there are 12 servings.
How many servings does the pot contain?
The number of servings is given by the quotient between the volume in the pot and the volume of each serving, so we have:
Volume in the pot = 3/4 gallon.Volume of each serving = 1/16 gallon.N = (3/4)*/(1/16) = 12
So there are 12 servings in the pot.
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if ending work in process contains 300 units that are 40omplete the number of equivalent units is
120 units are needed to complete the number of equivalent units if the ending work in the process contains 300 units.
Number of units = 300 units
Percentage of units completed = 40%
To determine the number of equivalent units for a display operation, you need to view the teams that are fully satisfied as well as the partly finished units in the cessation outcome in the process.
Equivalent units = Number of fully completed units + Equivalent units in finishing work in process
Number of equivalent units = 0 + (300 units x 40%)
Number of equivalent units = 0 + 120 units
Number of equivalent units = 120 units
Therefore, we can conclude that the number of equivalent units is 120 units.
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The complete question is-
if the ending work in the process contains 300 units that are 40% complete the number of equivalent units is?
Write the quadratic function in the form f(x)=a(x-h)^2+k. Then, give the vertex of its graph. Finally, graph the function by plotting the vertex and four additional points, two on each side of the vertex. f(x)=-2x^2+16x-35
Answer:
\(f(x) = -2(x - 4)^2 -3\)
Vertex = (4, -3)
Graph in the image attached, additional points:
(2, -11), (3, -5), (5, -5), (6, -11)
Step-by-step explanation:
The vertex of f(x) can be found using the formula:
\(x_{vertex} = -b/2a\)
\(x_{vertex} = -16 / (-4)\)
\(x_{vertex} = 4\)
to find y_vertex, we use x_vertex in f(x):
\(f(x_{vertex}) = -2 * 4^2 + 16*4 - 35\)
\(f(x_{vertex}) = -3\)
So the vertex is (4, -3)
To write the function in the form \(f(x)=a(x-h)^2+k\), we just need to calculate h = -b/2a and then find k:
\(h = -b/2a = -16/(-4) = 4\)
\(f(x) = -2(x - 4)^2 + k = -2(x^2 - 8x + 16) + k = -2x^2 + 16x - 32 + k\)
Comparing both forms of f(x), we have:
\(-32 + k = -35\)
\(k = -3\)
So we have:
\(f(x) = -2(x - 4)^2 -3\)
Now let's find the four additional points.
Two points to the left: x = 3 and x = 2
\(f(3) = -2 * 3^2 + 16*3 - 35 = -5\)
\(f(2) = -2 * 2^2 + 16*2 - 35 = -11\)
Two points to the right: x = 5 and x = 6
\(f(5) = -2 * 5^2 + 16*5 - 35 = -5\)
\(f(6) = -2 * 6^2 + 16*6 - 35 = -11\)
. Bella makes $7.50 an hour working at her job at the movie theater. If she worked 12 hours last week and 15.5 hours the week before, how much did she make total for the two weeks? (3pts – 1pt each for setting up equation, correct answer, correct label)
Find the quotient.
300 divided by 7.5= ?
Answer:
....try t out
The answer is 40
Answer:
Quotient=42
Step-by-step explanation:
a 16 ft ladder is leaning against a wall. if the top of the ladder slides down the wall at a rate of 2 ft/s, how fast (in ft/s) is the bottom moving along the ground when the bottom of the ladder is 8 ft from the wall?
The bottom of the ladder is moving away from the wall at a rate of 4 ft/s when the bottom is 8 ft from the wall.
The bottom of the ladder is moving away from the wall at a rate of 2 ft/s when the bottom is 8 ft from the wall. This is due to the fact that the ladder is leaning against the wall.
When the top of the ladder slides down the wall at a rate of
2 ft/s,
the bottom of the ladder will also be moving away from the wall at the same rate.
The rate of movement of the bottom of the ladder is determined by the angle of the ladder and its height.
To calculate the rate at which the bottom of the ladder is moving,
we need to use the Pythagorean Theorem.
Since
the height of the ladder is 16 ft
and the bottom of the ladder is 8 ft away from the wall,
the hypotenuse of the triangle will be the side of the triangle opposite the right angle and its length will be
16 - 8 = 8 ft.
Thus, the rate at which the bottom of the ladder is moving away from the wall is 8/2 = 4 ft/s.
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Step 1: -10 + 8x < 6x-4
Step 2: -10 <-2x - 4
Step 3: -6<-2x
Step 4:
What is the final step in solving the inequality - 2(5 -
4x) < 6x - 4
O X<-3
OX-3
O x<3
Ox>3
Answer:
0x>3 technically
Step-by-step explanation:
At step 3 you have -6<-2x
You want to get the x by itself on one side of the equation. Divide by -2 on both sides of the equation
-6÷-2<-2x÷-2
-6÷-2=3 and -2x÷-2=x
So you would have 3<x BUT when you divide an inequality by a negative, it flips the inequality sign.
So instead of 3<x your answer would be 3>x
Also, it would not be 0x, but 1x. Out of the choices you gave, the answer would be 0x>3 but if you want to actual answer it would be 1x>3 or just x>3
The final step in solving the given inequality is x < 3. The correct answer is option (C) x < 3.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The inequality is given as follows:
-2(5-4x) < 6x - 4
First, simplify the inequality as:
-2(5-4x) < 6x - 4
Distribute the -2 in the above inequality,
-10 + 8x < 6x - 4
Add 10 and subtract 6x from both sides,
-10 + 8x + 10 - 6x < 6x - 4 + 10 - 6x
2x < 6
Divide both sides by 2
x < 3
Therefore, the final step in solving the given inequality is x < 3.
Hence, the correct answer is option (C) x < 3.
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Multiply.
−2(8)= HELP WITH THIS TO
Answer:
-16
Step-by-step explanation:
yes
Or
Camille has a can of soup in the pantry. The circular lid has a radius of 3 inches. What is the lid's area?
Use 3. 14 for
The lid's area can be calculated using the formula for the area of a circle, which is A = πr^2, where A is the area and r is the radius.
So, for Camille's can of soup, the lid's area would be:
A = 3.14 x (3 inches)^2
A = 3.14 x 9 square inches
A = 28.26 square inches
Therefore, the lid's area is 28.26 square inches.
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A diamond has eight equilateral triangles as faces, as shown. The formula V = 0.4783
approximates the volume (in cubic millimeters) of the diamond, where s is the side length (in millimeters) of each edge. Approximate the length of each edge of the diamond.
V = 161 mm³
The length of each edge of the diamond is about
1
mm.
In equilateral triangles, 7.0 mm is the length of each edge of the diamond.
The equilateral triangle's definition?
An equilateral triangle is a triangle whose three sides are all the same length, commonly referred to as a "regular" triangle.
A triangle with all three sides equal and interior angles of 60 degrees is said to be equilateral. Triangle with an equal number of sides is known as an isosceles triangle.
V = 0.4783 S³ = 161
S³ = 161/0.47
= ∛ 161/0.47
≈ 7.0 mm
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In the figure particle 1 of charge q
1
=−4.90q and particle 2 of charge q
2
=+3.70q are fixed to an x axis. As a multiple of distance L, at what coordinate on the axis is the net electric field of the particles zero?
The net electric field of particle 1 and particle 2 will be zero at a coordinate on the x-axis that is a multiple of L/8.
The net electric field at a point on the x-axis due to particle 1 and particle 2 can be calculated using Coulomb's law:
Electric field due to particle 1: E1 = kq1/\(r1^{2}\)
Electric field due to particle 2: E2 = kq2/\(r2^{2}\)
Here, k is the electrostatic constant, q1 and q2 are the charges of particle
1 and particle 2 respectively, and r1 and r2 are the distances from the particles to the point on the x-axis.
To find the coordinate on the x-axis where the net electric field is zero, we need the magnitudes of E1 and E2 to be equal. Taking the magnitudes of the electric fields:
|E1| = |E2|
Using the expressions for E1 and E2:
k*|q1|/\(r1^{2}\) = k*|q2|/\(r2^2\)
Since the charges q1 and q2 are given as -4.90q and +3.70q respectively, and the magnitudes are equal:
(4.90q)/r = \(r1^2\)3.70q)/\(r2^2\)
Simplifying, we get:
\(r2^2\)/\(r1^2\) = 4.90/3.70
Taking the square root of both sides:
r2/r1 = \(\sqrt{(4.90/3.70)}\)
r2/r1 = sqrt\(\sqrt{(1.324)}\)
r2/r1 ≈ 1.150
Thus, the ratio of distances r2/r1 is approximately 1.150.
Since the particles are fixed to the x-axis, the distance between them is L, and the ratio r2/r1 is L/x, where x is the coordinate we are looking for.
Therefore, we have:
L/x ≈ 1.150
Solving for x, we find:
x ≈ L/1.150
Hence, the coordinate on the x-axis where the net electric field of the particles is zero is approximately L/1.150, or equivalently, a multiple of L/8.
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11/13% of a quantity is equal to what fraction of the quantity?
11/13% of a quantity is equal to 11/1300 fraction of the quantity.
What is Percent to Fraction?Percentage signifies for every hundred or for each. We display it as %. Since a percentage is expressed on a scale of 1 to 100, it is easy to comprehend. Converting percentage data to fractions is known as "percent to a fraction." As per the percent to fraction conversion instructions, the percentage can be written as a fraction by deleting the percent symbol and placing 100 in the denominator. Any percent can easily be converted to a fraction, and the opposite is also true.
How to Convert Percent to Fraction?To convert a percentage to a fraction, follow these three simple steps. Let's examine these three processes in more detail.
Leave out the percent sign.divide it by 100.Reduce the obtained fraction.Divide the given percentage by 100
\(\frac{11}{13}\)% \(=\frac{11}{13} \times \frac{1}{100} \\=\frac{11}{1300}\)
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Yoko sold a t-shirt at a festival and made a profit of $71. she made $4 for each t-shirt she sold. her total expense were $25 h.ow many t-shirts did she sell (please answer both A and B)
Lets say she sold x no of T shirt
she $4 for each T shirt
for x no. of T-shirt she made 4x , and her expenses were $25
but her $71 her profit , so from above condition,
we can write the equation 4x - 25 = 71
adding 27 from both sides, we get,
4x = 71 + 25 = 96.
dividing by 3 on both sides,
x = 96/ 4 = 24
she sold 24 T - shirts.
Select the correct answer from the drop-down menu.
The solution set for 6a²-a-5=0 is
(2,-5/6)
{2,-12/5)
{-1,-5/6)
(1.-5/6)
Answer:
{1, -5/6}
Step-by-step explanation:
(6a+5)(a-1) = 0
6a+5 = 0 (or) a-1 = 0
a = -5/6 (or) a = 1
you have $40 to spend on n gallons of gas that costs $3.25 per gallon.
Answer:
You can buy 12 gallons of gas.
Step-by-step explanation:
I took 40 and 3.25, then divided them.
I got a very large ugly decimal. When simplified it is 12.
Help!!!! please!!!!!
Answer:
60 or 70
Step-by-step explanation:
Answer:
The shape is a trapezium; so use the formula for solving area of a trapezium to solve it. Which is
1/2(a+b)×h
=1/2(10+6)×7
=1/2 × 16 × 7
= 8×7
=56
I’m having a bit of trouble really understanding this problem. Can I please get a answer for this? Thank you!
Answer:
flip it again
Step-by-step explanation:
then i will answer it
Answer:
I think the answer is 12,4
So 12 on the x axis and 4 on the y axis
which expression is equivalent to -14–6?
Answer:
-14+(-6) = -6+(-14)
Which equation can be used to find the value of x?
Responses
11x + 25x + 9x = 180
11x + 25x = 180
11x + 25x = 90
11x + 25x + 9x = 90
which of the following is equivalent to the radical expression below √8x^5
I really need help with this.
Find the mean, the median, and the mode(s), if any, for the given data. Round noninteger means to the nearest tenth. (If there ismore than one mode, enter your answer as a comma-separated list. If an answer does not exist, enter DNE.)18,3, 40, 19, 42, 48, 51, 43meanmedianmode(s)
The data are listed in ascending order to be:
\(3,18,19,40,42,43,48,51\)MEAN
The mean is the average of a data set. This can be calculated using the formula:
\(Mean=\frac{Sum\text{ }of\text{ }numbers}{Number\text{ }of\text{ }Numbers}\)From the question, we can calculate the mean to be:
\(\begin{gathered} Mean=\frac{3+18+19+40+42+43+48+51}{8}=\frac{264}{8} \\ Mean=33 \end{gathered}\)The mean is 33.
MEDIAN
The median is the middle of the set of numbers.
The middle terms are 40 and 42. Therefore, the median will be the average of the two numbers:
\(\Rightarrow\frac{40+42}{2}=41\)The median is 41.
MODE
The mode is the most common number in a data set.
The modes of the data are 3, 18, 19, 40, 42, 43, 48, and 51.
What is the importance and advantage of using graph representation when organizing your data?
The importance and advantage of using graph representation when organizing your data are that it makes data presentable, summarizing, better way of comparison of data.
An organized diagram or pictorial representation of the relationship between values or data is referred to as a graph. it is a a diagram that depicts a variable's variation in comparison to that of one or more other variables, such as a series of points, lines, line segments, curves, or areas.
The following are the three advantages of graphs:
It makes data look good and makes it easy to understand.It helps to concisely summarize the data.Better data comparison is made possible by it.Know more about graphs here: https://brainly.com/question/17267403
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Solve the system of equations below by graphing both equations with a
pencil and paper. What is the solution?
y=-x-1
y= x+3
A. (0,3)
B. (-2,1)
C. (-1,2)
O D. (0, -1)
32, 28, 36, 38, 40, 26, 29, 37 in least to greatest order
Answer:
26, 28, 29, 32, 36, 37, 38, 40
Step-by-step explanation:
a wooden cylinder beam of length 5 meters has a radius of 210cm. the wood density is 693kg/m
i) calculate the volume of the beam in cubic meters
ii) calculate the mass of the beam in kilograms.
Answer:
Cylinder Volume = π • r² • height
Volume = PI * .210 m^2 * 5
Volume = 0.6927211801 cubic meters
Wood has a mass of 693 / cubic meter
mass = 0.6927211801 * 693 = 480.06 kilograms
Step-by-step explanation:
If x to the first power is a line, and you multiply two lines together, what do you get? Think of the the exponent.
Answer: A quadratic equation (also called a parabola)
Step-by-step explanation:
A line can be written as:
f(x) = a*x + c
This is a polynomial with degree 1.
Now, of we have two lines:
f(x) = a*x + c
and:
g(x) = d*x + e
And we multiply them, we will get:
f(x)*g(x) = (a*x + c)*(d*x + e) = a*d*x^2 + a*e*x + c*d*x + c*e
We can rewrite this as:
= (a*d)*x^2 + (a*e + c*d)*x + (c*e)
This is a polynomial of degree = 2, this is a quadratic equation, then if you multiply two lines together, you get a quadratic equation (or a parabola)
Answer:
ax^2+ bx + c
Step-by-step explanation:
I get a parabola, that is, an equation of the second degree
give the numerical coefficient of the term x
the numerical coefficient is?
Answer:
1
Step-by-step explanation:
The numerical coefficient of every variable with no visible coefficient in front of it is always 1, since 1 multiplied by a number (or variable) is itself.
Label each item as factor by grouping or factor using substitution.
To factor a trinomial of the form
ax 2 + bx + c, find a factor pair of ac
that has the sum of b. Rewrite bx as a
sum of those factors. Then factor out
the GCF from the two groups of terms
to write the original trinomial as the
product of two binomials.
Answer:
To factor a trinomial of the form ax^2 + bx + c, you can use the following steps:
Step-by-step explanation:
To factor a trinomial of the form ax^2 + bx + c, you can use the following steps:
Find a factor pair of ac that has the sum of b. For example, if a = 2, b = -7, and c = -21, then the factor pair for -42 (2 * -21) that has the sum of -7 is (-7, -6).
Rewrite bx as a sum of those factors. In the example, -7x = -7x + (-6x).
Factor out the GCF (greatest common factor) from the two groups of terms. In the example, (2x - 7)(x - 6) = 2x(x - 6) - 7(x - 6) = 2x^2 - 14x + 12x - 42 = 2x^2 - 2x - 42.
Write the original trinomial as the product of two binomials. In the example, the trinomial 2x^2 + -7x + -21 can be factored as (2x - 7)(x - 6)
So the final factorization is (2x - 7)(x - 6)
9. Look at some of the printed letters in a textbook. The small horizontal
and vertical segments attached to the ends of the letters are called
serifs. Most of the letters in a textbook are in a serif typeface. The
letters on this page do not have serifs, so these letters are in a sans-
serif typeface. (Sans means "without" in French.) The figure shows a
capital letter A with serifs. Use the given information to write a
paragraph proof that the serif, segment HI, is parallel to segment JK.
Given: 21 and 23 are supplementary.
Prove: HI || JK
By considering the given information that angles 21 and 23 are supplementary and analyzing the properties of supplementary angles and parallel lines, we have proven that segment HI is parallel to segment JK.
To prove that segment HI is parallel to segment JK based on the given information that angles 21 and 23 are supplementary, we can utilize the properties of supplementary angles and parallel lines.
First, let's examine the given figure and information.
We have a capital letter A with serifs, where segment HI represents one of the serifs, and segment JK represents a horizontal line within the letter A.
To begin the proof, we'll make use of the fact that angles 21 and 23 are supplementary.
Supplementary angles are defined as two angles whose measures sum up to 180 degrees.
We can observe that angle 21 is an interior angle of triangle AHI, and angle 23 is an interior angle of triangle AJK.
Since angles 21 and 23 are supplementary, their sum is equal to 180 degrees.
Now, let's assume that segments HI and JK are not parallel.
In this case, if we extend lines HA and JA, they will eventually intersect at point P.
Since the angles formed at the point of intersection are supplementary (angle 21 + angle 23 = 180 degrees), it would imply that angle 21 and angle PJK, as well as angle 23 and angle PHI, are also supplementary.
However, this leads to a contradiction. In the original figure, we can observe that angle 21 and angle PJK do not form a supplementary pair since angle PJK is a right angle (90 degrees) in the letter A.
Therefore, our assumption that segments HI and JK are not parallel must be incorrect.
Consequently, we can conclude that segment HI is indeed parallel to segment JK.
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