The area of the first, second, third, and fourth circles will be 56.72 cm², 36.3 ft², 167.33 m², and 188.6 yd² respectively.
What is a circle?It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.
Then the radius and diameter are given below.
\(\rm r_1 = 4 \dfrac{1}{4} = \dfrac{17}{4} = 4.25 \ cm\\\\\\r_2 = \dfrac{d}{2} = \dfrac{6\frac{4}{5}}{2} = \dfrac{34}{10} = 3.4 \ ft\\\\\\r_3 = \dfrac{d}{2} = \dfrac{14.6}{2} = 7.3 \ m\\\\\\r_4 = 7\dfrac{3}{4} = \dfrac{31}{4} = 7.75 \ yd\)
Then the area of the circle is given as
Area = π × r²
Then the area of the first circle will be
Area = π × r₁²
Area = 3.14 × 4.25²
Area = 56.72 square cm
Then the area of the second circle will be
Area = π × r₂²
Area = 3.14 × 3.4²
Area = 36.3 square ft
Then the area of the third circle will be
Area = π × r₃²
Area = 3.14 × 7.3²
Area = 167.33 square m
Then the area of the fourth circle will be
Area = π × r₁²
Area = 3.14 × 7.75²
Area = 188.6 square yd
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Someone please help, i already asked this but i really need this!!!
Answer:
Step-by-step explanation:
Blue Triangles
Area of 1 blue triangle
Area = 1/2 B * H
B = 3 m
H = 4.5 m
Area = 1/2 * 3 * 4.5
Area = 1/2 13.5
Area = 6.75
Hold on. I forgot there were 4 triangles.
4 * 6.75 = 27 meters^2 of material
Green Base
Area = s * s
s = 3
Area = 3 * 3 = 9
How to solve adjacent angles?
Answer:
D
Step-by-step explanation:
1 + 4x and 57° are corresponding angles and are congruent , so
1 + 4x = 57 ( subtract 1 from both sides )
4x = 56 ( divide both sides by 4 )
x = 14
if the figure forms the base of a right solid 110 centimeters high, find the surface area
Answer:
\(60200cm^{2}\)
Step-by-step explanation:
(I am assuming that the units for the measurements in this question are all centimeters)
Surface area = 2 * (Area of Base) + (Perimeter of base)*(Height)
First, we'd need to solve for the area of the base by finding the area of the triangle and subtracting it from the area of the rectangle. The area of the rectangle is \(100 * 150 = 15000\). The area of the triangle is \(\frac{1}{2} * 120 * 90 = 5400\). (We can do this because it is a right triangle with leg lengths in the pattern of a 3-4-5 triangle.) Now, subtracting the area of the triangle from the rectangle, we get \(15000 - 54000 = 9600\). This is the area of the base.
Next, the perimeter of the base is \(100 + 150 + 90 + 120 = 460\). Multiplying this by the height, we get \(460 * 110 = 50600\).
Finally, we add 9600 and 50900 to get \(9600 + 50900 = 60200\).
Question 14(Multiple Choice Worth 1 points)
(03.03 MC)
The map shows the location of a mall, library, and school in a city:
Coordinate grid shown from negative 16 to positive 16 on x axis at intervals of 2, and negative 10 to positive 10 on y axis at intervals of 2. A triangle is shown with vertices labeled Library, Mall, and School. Library is the ordered pair negative 15, 6, Mall is the ordered pair 15, 6, and School is the ordered pair 15 and negative 10.
Mike traveled from the school to the mall and then from the mall to the library. Henry traveled from the school to the library. How many more miles did Mike travel than Henry?
10 miles
12 miles
34 miles
46 miles
Answer: mike traveled 34 miles
Three students from a 16 student class will be selected to attend a meeting. 6 of the students are female
I think you want 8/3 or 2.666666 or mabye 37%
0.000549 in scientific notation
Answer: 5.49 × 10-4
Step-by-step explanation:
When you move the decimal over move it over to the right by 4 units.
When you move right it is (-) negative. So you get 5.49 x 10-4.
125x ^ 3 - 27 = 0
Solve this by grouping
The solution to the equation 125x³ - 27 = 0 is (5x−3)(25x ^2 +15x+9)
What is an equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculationsolving the equation 125x³ - 27 = 0 by grouping
Rewriting 125x^ 3 −27 as (5x) ^3 −3³
The difference of cubes can be factored using the rule:: a ^3 −b^ 3 =(a−b)(a^ 2 +ab+b^ 2 )
Polynomial 25x^ 2 +15x+9 is not factored since it does not have any rational roots.
Hence, (5x−3)(25x ^2 +15x+9)
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I’m stuck on this problem can someone help with this 3(4x+3)?
Answer:
12x + 9 this is probably right
1.Write the expression in expanded form. The subscript number can be write in
normal form. E.g. X1 + X1Y1, do not forget the correct parenthesis and the correct
order. *
2.For the equation in above evaluate the notation using the values below. Please
enter the exact value.
X1 =0
Y1 = 5
Z1 = 0
X2 = 1
Y2 = 26
Z2 = -2
X3 = 12
Y3 = -2
Z3 = 3
X4 = -1
Y4 = 25
Z4 = 24
Answer:
(a) Expanded form:
\(((X_1 + X_1Y_1) - X_1Z_1) + ((X_2 + X_2Y_2) - X_2Z_2) + ((X_3 + X_3Y_3) - X_3Z_3) + ((X_4 + X_4Y_4) - X_4Z_4)\)
(b) The value of the expression: -21
Step-by-step explanation:
Given
\(\sum \limit^4_{i=1}\ ((X_i+X_iY_i) - X_iZ_i)\)
Solving (a): The expanded form:
This means that we substitute the values of i from 1 to 4 in the above expression.
So, the expression becomes:
\(((X_1 + X_1Y_1) - X_1Z_1) + ((X_2 + X_2Y_2) - X_2Z_2) + ((X_3 + X_3Y_3) - X_3Z_3) + ((X_4 + X_4Y_4) - X_4Z_4)\)
Solving (b): The value of the expression
To do this, we simply substitute the given values of X1, X2....... in the expression.
This gives:
So, the expression becomes:
\(((0 + 0*5) - 0*0) + ((1 + 1*26) - 1*-2) + ((12 + 12*-2) - 12*3) + ((-1 + -1*25) - -1*24)\)
Simplify each bracket
\(((0 + 0) - 0) + ((1 + 26) +2) + ((12 -24) - 36) + ((-1 -25) +24)\)
\(0 + 29 -48 -2\)
\(-21\)
Hence, the result of the expression is -21
F(x)=2x^3 -7x +4
Determine the intervals on which the function is positive on (-3,3).Give the boundaries of the intervals rounded to four decimals
The required f(x) is positive on the intervals (-2,1) and (1.1547,3).
What is Function?A function in mathematics from a set X to a set Y assigns precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two variable quantities.
According to question:To determine the intervals on which the function is positive on the interval (-3,3), we need to find the x-values for which f(x) is greater than zero (i.e., positive).
First, we can find the critical points of the function by finding where f(x) = 0:
\($\begin{align*}f(x) &= 2x^3 -7x +4 \0 &= 2x^3 -7x +4 \&= (x-1)(2x^2+2x-4) \&= (x-1)(2(x-1)(x+2)) \\end{align*}\)
So the critical points are x = 1 and x = -2.
Next, we can test the sign of f(x) on different intervals. Since f(x) is a polynomial function and is continuous on the interval (-3,3), we only need to test the sign of f(x) at the critical points and at the endpoints of the interval:
f(-3) &= 2(-3)³ -7(-3) +4 = -47 <0
f(-2) &= 2(-2)³ -7(-2) +4 = 0
f(1) &= 2(1)³ -7(1) +4 = -1 < 0
f(3) &= 2(3)³ -7(3) +4 = 47 > 0
Therefore, f(x) is positive on the intervals (-2,1) and (1.1547,3), where the boundaries of the intervals are rounded to four decimals. Therefore, the answer is:
\($$\boxed{(-2,1) \text{ and } (1.1547,3)}$$\)
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Edward and Tiffany were comparing the distance they ran over a week. If Edward ran 11.90 miles and Tiffany ran 7.9 miles, how far did they run total?
PLS HELPP!!! FAST.
Answer:
19.8 miles!!!!!!!!!+!
Answer:
The answer is
→ 19.8 miles
Step-by-step explanation:
Edward ran 11.90 miles in a week.
Tiffany ran 7.9 miles in a week.
The question is asking how far they ran in total.
Well, to answer that we have to set up what we have to add.
\(11.90+7.9=19.8\)
Therefore, 19.8 is your answer.
Hope this helped! :^)
write a lab report on density
You don't give much information but I will give you the definition of "density".
In all simpleness, the definition of density is the compactness of a substance.
Density can be found with the formula; p = m/v
p = density
m = mass
v = volume
Best of Luck!
An apple pie is divided into eight equal slices with each slice being 280 calories. How much calories are in the entire pie
Answer:
2240
Step-by-step explanation:
280*8= 2240
how to solve a pair of equations
42. Let f be a function from the set A to the set B. Let S and T be subsets of A. Show that
a) f(S ∪ T)=f(S) ∪ f(T).
b) f(S ∩ T) ⊆ f(S) ∩ f(T).
Start with any random elements of sets and compute LHS and RHS individually.
a) The proof of f(S ∪ T) = f(S) ∪ f(T) is explained below.
b) The proof of f(S ∩ T) ⊆ f(S) ∩ f(T) is expliane dbelow.
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
Let, The set A = {1, 2, 3, 4, 5} and B = {2, 4, 5}.
Therefore, S = {1, 2, 3} and T = {1, 4, 5}.
Now, f(S ∪ T) = {1, 2, 3, 4, 5} and f(S) ∪ f(T) = {1, 2, 3} ∪ {1, 4, 5}.
Hence, f(S ∪ T)=f(S) ∪ f(T).
Now, f(S ∩ T) = {1} and f(S) ∩ f(T) = {1, 2, 3} ∩ {1, 4, 5} = {1}.
Therefore, f(S ∩ T) ⊆ f(S) ∩ f(T). (⊆ implies improper subset)
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GEOMETRY 100 POINTS
Find the length of BC
Answer:
x = 16
Step-by-step explanation:
Opposite sides are equal in a parallelogram
AD = BC
5x - 12 = 3x + 20
5x - 3x = 20 + 12
2x = 32
x = 32/2
x = 16
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.
Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.
To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.
Let's start with the first equation:
2 + x = 5
Subtract 2 from both sides:
x = 3
Now let's move on to the second equation:
x + 1 = 4
Subtract 1 from both sides:
x = 3
Notice that we got the same value of x for both equations, so they are equivalent.
Next, let's look at the third equation:
9 + x = 6
Subtract 9 from both sides:
x = -3
Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.
Now, let's move on to the fourth equation:
x + (-4) = 7
Add 4 to both sides:
x = 11
This value of x is also different from the first two equations, so it is not equivalent to them.
Finally, let's look at the fifth equation:
-5 + x = -2
Add 5 to both sides:
x = 3
Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.
So, correct options are A, B and E.
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Complete question is:
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
- 5 + x = - 2
PLEASE HELO ME!!! PLSSSS
Answer:
Choice A
Step-by-step explanation:
<4 and <5 are alternate interior angles.
Answer:
angle 3 and 6
Step-by-step explanation:
They are on the other sides of eachother and are both in the interior.
If nine of every 11 trick-or-treaters that came to your house last Halloween were dressed as pirates what proportion of trick-or-treaters were not dressed as pirates
Answer:
11 - 9 = 2 trick-or-treaters out of 11 were not dressed as pirates so the proportion is 2/11.
Answer: Ratio is 2:11
Step-by-step explanation:
So your ratio of pirates to non-pirates would be 9:11
So you subtract number of pirates from total trick-or-treaters and get 2.
So the proportion of non-pirates would be 2:11.
consider the trial on which a 3 is first observed in successive rolls of a six-sided die. let a be the event that 3 is observed on the first trial. let b be the event that at least two trials are required to observe a 3. assuming that each side has probability 1/6, find (a) p(a), (b) p(b), and (c) p(a ub).
P(A) is the probability of observing 3 on first trial. P(B) is probability of observing 3 after at least 2 trials. P(A U B) is total probability of observing 3.
(a) The probability of observing a 3 on the first trial is 1/6. So, p(a) = 1/6.
(b) The probability of not observing a 3 on the first trial is 5/6.
If a 3 is not observed on the first trial, then the same experiment will be repeated with a 5/6 chance of not observing a 3 again.
This can be represented as (5/6)^2.
The probability of not observing a 3 on the first two trials is (5/6)^2.
So, the probability of observing a 3 on the third trial is
1 - (5/6)^2
This can be represented as
1 - (5/6)^n where n is the number of trials
The probability of requiring at least two trials to observe a 3 is the sum of the probabilities of observing a 3 on the third, fourth, fifth, etc. trials. This is equivalent to the sum of an infinite geometric series. The sum can be calculated using the formula
S = a/(1 - r) where S is the sum, a is the first term, and r is the common ratio.
In this case, a = 1 - (5/6)^2 and r = 5/6. So, the sum is S = (1 - (5/6)^2)/(1 - 5/6) = 6/36 = 1/6. Therefore, p(b) = 1/6.
(c) The probability of observing a 3 on the first trial or at least two trials is the sum of p(a) and p(b). So, p(a or b) = p(a) + p(b) = 1/6 + 1/6 = 1/3.
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In the town of Centralburg (Figure 1), which is laid out in a uniform block grid, the grocery store is three blocks East and four blocks North of the post office. Which of the following is a correct equation for the quantities represented in this scenario?
Answer:
tan(θ)= dn/de
θ=arctan(dn/de)
Step-by-step explanation:
ach ant has 6 legs. How many legs do 3 ants have?
Ants 1 2 3
Legs 6 ?
Answer:
Step-by-step explanation:
the answer is 18 I think?
Answer:
18
Step-by-step explanation:
6 (legs) x 3 (ants) = 18 legs
It can also be represented as 6+6+6 (18)
hope this helps :)
The equation cos(35•) = a/25 can be used to find the length of BC what is the length of BC round to the nearest tenth
If 20% of a number is 72 and 50% of the same number is 180, find 30% of that number.
Answer:
.20x = 72, so x = 360
.30(360) = 108
There are 31 horses competing in a show, how many ways can the blue,red,and yellow ribbons be awarded
If there are 31 horses competing in a show, then the blue, red, and yellow ribbons can be awarded in 26970 different ways.
As per the question statement, 31 horses are competing in a show.
We are required to calculate the number of ways in which the blue, red and yellow ribbons can be awarded.
To solve this question, first, we need to know a basic rule of horse shows, which is the 1st place or the winner is awarded with a blue ribbon, the second place or the runners-up is awarded with a red ribbon and the third place or the second runners-up is awarded with a yellow ribbon.
That is, in simpler terms, we have to calculate the number of different ways, in which the first, second and third places can be achieved between 31 different horses, each having equal probability of winning.
To solve this question, we just need to know the formula of permutation which goes as \([(nPr)=\frac{n!}{(n-r)!} ]\), i.e., we are to select an ordered set or "r" from a set of "n".
As per our question, (n = 31) and (r = 3), and using these in the above mentioned formula of permutation, we get
\((31C)=\frac{31!}{(31-3)!}=\frac{31!}{28!} =\frac{28!*29*30*31}{28!}=(28*29*30)=26970.\)
That is, the blue, red and yellow ribbons can be awarded in a show with 31 horses as contestants in 26970 different ways.
Probability: In mathematics, probability of an event is the extent to which it is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.Permutation: In mathematics, a permutation of a set is an arrangement of its members into a particular sequence, or if the set is already ordered, a rearrangement of its elements.To learn more about permutations, click on the link below.
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6x³ + 3x
how do you factor out the GCF in this question??
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to factor out the GCF in the expression
\(\star~\star\mathrm{6x^3+3x}~\star~\star\)
\(\triangle~\fbox{\bf{KEY:}}\)
Divide every single term of the expression by the GCF (Greatest Common Factor).So let's divide.
But first. we should work out the GCF.
Both terms have 3x in common, so we divide both terms by 3x:
\(\mathrm{6x^3+3x}\)
\(\mathrm{3x(2x^2+1)}\)
To ensure that we've factored correctly, we can always use the distributive property, distribute 3x and see whether or not we end up with \(\mathtt{6x^3+3x}\).
So the answer is
\(\mathrm{3x(2x^2+1)}\)
Notice I put parentheses around 2x²+1. This indicates that 3x is multiplied times both 2x² and 1.
Hope it helps you out! :D
Ask in comments if any queries arise.
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work out the area of a circle with diameter 1.8cm. Take \(\pi\) to be 3.142 and give your answer in 1 decimal place.
Area of a circle is pi x r ^2
R = diameter/2
R = 1.8/2 = 0.9
Area = 3.142 x 0.9^2
Area = 2.5 square cm.
Please help me !!!
Question 1 of 15
Which algebraic rule describes the translation of quadrilateral HIJK to
quadrilateral HTJK?
79
199
K
23456
H
OA. (x,y)
(x+6, y+4)
OB. (x, y)
(x+1, y-2)
OC. (x,y) - (x+1, y-8)
OD. (x, y) - (x-8, y+1)
The algebraic rule describes the translation of quadrilateral HIJK to quadrilateral H'I'J'K' is (x, y) => (x+1, y-8)
What in mathematics is a quadrilateral?
A quadrilateral, a two-dimensional shape, is made up of four sides, four vertices, and four angles. The most prevalent shapes are concave and convex. Also included in the list of convex quadrilateral subgroups are trapezoids, parallelograms, rectangles, rhombuses, and squares.
Given: quadrilateral HIJK to that translated H'I'J'K'
To determine the algebraic rule, we need to get the coordinates of HIJK and H'I'J'K' and then subtract them to get the translation:
H => (x, y) = (4, 6) | H' => (x, y) = (5, -2)
I => (x, y) = (6, 4) | I' => (x, y) = (7, -4)
J => (x, y) = (4, 2) | J' => (x, y) = (5, -6)
K => (x, y) = (4, 2) | K' => (x, y) = (3, -6)
Using points H and H' (you can use any point):
The difference in x is 5-4 = +1 => x+1
The difference in y is -2-6 = -8 => y-8
Therefore, the algebraic rule describes the translation is (x, y) => (x+1, y-8). Option C is the answer
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16 families went on a trip which cost them Rs 2,16,352. How much did each
family pay?
Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522
Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.
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Answer:
Step-by-step explanation
1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.
Now let's check if this result is correct:
1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.
So we have shown that each family paid **Rs 13,522** for the trip
write 1/4 + 1/4+1/4+1/4+1/4+1/4+1/4 as a multiplication problem then find the product
9514 1404 393
Answer:
7(1/4) = 7/4 = 1 3/4
Step-by-step explanation:
Multiplication is used to simplify repeated addition. The multiplier represents the number of times the sum includes the repeated value.
Here, the term 1/4 appears in the sum 7 times. That means we can write the equivalent expression ...
7 × 1/4 . . . . written as a multiplication expression
The product is found by multiplying the numerator of the fraction by the integer factor.
7 × 1/4 = 7/4
This improper fraction can be written as a mixed number.
7/4 = 1 3/4 . . . . the value of the sum
Answer:
1/4 + 1/4+1/4+1/4+1/4+1/4+1/4
(1/4) x 7
Step-by-step explanation: