The area of the pattern is calculated by finding the area of the circle, semicircles, and quarter-circles separately and then adding them together. The area of the pattern is approximately 1005.31 cm^2.
Explanation:To find the area of the pattern, we need to calculate the area of the circle, semicircles, and quarter-circles separately. The area of a circle is found using the formula A = πr^2, where r is the radius. So, the area of the circle is A = π(8)^2 = 64π cm^2. The area of a semicircle is half the area of a circle, so it is 32π cm^2. The area of a quarter-circle is a quarter of the area of a circle, which is 16π cm^2. To find the total area of the pattern, we add the areas of the circle, semicircles, and quarter-circles: 64π + 4(32π) + 8(16π) = 64π + 128π + 128π = 320π cm^2. Rounding to the nearest hundredth, the total area of the pattern is approximately 1005.31 cm^2.
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Finding the areas of the circles, semicircles, and quarter-circles separately and combining them together yields the pattern's overall area. The pattern's estimated area is 1005.31 cm^2.
To determine the area of the pattern, individual areas of the circle, semicircles, and quarter-circles are computed separately.
Utilizing the formula
A = πr^2
for a circle with a radius (r) of 8 cm, the circle's area is 64π cm^2.
The semicircles, constituting half the circle's area, total 32π cm^2 each.
Quarter-circles, representing a quarter of the circle's area, contribute 16π cm^2 each.
Combining these, the pattern's total area is calculated as 64π + 4(32π) + 8(16π) = 320π cm^2.
Rounded to the nearest hundredth, the total area is approximately 1005.31 cm^2.
This comprehensive approach ensures the accurate summation of all constituent shapes within the intricate pattern.
I don't understand this please explain step by step
Answer:
The answer is C.
Step-by-step explanation:
Think about it as substitution.
The equation given to you is 15n=10.
They are telling you that n is equal to 2/3.
So now, this is where you do the substitution.
1. Substitute 2/3 in for n.
15(2/3)=10
2. Determine if true.
15·2/3=10
3. Are they the same?
10=10
So now you know your answer is C. :)
which functions are symmetric with respect to the y axis
Answer:
A, B, and D
Step-by-step explanation:
Only the functions that have x by itself between the absolute value signs (A, B, and D) are symmetric with respect to the y-axis .
Placing a constant outside the absolute value signs moves the function up or down the y-axis but retains the symmetry.
Adding a constant inside the absolute value signs (as in C and E) moves the axis of symmetry to the left or right of the y-axis.
In the diagram, both A and B are symmetric with respect to the y-axis, but C has been shifted three units to the left.
The product of 3 consecutive odd numbers is 2,145. Enter a simplified expression for finding the numbers. Let n be the first odd number.
Answer:
11, 13 and 15.
Step-by-step explanation:
Let's say that the odd number is "x". If x is for example 15, then the next ODD number would be 15+2=17 and the one after that would be 15+2+2=15+4=19.
Applying that here, we get:
Odd number* the next odd number*the next odd number=2145
x*(x+2)*(x+4)=2145
x*(x^2+4x+2x+8)=2145
x^3+6x^2+8x=2145
By solving the polynomial, you get x=11.
Which makes our three numbers: 11, 13 and 15.
11*13*15=2145. The answer checks.
Final answer:
To find the three consecutive odd numbers whose product is 2,145, set up and solve an equation for n, the first odd number. The solution is n = 11, so the three consecutive odd numbers are 11, 13, and 15.
Explanation:
To find the three consecutive odd numbers whose product is 2,145, we can set up an equation and solve for n, the first odd number:
Let n be the first odd number
Then, the next two consecutive odd numbers would be n + 2 and n + 4
We can write the equation as: n x (n + 2) x (n + 4) = 2,145
Expanding this equation, we have: n³ + 6n² + 8n - 2,145 = 0
By factoring or using a numerical method, we can find that n = 11
So, the three consecutive odd numbers are 11, 13, and 15.
rectangle ABCD is graphed in the coordinate plane. the following are the vertices of the rectangle: A(-6,-4) B(-4, -4), C(-4, -2), and D(-6,-2) what is the perimeter of rectangle ABCD
Answer:
qwssfgbbbnjhbgbbnnbnnnnnnnj
Hello what is the equation I got the height but what’s the equation I’m stuck plz help
Answer:
h = 20 cm
Step-by-step explanation:
The volume (V) of a square based prism is
V = area of base × h ( h is the height )
area of square base = 9 × 9 = 81 cm²
Hence
81h = 1620 ← equation to be solved
Divide both sides by 81
h = 20 cm
Help with this question
Answer:
- 2
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ 3, 7 ] and from the graph
f(b) = f(7) = 2
f(a) = f(3) = 10, hence
average rate of change = [tex]\frac{2-10}{7-3}[/tex] = [tex]\frac{-8}{4}[/tex] = - 2
which value would make the statement true 2/?>4/12
Answer: Interval Notation (0, 6)
Graph: 0 o--------------o 6
Step-by-step explanation:
[tex]\dfrac{2}{x}>\dfrac{4}{12}\implies \dfrac{2}{x}>\dfrac{1}{3}\\\\\text{Restriction: Since the denominator cannot be zero, }x\neq 0\\\\\text{First, set the left side EQUAL to the right side and solve:}\\\dfrac{2}{x}=\dfrac{1}{3}\quad \text{cross multiply}\rightarrow 2(3)=x\quad \rightarrow \quad 6=x\\\\\\\text{Next, choose your test points}\\\bullet \text{to the left of 0: I choose -1}\\\bullet \text{between 0 and 6: I choose 1}\\\bullet \text{to the right of 6: I choose 8}[/tex]
[tex]\text{Now, plug each of the test points into the inequality to see which one(s)}\\\text{make a true statement.}\\\\\dfrac{2}{-1}>\dfrac{1}{3}\implies -2>\dfrac{1}{3}\quad FALSE\\\\\\\dfrac{2}{1}>\dfrac{1}{3}\implies 2>\dfrac{1}{3}\quad \boxed{TRUE!}\\\\\\\dfrac{2}{8}>\dfrac{1}{3}\implies -2>\dfrac{1}{3}\quad FALSE[/tex]
So, the solution is: every value between 0 and 6
2/x > 4/12
We can plug each of the numbers given in to verify.
2/4 = 4/8 = 6/12 > 4/12 √ this is correct
2/6 = 4/12 > 4/12 × this is incorrect
2/12 > 4/12 × this is incorrect
2/24 = 1/12 > 4/12 × this is incorrect
Your answer is A
3. Consider this dilation. (a) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
(b) What is the scale factor? Explain.
Answer:
the image of the dilation a reduction or an enlargement of the original figure
Step-by-step explanation:
The scale factor will be within the figure
Answer:
Reduction, 1/2
Step-by-step explanation:
We can already see that the prime figure is smaller, so we can justify that it is a reduction.
We can look at the points of the original figure and if we divide them by 2, we get the prime figure coordinates so we can conclude that the scale factor is 1/2.
What is the measure of the angle
Answer:
pie
Step-by-step explanation:
since line CT passes through point A (center) it is doameter (straight line)
its measure is 180° = pie radian
Please help, my teacher never explained how to do this!
Answer:
First, you have to calculate the angles.
3x-2 + 4x +2x -12 + 2x + 3x + 10
14x -4 = 360
14x = 364
x = 26
So, the angles are:
3x -2 = 76
4x = 104
2x -12 = 40
2x = 52
3x + 10 = 88
Step-by-step explanation:
a cylindrical vase is filled with soil.if the height of the vase is 6 centimeters and the vase is 471 cubic centimeters, what is the diameter of the vase?
[tex]\bf \textit{volume of a right-circular cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=6\\ V=471 \end{cases}\implies 471=\pi r^2(6)\implies \cfrac{471}{6\pi }=r^2 \\\\\\ \sqrt{\cfrac{471}{6\pi }}=r\implies \stackrel{diameter = 2\times radius}{d=2\left( \sqrt{\cfrac{471}{6\pi }} \right)}\implies d\approx 9.997[/tex]
What is the surface area of the rectangular prism
Answer:
The answer is C.
Step-by-step explanation:
To solve this problem, first do the calculations (twice per equation | example below.
6 x 8 x 2 = 96
8 x 11 x 2 = 176
6 x 11 x 2 = 132
Then, add of your products together to find your answer (example below).
132 + 176 + 96 = 404
Therefore, C is the answer.
Lauren,Amanda,and Cami each buy the same pizza.Cami eats 1/2 of her pizza.Amanda eats less than Cami.Lauren eats more than Cami.Write two fractions for both Amanda and Lauren to show how much pizza the girls eat.
Amanda could eat 3/8 of her pizza and Lauren could eat 2/3 of her pizza.
Explanation:To find out how much pizza Amanda and Lauren each eat, let's start with Cami who eats 1/2 of her pizza. Since Amanda eats less than Cami, we can represent her fraction as a fraction smaller than 1/2. For example, Amanda could eat 3/8 of her pizza. On the other hand, since Lauren eats more than Cami, we can represent her fraction as a fraction larger than 1/2. For example, Lauren could eat 2/3 of her pizza.
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What is the area of this trapezoid? Enter your answer in the box. units2 A rectangle with a length of 10 and a height of 9 has two right triangles on each side of it with short leg lengths of 7.
the area of the trapezoid is 64
90+31.5x2 = 153
153 units squared is the area of the trapezoid.
Convert the mixed number 31/4 to a percent
Answer:
3 1/4 = 325%
or
31/4ths = 775%
whichever is your intended fraction
Step-by-step explanation:
what is the difference between the longest and the shortest pencil
Answeron:
Du plus gras au plus sec : 9b - 8b - 7b - 6b - 5b - 4b - 3b - 2b - B - HB - F - H - 2h - 3h - 4h - 5h - 6h - 7h - 8h - 9h
The correct option is D.
The difference between the longest and shortest pencils is **7 inches**.
The difference between the measurements of the longest and shortest pencils can be calculated based on the given data. Let's break it down:
1. **Line Plot 1**: The longest pencil measures **7 inches**, and the shortest pencil is **[tex]$2 \frac{1}{2}$[/tex] inches** long. The difference is:
[tex]\[7 \text{ in} - 2 \frac{1}{2} \text{ in} = 4 \frac{1}{2} \text{ inches}\][/tex]
2. **Line Plot 2**: The longest pencil measures **7 inches**, and the shortest pencil is **[tex]$2 \frac{1}{4}$[/tex] inches** long. The difference is:
[tex]\[7 \text{ in} - 2 \frac{1}{4} \text{ in} = 4 \frac{3}{4} \text{ inches}\][/tex]
3. **Line Plot 3**: The longest pencil measures **7 inches**, and the shortest pencil is **[tex]$2 \frac{3}{8}$[/tex] inches** long. The difference is:
[tex]\[7 \text{ in} - 2 \frac{3}{8} \text{ in} = 4 \frac{5}{8} \text{ inches}\][/tex]
Therefore, the differences are as follows:
- Line Plot 1: **[tex]$4 \frac{1}{2}$[/tex] inches**
- Line Plot 2: **[tex]$4 \frac{3}{4}$[/tex] inches**
- Line Plot 3: **[tex]$4 \frac{5}{8}$[/tex] inches**
Based on this information, the correct answer is **D. 7 inches**.
The complete question is here:
What is the difference between the length of the longest pencil and the shortest pencil?
A. [tex]$1 \frac{1}{2}$[/tex] inches
B. 3 inches
C. [tex]$3 \frac{1}{2}$[/tex] inches
D. 7 inches
I appreciate anyone who helps me solve this math problem for Apex!
Answer:
Option C
Step-by-step explanation:
We can easily see the solution by realizing that the quadratic function
y = x^2 + 2 has a discontinuity at x =1 (white dot at the graph)
So, the solution must have
y = x^2 + 2 , x < 1
And the only option in which this applies is Option C.
use the models below to complete the sentence s.The models show wholes and parts.There are 3 wholes,each divided into fourths.
Each part is 1/4 of a whole. There are 12/4 in all. 12/4=3
Each part is 1/4 of a whole and there are 12/4 in all which is if the models show wholes and parts.There are 3 wholes,each divided into fourths.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
The model is given in the picture.
The models show wholes and parts.There are 3 wholes,each divided into fourths.
From the data given in the question:
Each part is 1/4 of a whole.
There are 12/4 in all.
= 12/4
= 3
Thus, each part is 1/4 of a whole and there are 12/4 in all which is if the models show wholes and parts.There are 3 wholes,each divided into fourths.
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One side of a rectangle is 4 inches longer than the other side. The area of the rectangle is 21 square inches. Find the lengths of each side.
Answer:
l = 7 in; w = 3 in
Step-by-step explanation:
The formula for the area of a rectangle is
A = lw
Data:
A = 21 in²
l = w + 4
Calculation:
21 = (w + 4) × w
21 = w² + 4w
w² + 4w - 21 = 0
(w + 7)(w - 3) = 0
w + 7 = 0 w - 3 = 0
w = -7 w = 3
We reject the negative value, so w = 3 in.
21 = l × 3
l = 7
The rectangle is 7 in long and 3 in wide.
A supersonic jet was flying at a constant velocity starting 8,400 kilometers west of U.S. airspace. It
flew one-third of the way to US, airspace in 2 hours. What was the jet's velocity?
Write your answer as a whole number. blank
kilometers per hour to the east
Submit
9514 1404 393
Answer:
1400 km/hour to the east
Step-by-step explanation:
We assume the jet is flying directly toward US airspace, so is flying east. The speed is ...
speed = distance/time
speed = ((8400 km)/3)/(2 h) = 1400 km/h
The jet's velocity is 1400 km per hour to the east.
Final answer:
The velocity of the supersonic jet traveling one-third of the way to U.S. airspace is 1400 km/h to the east, calculated by dividing the distance covered (2800 km) by the time taken (2 hours).
Explanation:
The supersonic jet's velocity can be determined by calculating the distance it flew and the time taken to cover that distance. The jet started 8400 km west of U.S. airspace and flew one-third of that distance, which is 2800 km (8400 km / 3). It took 2 hours for the jet to cover this distance. So, to find the velocity, we use the formula velocity = distance / time.
V = 2800 km / 2 hours = 1400 km/h to the east.
A bag contains 4 red, 3 yellow, 3 blue, and 2 white marbles, for a total of 12 marbles. If Lucia randomly picks two marbles from the bag without putting the first marble back, what is the probability that the first marble is red and the second is white?
Answer choices:
A. 2/144
B. 3/144
C. 2/33
D. 2/12
Answer: 2/33 hoped this helped you
Step-by-step explanation:
The probability that Lucia picks a red marble first and a white marble second from the bag without replacement is
2 / 33, found by multiplying the individual probabilities of each event. Hence option C is correct.
The question asks about the probability that Lucia randomly picks a red marble first and a white marble second from a bag containing marbles of various colors, without replacement. To calculate this probability, we need to consider the total number of marbles and the number of favorable outcomes for both events happening consecutively.
With 4 red and 2 white marbles in the bag, the probability of picking a red marble first is
P(Red) = Number of red marbles / Total number of marbles
P(Red) = 4 / 12 = 1 / 3
After picking a red marble, there are 11 marbles left, including 2 white marbles. The probability of then picking a white marble is
P(White | Red) = Number of white marbles / Total number of marbles remaining
P(White | Red) = 2 / 11
The combined probability is then the product of the two individual probabilities:
P(Red and White) = P(Red) X P(White | Red)
P(Red and White) = (4 / 12) X (2 / 11)
P(Red and White) = 8 / 132 = 2 / 33.
Thus, the correct answer is 2 / 33, which corresponds to option C.
Find the equation of the line that passes through the point (−3, −4) and is parallel to the line that passes through the points (−5, 1) and (7, −3).
Answer:
[tex]y = -\frac{1}{3}x - 5[/tex]
Step-by-step explanation:
To write the equation of a line use the point slope formula [tex]y - y_1 = m(x-x_1)[/tex]. Find m by using the slope formula with the points.
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{1--3}{-5-7} =\frac{4}{-12} =-\frac{1}{3}[/tex]
Since the line is parallel, it will have the same slope.
Substitute m = -1/3 and (-3,-4).
[tex]y --4 = -\frac{1}{3}(x --3)\\y + 4 = -\frac{1}{3}(x+3)\\y +4 = -\frac{1}{3}x - 1\\y = -\frac{1}{3}x - 5[/tex]
Final answer:
The equation of the line that passes through the point (-3, -4) and is parallel to a given line is y = -1/3x - 5. This is found by calculating the slope of the given line and then using the point-slope form to find the equation for the parallel line.
Explanation:
The student has asked for the equation of a line that passes through point
(-3, -4) and is parallel to another line. First, we need to find the slope of the given line that passes through points (-5, 1) and (7, -3). The slope (m) is calculated by using the difference in y-coordinates over the difference in x-coordinates (rise over run), which is:
m = (y2 - y1) / (x2 - x1) = (-3 - 1) / (7 - (-5))
m = (-4) / (12) = -1/3
Since parallel lines have the same slope, our new line will also have a slope of -1/3. Using the point-slope form of a line's equation, y - y1 = m(x - x1), and substituting the point (-3, -4) and the slope -1/3, we get the equation of the parallel line:
y - (-4) = -1/3(x - (-3))
y + 4 = -1/3(x + 3)
To write it in slope-intercept form (y = mx + b), we distribute the slope and simplify:
y + 4 = -1/3x - 1
y = -1/3x - 5
Therefore, the equation of the line parallel to the given line and passing through the point (-3, -4) is y = -1/3x - 5.
Suppose Cone A is similar to Cone B and the scale factor between the solids is 3:2, respectively. If the height of Cone A is 15 inches, determine the height of Cone B. 20 inches
15 inches
10 inches
5 inches
Answer:
[tex]10\ inches[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
Let
x----> the height of cone B
using proportion
[tex]\frac{3}{2}=\frac{15}{x} \\ \\x=2*15/3\\ \\x=10\ in[/tex]
HELP QUICKLY
The height of a rocket a given number of seconds after it is released is modeled by h(t)=-16t^2 + 32t + 10. What does t represent?
Im not sure if my anwser is correct
You're correct, t represents seconds
A juice shop needed 360 oranges to make 40 L of fresh squeezed juice how many oranges will be needed to make 60 L of fresh squeezed juice
Answer:
540 oranges
Step-by-step explanation:
360 Oranges=40L
40*3/2=60
360*3/2=540
Answer:
540
Step-by-step explanation:
First you have to divide 360 by 40. 360/40 = 9. So that means 9 oranges are needed to make 1 L of fresh squeezed juice.
Now since you know how many oranges are needed for 1 L, you have to find out how many are for 60. To do that you need to multiply 60 and 9. 60*9 = 540.
540 is your answer.
Hope this helped.
Solve each of the following equations. Show its solution set on a number line. Check your answers. |x+5|=−3
There is no solution for the given equation |x+5|=−3.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The equation |x+5| = -3 has no solutions in the real number system because the absolute value of any real number is always non-negative, and can never be negative.
Therefore, there are no values of x that make the left-hand side of the equation equal to -3, and the equation has no solutions.
Graphically, this means that there is no point on the number line where the distance from that point to -5 is equal to -3.
The solution set for the equation |x+5| = -3 is the empty set .
Hence, for the given equation |x+5|=−3 has no solution.
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Answer to this math question
Answer:
[tex]4\frac{2}{3}[/tex]
Step-by-step explanation:
This is a recurring decimal.
Let x = 4.666666... ⇒ (1)
10x = 46.66666... ⇒ (2)
Subtract equation (1) from equation (2)
10x = 46.66666..
- x = 4.666666...
9x = 42.0000.....
9x = 42
x = 42/9
= 14/3
=[tex]4\frac{2}{3}[/tex]
What is a real word example or use of surface area
A real life use of Surface area is when we need to figure out how much paint is needed to paint something. Paint can only cover so much surface area so we must figure out Surface area before it is painted.
Another example is in fashion when making clothes. You need to know the surface area of fabric so that there is enough cloth to fit a model and make a garment.
Answer:
Finding the area of a yard/centimeter.
Step-by-step explanation:
A house or let's say a building can be used as an example.
How to find the answer:
You would times length times width. (Up and bottom) Decimal or not, you would get your answer.
How can find the area
180 - 11 = 169
So b = 169 degrees.
URGENT !!!!!!!!!!!!!
Answer:
51
Step-by-step explanation:
Process exponents and division before performing addition, that is
49 + 64 ÷ 32 ← perform division
= 49 + 2 ← finally addition
= 51