Answer:
25.5°, 25.5°, 129° and 51°, 64.5°, 64.5°
Step-by-step explanation:
if you read the problem carefully you will notice that there are actually 2 ways of solving this problem. the first is by looking at the arc as if it is across from angle A, while the second is so the arc is across from side BC and bisected by point A (because the triangle is isosceles).
first way:
102/2=51°=m∠A
180-51=129°=m∠B+m∠C
129/2=m∠B=m∠C=64.5°
answers: 64.5°, 64.5°, 51°
second way:
102/2=51
51/2=m∠B=m∠C=25.5°
180-51=129°=m∠A
answers: 25.5°, 25.5°, 129°
Hope this helps!:)
The central angle BOC is twice the measure of arc BC, so it is 204°. Since the circle is 360°, the sum of the other two angles is 156°. Being an isosceles triangle, angles ABC and ACB are equal, thus each is 78°.
Explanation:To find the measure of the angles of an isosceles triangle ABC inscribed in a circle, with the measure of arc BC being 102°, we utilize the properties of a circle and the fact that an isosceles triangle has two equal angles. In a circle, the angle subtended by an arc at the center is twice the angle subtended on the circumference. Thus, if the measure of arc BC is 102°, the central angle BOC would be 204° (since it's twice the angle at the circumference).
This central angle separates the circle into two segments, one of which is the base of the isosceles triangle. The other two angles of the triangle, angles A and ABC or ACB (since it's an isosceles triangle, these angles are equal), will each occupy the remaining portion of the circle that amounts to 360° - 204° = 156°. Since the angles at B and C are equal in an isosceles triangle, we divide the remaining 156° by 2 to find each angle. Therefore, angle A = 204°, and each of the other two angles is 78°.
Zack buys some oranges from a store. The oranges cost $4.00 for 2 pounds. He wants to buy more fruit, but at the same price per pound as the oranges. Which of the following fruits could Zack buy?
A.
bananas at $2.00 for 5 pounds
B.
strawberries at $9.00 for 3 pounds
C.
peaches at $6.00 for 3 pounds
D.
blueberries at $8.00 for 2 pounds
For this case, I should find the unit cost per pound of orange.
[tex]\frac {4} {2} = 2 \frac {dollars} {libra}[/tex]
Zack wants to buy at the same price per pound.
Then, you can buy peaches:
[tex]\frac {6} {3} = 2 \frac {dollars} {pound}[/tex]
Answer:
Option C
Peaches at $ 6.00 for 3 pounds
Match the following reasons with the statements given. Given: R = Q AS = AT Prove: RS = QT. 1. ∠R = ∠Q, AS = AT Given 2. ∠5 = ∠6 Base ∠'s of isosceles triangle are = 3. ∠4, ∠5 are supplementary and ∠6, ∠7 are supplementary Exterior sides in opposite rays 4. ∠4 = ∠7 CPCTE 5. Triangle RAS congruent to Triangle QAT Two ∠'s supplementary to equal ∠'s are = 6. RS = QT AAS
∠R = ∠Q, AS = AT Given
∠5 = ∠6 Base ∠'s of isosceles triangle are =
∠4, ∠5 are supplementary and ∠6, ∠7 are supplementary Exterior sides in opposite rays
∠4 = ∠7 Two ∠'s supplementary to equal ∠'s are =
Triangle RAS congruent to Triangle QAT AAS
RS = QT CPCTE
Answer:
∠R = ∠Q, AS = AT Given
∠5 = ∠6 Base ∠'s of isosceles triangle are =
∠4, ∠5 are supplementary and ∠6, ∠7 are supplementary Exterior sides in opposite rays
∠4 = ∠7 Two ∠'s supplementary to equal ∠'s are =
Triangle RAS congruent to Triangle QAT AAS
RS = QT CPCTE
Step-by-step explanation:
When you divide a unit fraction by a whole number number, will the quotient be greater than or less than the unit fraction?
Answer:
it will be less than
Step-by-step explanation:
Answer:less than
Step-by-step explanation:
The following table represents a quadratic function which of the following are true of the graph hat represents the same quadratic function select all that apply
Answer:
Step-by-step explanation:
The graph has a relative minumum. TRUE Actually, I'd call it an absolute minimum, since 5 is the smallest y value and the graph opens up.
The graph shown has a vertex at (0, 5) TRUE. This point is also the absolute minimum of the function.
The graph opens up. TRUE
The graph has neither one nor two x-intercepts. The graph never crosses or touches the x-axis.
Answer:
A,B,C,F
Step-by-step explanation:
everything above was right except that there were more answers! For Algebra Nation the photo is incomplete and doesnt show the last two questions. I just took the test
if y=2×-3 determine the value of y when x=-15
Answer:
-33Step-by-step explanation:
Put x = -15 to the equation y = 2x - 3:
y = 2(-15) - 3 = -30 - 3 = -33
Answer:
y = 27
Step-by-step explanation:
[tex]y=2x-3[/tex]
[tex]y=2(15)-3[/tex]
[tex]y=30-3[/tex]
[tex]y=27[/tex]
Use the Distributive Property to write each expression in expanded form.
a. 3(x + 7) b. 5(5 - x) c. 2(4x - 8) d. (x + 4)(x + 2)
A. 3x+21
B. 25-5x
C.8x-16
D.x^2+6x+24
a. 3x + 21
b. 25 - 5x
c. 8x - 16
d. x^2 +6x + 8
On May 9, 2014 Jason made a deposit of $650.00. What is his balance after this transaction?
A) $540.28
B) $832.45
C) $1190.28
D) $1548.11
Answer:
What did he have before?
Step-by-step explanation:
A is the correct answer
i need to know how long the ramp is
Answer:
20.6
Step-by-step explanation:
Use the trig function Cosine to find the length of the ramp. The cosine function is defined as the ratio adjacent side over hypotenuse. The base 20 is the adjacent side to the angle 14 while the length of the ramp is the hypotenuse. Using the function we write, cos 14 = 20 / x. Solve for x.
Cos 14 = 20 / x
x*Cos 14 = 20
x = 20 / cos 14
x = 20.6
Answer:
Your can times them all up
Step-by-step explanation:
Priyanka and Ethan were asked to find an explicit formula for the sequence -3,-14,-25,-36,...
Answer:
[tex]a_{n}[/tex] = 8 - 11n
Step-by-step explanation:
These are the terms of an arithmetic sequence with n th term
[tex]a_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference
here a = - 3 and
d = - 14 - (- 3) = - 14 + 3 = -11, thus
[tex]a_{n}[/tex] = - 3 - 11(n - 1)
= - 3 - 11n + 11
= 8 - 11n
The explicit formula for the sequence -3, -14, -25, -36, ... is An = -11n + 8.
The student asked for an explicit formula for the sequence -3, -14, -25, -36, and so forth. We notice that each term decreases by 11 from the previous term. To find an explicit formula, we can use the arithmetic sequence formula which is given by An = A1 + (n - 1)d, where An is the n-th term, A1 is the first term, n is the term number, and d is the common difference between the terms.
For the given sequence, the first term A1 is -3 and the common difference d is -11. Substituting these values into the formula, we get An = -3 + (n - 1)(-11). We can simplify this to An = -3 - 11n + 11, which simplifies further to An = -11n + 8. Hence, the explicit formula for the given sequence is An = -11n + 8.
Figure 1 is a square pyramid. Figure 2 is a right triangular prism.
Complete the following statement about Figures 1 and 2.
The surface area of Figure 1 is ___ square centimeters ___ than the surface area of Figure 2.
Answer:
the answer is
The surface area of Figure 1 is 10.2 square centimeters Less than the surface area of Figure 2.
Step-by-step explanation:
Figure 1
area of a square = s2
=9squared
=81 sq cm
area of triangle = 1/2 bh
=1/2 (9cm) (14cm)
=63 sq. cm
find surface area
SA = 81 sq. cm + 4(63 sq. cm)
SA = 81 sq. cm + 252 sq. cm
SA = 333 sq. cm
Figure 2 Calculation
area of rectangle = lw
a = (12cm) (8 cm)
a = 96 sq. cm
area of triangle = 1/2 bh
=1/2 (8 cm) (6.9 cm)
= 27.6 sq. cm
total surface are of figure 2
SA = 3 (96 sq.cm) + 2 (27.6 sq. cm)
SA = 288 sq. cm + 55.2 sq. cm
SA = 343.2 sq. cm
find the difference between figure 1 and figure 2
343.2 sq. cm - 333 sq. cm = 10.2 sq. cm
Final answer:
We cannot complete the statement definitively about the surface area comparison between the square pyramid and the triangular prism without specific measurements. However, if we knew the dimensions, we could use the principle that surface area scales with the square of the linear dimensions to compare the two.
Explanation:
To complete the statement about the surface areas of Figure 1 (a square pyramid) and Figure 2 (a right triangular prism), we need to consider how areas scale with the dimensions of the shapes. Salviati's example illustrates that surface areas scale with the square of the linear dimensions, which is an important concept in geometry. Applying this concept to two triangles where one is larger than the other with linear dimensions twice as long, the larger triangle will have an area four times greater (area scales with the square of the linear dimensions).
Correct solution #1: Since the larger triangle's sides are twice as long, its area is 22 = 4 times more than the smaller triangle. If we applied similar reasoning and knew the dimensions of Figure 1 and Figure 2, we could compare their surface areas. However, with the provided information, we cannot definitively complete the given statement about the surface area of the pyramid relative to the prism without the specific measurements of each figure.
By understanding that the surface area of shapes scales with the square of their dimensions and using examples like cutting the larger triangle into four smaller ones (correct solution #2), we can tackle the surface area comparison confidently, provided we have the necessary dimensions.
at a bookstore, 8 similar books cost y dollars. what is the price of 3 such books?
[tex]\bf \begin{array}{ccll} books&price\\ \cline{1-2} 8&y\\ 3&x \end{array}\implies \cfrac{8}{3}=\cfrac{y}{x}\implies 8x=3y\implies x=\cfrac{3}{8}y[/tex]
Final answer:
To determine the price of 3 books when given the cost of 8 similar books, you divide the total cost by 8 to find the price per book, then multiply this price by 3.
Explanation:
The student asked: At a bookstore, 8 similar books cost y dollars. What is the price of 3 such books? To find the price of one book, we divide the total cost y by the number of books, which is 8. Let's call the price of one book x. So, x = y/8.
To find the price of 3 books, we multiply the price of one book by 3. Hence, the price of 3 books would be x times 3 or (y/8) times 3, which can be simplified to 3y/8.
Thus, the price of 3 such books is 3y/8 dollars.
The following equation is being multiplied by the LCD. Complete the multiplication to eliminate the denominators
x+2/3x - 1/x-2 = x-3/3x
(3x)(x-2) [x+2/3x - 1/x-2] = (3x)(x-2) [x-3/3x]
The resulting equation is
x+2-1 = x-3
3x(x+2)-(x-2) = x-3
(x-2)(x+2)-1 = (x-3)(x-2)
(x-2)(x+2)-3x=(x-2)(x-3)
After multiplying by the LCD, the denominators are eliminated, resulting in the equation (x-2)(x+2) - 3x = (x-2)(x-3). Further simplifying this equation, we obtain x^2 - 3x - 4 = x^2 - 5x + 6 which can then be solved with algebraic methods.
Explanation:To solve the given equation by multiplying each term by the lowest common denominator (LCD), which is 3x(x-2), we need to eliminate the fractions first.
The given equation is:
(x+2)/(3x) - 1/(x-2) = (x-3)/(3x)
After multiplying each term in the equation by the LCD, we have:
3x(x-2) * ((x+2)/(3x)) = (x-2)(x+2)3x(x-2) * (-1/(x-2)) = -3x3x(x-2) * ((x-3)/(3x)) = (x-2)(x-3)Now, we can write the new equation without denominators:
(x-2)(x+2) - 3x = (x-2)(x-3)
Next, we simplify it:
x^2 + 2x - 2x - 4 - 3x = x^2 - 3x - 2x + 6
x^2 - 3x - 4 = x^2 - 5x + 6
This equation can now be simplified or solved using algebraic methods such as combining like terms or moving all terms to one side in preparation for factoring or applying the quadratic formula.
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Answer:
(x-2)(x+2) - 3x = (x-2)(x-3)
Step-by-step explanation:
~~THIS IS MULTIPLE CHOICE ~~
someone help me please I'm honestly lost
(PiCtUrE AtTaChEd)
Answer:
Derek delivers 10 magazines per hour.
Step-by-step explanation:
in the bottom of the table, M(h), the magazine number decreases by 10 every hour. So it takes him 1 hour for every 10 magazinesderek delivers ten magazines per hr
Write down the nth term of the following sequence:
7 2 -3 -8 -13
With steps and explanation please,!!
Answer:
see explanation
Step-by-step explanation:
This is an arithmetic sequence with n th term
• [tex]a_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference
d = 2 - 7 = - 3 - 2 = - 5 and a = 7, hence
[tex]a_{n}[/tex] = 7 - 5(n - 1) = 7 - 5n + 5 = 12 - 5n
[tex]a_{n}[/tex] = 12 - 5n ← n th term formula
help me answer the quesyion for 13 points
Answer: it is (-2,2)
Step-by-step explanation:
You go on the -2 point on the x axis and 2 block up from that point to get (-2,2).
Micha made a scale model of the Empire State Building. The building has an actual height of 381 meters. Micha’s model used a scale in which 1 cm represents 50 meters. What is the height in centimeters of michas model?
Micha's scale model of the Empire State Building is 7.62 centimeters tall
To determine the height in centimeters of Micha's scale model of the Empire State Building, we use the given scale where 1 cm represents 50 meters.
First, we find the scale factor for the actual height of the Empire State Building, which is 381 meters.
Using the scale, the calculation is as follows:
Actual height of Empire State Building = 381 m.
Scale ratio = 1 cm : 50 m.
Height of model in cm = Actual height (in meters) \/ Scale ratio (meters per cm).
Height of model in cm = 381 m / 50 m/cm.
Height of model in cm = 7.62 cm.
Therefore, the height of Micha's model is 7.62 centimeters.
Pls answer this pls
Answer:
nearsighted: A, C, Efarsighted: B, Dmost nearsighted: Emost farsighted: DStep-by-step explanation:
Since the questions are about which numbers are positive or negative and which have the largest magnitude, it is convenient to arrange them in order from least to greatest:
-3.00 (E), -2.25 (A), -1.50 (C), 1.00 (B), 3.25 (D)
Nearsighted patients are those with negative prescriptions: E, A, C.
Farsighted patients are those with positive prescriptions: B, D.
The most nearsighted patient has the most negative prescription: E
The most farsighted patient has the most positive prescription: D
Point B is the midpoint of AC
Which statements about the figure must be true? Check all
that apply
a)
b)
c) <ВС = 1/2 AC
d)
e) DB congruent BC
f) 2m
BC=1/2 AC must be true because B is a mid point so BC=AB=1/2AC
Given that B is the midpoint of AC
AC= AB + BC
Since AB = BC
AC = 2 [tex]\times[/tex] BC
so BC = [tex]\frac{1}{2} \times[/tex]AC
If the Length of BC = Length of BD then they are said to be congruent.
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HELP NOW PLEASE. The yearly attendance at a ballpark is shown in the table. Which answer describes the average rate of change from Year 2 to Year 5?
I think the last one. Sorry if I’m wrong. Minus year 2 and 5
Answer:
Option. A is the correct option.
Step-by-step explanation:
The yearly attendance at a ballpark is shown in the table attached.
We have to describe the average rate of change in attendance from year 2 to year 5.
Since rate of change in the attendance will be described by [tex]\frac{\text{Difference in attendance}}{\text{Difference in years}}[/tex]
Therefore, average change in attendance = [tex]\frac{\text{Attendance in year 5 - attendance in year 2}}{\text{5-2}}[/tex]
= [tex]\frac{333.7-298.3}{5-2}=\frac{35.40}{3}[/tex]
= 11.80 thousands per year
≈ 11800 people per year
Therefore, there is an average rate of change of 11800 people per year from year 2 to year 5.
Option A. is the answer.
Mrs. Jenkins just finished grading her math tests. The average score on her test was 93%. However, she forgot to grade Billy's paper. Billy scored 80% on the test. What is going to happen to the class average, once she includes Billy's score?
A.
The class average will stay the same.
B.
The class average will go up.
C.
The class average will go down.
D.
There is not enough information.
Including Billy's score of 80% will lower the class average from 93% because his score is below the initial average.
Explanation:When including Billy's test score of 80% into the class average that was previously 93%, the class average will definitely go down. This is because Billy's score is lower than the class average, so when it is factored into the overall calculation, it will decrease the average. Hence, the correct answer to the question is: C. The class average will go down.
Shelf A had 40 books and Shelf B had 16 books. After Katrina borrowed an equal number of books from Shelf A and Shelf B, there were 3 times as many books on Shelf A than Shelf B. How many books did Katrina borrow altogether?
Answer:
8 books; 4 from each shelf
Step-by-step explanation:
let x represent equal number of books from each shelf
from shelf A = 40 -x
from shelf B = 16 -x
shelf A has 3 times as many books than shelf B
3(16- x) = 40 -x
48 -3x = 40 -x
48 - 40 = -x + 3x
8 = 2x
x = 4
altogether she borrowed 4 + 4 = 8 books
Write the equation in exponential form. Log 4 1/16 =-2
Answer:
see explanation
Step-by-step explanation:
Using the rule of logarithms
• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Hence
with b = 4 and n = - 2
[tex]log_{4}[/tex] [tex]\frac{1}{16}[/tex] = - 2, then
[tex]\frac{1}{16}[/tex] = [tex]4^{-2}[/tex] ← in exponential form
ANSWER
The exponential form is
[tex] \frac{1}{16} = {4}^{ - 2} [/tex]
EXPLANATION
The given logarithm is
[tex] log_{4}( \frac{1}{16} ) = - 2[/tex]
We want to write the given logarithm in exponential form:
We take the antilogarithm of both sides to obtain:
[tex] {4}^{log_{4}( \frac{1}{16} )} = {4}^{ - 2} [/tex]
We simplify the left hand side to obtain:
[tex] \frac{1}{16} = {4}^{ - 2} [/tex]
Hence the exponential form is
[tex] \frac{1}{16} = {4}^{ - 2} [/tex]
Answer, please, hurry! :(
Answer: 10 square units
Answer:6 square units
Step-by-step explanation: count the top its 6 plus i did the test for my brother
How many times greater is the value of 0.03 than the value of 0.003
Answer:
The answer .03 is 10 times greater than .003
Step-by-step explanation:
.003 x 10= .03
Final answer:
The value of 0.03 is ten times greater than the value of 0.003. This is evident by observing that 0.03 is expressed as 3 x 10^-2 while 0.003 is expressed as 3 x 10^-3, showing 0.03 is one decimal place to the left of 0.003.
Explanation:
The value of 0.03 is ten times greater than the value of 0.003. This conclusion is reached by observing the placement of the decimal point. For each power of ten we move to the right, the number becomes 1/10 the size of the previous number. Conversely, moving one place to the left (making the number ten times bigger), we increase the value of the number by a factor of 10.
Expressing these numbers with negative exponents, we have:
0.03 as 3.0 x 10-2 (three and zero tenths times ten to the negative second power)0.003 as 3.0 x 10-3 (three and zero tenths times ten to the negative third power)As illustrated above, since 10-3 is one factor of 10 smaller than 10-2, the value 0.03 is ten times greater than 0.003.
in 5 rounds of a game, jill scored -3, 8, 9, -7, and 13. what integer represents her average score for 5 rounds?
-3+8+9+-7+13 divided by 5 which is 4
The integer represents her average score for 5 rounds will be 4.
What is the interpretation of average?Arithmetic mean is the best central measure available for representing the values of a data set. It is also called average of the values of the considered data set. It serves as one representation of the values of the data set. If for a data set, only its average is given, then we can't say much about the values of the data set. Average provides ill information in case of skewed data.
WE have given that 5 rounds of a game, jill scored -3, 8, 9, -7, and 13.
Then total number of score = - 3+8+9+-7+13
= 20
The total number of round in game = 5
Therefore,
Average = the total number of score/ number of rounds
Average = - 3+8+9+-7+13 / 5
Average = 20/5
Average = 4
Hence, the integer represents her average score for 5 rounds will be 4.
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A pre-image point is rotated 90° clockwise. If the pre-image point had the coordinates (3, -5), what are the coordinates of its image point?
(-5, -3)
(5, 3)
(-3, 5)
(-3, -5)
A pre-image point is rotated 90° clockwise. If the pre-image point had the coordinates (3, -5), what are the coordinates of its image point?
(-5, -3)
(5, 3)
(-3, 5)
(-3, -5)
Next Question
Ask for help
Turn it in
(5,3)
Explanation1. Determine the rule for this rotation
(x,y) ---> (-y,x)
2. Plug in
(3, -5) ----> (5,3)
Answer
(5,3)
Answer:
( -5, -3) .
Step-by-step explanation:
Given : A pre-image point is rotated 90° clockwise. If the pre-image point had the coordinates (3, -5).
To find : what are the coordinates of its image point.
Solution : We have given that
Parent coordinates (3, -5)
If the point is rotated 90° clockwise.
By the rotation rule of 90° clockwise (x ,y) →→ ( y , -x) .
Then (3 ,-5) →→ ( -5, -3)
Therefore, ( -5, -3) .
The range of the set of data below is 9
7. 16, 8, 16, 14, 10, 9, 8, 11, 12, 13, 18
True
False
False, The claim that the range of the data set (16, 8, 16, 14, 10, 9, 8, 11, 12, 13, 18) is 97 is false. The actual range is the difference between the largest and smallest values, which is 10.
The task is to determine whether the statement that the range of the provided data set is 97 is true or false. First, let's define the range. It is the difference between the smallest and largest numbers in a data set. Looking at the data provided: 16, 8, 16, 14, 10, 9, 8, 11, 12, 13, 18, we find the smallest value to be 8 and the largest to be 18.
To calculate the range, we subtract the smallest number from the largest: 18 - 8 = 10. Consequently, the initial claim that the range is 97 is false. The correct range of this data set is, in fact, 10.
The given statement the range of the set of data below is 9 is false.
The correct answer is False.
To find the range of a set of data, we subtract the smallest value from the largest value.
Step 1: Identify the smallest and largest values in the data set.
Smallest value: 7
Largest value: 18
Step 2: Calculate the range.
Range = Largest value - Smallest value
Range = 18 - 7
Range = 11
Step 3: Compare the calculated range with the given range.
Given range = 9
Calculated range = 11
Since the calculated range (11) does not match the given range (9), the statement "The range of the set of data below is 9" is False.
The range of a data set measures the spread or dispersion of the data. It is calculated by finding the difference between the largest and smallest values in the data set. In this case, the smallest value is 7 and the largest value is 18. Therefore, the range is 18 - 7 = 11. This contradicts the given range of 9, making the statement false. In summary, the correct answer is False, and the range of the given data set is 11.
Complete question:
The range of the set of data below is 9
7. 16, 8, 16, 14, 10, 9, 8, 11, 12, 13, 18
True
False
factor completely, 128x 2 +96xy + 18y 2
Answer:
[tex]2(8x+3y)^2)[/tex]
Step-by-step explanation:
The given expression is [tex]128x^2+96xy+18y^2[/tex].
We factor the GCF to get:
[tex]2(64x^2+48xy+9y^2)[/tex]
This can be rewritten as:
[tex]2[(8x)^2+2(3\times8)xy+(3y)^2][/tex]
We can observe that the quadratic trinomial is a perfect square)
[tex]2(8x+3y)^2)[/tex]
Therefore the completely factored form of the given trinomial is [tex]2(8x+3y)^2)[/tex]
Match the people with their accomplishments. 30 points!!
Answer:
View the picture please!
Step-by-step explanation:
A target with a diameter of 14cm has 4 scoring zones by concentric circles. The diameter of the center circle is 2 cm. The width of each ring is 2 cm. A dart hits the target at a random point. Find the probability that it will hit a point in the outer (yellow) ring
Answer:
[tex]48.98\%[/tex]
Step-by-step explanation:
we know that
The probability that it will hit a point in the outer (yellow) ring is equal to divide the area of the yellow ring by the total area of the target
step 1
Find the area of the yellow ring
[tex]A=\pi [7^{2} -5^{2}][/tex]
[tex]A=24\pi\ cm^{2}[/tex]
step 2
Find the total area of the target
[tex]A=\pi [7^{2}][/tex]
[tex]A=49\pi\ cm^{2}[/tex]
step 3
Find the probability
[tex]24\pi/49\pi=0.4898[/tex]
Convert to percentage
[tex]0.4898*100=48.98\%[/tex]
Answer:
0.38468
Step-by-step explanation:
To know the probability we need to know the area of the yellow zone and the area of the rest. So, the yellow circle (that contains white, red and blue circle) has a radius of 1+2+2+2=7. Then the area is
Area yellow= [tex]\pi r^{2}= \pi *7^{2}=49\pi.[/tex]
But, the yellow zone is yellow circle - blue circle.
Area blue = [tex]\pi r^{2}= \pi *(1+2+2)^{2}=\pi *5^{2}=25\pi.[/tex]
Then, the yellow zone will be [tex]49\pi-25\pi=24\pi.[/tex]
Area target= 14*14 = 196.
So, the probability is the yellow zone divided by the target (total area):
P = [tex]\frac{24\pi}{196}= \frac{6\pi}{49}= 0.38468.[/tex]