NO LINKS!!! Find the probability that a randomly chosen point in the figure lies in the shaded region area.
Answers
#36
Area of rectangle
12(8)96Area of 6 circles.
6(π)(8/4)²6π(4)24π75.4Probability
75.4/960.78#2
Area of whole
(2+6)(6+10)8(16)144Area of two rectangles
2(10)(2)40So
Probability
144-40/144104/1440.7#3
Area of whole circle
π(4+4+2)²100πArea of inner circle(not shaded)
π(2)²4πArea of shaded circle
π(4+2)²36πProbability
16π-4π/96π12π/96π3/8Answer:
To find the probability that a randomly chosen point in the figure lies in the shaded region, we need to divide the area of shaded region by the total area of the figure.
Question 36Total Area
Area of a rectangle = width × length = 8 × 12 = 96 units²
Shaded Region Area
This is made up of 6 congruent circles.
The radius of each circle is 1/6 of the length of the rectangle (or 1/4 of the width).
⇒ radius = 12/6 = 2 units
Area of a circle = πr² = π(2)² = 4π units²
⇒ Shaded region area = 6 circles = 6 × 4π = 24π units²
Probability
= Shaded region area ÷ total area
= 24π ÷ 96
= 0.7853981634...
= 78.5% (3 s.f.)
Question 37Total Area
Area of a rectangle = width × length = 16 × 8 = 128 units²
Shaded Region Area
The easiest way to calculate this is to subtract the un-shaded areas from the total area:
⇒ Shaded region area = 128 - 2(2 · 10) = 88 units²
Probability
= Shaded region area ÷ total area
= 88 ÷ 128
= 0.6875
= 68.8% (3 s.f.)
Question 38Total Area
The radius of the largest circle is the sum of the individual given radii.
⇒ Area of a circle = πr² = π(4 + 4 + 2)² = 100π units²
Shaded Region Area
= Area of a circle with radius (4 + 2) - area of circle with radius 2
= π(6)² - π(2)²
= 32π units²
Probability
= Shaded region area ÷ total area
= 32π ÷ 100π
= 0.32
= 32%
Related Questions
The ratio of the sides of rectangle LMNP to the sides of rectangle TUVW is 1:4. The length of LM is 3.6 in, and the length of UV is 16 in.
What is the difference between the areas of the two rectangles?
A. 226 in2
B. 172.8 in2
C. 211 in2
D. 216 in2
Answers
graph h(x)=(x-1)^2-9
Answers
The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.
The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.
The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.
The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).
Based on this information, we can draw the following conclusions:
The graph will be a U-shaped curve with the vertex at (1, -9).
The vertex represents the minimum point of the parabola since it opens upward.
The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.
The graph will extend indefinitely in both directions.
To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.
Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.
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2) Ayanda wants to invest R200 000. The bank offers him 2 options for his
6 year investment.
Option 1: 12% Simple interest p.a.
Option 2: 9,5% Compound interest p.a.
4.2.1) Calculate the return on Ayanda's investment using Option 1.
●
●
4.2.2) Calculate the return on Ayanda's investment using Option 2.
4.2.3) Which option will render the most money?
Answers
Answer:
4.2.1) R140 000
4.2.2) R144 758.28
4.2.3) Option 2
Step-by-step explanation:
To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.
\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)
Given values:
P = R200 000r = 12% = 0.12t = 6 yearsSubstitute the given values into the formula and solve for I:
\(I=200000 \cdot 0.12 \cdot 6\)
\(I=24000 \cdot 6\)
\(I=144000\)
Therefore, the return on Ayanda's investment using Option 1 is R144000.
\(\hrulefill\)
To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.
\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)
Given values:
P = R200 000r = 9.5% = 0.095t = 6 yearsSubstitute the given values into the formula and solve for I:
\(I=200000(1+0.095)^6-200000\)
\(I=200000(1.095)^6-200000\)
\(I=200000(1.72379142...)-200000\)
\(I=344758.28426...-200000\)
\(I=144758.28426...\)
\(I=144758.28\)
Therefore, the return on Ayanda's investment using Option 2 is R144758.28.
\(\hrulefill\)
Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.
Can u do 25 and how to do it
Answers
Answer:
f(- 1) = 10
Step-by-step explanation:
using the rule of exponents
\((\frac{a}{b}) ^{-1}\) = \((\frac{b}{a}) ^{1}\) = \(\frac{b}{a}\)
to find f(- 1) substitute x = - 1 into f(x)
f(- 1) = 5\((\frac{1}{2}) ^{-1}\) = 5 × \(\frac{2}{1}\) = 5 × 2 = 10
i only need the answer for #6
Answers
Greetings !
The function has no undefined points nor domain constraints Therefore, the domain is
\(domain \: of \: 3 {}^{x} = \\ interval \: notation \: ( - \infty ,\infty ) \\ solution \: - \infty < x < \infty \\ \\ \)
The range of an exponential function of the form
\(c.n {}^{ax + b} + k \: is \: f(x) > k \\ k = 0,f(x) > 0\)
And also the range is given as
\(range \: of \: 3 {}^{x} = \\ solution \: x > 0 \\ interval \: notation \: (0,\infty )
Hope it helps!
PLEASE HELP PLEASE PLEASE HELP
Answers
Answer:
2:3
Step-by-step explanation:
Simplica Los dos numeros
6 ÷ 3 = 2
9 ÷ 3 = 3
Simon began a weight-loss program. He loses weight every two weeks. His weight, in pounds, t months after he began the weight-loss program, is shown by the following expression.
210(0.94)2t
Which statement below best describes the base, 0.94?
A. Simon's weight before he beganm the weight-loss program
B.the rate which Simon loses weight
C. the monthly decrease in Simon's weight
D. the numbers of times Simon has lost weight since he began the weight-loss program
Answers
helo please find the values of x and y
Answers
Answer:
x=5
y=20
Step-by-step explanation:
abc =def
3X-3=12
X=(12+3)\3 =5
AND 7X+Y=55
Y=20
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
A/60
B/45
C/105
The measurement of angle A is
The measurement of angle B is
The measurement of angle Cis
Answers
The second pair of points representing the solution set of the system of equations is (-6, 29).
To find the second pair of points representing the solution set of the system of equations, we need to substitute the x-coordinate of the second point into one of the equations and solve for y.
Given the system of equations:
y = x^2 - 2x - 19
y + 4x = 5
Substituting the x-coordinate of the second point (-6) into equation 2:
y + 4(-6) = 5
y - 24 = 5
y = 5 + 24
y = 29
Therefore, the second pair of points representing the solution set of the system of equations is (-6, 29).
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Question
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
y = x2 − 2x − 19
y + 4x = 5
The pair of points representing the solution set of this system of equations is (-6, 29) and
_________.
Will mark the brainliest
Answers
Answer:
i have no idea
Step-by-step explanation:
Answer:
Step-by-step explanation:
put the g 3 first
3+1/3-1=2
f 2 = 3(2)-7=-1
Suppose that a poll taken 10 years ago found that 55% of parents spank their children. Suppose a recent poll of 500 adults with children finds that 242 indicated that they spank their children. Complete parts (a) and (b) below. (a) Assuming parents' attitude toward spanking has not changed since the original poll, how many of the 500 parents surveyed would be expected to spank their children?
Answers
Answer:
Of the 500 parents surveyed 275 would be expected to spank their children.
Step-by-step explanation:
Let the random variable X represent the number of parents who spank their children.
It is provided that, from previous studies, p = 55% of parents spank their children.
A random sample of n = 500 adults were selected.
The event whether a parent spank their children is independent of other parents.
The random variable X thus follows a Binomial distribution with parameters n = 500 and p = 0.55.
The expected value of a Binomial random variable is:
\(E(X)=np\)
\(=500\times 0.55\\=275\)
Thus, of the 500 parents surveyed 275 would be expected to spank their children.
From the 500 parents surveyed, the number of parents that will be expected to spank their children is 275 parents.
Number of parents surveyed = 500
Percentage of parents that spank their children = 55%
Therefore, from the 500 parents surveyed, the number of parents that will be expected to spank their children will be:
= 55% × 500
= 0.55 × 500
= 275
Therefore, the number of parents will be 275 parents.
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1
In a circle, the coordinates of the endpoints of
a diameter are (4,5) and (10,1). What are the
coordinates of the center of the circle?
Answers
Answer: (7,3)
Step-by-step explanation:
Find the midpoint of the diameter to find the center
mid-point formula
\((\frac{(x_{1} +x_{2)} }{2} ,\frac{(y_{1} +y_{2} )}{2} )\)
Using points (4,5) and (10,1)
\((\frac{4+10}{2} , (\frac{5+1}{2} )\\(\frac{14}{2},\frac{6}{2}) \\\\(7,3)\)
The coordinates of the center of the circle are (7, 3).
Given that, in a circle, the coordinates of the endpoints of a diameter are (4,5) and (10,1).
What is the midpoint of a line segment?A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.
The formula to find the midpoint of line segment is (x, y) = [(x1+x2)/2, (y1+y2)/2]
The center of the circle is midpoint of a diameter
Here, (x, y) = ((4+10)/2, (5+1)/2)
= (14/2, 6/2)
= (7, 3)
Therefore, the coordinates of the center of the circle are (7, 3).
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consider a normal population with u= 75 and o= 10. a sample of at least which size needs to be obtained in order to achieve a standard error or om= 2.00 or less.
Answers
n = 25
=====================================================
Explanation:
The standard error formula for the mean is
\(\sigma_{M} = \frac{\sigma}{\sqrt{n}}\\\\\)
Since we want this 2.00 or less, this means,
\(\sigma_{M} \le 2.00\\\\\frac{10}{\sqrt{n}} \le 2.00\\\\10 \le 2.00\sqrt{n}\\\\2.00\sqrt{n} \ge 10\\\\\sqrt{n} \ge \frac{10}{2.00}\\\\\sqrt{n} \ge 5\\\\n \ge 5^2\\\\n \ge 25\\\\\)
The sample size needs to be n = 25 or larger.
In other words, the sample size needs to be at least 25.
e these word problems. Check your answers.
A man had paid $175.50 in interest at the end of three years. How much had he borrowed at 9% per year?
(The problem gives you the interest, rate, and time. You need to find the principal.)
Answers
Answer:47.38
Step-by-step explanation:175.50/100 x27im not that sure
Evaluate the expression 2(8 − 4)2 − 10 ÷ 2. (5 points)
Answers
Answer:
11
Step-by-step explanation:
2(8−4)(2)− 10/2
=11
___________________________________________________________
EASY
yourwelcome
S-348
a-1.7 t
Area
Perimeter
Type
s = 3.3 yds
a = 1 65 yds
Area
Perimeter:
Type:
7)
s=5.4 mm
a = 2.57 mm
Area:
Perimeter:
Type:
Identify and Calculate the Area and Perimeter for ea
2)
a-8.2 yds
c-94 yds
Area
Perimeter.
Type:
5)
a
b
Ares
8)
a 66 cm
Triangle
h
Perimeter
Type.
Area
b-4.6 yds
a
h- 5.98 cm
Trapezoi
a=2.5 cm
a-1.25 cm
Perimeter
Type
Can someone solve help solve these???
Answers
Is 3 the coefficient of s/3?
Answers
The coefficient of s/3 is 1/3.
s/3 = (1/3)s
No, 3 is not the coefficient of s/3.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
s/3
This can be written as (1/3)s.
The coefficients of an equation are the non-zero values along with the variables.
Example:
ax² + bx + 3
The coefficients of this equation are a, and b.
The coefficient for the expression s/3 is 1/3.
Thus,
The coefficient of s/3 is 1/3.
s/3 = (1/3)s
No, 3 is not the coefficient of s/3.
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Clean Machine is Middletown's premier house cleaning service. The company used 2,920 gallons of soap last year, and 35% less this year. How many gallons of soap did the company use this year?
Answers
Answer:
Step-by-step explanation:)
Need help with question
Answers
Answer:
f(2) = 1
x = 0
Step-by-step explanation:
f(2) = 1 since y=1 when x=2.
f(0) = -3 since x=0 when y=-3
This is a picture of a cube and the net for the cube.
What is the surface area of the cube?
Responses
Answers
The surface area of the cube is 384 mm².
What is a cube:A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Since there are six square that makes up a cube, to find the surface area of the cube, we find the area of one of the square and multiply by six
A = 6L²...................... Equation 1Where:
A = Surface area of the cubeL = Length of the side of the cubeFrom the question,
Given:
L = 8 mmSubstitute this value into equation 1
A = 6×8²A = 6×64A = 384 mm²Hence the right option is D. 384 mm².
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b. What is the area of the surface of Crater Lake?
Give a step by step explanation
Answers
Answer: 23.76 miles
Step-by-step explanation:
You are basically finding the perimeter for question a
given that perimeter is \(\pi\)d
Subsitute the values
So perimeter = \(\pi\) x 5.5 = 5.5 \(\pi\) miles = 17.28 miles (2.d.p)
For question b, the area of the surface of Crater lake is finding its area
Given that area of a circle is \(\pi r^{2}\)
Substitute the values
Because 5.5 is the diameter, to find the radius, divide by 2 to get 2.75
Area = 2.75^2 x \(\pi\) = 7.5625\(\pi\) = 23.76 miles^2 (2.d.p)
What is the justification for each step in the solution of the equation?
23x−13=2(x+2)
23x−13=2(x+2) Given
2x−1=6(x+2)
2x−1=6x+12
2x=6x+13
−4x=13
x=−134
Answers
The justification for each step in the solution of the equation are as follows:
2/3x − 1/3 = 2(x + 2) -- GivenBy the multiplication property of an equation: 2x − 1 = 6(x + 2)By the distributive property of an equation: 2x − 1 = 6x + 12Collect and evaluate the like terms: 2x = 6x + 13By the subtraction property of an equation: −4x = 13By the division property of an equation: x =−13/4How to determine the justification for each step in the solution of the equation?The equation is given as
23x − 13 = 2(x + 2)
Based on the solutions, we can rewrite the given equation as follows
So, we have
2/3x − 1/3 = 2(x + 2)
So, the justification for each step in the solution of the equation are as follows:
2/3x − 1/3 = 2(x + 2) -- Given
By the multiplication property of an equation, we have
2x − 1 = 6(x + 2)
By the distributive property of an equation, we have
2x − 1 = 6x + 12
Next, we collect and evaluate the like terms
2x = 6x + 13
By the subtraction property of an equation, we have
−4x = 13
By the division property of an equation, we have
x =−13/4
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The length of a rectangular yard is 5 less than twice the width. The perimeter of the yard is 80 meters. Find
the dimensions of the yard
Answers
width=15
the explanation is in the attached picture
Five cards are dealt from a standard deck. What is the probability that at least four of them are hearts?
Answers
Step-by-step explanation:
To calculate the probability of getting at least four hearts when dealing five cards from a standard deck, we can use the concept of combinations and probability.
There are a total of 52 cards in a standard deck, and 13 of them are hearts (assuming no jokers). So the probability of drawing a heart on the first card is 13/52, or 1/4.
Now, there are two possible scenarios that would result in at least four hearts:
Four hearts and one non-heart: This can happen in C(13,4) * C(39,1) ways, where C(n, k) is the number of combinations of n items taken k at a time. The first part C(13,4) represents choosing 4 hearts out of 13, and the second part C(39,1) represents choosing 1 non-heart out of the remaining 39 cards. The total number of ways to choose 5 cards from 52 is C(52,5).
Five hearts: This can happen in C(13,5) ways, where C(13,5) represents choosing all 5 hearts out of 13.
So, the total number of favorable outcomes is C(13,4) * C(39,1) + C(13,5), and the total number of possible outcomes is C(52,5). Therefore, the probability of getting at least four hearts is:
P(at least 4 hearts) = (C(13,4) * C(39,1) + C(13,5)) / C(52,5)
Plugging in the values and simplifying, we get:
P(at least 4 hearts) = (C(13,4) * C(39,1) + C(13,5)) / C(52,5)
= (715 * 39 + 1287) / 2,598,960
= 27,885 / 2,598,960
≈ 0.0107566
So, the probability of getting at least four hearts when dealing five cards from a standard deck is approximately 0.0107566 or about 1.08%.
The graph below shows the solutions to which inequality?
A. x^2-3x+3 ≥0
B. x² + 3x-3 <0
C. x²-3x+3<0
D. x² + 3x-3>0
Answers
The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.
option B.
What is the solution of the inequality?The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;
The solution of the graph,
x > -4 and x < 1
The first equation with "≥" is ruled out because the graph doesn't have a thick dot.
Let's simplify the second expression;
x² + 3x - 3 < 0
solve using quadratic formula;
x > -3.79 or x < 0.79
The third expression is ruled out since its solution will be complex.
For the last expression;
x² + 3x - 3 > 0
x < -3.79 or x > 0.79
Thus, the correct inequality expression is x² + 3x - 3 < 0.
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The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days: Temperature, x | 72 85 91 90 88 98 75 100 80 No. of absences, y | 3 7 10 10 8 15 4 15 5 a) Find the equation of the regression line for the data. b) Assuming that the variables x and y have a significant correlation, what is the predicted number of absences when the temperature is 91? c) Calculate the correlation coefficient. d) Calculate the standard error for the model.
Answers
The equation of the regression line is y=-30.27+0.449x and predicted number of absences when the temperature is 910= 10.589
See table for sum of values.
The regression equation is:
y=α+βx
β = \(\frac{Sxx}{Syy}\)=6995-97799779\(\frac{6995-9\times\frac{779}{9}\times\frac{77}{9}}{68613-9(\frac{779}{9} )2}\)= 0.449
α=y-βx= 779-(0.449)7799 = =-30.27
The equation is y=-30.27+0.449x
Where y = predicted variable; x = independent variable = 0.449; - 30.27 = intercept/ slope
Constructing a 91% prediction interval for y:
x = 910
Inputting x = 91 into the regression equation : y = 0.449(91) - 30.27
y = 40.859 - 30.27 = 10.589
Prediction interval = y pm error margin
To save computing time, error margin (E) can be obtained using the online error margin calculator.
Obtained error margin (E) value = 2.3398
(10.589- 2.3398, 10.589+ 2.3398)
(8.2492, 12.9288)
(8, 13)
The equation of the regression line is y=-30.27+0.449x and predicted number of absences when the temperature is 910= 10.589
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i need help asap due tonight
Answers
Answer:
4
Step-by-step explanation:
multiply 10 by w and 3
equation becomes 10w+30=70
subtract 30 by both sides
equation becomes 10w=40
divide both sides by 10
equation becomes w=4
your answer is 4!
Explanation: 10 (4+3)=70. 4+3 is 7. And 7x10 is 70. :) hope I helped!
Hello please answer :) will give brainlst
Answers
Answer:
A. It is an atom
Step-by-step explanation:
That shows CO2 in the form of an atom
Answer:
D
Step-by-step explanation:
The answer is compound because a compound is a mixture of the two or the formed final product. It is basically the final result after adding those two together. It's also known as your solution. It isn't C a mixture because a mixture would just be a mix of the the molecules they wouldn't be bonded(attached to one another).
Hope this helps you out :)
Since my uncles farmyeard apperas to be overrun with gos and chickens i asked him hom many of each did he have he responded that his dog and chicked had a total of 148 legs and 60 heads. hime mmay of each does he have
Answers
There are 14 dogs and 46 chickens in the farmyard.
The supposition that there are d dogs and c chickens.
Each chicken has two legs, but each dog has four.
Consequently, the total number of legs may be written as follows:
4d + 2c
Since we are aware that there are 148 legs in total, we can construct the following equation:
4d + 2c = 148
We may create another equation since we know that there are a total of 60 heads (dogs and chickens):
d + c = 60
Now that we have two equations with two variables, we may answer them both at the same time.
2d + 2c = 120 is the result of multiplying the second equation by two.
When we deduct this from the first equation, we obtain 2d = 28.
So, d = 14.
Reintroducing this into the second equation, we get:
14 + c = 60
So, c = 46.
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Find the Value of x. I WILL GIVE YOU BRAINLIEST!!!!! +to the person who answers first)
Answers
Answer:
hi
Step-by-step explanation:
5x+10+2x+10+90=180
5x+2x=180-10-10-90
7x=70
x=10
have a nice day