Answers
The probability that a point chosen at random lies in the shaded region is 0.28
Calculating the area of a shaded region and probabilityFrom the question, we are to find the probability that a point chosen at random lies in the shaded region.
The shaded region is a triangle.
The probability that a point chosen at random lies in the shaded region = Area of the triangle / Area of the circle
First, we will calculate the unknown side of the triangle
Let the unknown side be x.
Then, from the Pythagorean theorem, we can write that
12² = 6² + x²
144 = 36 + x²
x² = 144 - 36
x² = 108
x = √108
x = 6√3
From formula,
Area of a triangle = 1/2 × base × height
Area of the triangle = 1/2 × 6 × 6√3
Area of the triangle = 18√3 square units
Now, we will determine the area of the circle
Area of a circle = πr²
Where r is the radius
From the given information,
Diameter of the circle = 12
But,
Radius = Diameter / 2
Therefore,
r = 12/2
r = 6
Thus,
Area of the circle = 3.14 × 6²
Area of the circle = 113.04 square units
Now,
The probability that a point chosen at random lies in the shaded region = 18√3 / 113.04
The probability that a point chosen at random lies in the shaded region = 0.2758
The probability that a point chosen at random lies in the shaded region ≈ 0.28
Hence, the probability is 0.28
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Related Questions
The ale tax on a car that old for $13,500 i $910. At thi rate, how much higher i the tax on a car that ell for $16,500
Answers
The tax on a car that sells for $16,500 at the rate of 6.7% is $195.5 higher.
What is the percentage?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
We have,
First car price is = $13,500
and tax of the first car is = $910
Second car price is = $16,500
and tax of the second car is = ?
so,
$13,500 ----- 100,
$910 ----- x
x = 910 * 100 / 13500
x = 6.7
therefore, the rate of tax is 6.7%
so, we will calculate the tax for the second car,
$16,500 ----- 100,
y ----- 6.7
y = 6.7 * 16,500 / 100
y = $1105.5
difference of tax price between two cars = $1105.5 - $910 = $195.5
Hence, the tax on a car that sells for $16,500 at the rate of 6.7% is $195.5 higher.
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Find the length of the third side. If necessary, write in simplest radical form.
Legs- 9 and 7
Hypotenuse-?
Answers
You do 9^2 + 7^2 = x^2
81+49=x^2
130=x^2
Square root of 130 is
A decimal so simplistic radical form is square root 130
Answer:
√130
Step-by-step explanation:
|
? | 7
|
---------------------------
9
a² + b² = c²
7² + 9² = c²
49 + 81 = c²
130 = c²
√130 = √c²
√130 = c
I hope this helps!
Select the values that make the inequality h<3h<3 true. (Numbers written in order from least to greatest going across.) -5 -2 0 2 2.9 2.99 2.999 3 3.001 3.01 3.1 4 6 8 11
Answers
The values that make the inequality, h < 3h < 3, true are the values of h in the range 0 < h < 1. The values -5, -2, 0, 2, 2.9, 2.99, 2.999, 3, 3.001, 3.01, 3.1, 4, 6, 8, 11, are larger or smaller than the values make the inequality true.
What is an inequality in mathematics?An is a comparison between two expressions, using non equal expressions, such as ≥, >, ≠, <, or ≤ symbols.
The specified inequality is; h < 3·h < 3
When h < 3·h, we get;
h is a positive number larger than 0, such that we get;
When h < 0, 3·h < h
Therefore; h > 0
The inequality, 3·h < 3, indicates;
3·h < 3
h < 3/3 = 1
h < 1
Which indicates that we get;
0 < h < 1
Therefore, non of the values make the inequality, h < 3·h < 3
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Line d passes through points (6, 9) and (2, 4). Line e passes through points (5, 3) and
(10, 7). Are line d and line e parallel or perpendicular?
PLEASE HELP ASAP, WILL GIVE 10 POINTS, BRAINELST, 5 STAR, AND RATING!
Answers
Answer:
Neither
Step-by-step explanation:
Line d:
m = 4-9/2-6 = -5/-4 = 5/4
Line e:
m = 7-3/10-5 = 4/5
It would be neither because if it was perpendicular, one of the slopes' would have to be negative.
a 36 year old woman on chronic cyclosporine treatment for bilateral lung transplantation visits the emergency department complaining of extreme headache, nausea and vomiting. her exam is notable for bp 239/165, normal cardiac exam, bibasilar pulmonary rales, and 1 lower extremity edema. ekg showed asymmetric inverted t-waves in i, avl, and v4-6. in an effort to acutely control her blood pressure, which of the following is true?
Answers
The best treatment for this patient's acute blood pressure control is to administer an intravenous (IV) antihypertensive medication such as labetalol or nitroprusside. Additionally, it is important to assess for underlying causes of her elevated blood pressure such as infection, kidney disease, or heart failure.
What is blood pressure?
Blood pressure (BP) is indeed the force exerted by moving blood against blood vessel walls. The heart's action of trying to pump blood through the blood vessels is largely responsible for this pressure. The pressure in the major arteries is meant when the term "blood pressure" is used without qualification. Systolic pressure, or the highest pressure during one heartbeat, is typically expressed as the ratio of diastolic pressure, or the lowest pressure between two heartbeats, in blood pressure measurements. It is expressed as a millimetre of mercury (mmHg) just above atmospheric pressure in the immediate vicinity. Along with respiratory rate, pulse rate, oxygen levels, and body temperature, blood pressure is among the vital signs that medical professionals consider when assessing a patient's health.
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A safe-breaker is attempting to crack a safe with a 7-combination code. So far they have worked out that: the first digit is double the third digit the code is a palindrome (it reads the same if it is reversed) the fourth number is 7 the third number is one less than the sixth number the second number is 3 less than the fourth number.
Answers
The correct 7 digit combination safe-breaker code which is a palindrome is given by 6437346.
What is a Palindrome?A palindrome is a number that reads the same both forward and backward in mathematics. Examples of palindromes include 353, 787, and 2332.
The following straightforward procedure may be used to find other palindromes given any set of integers.
Start with any number in step one. Identify it as original number. Reverse the original number's digits.
Call the number whose numbers have been reversed in step two. The new number should be added to your original one.
Call the number discovered by combination of the new number with the test number.
Step 3: You're finished if the test number is a palindrome. If the test number is incorrect, use your original number instead and complete the previous procedures using your test number.
How to solve?
Let the seven-digit code be given by abcdefg. As it is palindrome therefore, a=g, b=f, c=e, and d=d. Also, first digit is double than third digit that is a=2c.
As per the question d=7, c=f-1 and,
b=7-3 = 4.
Since the number is palindrome so b=f. Therefore f=4.
Now, c=f-1 => c = 4-1 = 3, and c = e = 3.
Also, a=2c => a=6.
Thus, the numbers are a=6, b=4, c=3, d=7, e=3, f=4, g=6 and the combination is 6437346.
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On a number line, point d is at -6, and point e is at 8. point f lies between points d and e. if is , where does point f lie on the number line? point f is at on the number line.
Answers
The point F lies on 4.5 in the number line.
What is the number line?
The number line is a One dimensional representation of point referring by a number only.
We know that if a point divides a line joining the points at x, y in the number line respectively in m:n ratio then that point lies on
= (my+nx)/(m+n) in the number line.
Here in the given problem that,
Point D lies on -6 in the number lin
Point E lies on 8 in the number line
And F lies between D and E points and DE:EF = 3:1
So the point F clearly divides the staright line DE joining the point D at -6 and E at 8 in 3:1 ratio.
So the point F lies on = (1*(-6)+3*8)/(3+1) = (-6+24)/4 = 18/4 = 4.5
Hence, the point F lies on 4.5 in the number line.
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Consider the scatter plot, its line of best fit, and the corresponding residual plot of each data set. State whether a linear model is appropriate for the data and justify your answer.
Linear regression equation: y = 14.08x - 163.13, r = 0.9746
Answers
No, a linear model is not appropriate for the data because; the residual plot indicates that the residuals are far off the horizontal.
Is a linear model appropriate for the data given?It follows from the task content that it is required to determine if a linear model is appropriate for the given data.
By observation of the scatter plot and the line of best fit; it is evident that the residuals are large (meaning that actually values are far off the predicted values).
Conclusively, the residual plot is a confirmation of the inappropriateness of a linear model for the given data. This follows from the fact that the residuals are large as evident in the how far the residual plot points are to the horizontal.
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Convert 460000 milligrams into pounds. Round your answer to the nearest hundredth.
Answers
Answer:
460000 milligrams converted to pounds would be 1.01 pounds.
Step-by-step explanation:
2 websites sell the same type of headphone cost of headphone in website A is 49.95 and the postage is 4.39. The headphones in website B is 47.68 and the postage is 6.95. Including the postage which website is cheaper and by how much
Answers
Answer:
Website A is cheaper by 29 cents
Step-by-step explanation:
A
49.95 + 4.39 = 54.34
B
47.68 + 6.95 = 54.63
54.63 - 54.34 = 0.29
Answer:
the difference is 0.29 cents
website A is cheaper
Step-by-step explanation:
(47.68 + 6.95) - (49.95 + 4.39)
54.63 - 54.34 = 0.29
Segment BD bisects angle ABC measure angle ABC equals 7x. The measure angle ABD equals 3x+25. Find the measurement of angle DBC
Answers
The measurement of angle DBC is 100°. It can be obtained by the properties of bisector of an angle and algebriac multiplication.
What is angle bisector?
An angle bisector is the ray or line segment that divides the angle into two equal parts.
Since the segment BD bisects angle ABC hence,
∠ABC = ∠ABD+∠DBC ..... (1)
Also, since segment BD bisects angle ABC hence,
∠ABD = ∠DBC
Use this fact in equation (1)
∠ABC = ∠ABD+∠ABD
∠ABC =2 ∠ABD
Now, substitute values and use algebriac multiplication.
7x = 2(3x+25)
7x = 6x+50
7x - 6x= 50
x=50
Now, substitute the value of x in the expression of ∠ABD.
∠ABD = 3x+25
∠ABD = 3(50)+25
∠ABD = 100
Now, since ∠ABD = ∠DBC hence, ∠DBC = 100.
Hence, the measurement of angle DBC is 100°.
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A box of cereal states that there are 99 calories in a
3/4 cup serving. What is the unit rate for calories per cup? How many calories are there in 4 cups of the cereal?
Answers
The number of calories in one cup is 132 calories and the number of calories in 4 cups is 528 calories.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a box of cereal states that there are 99 calories in a 3/4 cup serving.
The number of calories per cup is calculated as,
3 / 4 cup = 99 calories'
1 cup = 99 x (4 / 3 )
1 cup = 132 calories
The number of calories for 4 cups of cereal,
1 cup = 132 calories
4 cup = 132 x 4 calories
4 cup = 528 calories
Therefore, the number of calories in one cup is 132 calories and the number of calories in 4 cups is 528 calories.
Therefore, the number of calories in one cup is 132 calories and the number of calories in 4 cups is 528 calories.
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find an equation in standard form for the ellipse with the vertical major axis of length 6 and minor axis of length 4. (2 points)
Answers
Standard form of ellipse has equation [tex]\frac{y^2}{a^2} +\frac{x^2}{b^2} =1[/tex] where, a and b are the halves of the length of major and minor axis respectively.
Given that,
Length of major axis(2a)=6.
So
a=6/2
=3
Length of minor axis(2b)=4.
So
b=4/2
=2
Putting in equation of standard ellipse. We get
[tex]\frac{y^2}{3^2} +\frac{x^2}{2^2} =1[/tex]
After simplifying
4y² + 9x² = 36
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A cylindrical rod of steel (e = 207 gpa) having a yield strength of 310 mpa is to be subjected to a load of 11,100 n. If the length of the rod is 500 mm, what must be the diameter to allow an elongation of 0. 38 mm?.
Answers
the diameter to allow an elongation of 0. 38 mm therefore required diameter is 7.65 mm
Given the data in the question;
F = 11100 N
l₀ = 310 mm = 0.31 m
E = 207 GPa = 207 × 10⁹ N/m²
Δl = 0.38 mm = 0.0005 m
So, lets assume the deformation is elastic;
d₀ = √( [4l₀F] / [πEΔl] )
we substitute
d₀ = √( [4 × 0.38 × 11100] / [π × (207 × 10⁹) × 0.0005]] )
d₀ = √( 10123.2 / 172787595.947 )
d₀ = √( 5.85875 × 10⁻⁵ )
d₀ = 0.007654 m
d₀ = ( 0.007654 × 1000 )mm
d₀ = 7.65 mm
Therefore, required diameter is 7.65 mm
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7. A tour guide charges $28 to take four people on a tour. How much does the tour guide charge per person?
Answers
Answer: $7
Step-by-step explanation:
We know that $28 for four people.
So we take 28 divided by 4 and we get $7 per people
40 PIONTS FOR ANSWERING 2 Q'S, I WILL PICK BRIANLISET
my equation for Q 7: C=2.7m+1.95
8. For the Raleigh company write an equation in point-slope form to represent the amount charged, C, for m number of miles for the company in Raleigh, NC.
9. Write an equation in standard form to represent the amount charged, C, for m number of miles for the company in Raleigh.
Answers
Answer:
8.m = ∞
9.[tex]m=\frac{20c-39}{54}[/tex]
Step-by-step explanation:
8.The equation is a vertical line, so the slope is ∞
so the answer for 8. is m = ∞
9.Switch sides:
2.7m + 1.95 = c
Multiply both sides by 100:
2.7m · 100 + 1.95 · 100 = c · 100
Refine:
270m + 195 = c · 100
Move 195 to the right side so it would be: 270m = c · 100 - 195
And now Divide both sides by 270
[tex]\frac{270m}{270}[/tex] = [tex]\frac{c*100}{270}[/tex] - [tex]\frac{195}{270}[/tex]
And now all that's left is to Simplify it
so the answer for answer 9. is [tex]m=\frac{20c-39}{54}[/tex]
Can someone please help me
Answers
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.
The expressions that are simplified are:
[tex]n^{4}[/tex]
[tex]\frac{1}{n^{-5}}[/tex]
[tex]\frac{1}{n^3}[/tex]
Options A, B, and E are the correct answer.
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,
[tex]n^{4}[/tex]
This is already simplified.
[tex]\frac{1}{n^{-5}}[/tex]
This is already simplified.
[tex]n^6 . n^{-8}[/tex]
= [tex]n^{6 - 8}[/tex]
= [tex]n^{-2}[/tex]
[tex]n^7 . p^8[/tex]
= [tex]n^{7 + 8}[/tex]
= [tex]n^{15}[/tex]
[tex]\frac{1}{n^3}[/tex]
This is already in simplified form.
Thus,
The expressions that are simplified are:
[tex]n^{4}[/tex]
[tex]\frac{1}{n^{-5}}[/tex]
[tex]\frac{1}{n^3}[/tex]
Options A, B, and E are the correct answer.
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5 divided by 19 vvchgdvbdvvvdbbxbvxvvdhhsjjshhhdbhshhhdhhshshhshdggdhshgdgfduhf
Answers
Find the length of the segment connecting (-4, 3) and (-5,2). Provide
an answer accurate to the nearest tenth.
Answers
The length of the segment connecting (-4, 3) and (-5,2) is 1.4.
How to find length of segment?The length of a line segment can be measured by measuring the distance between its two endpoints.
Therefore, the length of the segment connecting (-4, 3) and (-5,2) can be found as follows:
length of the segment = √(2 - 3)² + (-5 + 4)²
length of the segment = √(-1)² + (-1)²
length of the segment = √1 + 1
length of the segment = √2
length of the segment = 1.41421356237
length of the segment = 1.4
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almost every american adult has this thing
Answers
Answer: omm
but I need this so
Step-by-step explanation:
Can anybody help me with this?
Answers
The Height of trees are equal after 4 years and the height is 54 inches.
What is linear equation?A linear equation is a equation which draws straight line on the plot
when plotted.
Given,
Height of tree A at the time of planting = 38 inches
Height of tree B at the time of planting = 22 inches
Each year tree A grow = 4 inches
Each year tree B grow = 8 inches
Let's make an equation for the height of the trees,
H = 38 +4t
H = 22+8t
Now the time when height of both the trees will equal
38 + 4t = 22 + 8t
4t = 16
t = 4
Hence , After 4 years the height of both the trees will equal and the height of both the trees after 4 years will be 54 inches.
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Four more than twice the sum of a number and three is negative 5
Answers
Answer: It is A
Step-by-step explanation:
In 1972, about 22 crushed beverage cans weighed one pound. In 2002, beverage cans were lighter and about 34 crushed beverage cans weighed one pound. Every minute of every day, an average of 113,204 beverage cans are recycled. A: About how many pounds of beverage cans are recycled in an hour?
B: About how many tons of beverage cans are recycled in an average day?
C: About how many kilograms of beverage cans are recycled in a day?
Answers
A) The number of pounds that the beverage cans are recycled in an hour is 119772 pounds
B) The number of tons that the beverage cans are recycled in an average day is 2397 ton
C) The number of Kilograms that the beverage cans are recycled in a day is 57528000 kg
What is a pound?The pound is the main unit of sterling, and the term "pound" is frequently used to refer to British currency in general, which is often qualified in foreign contexts as the British pound or the pound sterling.
In 2002 about 34 beverages can weigh one pound.
In one minute 113204 beverage cans are recycled.
In one hour, 60 minutes number of beverage cans recycled=113204×60
=6792240
34 beverage cans weight 1 pound
1 beverage cans weight=1/34 pounds
A) 6792240 beverage can weigh=1
=(1/34)(6792240) pound
=119771.765 pound
≈119772 pound
B) So, In 24 hours, no. of pounds recycled
=119772×24 pound
=119772×24×0.0005 ton
=2397.26 ton
≅2397 ton in one day.
C) So, In 24 hours, no. of tons recycled
=2397×24 ton
=2397×24×1000 kg
=57528000 kg
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the hudson valley renegades stadium hold a maximum of 4,505 people. During the height of their popularity, they sold out 219 consecutive games. how many tickets were sold during this time?
Answers
Answer:
Step-by-step explanation:
4,505 tickets were sold 219 times.
4,505 x 219
The answer is 986,595
In the figure below, points D, B, E, F, and lie in plane X.
Points A and C do not lie in plane X.
For each part below, fill in the blanks to write a true statement.
Answers
The blanks are filled as below
(b) G and E are distinct points that are collinear.(c) F, D, B, and G are distinct points that are coplanar.(d) Suppose line AD is drawn on the figure. Then AD and AC are distinct lines that intersect.What are collinear points?Collinear points are those that are situated along a single straight line.
Collinear points are those that are on a line either close to or far from another point, it can be more than two points.
While coplanar points imply lying on the same plane
In the diagram,
E, F, and G are collinear points
D, B, E, F, and G are coplanar points
A, B, and C are another collinear points
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Gianna can wash 6 cars in 2 hours. At this rate, how many cars can Gianna wash in 5 hours?
Answers
Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.
What is unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
According to the given question:
Gianna can wash 6 cars in 2 hours
Therefore, in 1 hour she can wash 6/2 cars which is 3 cars.
Gianna's rate of washing cars is 3 cars per hour
Hence by unitary method, Gianna at this rate can washes 5 x 3 cars that is 15 cars.
Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.
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REASONING 11. Can the value of o*g_{2}(- 4) * befounc ? What about the value of log ? Why or why not ? What does this tell you about the domain of log ?
Answers
-4 = 2x ( if logbA = B , then A = bB)
Now take the value of x whatever you want and you are neither going to obtain a negative number nor zero.
So negative number and zero can't be the domain of logarithmic function.
Now it is clear that why log2(0) can't be obtained because exponential function is always positive.
So
Domain of logb(x) is positive real numbers or
x > 0 .
Write an inequality that could be used to represent all solutions for x: the quotient of a number and three minus twelve is less than 12
Answers
We can write the given statement as inequality as -
-(x/9) < 12
What is linear inequality? What is the law of Reversal and law of Trichotomy? What is the general equation of a Straight line?Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols.
y > mx + cy < mx + cy ≥ mx + cy ≤ mx + cReversal property : If (a > b) then (b < a) and if (a < b) then (b > a).
Law of Trichotomy : The "Law of Trichotomy" says that - only one of the following is true : (a < b) or (a = b) or (a > b).
The general equation of a straight line is y = mx + c
Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}We have the following statement -
"the quotient of a number and three minus twelve is less than 12".
We can write the inequality as -
-(x/9) < 12
Therefore, we can write the given statement as inequality as -
-(x/9) < 12
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PLEASE HELP ME
What is the y-intercept of this line?
I keep getting confused someone please help me and explain it better to me
Answers
Answer:
2
Step-by-step explanation:
The y-intercept is the point at which the graph crosses the y-axis.
(I have marked it in blue on the attached graph).
From inspection of the given graph, the line crosses the y-axis at point (0, 2). So the y-intercept is 2.
Please Help me With this ASAP (20 Points)
Answers
Answer:
200*1-0.95-0.95+0.9025
200*1-1.9+0.9025
200*0.0025
0.5
