Answers
Solution:
Given the circle with center A as shown below:
The plane travels 120 feet counterclockwise from B to C, thus forming an arc AC.
The length of the arc AC is expressed as
[tex]\begin{gathered} L=\frac{\theta}{360}\times2\pi r \\ \text{where} \\ \theta\Rightarrow angle\text{ (in degre}e)\text{subtended at the center of the circle} \\ r\Rightarrow radius\text{ of the circle, which is the }length\text{ of the control line} \\ L\Rightarrow length\text{ of the arc AC} \end{gathered}[/tex]Given that
[tex]\begin{gathered} L=120\text{ f}eet \\ \theta=80\degree \\ \end{gathered}[/tex]we have
[tex]\begin{gathered} L=\frac{\theta}{360}\times2\pi r \\ 120=\frac{80}{360}\times2\times\pi\times r \\ cross\text{ multiply} \\ 120\times360=80\times2\times\pi\times r \\ \text{make r the subject of the equation} \\ \Rightarrow r=\frac{120\times360}{2\times\pi\times80} \\ r=85.94366927\text{ fe}et \end{gathered}[/tex]Hence, the length of the control line is 85.94366927 feet.
Related Questions
22% of the squirrels in Cititon Park are gray. What is the probability that, in a random sample of 322
squirrels, fewer than 71 are gray squirrels? Use a normal approximation to compute your answer.
Round your answer to 4 decimal places.
Answers
The probability is 0.4841 .
Probability theory is the name of the branch of mathematics that deals with probability.
Although there are many ways to interpret the concept of probability, probability theory approaches it in a formal mathematical manner by articulating it through a set of axioms. These axioms typically formalize probability in terms of a probability space, which connects a sample space of possible outcomes to a measure that accepts values between 0 and 1. Statistical mechanics or sequential estimation are two examples of how probability theory approaches can be used to describe complicated systems when only a piece of their state is known. A significant achievement in twentieth-century physics was the description of the probabilistic nature of physical events at the atomic scale in terms of quantum mechanics.Given n = 322
p = 0.22
We know that from probability
μ = n × p = 0.22 ×322 = 70.84
σ = √(p × n×(1-p)) = 7.43
Now (P < 71) = P<70.84
Solving we get
P(z<-0.045)
= 0.48405
Therefore the probability is 0.4841
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pythagorean theorem
Answers
Your answer may need to be rounded depending on what your teacher requires
Step by step
Pythagorean theorem
a^2 + b^2 = c^2
a^2 + 2^2 = 8^2
a^2 + 4 = 64
Subtract 4 from each side
a^2 + 4 - 4 = 64 - 4
a^2 = 60
Take the square root of both side
a= 7.75 units
Answer:
7.75 units squared
Step-by-step explanation:
NO LINKS!! Please help me with this probability question
Answers
===========================================================
Explanation:
Define these two events
A = father born in Michigan
B = mother born in Michigan
The notation ~A and ~B represent the opposite of each defined event above.
According to the table
P(A) = 0.48
P(B) = 0.73
If A and B were independent, then P(A and B) = P(A)*P(B) = 0.48*0.73 = 0.3504 = 35.04% but this contradicts the 29% in the "father born in Michigan" column and "mother born in Michigan" row. The table states that P(A and B) = 0.29 should be the case instead of 0.3504.
Because of this contradiction, this means P(A and B) = P(A)*P(B) is false and therefore A and B are NOT independent
--------------------------------------
Another way to look at it:
P(A) = 0.48
P(A given B) = P(A and B)/P(B)
P(A given B) = 0.29/0.73
P(A given B) = 0.39726 approximately
If A and B were independent, then P(A) and P(A given B) would be the same value. However, they are not. This is another way to see why the events are NOT independent
Through similar calculations, P(B given A) = P(A and B)/P(A) = 0.29/0.48 = 0.6042 approximately which doesn't match with P(B) = 0.73; if A and B were independent then P(B) needs to be equal to P(B given A).
write 1.09 × 10^-4 in standard notation
Answers
1.09 × 10^-4 in standard form is
[tex]\text{ 1.09 x 10}^{-4}[/tex]Find (f - g)(x)
f(x) = 3x² - 2x
g(x) = 9x²2 - x + 7
A. -6x²-x-7
B. 6x²-x+7
C. 12x²-x-7
D. -6x²-3x - 7
Answers
The solution to the given function is (f-g)(x) = -6x² - x - 7.
What is a function?
Function, in mathematics, an expression, rule, or law that defines a relationship between : one variable (the independent variable) and another variable (the dependent variable).
A function is an equation with a single solution for y for each value of x. Each input of a particular type receives exactly one output when using a function. Instead of y, a function is frequently named f(x) or g(x). When x equals 2, we should determine our function's value because f(2) says to do so.
Given: f(x) = 3x² - 2x
g(x) = 9x² -x + 7
To find: ( f - g )(x)
thus (f-g)(x)= 3x² - 2x - ( 9x² - x + 7)
(f-g)(x) = -6x² - x - 7
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. Fritz spent two days last week writing his report and
another three days this week. In the last ten working
days, what fraction of the time has he been working
on his report?
Answers
Answer:
1/2
Step-by-step explanation:
5/10 which is the same as 1/2
give the answer, which of the following are composite numbers? 4 9 15 3 5
Answers
Given
we are given numbers 4, 9, 15, 3, 5
Required
we need to find which of the above numbers are composite.
Explanation
Here
[tex]\begin{gathered} 4=2\times2 \\ 9=3\times3 \\ 15=3\times5 \\ 3=3\times1 \\ 5=5\times1 \end{gathered}[/tex]clearly 4, 9, 15 have factors other than 1 and itself.
so 4, 9 and 15 are composite numbers
the wholesale price for a pair of shoes is $5.50. A certain department store marks up the wholesale price by 40%. Find the price of shoes in the department store.
Answers
EXPLANATION
Price of shoes = $5.50
Markup= 40%
Let's call x to the unknown final price.
The markup percentage relationship is given by the following formula:
[tex]\text{Markup =( }\frac{Selling\text{ Price}-\text{Cost Price}}{\text{Cost Price}})\cdot100[/tex]Replacing terms:
[tex]\text{40}=(\frac{x-5.5}{5.5})\cdot100[/tex]Multiplying both sides by 5.5:
[tex]40\cdot5.5=(x-5.5)\cdot100[/tex]Dividing both sides by 100:
[tex]\frac{40\cdot5.5}{100}=x-5.5[/tex]Adding 5.5 to both sides:
[tex](\frac{40\cdot5.5}{100})+5.5=x[/tex]Simplifyng the fraction:
[tex]2.2+5.5=x[/tex]Adding numbers:
[tex]\text{7}.7\text{ = x}[/tex]Switching sides:
[tex]x=7.7[/tex]Answer: The final price of the shoes in the deparment store is $7.7
The area of the desert is 25,000 square miles a scale drawing of the desert has a scale drawing 10 square inches. What is the scale of the map?
Answers
The scale of the map is 1 square inches = [tex]10^{13}[/tex] square inches.
Given that:-
Area of the desert = 25,000 square miles
Area of the desert in the map = 10 square inches
We have to find the scale of the map.
We know that,
1 mile = 63360 inches
Hence, conversion of square miles to square inches:-
1 mile * 1 mile = 63360 inches *63360 inches
1 square mile = 4,01,44,89,600 square inches
25,000 square miles = 40144893600*25000 = 10,03,62,24,00,00,000 square inches =[tex]10.036224 *10^{13}[/tex] ≈ [tex]10*10^{13}[/tex] square inches.
Now, we can say that [tex]10*10^{13}[/tex] square inches is scaled to 10 square inches.
Hence, the scale of the map is :-
1 square inches = [tex]10^{13}[/tex] square inches.
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Estimate sqrt(37) to the nearest tenth. Then locate sqrt(37) on a number line.137 =(Round to the nearest tenth as needed.)
Answers
The given number is
[tex]\sqrt{37}[/tex]Which is equal to 6,0827625302982196889996842452021...
However, rounded to the nearest tenth is
[tex]\sqrt{37}\approx6.1[/tex]The image below shows the number graphed on a number line.
Mr. Rodriquez is purchasing throphies for each trophies for each child that play little ldag
Answers
From the information provided, Mrs Rodriguez wants to spend nothing more than $7.00 per trophy. That means she can spend less than $7.00 if she has to, but she cannot spend anything above that amount.
Therefore, the correct answer is option 2, and that is;
5 trophies for $30.00
With other options given, she would be spending above $7.00 per trophy
What is the answer to this?
Answers
Answer: 4/7
Step-by-step explanation:
There are 7 students with brothers, 4 of which have sisters.
So, the probability is 4/7.
3х2 + 14х — 49 = 0solve for x
Answers
The given expression 3x^2 +14x-49=0
we will de factorization tos solve for x
[tex]\begin{gathered} 3x^2+14x-49=0 \\ 3x^2-7x+21x-49=0 \\ (3x^2-7x)+(21x-49)=0 \\ \text{Taking x common from (}3x^2-7x)=x(3x-7) \\ \text{Taking 7 common from }(21x-49)=7(3x-7) \\ (3x^2-7x)+(21x-49)=0 \\ x(3x-7)+7(3x-7)=0 \\ \text{Taking (3x-7) common} \\ (3x-7)(x+7)=0 \\ \text{ Thus, for} \\ \text{(3x-7)=0} \\ 3x=7 \\ x=\frac{7}{3} \\ \text{and for (x+7)=0} \\ x+7=0 \\ x=-7 \end{gathered}[/tex]The value of x is -7 and 7/3
Answer : x = -7 and x = 7/3
find perimeter and area of each triangle round to nearest hundredth
Answers
Given is a right angled triangle. Consider the figure,
Using the trignoetric funcyion tan, we have,
[tex]\begin{gathered} \tan 18=\frac{a}{12} \\ a=12\times\tan 18=3.89 \end{gathered}[/tex]Now, as we have base, a = 3.89 and height c = 12, the perimeter can be calcualted as,
[tex]\begin{gathered} P=a+c+\sqrt[]{a^2+c^2} \\ \text{ =3.89+12+}\sqrt[]{3.89^2+12^2}=28.5=29 \end{gathered}[/tex]Now, the area can be calculated as,
[tex]\begin{gathered} A=\frac{1}{2}ac \\ \text{ =1/2}\times3.89\times12=23.34=23 \end{gathered}[/tex]Please see photo I think it is the first answer but I wanted to confirm
Answers
Hello
The sample which she has to study is 200
The answer to this question is option A
Part A and B answer snd explaintion please
Answers
Answer:
Step-by-step explanation:
63 and 117
Thank for helping have a great rest of your night
Answers
The number of red balloons is 5.
The number of blue balloons is 7.
The number of yellow balloons is 12.
ExplanationTo find the probability of randomly selected a yellow balloon
[tex]P=\frac{number\text{ of red balloons}}{total\text{ number of balloons}}[/tex][tex]\begin{gathered} P=\frac{12}{5+7+12} \\ P=\frac{12}{24} \\ P=\frac{1}{2} \end{gathered}[/tex]AnswerHence the correct option is C that is 1/2.
HELP ME ASAPPP
Mr. Anderson worked with the following number of students each year.
42 in 2023-2024
256 in 2022-2023
195 in 2021-2022
228 in 2020-2021
174 in 2019-2020
136 in 2018-2019
216 in 2017-2018
204 in 2016-2017
151 in 2015-2016
What would we call 42 in this situation?
A.
Mean Absolute Deviation
B.
Mode
C.
Outlier
D.
Range
Answers
Notice how 42 is a much smaller number than 256,195,174, etc? the number that is much bigger or smaller from the other numbers is called an outlier.
Human hair grows at a rate of about 6.849×10-4 cm per hour to 2.329×10−2 cm per hour. The rate depends on gender, genetics, age, and health. Find the difference between the high end and the low end of the range. Express your answer in scientific notation rounding to 2 decimal places.
Answers
Answer:
2.×10^-2 cm/h . . . . rounded to 2 dp
2.26×10^-2 cm/h . . . . rounded to 3 sf
Step-by-step explanation:
You want the difference in growth rates between 6.849×10^-4 cm per hour and 2.329×10^-2 cm per hour.
DifferenceThe difference of two numbers written in scientific notation requires that they have the same power-of-ten multiplier.
2.329×10^-2 - 6.849×10^-4
= 2.329×10^-2 - 0.06849×10^-2 = 2.26051×10^-2 = 0.0226051
RoundingThe question asks for the answer rounded to 2 decimal places and expressed in scientific notation.
0.0226051 ≈ 0.02 = 2×10^-2 . . . . cm per hour
It makes more sense to round the mantissa to 2 decimal places, meaning the value is rounded to 3 significant figures.
2.26051×10^-2 ≈ 2.26×10^-2 . . . . cm per hour
What is the product of 840 and 4.6 x 102 expressed in scientific notation?
Answers
We can rewrite the expression:
[tex]840\times4.6\cdot10^2=8.4\cdot10^2\times4.6\cdot10^2[/tex]The product is,
[tex](8.4\times4.6)(10^2\times10^2)=(38.64)(10^{2+2})=38.64\times10^4[/tex]Sketch a graph of 6 x + 4 y = 4
Answers
The graph of 6x + 4y = 4 can be sketched as shown in the image attached below.
How to Sketch the Graph of a Linear Equation?A linear equation can be expressed in standard form as Ax + By = C, where A, B, and C are integers. Also, it can be rewritten in slope-intercept form as y = mx + b, where b is the y-intercept and m is the slope of the equation.
In order to graph an equation, we can easily determine what the slope (m) and the y-intercept (m) of the graph would be when we rewrite the equation in slope-intercept form.
Given the equation in standard form as, 6x + 4y = 4, rewrite it in slope-intercept form:
6x + 4y = 4
4y = -6x + 4
y = -6x/4 + 4/4
y = -3/2x + 1
This means that the slope of the graph you'd sketch will be -3/2, and the line must intercept the y-axis at 1, because the y-intercept is 1.
The graph is shown below.
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I need help with this worksheet that’s due tomorrow for algebra 1 it’s about Characteristics of Quadratic Functions
Answers
We have the following quadratic Function in a graph:
Now, we solve one aspect at a time:
Zeros
Let's remember that the zeros or roots of the quadratic function are those values of x for which the expression is 0. Graphically, the roots correspond to the abscissae of the points where the parabola intersects the x-axis.
By looking at the graph we can identify these, which in this case it is:
[tex](-2,0)[/tex]Axis of symmetry
Recall that the graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola.
By looking at the graph we can identify this, which in this case it is:
[tex]x=-2[/tex]Max or min
In mathematical analysis, the maxima and minima of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range or on the entire domain.
By looking at the graph we can identify this, which in this case it is:
[tex]y=0[/tex]Vertex
Remember that the vertex of a quadratic equation or parabola is the highest or lowest point of the graph corresponding to that function. The vertex lies in the plane of symmetry of the parabola; whatever happens to the left of this point will be an exact reflection of what happens to the right.
By looking at the graph we can identify this, which in this case it is:
[tex](-2,0)[/tex]can you please list 1-6 if they are rational irrational integer whole and natural
Answers
1. -14/2 = -7 Integer, Rational
2. √64 = 8 Natural, Whole, Integer, Rational
3. 0 Whole, Integer, Rational
4. π Irrational
5.
[tex]0.\bar{45}[/tex]can be expressed as a fraction, then it's rational
6. 3/8 Rational
Find anequation for the perpendicular bisector of the line segment whose endpoints are(-8, 4) and (-4,-8).
Answers
to solve this question, we need to difine our variables
we have values for end points as
x1 = -8
y1 = 4
x2 = -4
y2 = -8
next we can find the slope of the equation
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{-8-4}{-4-(-8)} \\ \text{slope}=\frac{-12}{4} \\ \text{slope}=-3 \end{gathered}[/tex]step 2
let's find the mid-point using mid-point formula
[tex]\begin{gathered} md=\frac{x_1+x_2}{2},\frac{y_2+y_1}{2} \\ md=\frac{-8+(-4)}{2},\frac{-8+4}{2} \\ md=-6,-2 \end{gathered}[/tex]mid-point = (-6, -2)
now we know the perpendicular line travels (-6 , -2) and has a slope of -3
equation of a straight line => y = mx + c
we can solve for c to find the equation.
[tex]\begin{gathered} y=mx+c \\ -2=(-3)(-6)+c \\ -2=18+c \\ c=-2-18 \\ c=-20 \end{gathered}[/tex]note: m = slope
c = intercept
the equation of the perpendicular bisector can be written as
y = -3x - 20
[tex]y=-3x-20[/tex]please help me ASAP!!
Answers
We have to solve:
[tex]\begin{gathered} 2^x-3=(x-6)^2-4_{} \\ 2^x-3+4=(x-6)^2 \\ 2^x+1=(x-6)^2 \end{gathered}[/tex]We can not write a explicit expression to find the value of x, but we can test each option to see which one is correct:
[tex]\begin{gathered} x=5 \\ 2^5+1=(5-6)^2 \\ 33=(-1)^2\longrightarrow\text{Not true} \end{gathered}[/tex][tex]\begin{gathered} x=3 \\ 2^3+1=(3-6)^2 \\ 8+1=(-3)^2 \\ 9=9\longrightarrow\text{True} \end{gathered}[/tex][tex]\begin{gathered} x=4 \\ 2^4+1=(4-6)^2 \\ 17=(-2)^2\longrightarrow\text{Not true} \end{gathered}[/tex][tex]\begin{gathered} x=-2 \\ 2^{-2}+1=(-2-6)^2 \\ \frac{1}{4}+1=(-8)^2\longrightarrow\text{Not true} \end{gathered}[/tex]Answer: x=3
Graph the line that is perpendicular to the line
7x+8y= 16 and passes through the
point (7, 2).
Answers
The general equation of the line is 7x+8y−65=0 when the line equation is 7x+8y=16 and the point is (7,2) and is perpendicular to the given line.
What is line?A line is a one-dimensional figure with no width and only length. A line is made up of a series of points that extend in opposite directions indefinitely. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.
What is equation of line?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. This number c is known as the y-axis intercept.
here, the given equation is 7x+8y=16 and point is (7,2).
by the relation y = mx + c we will find the value of slope for the line.
8y=-7x+16
y=(-7/8 ) x+16
on comparing relation,
m=[tex]\frac{-7}{8}[/tex]
y=mx+b
b=y1-m.x1
b=2-(-7/8).7
b=65/8
y=(-7/8)x+65/8
final equation,
7x+8y=65
The required equation of the line is 7x+8y=65 for the given point and line.
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Pls help I’ll mark brainliest im too tired for this
Answers
Answer:
309.8$
Step-by-step explanation:
450.60 - 35.20*4
= 309.8
:]
Create your own thought experiment explaining why a negative divided by a negative is a positive.
Answers
Dividing two negative numbers results in a positive number.A negative number divided by a negative number produces a positive result since two negatives equal a positive.
Explaining why a negative divided by a negative is a positive
The quotient is positive when two negative values are divided.The same guidelines apply to multiplication. Divided by another negative integer, a negative number always yields a positive number.divided equally by.The solution cannot be or any other negative number because it is positive. Divide two negative numbers, and you'll always get a positive number as the result.For instance, dividing -4 by -2 yields 2.The negatives cancel out when both numbers are negative, hence the outcome is always a positive number. Consider that you are taking part in a game that uses red and black chips.You will win one dollar (+1) at the end of the game for each black chip you have.You must pay one dollar for every red chip you possess.Assume that at some time throughout the game you have numerous bags of black chips and several bags of red chips. These chips are currently bundled together in bags of five.You make $15 if someone offers you three bags of black chips.(3)(5)=15.You lose 15 bucks if someone steals three of your bags of black chips.(-3)(5)=-15.You lose $15 if someone gives you three bags of red chips.(3)(-5)=-15.You lose $15 if someone gives you three bags of red chips.(3)(-5)=-15.You make 15 bucks if someone steals three of your bags of red chips.(-3)(-5)=15.The crucial concept is that negative numbers signify variations rather than totals.Saying that you have four slices of bread is illogical.However, it makes logical to state that since you had 4 slices of bread, the new number of slices you possess is 4.
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Please help with this math problems! This is due in a few hours!
Answers
(i) The vertex's x-coordinate is 25.
(ii) The maximum height of the cannonball is 12.48 meters.
(iii) Total horizontal distance that a cannon ball can travel is 50 meters.
(iv) Total horizontal distance that a cannon ball can travel with decreased angle is 22.5 meters.
(v) Distance the cannonball traveled before reaching the maximum height is 25 meters.
What is coordinate?
A pair of values is used to specify a point's placement on a coordinate plane using both horizontal and vertical distinctions from the two separate axes. usually represented by a pair of x-values and y-values (x,y).
(i) They are both at y = 4 and separated by (40-10) = 30
The symmetry line is halfway between 40 and 10
Consequently, the vertex's x-coordinate is 25.
(ii) y = -0.01x2 + 0.5x,
a = -0.01,
b = 0.5,
-b/2(a) = -0.5/(2X-0.01) = 0.5/0.02, and so on.
y=-0.01*2+0.5(25) =12.48 meters
The maximum height of the cannonball is 12.48 meters.
(iii) Total horizontal distance that cannon ball can travel is (0,0)-(50,0)= 50 meters.
(iv)Total horizontal distance that cannon ball can travel with decreased angle is (0,0)-(22.5,0) =22.5 metres
(v) Distance cannon ball travelled before reaching the maximum height is [(0,0)-(50,0)]/2 =25 meters
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Convert 21,510 ft to mi
Answers
Answer:
4.0738636
Step-by-step explanation: