Answer:
The length of the arc is 20 miles.
Step-by-step explanation:
We know that an arc formed by an angle of 1 radian in a circle of radius of 1 mile will have a length of 1 mile.
If the radius is 5 miles, an arc of 1 radian will have a length of 5 miles.
Then, if the angle is 4 radians, and the radius is 5 miles, we will have an arc length of:
[tex]\text{arc length}=\text {angle} \cdot \text {radius}=4\cdot 5 =20\;\text{miles}[/tex]
What is the sign of f
Answer:
The sign of f is used to symbolize many things. In physics it is commonly used to mean frequency and in music it is used to symbolize forte, which means loud.
Want Brainliest? Get this correct Which of the following is the quotient of the rational expressions shown below?
Answer:
[tex]\dfrac{4x^2+12x+5}{6x^2-3x}[/tex]
Step-by-step explanation:
Invert the denominator and multiply.
[tex]\dfrac{2x+5}{3x}\div\dfrac{2x-1}{2x+1}=\dfrac{2x+5}{3x}\cdot\dfrac{2x+1}{2x-1}\\\\=\dfrac{(2x+5)(2x+1)}{(3x)(2x-1)}=\boxed{\dfrac{4x^2+12x+5}{6x^2-3x}}\qquad\text{matches choice A}[/tex]
Answer:
[tex]\frac{4x^2+12x+5}{6x^2-3x}[/tex]
Step-by-step explanation:
After using the reciprocal of the second term, the denominator will multiply out to be [tex]6x^2-3x[/tex]. There is only one option with that as the denominator so it must be the correct answer.
Suppose you were given the function F(x)=x^4-2x^3+3x^2-10x+3 and the factor (x-2). What is the value of a?
Answer:
Hope it helps..........The given the function F(x)=x^4-2x^3+3x^2-10x+3 and the factor (x-2). Hence, the value of x is 7.5.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
The given the function F(x)=x^4-2x^3+3x^2-10x+3 and the factor (x-2).
here x = 2
Substitute in the function;
F(x)=x^4-2x^3+3x^2 - ax+3
F(2) = 2^4-2(2)^3+3(2)^2 - a(2) +3
F(2) = 16 - 16 + 12 - 2a +3
F(2) = 15 - 2a
15 - 2a = 0
15 = 2a
a = 7.5
Hence, the value of x is 7.5
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Determine whether the point (–3,–6) is in the solution set of the system of inequalities below. x ≤ –3 y < 5∕3x + 2
Answer:
The point (–3,–6) is not in the solution set of the system of inequalities below.
x ≤ –3 y < 5∕3x + 2
Step-by-step explanation:
Given point (-3, -6)
inequality
x ≤ –3
It means that value of x should be less than or equal to -3
since in point (-3,-6) , -3 is point for representing x which is equal to -3 and hence satisfy the criteria for valid value of x,
thus, -3 lie in the solution set of inequality x ≤ –3
lets now see for y = -6
to do that we will put x = -3 in the given below inequality
y < 5∕3x + 2
y < 5∕3*-6 + 2
y < -10 + 2
y < - 8
Thus, inequality suggests that value of y should be less than -8.
but here y is -6, if we see number line -6 is greater than -8 and hence does not belong to the solution set y < 5∕3x + 2 when x = -3
Thus, the point (–3,–6) is not in the solution set of the system of inequalities below. x ≤ –3 y < 5∕3x + 2
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle. A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n. Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle) Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles) Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p Step 4: So, m∠m + m∠n = m∠p In which step did the student first make a mistake and how can it be corrected? Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles) Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles) Step 2; m∠p − m∠o = 90 degrees (alternate interior angles)
Answer:
(A)Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle)
Step-by-step explanation:
In the triangle, the exterior angle = pThe adjacent interior angle =oThe two opposite angles are marked m and nThe steps followed by the student are:
Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle)
Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
We observe that the student made a mistake in Step 1, it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle).
p is outside the triangle, therefore it cannot form one of the angles in the triangle.
If a linear function passes through two points (x1, y1) and (x2, y2), what is the average value of the function on the interval from x1 to x2
Answer:
(y1+y2)/2
Step-by-step explanation:
adding and dividing by the total is the way to calculate the average
Can Someone help me!!! I need this ASAP! What number? Increased by 130% is 69? FYI: the answer is less than 69
Answer:
Hey there!
There are a few ways you could solve this problem, but the easiest would to be writing an equation.
You could say-
2.3x=69
Divide by 2.3
x=30
Hope this helps :)
Answer:
30
Step-by-step explanation:
the answer is 30 bc increasing something by 130% is multiplying it by 2.3 so technically you have to divide 69 by 2.3 which equals to 30
What is the length of Line segment A C? Round to the nearest tenth.
Step-by-step explanation:
To find AC we use tan
tan ∅ = opposite / adjacent
From the question
15 is the opposite
AC is the adjacent
tan 55 = 15 / AC
AC = 15 / tan 55
AC = 10.503
AC is 11 to the nearest tenthHope this helps you
Answer:
A: 10.5 m
Step-by-step explanation:
it's what i think it is, i may be wrong! hope this helps!!~
2. A ski lodge offers two weekend packages. Package A provides 2 nights and 3 meals for $280. Package B provides 2 nights and 5 meals for $320. Write and solve a system of equations to find the costs per night and per meal. (Assume the cost per night and cost per meal are the same for both packages.) Use n to represent the cost per night and m to represent the cost of each meal. (8 points) Step 1: The equation representing package A is given. Complete the system of equations by writing an equation to represent package B. (1 point) Package A: 2n + 3m = 280 Package B: ___________________ Step 2: Select a method for solving the system. Which method did you choose? Why? (2 points) Step 3: Solve the system of equations to find the costs per night and per meal. Show your work.(3 points) Step 4: Explain the meaning of the solutions for m and n. (2 points: 1 point each)
Answer:
see below
Step-by-step explanation:
Package A
2n + 3m = 280
Package B
2n + 5m = 320
Using elimination to eliminate n since the coefficient is the same
Subtracting the A equation from the B equation
2n + 5m = 320
-2n - 3m = -280
------------------------
2m = 40
Divide by 2
2m/2 = 40/2
m = 20
Now finding n
2n+3m = 280
2n +3(20) = 280
2n+60 = 280
Subtract 60 from each side
2n +60-60= 280-60
2n = 220
Divide by 2
2n/2 = 220/2
n = 110
The cost per night is 110 and the cost per meal is 20
m∠1=28°, m∠6=65°, m∠5=65°. Find m∠MAX
Answer:
<MAX = 93
Step-by-step explanation:
Since <MAX is technically <1 + <5, we know that <1 is 28 and <5 is 65. We can add both of these angles up to solve for <MAX, which is 28 + 65 = 93.
The angle of MAX is 93 degrees.
What is addition?The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
Since m∠MAX = m∠1 + m∠5,
we know that m∠1 = 28 and m∠5 = 65.
To solve for m∠MAX, which is 28 + 65 = 93.
Thus, the angle of MAX is 93 degrees.
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A survey of 61,647 people included several questions about office relationships. Of the respondents, 26% reported that bosses scream at employees. Use a 0.05 significance level to test the claim that more than ¼ of people say that bosses scream at employees.
Step-by-step explanation:
n = 61,647, p = 0.26, q = 0.74
μ = p = 0.26
σ = √(pq/n) = 0.00177
At 0.05 significance, z = 1.96.
0.26 ± 1.96 × 0.00177
(0.257, 0.263)
0.25 is outside of the confidence interval, so we can conclude with 95% confidence that the proportion is greater than 0.25.
Let S be a sample space and E and F be events associated with S. Suppose that Pr (Upper E )equals 0.6, Pr (Upper F )equals 0.2 and Pr (Upper E intersect Upper F )equals 0.1. Calculate the following probabilities. (a) Pr (E|F )(b) Pr (F|E )(c) Pr (E| Upper F prime )(d) Pr (Upper E prime | Upper F prime )
Answer:
(a)0.5
(b)0.17
(c)0.625
(b)0.375
Step-by-step explanation:
Pr(E)=0.6
Pr(F)=0.2
[tex]Pr(E\cap F)=0.1.[/tex]
(a)Pr (E|F )
[tex]Pr (E|F )=\dfrac{Pr(E \cap F)}{Pr(F)} \\=\dfrac{0.1}{0.2}\\\\=0.5[/tex]
(b)Pr (F|E )
[tex]Pr (F|E )=\dfrac{Pr(E \cap F)}{Pr(E)} \\=\dfrac{0.1}{0.6}\\\\=0.17[/tex]
(c)Pr (E|F')
Pr(F')=1-P(F)
=1-0.2=0.8
[tex]Pr(E \cap F')=P(E)-P(E\cap F)\\=0.6-0.1\\=0.5[/tex]
Therefore:
[tex]Pr (E|F' )=\dfrac{Pr(E \cap F')}{Pr(F')} \\=\dfrac{0.5}{0.8}\\\\=0.625[/tex]
(d)Pr(E'|F')
[tex]P(E'\cap F')=P(E \cup F)'\\=1-P(E \cup F)\\=1-[P(E)+P(F)-P(E\cap F)]\\=1-[0.6+0.2-0.1]\\=1-0.7\\=0.3[/tex]
Therefore:
[tex]Pr (E'|F' )=\dfrac{Pr(E' \cap F')}{Pr(F')} \\=\dfrac{0.3}{0.8}\\\\=0.375[/tex]
At a DBE lecture of 100 students, there are 29 women and 23 men. Out of these students, 4 are teachers and 24 are either men nor teachers. Find the number of women teachers attending the lecture
Answer:
20 teachers
Step-by-step explanation:
Because if you take 100 and minus it by 29, 23, 4 and 24 you get 20.
The total number of hamburgers sold by a national fast-food chain is growing exponentially. If 3 billion had been sold by 2003 and 9 billion had been sold by 2010, how many will have been sold by 2013
Answer:
F(10) = 14.41 Billion
The total number of hamburgers that will have been sold by 2013 is 14.41 billion.
Step-by-step explanation:
The exponential function representing the total number of hamburgers sold by a national fast-food chain which grows exponentially can be expressed as;
f(t) = p(a)^t
In 2003, t = 0 and f(0) = 3 Billion
f(0) = p = 3 billion
The initial value p = 3 billion
In 2010, t = (2010-2003) = 7
f(7) = p(a)^7 = 9 billion
3(a)^7 = 9
a^7 = 9/3 = 3
a = 3^(1/7)
Therefore, the function f(t) is;
f(t) = 3(3)^(t/7) .......2
In 2013, t = (2013 - 2003) = 10
Substituting t = 10 into equation 2;
f(10) = 3(3)^(10/7)
F(10) = 14.41195997001 Billion
F(10) = 14.41 Billion
The total number of hamburgers that will have been sold by 2013 is 14.41 billion.
Find the missing side. Round your answer to the nearest tenth.
Answer:
answer is a 107 hope it halp u
Answer:
24.9
Step-by-step explanation:
To do this, we set cos(58) to 15/x.
Using a calculator and some math, we get x is about 24.9.
Here is why we do that:
Since cosine is adjacent over hypotenuse, and we have the adjacent but not the hypotenuse, we can use that to create an equation.
Hope this helped!
What is the solution to the system of linear equations below?
x+4y=22
2x+y=9
Answer:
[tex]\boxed{\sf \ \ \ x = 2 \ \ and \ \ y = 5 \ \ \ }[/tex]
Step-by-step explanation:
hello, we have two equation
(1) x + 4y = 22
(2) 2x + y = 9
let's multiply (1) by 2 and subtract (2)
2x + 8y - (2x + y) = 2*22 - 9 = 44 - 9 = 35
<=> 2x + 8y -2x -y = 35
<=> 7y = 35
<=> y = 35/7 = 5
we replace this value in (1) and it comes
x + 4*5 = 22
<=> x = 22 - 20 = 2
so the solution is
x = 2 and y = 5
hope this helps
Two cities whose longitudes are 10E and 20W on the equator are apart
Step-by-step explanation:
to be honest I'm not sure how to do
CAN SOMEONEHELP PLS ASAP
Answer:
a ≈ 2.2
Step-by-step explanation:
Using the Cosine rule in Δ ABC
a² = b² + c² - 2bc cos A
Here b = 3, c = 4 and A = 32° , thus
a² = 3² + 4² - (2 × 3 × 4 × cos32° )
= 9 + 16 - 24cos32°
= 25 - 24cos32° ( take the square root of both sides )
a = [tex]\sqrt{25-24cos32}[/tex] ≈ 2.2
Please need help Please
Answer: 14/11
Step-by-step explanation:
When 14/11 is multiplied by 1/4, you get a repeating decimal. All repeating decimals are rational.
Hope it helps <3
the construction of creating the perpendicular bisector of PQ is started below. How would the construction be different if you changed the compass setting in the next step of the perpendicular bisector construction?
Answer: It will not create a perpendicular bisector.
Explanation:
If the compass is the same setting as the first arc and drawn from point B, the points of intersection of the arcs will pass through the midpoint of AB (thus creating a perpendicular bisector).
If you change the setting of the compass and draw an arc from point B, the points of intersection of the arcs will still create a perpendicular line but will not pass through the midpoint of AB (creating a perpendicular line but not a perpendicular bisector).
A perpendicular bisector divides a line segment into two equal segments.
If the compass setting is changed, the line will not be bisected.
To bisect a line, the positioning of the compass must be done as follows:
Place the compass at the endpoint of the line segment, then draw an arcRepeat the above process for the other endpoint of the line segment.Trace the point of intersection of the two arcs, to the line that is being bisected.The above points are what is being done in the given construction.
Any step or setting other than that, would not create a perpendicular bisector.
Hence, if the compass setting is changed, the perpendicular bisector of the line would not be drawn.
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A person has a bag containing dimes and nickels. There are a total of 120 coins in the bag, and the total value of the coins is $9.25. Determine how many dimes and nickels are in the bag. There are _____dimes. There are _____ nickels.
Answer:
There are 65 dimes. There are 55 nickels.
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the number of dimes
y is the number of nickels.
There are a total of 120 coins in the bag
This means that x + y = 120.
The total value of the coins is $9.25.
The dime is worth $0.10 and the nickel is worth $0.05. So
0.1x + 0.05y = 9.25
System:
[tex]x + y = 120[/tex]
[tex]0.1x + 0.05y = 9.25[/tex]
From the first equation:
[tex]y = 120 - x[/tex]
Replacing in the second:
[tex]0.1x + 0.05y = 9.25[/tex]
[tex]0.1x + 0.05(120 - x) = 9.25[/tex]
[tex]0.1x + 6 - 0.05x = 9.25[/tex]
[tex]0.05x = 3.25[/tex]
[tex]x = \frac{3.25}{0.05}[/tex]
[tex]x = 65[/tex]
[tex]y = 120 - x = 120 - 65 = 55[/tex]
There are 65 dimes. There are 55 nickels.
Legal descriptions tend to prefer neat straight lines from point to point, regardless of describing a square, rectangle, triangle or even a smooth circle. When might a property boundary end up being a squiggly line?
Answer:
When describing a property line drawn down the center of a creek bed
A tank contains 3,000 L of brine with 16 kg of dissolved salt. Pure water enters the tank at a rate of 30 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. (a) How much salt is in the tank after t minutes
Answer:
The amount of salt in the tank after t minutes is
y= 16e^(t/100)kg
Step- by-step Explanation
The tank contain 3000L of the brine
The rate is 30L/ min
The solution is mixed thoroughly, therefore, the rate in= rate out
dy/dt= rate in to the tank= rate out of the tank
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
Terry has a collection of 50 coins. There are only quarters and dimes in the collection. The total value of the coins is $8.00. How many dimes does he have?
Answer:
30 dimes and 20 quarters
30×.10=$3.00
20×.25=$5.00
30+20=50
$3+$5=$8
A data set includes 104body temperatures of healthy adult humans having a mean of 98.7degreesFand a standard deviation of 0.66degreesF.Construct a 99%confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6degreesFas the mean body temperature?
Answer:
The 99% confidence interval estimate of the mean body temperature of all healthy humans is between 98.53ºF and 98.87 ºF. 98.6ºF is part of the interval, so the sample suggests that the use of 98.6ºF as the mean body temperature is correct.
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 104 - 1 = 103
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 103 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.624
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.624\frac{0.66}{\sqrt{104}} = 0.17[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 98.7 - 0.17 = 98.53ºF.
The upper end of the interval is the sample mean added to M. So it is 98.7 + 0.17 = 98.87 ºF.
The 99% confidence interval estimate of the mean body temperature of all healthy humans is between 98.53ºF and 98.87 ºF. 98.6ºF is part of the interval, so the sample suggests that the use of 98.6ºF as the mean body temperature is correct.
Write a two column proof Given: AB || DC; BC || AE Prove: BC/EA = BD/EB
Answer:
AB || DC Given
∠ABE ≅ ∠CDB Alternate interior angles are congruent
BC || AE Given
∠CBD ≅ ∠BEA Alternate interior angles are congruent
ΔAEB is similar to ΔCBD AA Similarity Postulate
BC / EA = BD / EB Similar sides are proportional
A half marathon is 13.1 miles long. Leah is running a half marathon and has completed 7.75 miles. How many miles to
the finish line?
Answer:
5.35 more miles
Answer:
5.35 miles to the finish line
Step-by-step explanation:
Step one
13.1-7.75=
5.35
What is the range of this function?
Answer:
Step-by-step explanation:
The answer is 2,4,3 and -9
The range is the y value
A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Three hundred feet of fencing is used
dimensions of the playground that maximize the total enclosed area. What is the maximum area?
The smaller dimension is
feet
Answer:
50 ft by 75 ft3750 square feetStep-by-step explanation:
Let x represent the length of the side not parallel to the partition. Then the length of the side parallel to the partition is ...
y = (300 -2x)/3
And the enclosed area is ...
A = xy = x(300 -2x)/3 = (2/3)(x)(150 -x)
This is the equation of a parabola with x-intercepts at x=0 and x=150. The line of symmetry, hence the vertex, is located halfway between these values, at x=75.
The maximum area is enclosed when the dimensions are ...
50 ft by 75 ft
That maximum area is 3750 square feet.
_____
Comment on the solution
The generic solution to problems of this sort is that half the fence (cost) is used in each of the orthogonal directions. Here, half the fence is 150 ft, so the long side measures 150'/2 = 75', and the short side measures 150'/3 = 50'. This remains true regardless of the number of partitions, and regardless if part or all of one side is missing (e.g. bounded by a barn or river).
The initial population of a town in the year 2010 was 20 000. By 2014, the population had grown exponentially to 32 500 people. Write an equation to represent the population of the town (P) over time in years (n).
Answer:
P = 20000×1.625^(n/4)
Step-by-step explanation:
An exponential equation can be written using the given data:
value = (initial value)×(growth factor in period)^(n/(period))
Here, the growth is by a factor of 32500/20000 = 1.625, and the period is 4 years. Then your exponential equation is ...
P = 20000×1.625^(n/4)