Solution:
Given:
[tex]\text{radius of a circle, r = 16m}[/tex]The circumference (C) of a circle is given by;
[tex]\begin{gathered} C=2\pi r \\ \text{where;} \\ C\text{ is the circumference of the circle} \\ r\text{ is the radius} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} r=16m \\ \pi=3.14 \\ C=\text{?} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} C=2\pi r \\ C=2\times3.14\times16 \\ C=100.48m \end{gathered}[/tex]Therefore, the circumference of the circle is 100.48m
Math for Liberal Arts Lecture Class, Fall 2021 = Homework: Ch... Question 2, 1.1.3 Part 2 of 3 HW Score: Points: An election is held to choose the chair of a department at a university. The candidates are Professors Arg for short). The following table gives the preference schedule for the election. Use the table to complete pa Number of Voters 7 9 2 5 3 6 1st choice А A B D A 2nd choice B D D А E E 3rd choice D B E C B B 4th choice E C A B C D 5th choice C E C D A C (a) How many people voted in this election? ... 32 voters (Type a whole number.) (b) How many first-place votes are needed for a majority?
a) In this election voted: 7+9+2+5+3+6=32
b) For a majority you can follow the next rule:
The 50% of 32 is: 32*0.5=16, then, are needed at least 17 votes
c) Candidate A had 3 last-place votes, candidate B had 0 last-place votes, candidate C had 15 last-place votes, candidate D had 5 last-place votes and candidate E had 9 last-place votes.
Thus, the candidate with the fewest last-place votes is candidate B
3. In one linear function, when you subtracteach y-coordinate from the x-coordinate,the difference is 3. If the x-coordinate isnot greater than 10 and the y-coordinateis a positive whole number, how manyordered pairs are there?
Problem
3. In one linear function, when you subtract each y-coordinate from the x-coordinate, the difference is 3. If the x-coordinate is not greater than 10 and the y-coordinate is a positive whole number, how many ordered pairs are there?
Solution
Here are the conditions
x- y= 3
x <10
y >0
And then we have these as possible answers:
4-1 =3
5-2= 3
6-3=3
7-4=3
8-5=3
9-6=3
Then the total possible pairs are: 6
Which term is −20,155,392 for the following sequence, assuming that the pattern continues?
2, −12, 72, −432, …
a9
a10
a11
a12
The term that is the −20,155,392 in the sequence is a₁₀.
How to solve sequence?The sequence below is a geometric sequence.
Therefore, a geometric sequence can be represented as follows:
nth term = arⁿ⁻¹
where
a = first termn = number of termsr = common ratioTherefore, let's find which term is −20,155,392 for the sequence.
2, -12, 72, -432
r = -12 / 2 = 72 / -12 = -432 / 72 = -6
a = 2
Hence,
nth term = arⁿ⁻¹
−20,155,392 = 2 × -6ⁿ⁻¹
−20,155,392 / 2 = -6ⁿ⁻¹
- 10077696 = -6ⁿ⁻¹
6ⁿ⁻¹ = 10077696
6ⁿ⁻¹ = 6⁹
n - 1 = 9
n = 9 + 1
n = 10
Therefore, it's the 10th term.
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The term −20,155,392 is the tenth in the given geometric sequence.
The given sequence is below which is in a geometric pattern
2, -12, 72, -432
Here first term (a) = 2
The common ratio (r) = -12 / 2
The common ratio (r) = -6
We know that the nth term of the geometric sequence is
Tₙ = arⁿ⁻¹
Here Tₙ = −20,155,392
⇒ −20,155,392 = arⁿ⁻¹
Substitute the values of a and r in the above equation,
⇒ −20,155,392 = 2 × -6ⁿ⁻¹
⇒ −20,155,392 / 2 = -6ⁿ⁻¹
Apply the division operation,
⇒ - 10077696 = -6ⁿ⁻¹
⇒ 6ⁿ⁻¹ = 10077696
⇒ 6ⁿ⁻¹ = 6⁹
Equating exponents of the base
⇒ n - 1 = 9
⇒ n = 10
Therefore, the term −20,155,392 would be the tenth in the given sequence.
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Daniel ate 3 pieces of pizza. Jeremy ate 2 times that much. How many pieces of (p) did Jeremy eat?
Let:
x = pieces of pizza eaten by Daniel
y = Pieces of pizza eaten by Jeremy
Daniel ate 3 pieces of pizza. so:
[tex]x=3[/tex]Jeremy ate 2 times that much, so:
[tex]\begin{gathered} y=2x \\ so\colon \\ y=2(3) \\ y=6 \end{gathered}[/tex]Jeremy ate 6 pieces of pizza
Out of 441 applicants for a job 235 have over five years of experience and 106 have over five years of experience and have a graduate degreeWhat is the probability that a randomly chosen applicant has a graduate degree given that they have a five years of experience enter a fraction or round your answer to four decimal places if necessary
Probability that a randomly chosen applicant has a graduate degree given that they have a five years of experience = 106/441
Explanation:Total number of applicants, n(Total) = 441
Number of candidates that have over five years of experience, n(5 yrs) = 235
Probability that a randomly chosen applicant has over 5 years experience
[tex]\begin{gathered} P(5yrs)=\frac{n(5yrs)}{n(Total)} \\ \\ P(5yrs)=\frac{235}{441} \end{gathered}[/tex]Number of applicants that have over five years of experience and have a graduate degree, n(5 n g) = 106
Probability that a randomly selected applicant has over five years of experience and have a graduate degree
[tex]\begin{gathered} P(5\text{ n g\rparen = }\frac{n(5\text{ n g\rparen}}{n(Total)} \\ \\ P(5\text{ n g\rparen = }\frac{106}{441} \end{gathered}[/tex]Probability that a randomly chosen applicant has a graduate degree given that they have a five years of experience
[tex]\begin{gathered} P(g\text{ /5yrs\rparen = }\frac{P(5\text{ n g\rparen}}{P(5yrs)} \\ \\ P(g\text{ /5yrs\rparen = }\frac{106}{441}÷\frac{235}{441} \\ \\ P(g\text{ /5yrs\rparen=}\frac{106}{441} \end{gathered}[/tex]What is the solution to the equation below? √x+9 = 11 O A. x= 2 O B. X= √ O C. x = 42 D. x = 4
answer: D. x = 4
How many different choices of shirts does the store sell
Answer:
11
Explanation:
From the probability tree:
• There are 3 choices of small shirts.
,• There are 3 choices of medium shirts.
,• There are 3 choices of large shirts.
,• There are 2 choices of X-Large shirts.
Therefore, the number of different choices of shirts the store sells:
[tex]\begin{gathered} =3+3+3+2 \\ =11 \end{gathered}[/tex]There are 11 choices of shirts.
What is the value of the expression? (9 1/2−3 7/8) + (4 4/5−1 1/2)
By algebra properties, the sum of four mixed numbers is equal to the mixed number [tex]8\,\frac{37}{40}[/tex].
How to simplify a sum of mixed numbers
In this problem we find a sum of four mixed numbers. The simplification process consists in transforming each mixed number into a fraction and apply algebra properties. Then,
[tex]9 \,\frac{1}{2}[/tex] = 9 + 1 / 2 = 18 / 2 + 1 / 2 = 19 / 2
[tex]3\,\frac {7}{8}[/tex] = 3 + 7 / 8 = 24 / 8 + 7 / 8 = 31 / 8
[tex]4\,\frac{4}{5}[/tex] = 4 + 4 / 5 = 20 / 5 + 4 / 5 = 24 / 5
[tex]1 \,\frac{1}{2}[/tex] = 1 + 1 / 2 = 2 / 2 + 1 / 2 = 3 / 2
(19 / 2 - 31 / 8) + (24 / 5 - 3 / 2)
(76 / 8 - 31 / 8) + (48 / 10 - 15 / 10)
45 / 8 + 33 / 10
450 / 80 + 264 / 80
714 / 80
357 / 40
320 / 40 + 37 / 40
8 + 37 / 40
[tex]8\,\frac{37}{40}[/tex]
The sum of mixed numbers is equal to [tex]8\,\frac{37}{40}[/tex].
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What are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x² + x - 12?
Answer:
All the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x - 12 are 3/4 and -4/5.
I just need help finding the area of shape c.
We need to find the area of Shape C.
Please have a look at the diagram below:
To find x, we can use the Pythagorean Theorem on the right triangle.
[tex]\begin{gathered} 100^2+x^2=107^2 \\ \end{gathered}[/tex]Now, let's solve for x. The steps are shown below:
[tex]\begin{gathered} 100^2+x^2=107^2 \\ x^2=107^2-100^2 \\ x^2=11449-10000 \\ x^2=1449 \\ x=\sqrt[]{1449} \\ x=38.07 \end{gathered}[/tex]So, the top part (dotted line) is
[tex]\begin{gathered} x+100+x \\ =38.07+100+38.07 \\ =176.14 \end{gathered}[/tex]Now, we have a trapezoid. Let's find the area of the trapezoid:
[tex]\begin{gathered} A=\frac{1}{2}(b_1+b_2)h \\ A=\frac{1}{2}(100+176.14)(100) \\ A=13,807 \end{gathered}[/tex]Now, we need to subtract the area labeled (K) from the area of the trapezoid found.
--------------------------------------------------------------------------------
Area k is a triangle with side lengths 117, 117, and 176.14. Let's find the area of the triangle. The diagram is shown below:
Now, we will find h, the height of the triangle using Pythagorean Theorem.
[tex]\begin{gathered} 88.07^2+h^2=117^2 \\ h^2=117^2-88.07^2 \\ h^2=5932.6751 \\ h=\sqrt[]{5932.6751} \\ h=77.02 \end{gathered}[/tex]The area of the triangle (region K) is,
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A=\frac{1}{2}(176.14)(77.02) \\ A=6783.15 \end{gathered}[/tex]The area of region C is the area of trapezoid - area of region k (triangle). So, the area is >>>>
[tex]\begin{gathered} A=13,807-6783.15 \\ A=7023.85 \end{gathered}[/tex]Answer7023.85Select the similarity transformation(s) that make ABCD similar to EFGH.
Answer:
D
F
Explanation:
We would compare the coordinates of the corresponding vertices of rectangles ABCD and EFGH. We would compare vertices A and E. From the information given,
A = (1, - 2)
E = (- 2, 4)
If we apply (x, y)---(- x, - y) to A, it becomes (- 1, - - 2) = (- 1, 2)
If we apply (x, y)---(2x, 2y) to (- 1, 2), it becomes (2 * - 1, 2 * 2) = (- 2, 4)
Thus, the correct similarity transformation(s) that make ABCD similar to EFGH are
D
F
<
Z2
Find the midpoint m of z₁ = (9+7i) and Z₂ = (-7+7₂).
Express your answer in rectangular form.
m=
Re
The midpoint m of z₁ = (9+7i) and Z₂ = (-7+7i) is 1 + 7i .
Given complex numbers:
[tex]z_{1}[/tex] = (9 + 7i) and [tex]z_{2}[/tex] = (-7 + 7i)
compare these numbers with a1+ib1 and a2+ib2, we get
a1 = 9, a2 = -7 , b1 = 7 and b2 = 7.
Mid point of complex numbers = a1 + a2 /2 + (b1 + b2 /2)i
= (9 + (-7)/2 + (7 + 7 /2)i
= 2/2 + 14/2 i
Mid point m = 1 + 7i
Therefore the midpoint m of z₁ = (9+7i) and Z₂ = (-7+7i) is 1 + 7i
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Question 8 > Find the area of the trapezoid shown below 9 19 18 21 23 I Question Help ve
288 u²
1) Let's calculate the area of that trapezoid by plugging into the formula below the measures of the altitude, larger base, smaller one:
[tex]\begin{gathered} S=\frac{(B+b)h}{2} \\ S=\frac{(23+9)18}{2} \\ S=288 \end{gathered}[/tex]2) So that trapezoid has an area of 288 u²
Which of the followingrepresents this inequality?|4x – 61 > 10
Solution:
Given the absolute inequality below:
[tex]\lvert4x-6\rvert>10[/tex]From the absolute law,
[tex]\begin{gathered} \lvert u\rvert>a \\ implies\text{ } \\ u>a\text{ } \\ or \\ u<-a \end{gathered}[/tex][tex]\begin{gathered} When\text{ 4x-6>10} \\ add\text{ 6 to both sides of the inequality,} \\ 4x-6+6>10+6 \\ \Rightarrow4x>16 \\ divide\text{ both sides by the coefficient of x, which is 4} \\ \frac{4x}{4}>\frac{16}{4} \\ \Rightarrow x>4 \end{gathered}[/tex][tex]\begin{gathered} When\text{ 4x-6<-10} \\ add\text{ 6 to both sides of the inequality,} \\ 4x-6+6<-10+6 \\ \Rightarrow4x<-4 \\ divide\text{ both sides by the coefficient of x, which is 4} \\ \frac{4x}{4}<-\frac{4}{4} \\ \Rightarrow x<-1 \end{gathered}[/tex]Plotting the solution to the inequality, we have the line graph of the inequality to be
Hence, the correct option is D.
y - y1 = m (x - x1 ) write an equation in point slope form given point ( 4, -3 ) and m = 1
The point-slope form of a line is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Replacing with m = 1 and the point (4, -3):
y - (-3) = 1(x - 4)
y + 3 = x - 4
Graph the inequality on a plane. Shade a region below or above. Y < - 1
In order to graph the inequality on the coordinate plane, we first need to find it's border, which is delimited by the line below:
[tex]y=-1[/tex]This line is a straight line parallel to the x-axis and that passes through the y-axis at the point (0, -1). Since the original inequality has a "less" sign, we need to make this boundary line into dashes.
Now we can analyze the inequality:
[tex]y<-1[/tex]Since the signal is "<", we need to shade all the region of the coordinate plane for which y is below -1, this means that we have to paint the region below the line. The result is shown below:
Use the distributive property to simplify 10 - 5( -3-7m) completely .
Simplify the expression by using the distributive property.
[tex]\begin{gathered} 10-5(-3-7m)=10+(-5)\cdot(-3)+(-5)\cdot(-7m) \\ =10+15+35m \\ =25+35m \end{gathered}[/tex]So answer is 25 + 35m.
fred had a tray of brownies for his birthday. he ate 1/6 of the brownies by himself and his family ate 1/3 of the brownies how many brownies did fred and his family eat altogether
We want to know how many brownmies did Fred and his family eat together.
We will call to the total of the brownies by 1. On this case, after Fred ate 1/3 of the brownies, he will have:
[tex]1-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}[/tex]This means that he has left 2/3 of the brownies. After his family ate 1/6 of the brownies:
[tex]\frac{2}{3}-\frac{1}{6}=\frac{4}{6}-\frac{1}{6}=\frac{3}{6}=\frac{1}{2}[/tex]This means they will have left 1/2 of the tray of brownies, and that they ate half of it.
What are the coefficient(s) in the following expression:
x² + 2x-5xy-y+3y¹
2,4
A
B
C
D
1, 2, 5, 1,3
2,-5, 3
1, 2, 5, 1, 3
Step-by-step explanation:
based on the expression you wrote here, the correct answer is
1, 2, -5, -1, 3
since none of your answer options show this, you must have made a mistake either with the expression itself or with the answer options.
please choose in your original the one matching my answer above.
The area of a triangle is 5. two of the sides lengths are 4.1 and 2.5 and the included angle is obtuse. find the measure of the included angle, to the nearest tenth of a degree.
Given data:
The given area of the triangle is A=5.
The first side given is a=4.1.
The second side given is b=2.5.
The expression for the area of triangle is,
[tex]A=\frac{1}{2}ab\sin C[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} 5=\frac{1}{2}(4.1)(2.5)\text{ sin C} \\ \sin C=0.97561 \\ C=102.7^{\circ} \end{gathered}[/tex]Thus, the value of the angle is 102.7 degrees.
find the point that is symmetric to the point (-7,6) with respect to the x axis, y axis and origin
Answer:
[tex]\begin{gathered} a)(-7,-6)\text{ } \\ b)\text{ (7,6)} \\ c)\text{ (7,-6)} \end{gathered}[/tex]Explanation:
a) We want to get the point symmetric to the given point with respect to the x-axis
To get this, we have to multiply the y-value by -1
Mathematically, we have the symmetric point as (-7,-6)
b) To get the point that is symmetric to the given point with respect to the y-axis, we have to multiply the x-value by -1
Mathematically, we have that as (7,6)
c) To get the point symmetric with respect to the origin, we multiply both of the coordinate values by -1
Mathematically, we have that as:
(7,-6)
A yogurt stand gave out 200 free samples of frozen yogurt, one free sample per person. The three sample choices were vanilla, chocolate, or chocolate & vanilla twist. 115 people tasted the vanilla and 137 people tasted the chocolate, some of those people tasted both because they chose the chocolate and vanilla twist. How many people chose chocolate and vanilla twist?
So we are to find x
[tex]137-x+x+115-x=200[/tex][tex]\begin{gathered} 137+115-x=200 \\ 252-x=200 \\ -x=200-252 \\ -x=-52 \\ x=52 \end{gathered}[/tex]The final answer52 people chose chocolate and vanilla twistimage
Determine the value of x.
Question 17 options:
A)
x = 20°
B)
x = 45°
C)
x = 4.5°
D)
x = 90°
The value of the x in the rectangle is 4.5°
Rectangle:
A rectangle is a two-dimensional shape (2D shape) in which the opposite sides are parallel and equal to each other and all four angles are right angles
Given,
Here we have the rectangle with one angle as 90°.
Here we have to find the value of x.
We know that, we we divide the rectangle as two distinct right angled triangle.
We know that, the right triangles are triangles in which one of the interior angles is 90 degrees, a right angle.
So,
20x = 90
x = 90/20
x = 4.5°
Therefore, the value of x is 4.5°.
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23. At a company employing 140 people, 40% of the employees took the bus to work,and 5 % lived close enough to walk. The others drove cars. How many employeesdrive cars to work?Answer
Since the total percent of the employees is 100%
Since 40% of them took the bus
Since 5% walk
Add them and subtract the sum from 100% to get the percentage of who take the car
[tex]\begin{gathered} 40+5=45 \\ 100-45=55 \end{gathered}[/tex]Then 55% of the employees use cars
Since the total number of employees is 140, then
Let us find 55% of 140
Change 55% to a number by divide it by 100, then multiply it by 140
[tex]\begin{gathered} N=\frac{55}{100}\times140 \\ N=77 \end{gathered}[/tex]There are 77 employees who use cars
Select the correct answer.
What is the value of this logarithmic e ession?
log2 16 - log₂ 4
Answer:l og2(16)=x log 2 ( 16 ) = x in exponential form using the definition of a logarithm. If x x and b b are positive real numbers and b b does not equal ...
Step-by-step explanation:
what is the sum of -1 1/3 + 3/4
Here, we want to add two fractions
What we have to do here is to make the mixed fractin an improper one
To do this, we multiply the denominator by the standing number, and add to the numerator, then we place the value over the denominator
Thus, we have it that;
[tex]\begin{gathered} 1\frac{1}{3}\text{ = }\frac{4}{3} \\ -\frac{4}{3}+\frac{3}{4}\text{ = }\frac{-16+9}{12}=\text{ }\frac{-7}{12} \end{gathered}[/tex]Solve for k 4k – 6/3k – 9 = 1/3
hello
to solve this simple equation, we need to follow some simple steps.
[tex]4k-\frac{6}{3}k-9=\frac{1}{3}[/tex]step 1
multiply through by 3
we are doing this to eliminate the fraction and it'll help us solve this easily
[tex]\begin{gathered} 4k(3)-\frac{6}{3}k(3)-9(3)=\frac{1}{3}(3) \\ 12k-6k-27=1 \end{gathered}[/tex]notice how the equation haas changed suddenly? well this was done to make the question simpler and faster to solve.
step 2
collect like terms and simplify
[tex]\begin{gathered} 12k-6k-27=1 \\ 12k-6k=1+27 \\ 6k=28 \\ \end{gathered}[/tex]step three
divide both sides by the coefficient of k which is 6
[tex]\begin{gathered} \frac{6k}{6}=\frac{28}{6} \\ k=\frac{14}{3} \end{gathered}[/tex]from the calculations above, the value of k is equal to 14/3
What is the area of a rectangle with length of 6.5 feet (ft) and width of 2.5 ft?
The area of a rectangle is given by the formula
[tex]\begin{gathered} A=l\cdot w \\ \text{ Where l is the length and} \\ w\text{ is the width of the rectangle} \end{gathered}[/tex]So, you have
[tex]\begin{gathered} l=6.5\text{ ft} \\ w=2.5\text{ ft} \\ A=l\cdot w \\ A=6.5\text{ ft }\cdot2.5\text{ ft} \\ A=16.25\text{ ft}^2 \end{gathered}[/tex]Therefore, the area of this rectangle is 16.25 square feet.
Match each step with the correct expression to factor s2 + 78 + 6 by using the decomposition method.
We have the following:
[tex]s^2+7s+6[/tex]solving:
[tex]\begin{gathered} \text{step 1} \\ s^2+s+6s+6 \\ \text{step 2} \\ s\mleft(s+1\mright)+6\mleft(s+1\mright) \\ \text{step 3} \\ (s+1)(s+6) \end{gathered}[/tex]Exponential Regression
The table below shows the population, P. (in thousands) of a town after 12 years.
0
72
P 2400
3
2801.27
7
3608.71
12
14
4974.15 5426.17
19
6898.37
(a) Use your calculator to determine the exponential regression equation P that models the set of
data above. Round the value of a to two decimal places and round the value of b to three decimal
places. Use the indicated variables.
P =
(b) Based on the regression model, what is the percent increase per year?
96
(c) Use your regression model to find P when n = 13. Round your answer to two decimal places.
The population of the town after
P =
thousand people
(d) Interpret your answer by completing the following sentence.
years is
thousand people.
Considering the given table, it is found that:
a. The exponential regression equation is: P(t) = 2408.80(1.059)^t.
b. The yearly percent increase is of 5.9%.
c. P(13) = 5075.
d. The population of the town after 13 years is of 5075.
How to find the exponential regression equation?The exponential regression equation is found inserting the points into a calculator.
The points are given as follows:
(0, 2400), (3, 2801.27), (7, 3608.71), (12, 4974.15), (14, 5426.17), (19, 6898.37).
Using a calculator, the function is:
2408.80(1.059)^t.
The yearly percent increase rate is calculated as follows:
1 + r = 1.059
r = 1.059 - 1
r = 0.059
r = 5.9%.
Then in 13 years, the population will be given as follows:
P(13) = 2408.80(1.059)^13 = 5075.
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