The area of a circle with radius r is given by the following formula:
[tex]A=\pi r^2[/tex]The circumference of that circle is given by:
[tex]C=2\pi r[/tex]Finding the answerWe are given the area of the circle. With this data and the first formula we can construct an equation for the radius r. Once we find the radius of the circle we can use it to find its circumference. So first of all we take the first formula and we equalize it to 95.03:
[tex]95.03=\pi r^2[/tex]We can divide both sides by π:
[tex]\begin{gathered} \frac{95.03}{\pi}=\frac{\pi r^2}{\pi} \\ r^2=\frac{95.03}{\pi} \end{gathered}[/tex]Now we apply a square root to both sides:
[tex]\begin{gathered} \sqrt{r^2}=\sqrt{\frac{95.03}{\pi}} \\ r=\sqrt{\frac{95.03}{\pi}} \end{gathered}[/tex]And that's the radius of the circle. Then we can use this value in the formula of the circumference C:
[tex]C=2\pi *\sqrt{\frac{95.03}{\pi}}=34.6[/tex]AnswerThen the answer is 34.6 m.
Eugenia rolls a six-sided number cube. What is the probability that she gets anumber greater than 4?
A cube is six sided. The numbers which are greater than 4 in a cube are 5 and 6. So, there are two sides on the cube which has numbers greater than 4.
Hence, the number of desired outcomes, N=2.
Since the cube is six sided, the total number of outcomes, T=6.
So, the probability of getting a number greater than 4 while rolling a cube is,
[tex]P=\frac{N}{T}=\frac{2}{6}=\frac{1}{3}[/tex]Therefore, the probability of getting a number greater than 4 is 1/3.
Option B is correct.
what is 1 + 1 and two times 15
Solution
1 + 1= 2
2* 15= 30
HiI’m bad at math I decided to practice but get confused Not is not assignment
Solution
Name an acute angle for which each of the angles are associated in terms of trig ratios:
Trigonometry ratios include sine, cosine and tangent
The associated angles interms of relation to acute angle is which of them is equivalent
[tex]sin150=sin30[/tex][tex]tan225=tan45[/tex][tex]cos300=cos60[/tex]Solve 7sin(pi/6 * x) = 2 for the four smallest positive solutions
Answer:
x =0.55, 5.45, 12.55, 17.45
Explanation:
First, we divide both sides by 7. This gives
[tex]\sin(\frac{\pi}{6}x)=\frac{2}{7}[/tex]then taking the inverse sine of both sides gives
[tex]\frac{\pi}{6}x=2\pi n\pm\sin^{-1}[\frac{2}{7}][/tex]since
[tex]\sin^{-1}[\frac{2}{7}]=16.60[/tex]Therefore,
[tex]\frac{\pi}{6}x=2\pi n\pm16.60[/tex]Multpilying both sides by 6/π
[tex][/tex]what is the best estimate for the value of the expression? [tex] ( \frac{34}{8} - \frac{16}{3}) - \frac{14}{9} [/tex]A. -3B.[tex] - 2 \frac{1}{2} [/tex]C. 7D. [tex]7 \frac{1}{2} [/tex]
-95/34
Explanation:
[tex](\frac{34}{8}-\frac{16}{3})-\frac{14}{9}[/tex]Simplify the expresssion:
[tex]\begin{gathered} \text{LCM for the one in the bracket is 24} \\ \frac{34(3)-8(16)}{24}-\frac{14}{9} \\ \frac{102-128}{24}-\frac{14}{9} \\ =\text{ }\frac{-26}{24}-\frac{14}{9} \end{gathered}[/tex][tex]\begin{gathered} \frac{-26(3)\text{ -14(8)}}{72} \\ =\text{ }\frac{-78-112}{72}=\text{ }\frac{-190}{72} \\ =\frac{-95}{36} \end{gathered}[/tex]None of the options has this value.
There is likely an error in question.
1. Given that f(x)=x²-4 and that g(x)=√√x-1:
A. State (f-g)(x) and (fog)(x).
B. State
and determine its domain.
C. Determine whether each of the following functions is odd, even, or neither odd nor
even: f(x)=x²-4, g(x)=√√x-1.
D. State (g/f)(x) and find all vertical asymptotes.
Please show work! Thank you so much!
Given the functions are,
[tex]f(x)=x^2-4\\g(x)=\sqrt[3]{x-1}[/tex]
Then the subtraction of functions is given by,
[tex](f-g)(x)=f(x)-g(x)=x^2-4-\sqrt[3]{x-1}[/tex]
Again,
[tex](f\circ g)(x)=f(g(x))=f(\sqrt[3]{x-1})=(x-1)^{2/3}-4[/tex]
And,
[tex]\left(\frac{f}g{}\right)(x)=\frac{f(x)}{g(x)}=\frac{x^2-4}{\sqrt[3]{x-1}}[/tex], it exists when x not equals to 1.
So domain of the function is all real number except 1.
Since, [tex]f(-x)=(-x)^2-4=x^2-4=f(x)[/tex], then the function is an even function.
Since [tex]g(-x)=\sqrt[3]{-x-1}[/tex], so it is neither odd function nor even function.
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Which statement best explains the relationship betweenlines AB and CD?
GIven:-
An graph with two parallel lines.
To find:-
The given condition which sutis it.
Now we find two points form the line.
The points from the line AB is,
[tex](-4,-2),(4,4)[/tex]The points from the line CD is,
[tex](0,-3),(4,0)[/tex]Now the slope of AB is,
[tex]\frac{4+2}{4+4}=\frac{6}{8}=\frac{3}{4}[/tex]Now the slope of CD is,
[tex]\frac{0+3}{4}=\frac{3}{4}[/tex]The both slopes are equal so we have,
They are parallel because the slopes are equal.
(b) A company has 39 salespeople. A boardmember at the company asks for a list of the topsalespeople, ranked in order of effectiveness. How many such rankings are possible?0ExplanationCheck
Since 1 person cannot be in the top 4 salespeople more than once, then, we use combinations instead of permutations.
[tex]39C4=\frac{39!}{4!(39-4)!}[/tex]Simplify the expression,
[tex]39C4=\frac{39!}{4!35!}[/tex][tex]\begin{gathered} 39C4=\frac{39\ast38\ast37\ast36}{4\ast3\ast2\ast1} \\ 39C4=\frac{1974024}{24} \\ 39C4=82251 \end{gathered}[/tex]answer:
The 4 top list can be arranged in 82251 ways
+ Type a messageSend2Help Mark use completing the square with the algebra tiles to convert this standard form equation to vertexform. Draw the tiles using this method and show the algebraic steps that take you from this equation to itsequivalent vertex form. Then state the vertex.014Show Your WorkCorrect answer y=xThis assignment has been submitted and is no longer editable.Client time: 5/13/2021, 6:06:10 PM (America/Los_Angeles)Server time: 5/13/2021, 6:06:10 PM (-70.44)Missing.omeos StommKB
From the image.
we have
1 y
1 x^2
6 x
8 (1squares)
We can write the standard equation as
[tex]y=x^{2^{}}+\text{ 6x +8}[/tex]But we need to express it in vertex form y = a(x-h)^2 + k where (h,k) is the vertex
to complete the squares we need to express the equation as
y = (x^2+6x+8+__)-___
to complete the square we need to add +1 inside the parenthesis and -1 outside
y = (x^2+6x+8+1)-1
We can express the equation
y = (x+3)^2 -1
[tex]y=(x+3)^2-1[/tex]Find the equation of the axis symmetry:Find the x-intercept(s):and y-intercept(s):Find the coordinates of the vertex:
Step 1
Find the equation of the axis of symmetry
[tex]\begin{gathered} From\text{ the graph the zeroes are} \\ x=-2 \\ \text{and} \\ x=4 \end{gathered}[/tex][tex]\begin{gathered} \text{Hence the function is } \\ y=(x+2)(x-4) \\ y=x^2-4x+2x-8 \\ y=x^2-2x-8 \end{gathered}[/tex]The equation of symmetry is given as
[tex]\begin{gathered} x=\frac{-b}{2a} \\ b=-2 \\ a=1 \\ c=-8 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-(-2)}{2(1)} \\ x=\frac{2}{2}=1 \\ x=1 \end{gathered}[/tex]Step 2
Find the x-intercepts
[tex]\begin{gathered} \text{From the graph, the x-intercepts are}; \\ (4,0),(-2,0) \end{gathered}[/tex]Step 3
Find the y-intercepts
[tex]y\text{-intercept; (0,-8)}[/tex]Step 4
Find the coordinates of the vertex
[tex]The\text{ coordinates of the Vertex ; (1,-9)}[/tex]Express the number in scientific notation 6,340,000,000
Solution:
The number is given below as
[tex]6,340,000,000[/tex]Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form
Concept:
count the number from the last number and then stop in front of the first number 6 and then multiply in powers of 10
The general form of a scientific notation is given below as
By applying the concept, we will have
[tex]\begin{gathered} 6,340,000,000=6.34\times1,000,000,000 \\ 6,340,000,000=6.34\times10^9 \end{gathered}[/tex]Hence,
The final answer is
[tex]6.34\times10^9[/tex]5. What is the sum of 3 5/24, 6 7/24, and 9 9/24?,A. 14²/3B. 14 1/8C. 18 7/8D. 13 1/2
To answer this question, we can realize that we have mixed fractions. Then we need to add integers and fractions separately as follows:
1. We have:
[tex]3\frac{5}{24}+6\frac{7}{24}+9\frac{9}{24}[/tex]2. And this expression is equivalent to:
[tex]3+\frac{5}{24}+6+\frac{7}{24}+9+\frac{9}{24}[/tex]3. Now, we can add the integer parts, and the fractional parts separately as follows:
[tex](3+6+9)+(\frac{5}{24}+\frac{7}{24}+\frac{9}{24})[/tex]4. Therefore:
[tex]18+\frac{5+7+9}{24}=18+\frac{21}{24}[/tex]5. We finally need to simplify the fraction, and then we will have:
[tex]\begin{gathered} \frac{21}{24}=\frac{\frac{21}{3}}{\frac{24}{3}}=\frac{7}{8} \\ 18+\frac{7}{8}=18\frac{7}{8} \end{gathered}[/tex]In summary, therefore, we have that the sum of the above fractions is:
[tex]18\frac{7}{8}[/tex][Option C.]
find the probability of obtaining five heads when flipping five coins. express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
1/32
Explanation:In an experiment, we can only get head or tail:
Probability of getting a head = 1/2
Probability of obtaining five heads when flipping five coins:
[tex]\begin{gathered} \text{Probability = (1/2)}^{number\text{ of flips}} \\ \text{Probability = (1/2)}^5 \\ \end{gathered}[/tex][tex]\text{Probability = 1/32}[/tex](10) When using substitution to solve this system of equations, what is the result of the first step? Eq#1 y = 6x + 3 Eq#2 x + 2y = 5
Given data:
The first equation given is y = 6x + 3.
The second equation given is x + 2y = 5.
Subsitute (6x+3) for y in second equation.
[tex]x+2(6x+3)=5[/tex]Thus, the first option is correct.
Find three odd consecutive integers whose sum is 531
The number = 531
There are no three consecutive odd integers whose sum is 531
Because the difference between consecutive integer is 1
What is the probability that a student would randomly choose a school uniform outfit with a plaid skirt and black sneakers ?
Notice that as for the type of shoes, there are two possibilities either loafers or black sneakers.
Therefore, the probability of choosing black sneakers is 0.5.
On the other hand, after picking the black sneakers, there are 4 possibilities as to the sort of skirt/pants to use, and the probability of choosing a plaid skirt is 1/4=0.25.
Thus, the probability of randomly choosing a plaid skirt and black sneakers is
[tex]P(sneakers\cap plaid)=0.5*0.25=0.125[/tex]Therefore, the answer is 0.125 or 1/8 (both are correct).I need help with this practice problem Having a tough time completing step by step
we have the expression
[tex]\frac{cos(sin^{-1}(\frac{1}{2}))}{tan(cos^{-1}(-\frac{1}{2}))}[/tex]step 1
Find out the value of sin^-1 (1/2) and cos^-1(-1/2)
[tex]\begin{gathered} sin^{-1}(\frac{1}{2})=30^o \\ cos^{-1}(-\frac{1}{2})=120^0 \end{gathered}[/tex]substitute in the original expression
[tex]\frac{cos(30^o)}{tan(120^o)}=-\frac{1}{2}[/tex]Therefore
The answer is -1/21. This is a two part question. If you are going 65 kilometers per hour how many meters per second are you traveling? a) What conversions will you use to solve this problem? b) Complete the conversion. Show your work. Make sure to include units
The value of 65 km/hr in meter/second will be 18.05 m/sec by the method of "To convert km/hr to m/s ,multiply the quantity by 5/18."
What is kilometer per hour?A derived unit for both speed and velocity, kilometers per hour is a measurement that takes length in kilometers and time in hours. Although kph or kmph are also occasionally used, km/h is the correct abbreviation for this unit.
a. 65 KM/hour to metre/second
=65*5/18
=18.05 m/second
b. To convert km/hr to m/s ,multiply the quantity by 5/18.
as 1 KM=1000 m
1 hour=3600 seconds
x* 1000/3600
x*5/18
According to the formula "To convert km/hr to m/s, multiply the quantity by 5/18," 65 km/hr will equal 18.05 m/s.
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A function whose values repeat based on positions of a point that moves around a circle is called a sinusoid.
Given
A function moves around a circle
Find
Is the function sinusoidal
Explanation
Final Answer
Yes, the function is sinusoidal
3. Factor 3x from 12x2 + 15x 3
SOLUTION
In this question, we are meant to factor
[tex]\begin{gathered} 3xfrom12x^2+15x^3 \\ \text{Next, we factor in this manner,} \\ 3\text{ x ( }4x+5x^2\text{ )} \\ \text{CONCLUSION : The correct solution is 3 x ( 4 x + 5 x }^2\text{ )} \end{gathered}[/tex]write the equation of the line using the given slope and pointm=4 (2,6)
1) We can write the equation of the line, using this point (2,6) and the slope m=4.
2) So, let's plug into the slope-intercept form the point and the slope to find the y-intercept
[tex]\begin{gathered} y=mx+b \\ 6=4(2)+b \\ 6=8+b \\ 6-8=b \\ b=-2 \end{gathered}[/tex]3) Thus, we can write out the following equation:
[tex]y=4x-2[/tex]which represents the inverse of the fuction f(x)=4x?a. h(x) = x + 4xb. h(x) = x - 4c. h(x) = 3/4xd. h(x) = 1/4x
If we want to calculate the inverse, we have to solve for x the following equation
[tex]\begin{gathered} y=4x \\ x=\frac{y}{4} \end{gathered}[/tex]Therefore the inverse function is
[tex]h(x)=\frac{1}{4}x[/tex]f(x) = -x^2 + x + 13Find f(9)
To answer this question, we need to substitute the value of 9 into the quadratic function as follows:
[tex]f(9)=-(9)^2+9+13=-81+22\Rightarrow f(9)=-59[/tex]Therefore, the answer is f(9) = -59.
RewritingInstructions: Rewrite the equation in Slope-Intercept Form.y-2=-5(x- 2)Check
In general, the slope-intercept form of a linear equation is
[tex]\begin{gathered} y=mx+b \\ m,b\rightarrow\text{ constants} \end{gathered}[/tex]Thus, in our case,
[tex]\begin{gathered} y-2=-5(x-2) \\ \Rightarrow y-2=-5x+10 \\ \Rightarrow y=-5x+12 \end{gathered}[/tex]The answer is y=-5x+12The Fighting Irish won 7 games, lost 2 and tied 1. What percent of their games did they win?
N = Total number of games = 7
W = games won = 7 + 2 + 1 = 10
% games they won = W/N = 7/10 = 0.7 = 70%
Question 3: 11 ptsArating for the school bus, Bruce records the colors of all cars passing through an intersection. The tablethe results. Estimate the probability that the next car through the intersection will be black. Express youras a percent. If necessary, round your answer to the nearest tenth.
To find the probability that the next car through the intersection will be black divide the number of black car by the total number of cars.
The total number of cars is the sum of the number of cars of each color, which is 58.
[tex]P=\frac{9}{58}=0.155[/tex]Expressed as a percent it is 15.5%.
It means that the correct answer is the last choice.
Which ordered pair does not lie on the graph of Y=x/4+5?A (-8,3)B (-4,6)C (12,8)D (20,10)
Answer
B (-4, 6)
Step-by-step explanation
Given the expression:
[tex]y=\frac{x}{4}+5[/tex]Substituting x = -8, we get:
[tex]\begin{gathered} y=\frac{-8}{4}+5 \\ y=-2+5 \\ y=3 \end{gathered}[/tex]Then, the point (-8, 3) lies on the line.
Substituting x = -4, we get:
[tex]\begin{gathered} y=\frac{-4}{4}+5 \\ y=-1+5 \\ y=4 \end{gathered}[/tex]Then, the point (-4, 6) does not lie on the line, the point (-4, 4) does.
Need help with dilations mix
When you add/subtract values to the coordinates of a figure, its size doesn't change, you only move it to another location.
When you multiply the coordinates of a figure, you enlarge it, i.e. create a bigger figure proportional to the original one.
When you divide the coordinates of a figure, you reduce its size.
Since the figure was dilated and not moved, option F is incorrect.
To determine how much it was dilated select any point from the pre image and image and compare them.
For example
G (-2,1)
G'(-5,2.5)
To determine the coefficient used for the dilation divide the x-coordinate of the image point by the x-coordinate of the preimage point:
[tex]\frac{X_{G^{\prime}}}{X_G}=\frac{-5}{-2}=\frac{5}{2}[/tex]Now do the same to determine the coefficient used in the Y-coordinates:
[tex]\frac{Y_{G^{\prime}}}{Y_G}=\frac{2.5}{1}=2.5[/tex]2.5 expressed in fractions is 5/2
So the dilation made was (X,Y)→(2/5X,2/5Y)
The correct answer is E.
Find the surface area of this cone. I think the inside is hollow? Im not sure what to do with this problem to be honest
Let us start this problem by analyzing the area we want to calculate
.
To calculate the surface area we will divide the are in two parts:
[tex]\text{ The total area = Area of the base + area of the inner and outer cone}[/tex]The area of the base:
The area of the base can be calculated as the difference between the areas of the to disks , as follows:
[tex]\begin{gathered} \text{ Area of the base=Area of the outer disk - area of the inner disk} \\ =\pi(12)^2-\pi4^2 \\ \\ =128\pi \\ \end{gathered}[/tex]Where we use twice the formula for the area of a circle pi*radius^2, for the outer disk the radius is 12 and for the inner disk the radius is 4.
The lateral area of the two cones, the outer and the inner
Now we will calculate the lateral area of a cone (that is we will not include the base) this area is illustrated by the following draw:
The lateral area of a cone can be calculated using the next formula
[tex]\text{ Lateral area of a cone=}\pi r\sqrt{h^2+r^2}[/tex]Where h is the height of the cone, and r is the radius of the base, for the bigger cone we know from the figure that the height is 6 ft and the radius is 12 ft, for the smaller cone we also know from the figuere that the height is 3 ft and the radius is 4 ft. Therefore we can calculate:
[tex]\begin{gathered} \text{ Lateral area of the bigger cone= }\pi12\sqrt{6^2+12^2} \\ \\ =12\pi\sqrt{180} \end{gathered}[/tex]and
[tex]\begin{gathered} \text{ Lateral area of the smaller cone= }\pi4\sqrt{3^2+4^2} \\ \\ =4\pi\sqrt{25} \\ \\ =20\pi \end{gathered}[/tex]Finally, putting all the areas together we find that:
[tex]\begin{gathered} \text{ The total area= The area of teh base+ the lateral area of the two cones} \\ \\ =128\pi+12\sqrt{180}\pi+20\pi \\ \\ =148\pi+12\sqrt{180}\pi \\ \\ =148\pi+72\sqrt{5}\pi \end{gathered}[/tex]Arithmetic and Geometric Sequences. The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
From the information provided, observe that the three terms are connected by a common ratio.
The first term is multiplied by a value denoted as letter r (common ratio) to derive the second term. The second term is also multiplied by r to derive the third term, and so on.
Therefore;
[tex]\begin{gathered} 5\times r=4 \\ r=\frac{4}{5} \\ 4\times r=\frac{16}{5} \\ r=\frac{16}{5}\text{ / }\frac{4}{1} \\ r=\frac{16}{5}\times\frac{1}{4} \\ r=\frac{4}{5} \end{gathered}[/tex]From the above calculation, the common ratio is 4/5. Therefore, the 10th term in the sequence shall be;
[tex]\begin{gathered} T_n=a\times r^{n-1} \\ \text{Where;} \\ a=5,r=\frac{4}{5},n=\text{nth term} \\ T_{10}=5\times(\frac{4}{5})^{10-1} \\ T_{10}=5\times(\frac{4}{5})^9 \\ T_{10}=5\times\frac{262144}{1953125} \\ T_{10}=\frac{262144}{390625} \end{gathered}[/tex]The 10th term is as shown above. To round this figure to the nearest thousandth, we need to convert this fraction into a decimal.
Hence we would have;
[tex]\begin{gathered} T_{10}=\frac{262144}{390625} \\ T_{10}=0.67108864 \\ T_{10}\approx0.671\text{ (to the nearest thousandth)} \end{gathered}[/tex]