So,
From the graph, we can clearly state that:
In 2 mins, there were 0 calls.
In 3 mins, there was 1 call.
In 4 mins, there were 4 calls.
In 5 mins, there were 6 calls.
In 6 mins, there were 4 calls.
Then, the number of calls that were answered to in 6 mins or less were 0+1+4+6+4 = 15
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]The perimeter of a rectangular picture frame can be represented by the expression 6x,where x is one of the side lengths. Rewrite the expression as the sum of the four side lengths.
Perimeter is formed by 4 side lengths.
Divide perimeter in 4 parts
x= side length
P = 6x = x + x + 4x
then length of the other sides lengths is= 2x
So then ANSWER IS
P= x + x + 2x + 2x
The 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%
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).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
What is the equation of the graphed function?A. f(x) = -1/3x + 1B. f(x) = 3x + 1C. f(x) = 1/3x + 1D. f(x) = -3x + 1
If (x,y) is a point in the graph of a line then its coordinates x and y form a solution to the equation of that line. In slope-intercept form this equation looks like this:
[tex]y=mx+b[/tex]What we are going to do here is choose two points from the line in the picture and use them and the expression above to construct two equations for m and b.
As you can see (0,1) and (3,0) are part of the line so we have the following two equations:
[tex]\begin{gathered} 1=m\cdot0+b \\ 0=3m+b \end{gathered}[/tex]From the first equation we get b=1. If we use this value of b in the second equation we obtain the following:
[tex]\begin{gathered} 0=3m+b=3m+1 \\ 0=3m+1 \end{gathered}[/tex]We can substract 1 from both sides:
[tex]\begin{gathered} 0-1=3m+1-1 \\ -1=3m \end{gathered}[/tex]Then we divide both sides by 3:
[tex]\begin{gathered} -\frac{1}{3}=\frac{3m}{3} \\ m=-\frac{1}{3} \end{gathered}[/tex]Then we have this equation for the line in the picture (we take y=f(x)):
[tex]f(x)=-\frac{1}{3}x+1[/tex]AnswerThen the answer is option A.
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
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.
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]Nolan just drove at a constant rate for 5 hours here is now 340 miles from where he started. A. At what rate was he driving? B. Nolan has another 204 miles to go. If he continues to drive at the same rate, how long will it take him?
A) 68 mph. B) 3h
1) Gathering the data
time: 5 hours
Space= 340 miles
A) To find the rate, we can calculate it by simply writing a quotient between the Space and the time, (since Nolan is constantly moving
[tex]V=\frac{340}{5}=68\text{ mph}[/tex]So Nolan was at 68 mph
B) We can find out by setting a proportion since it's been said that the speed is constant. 340 miles have already been driven there are 204 miles to go.
340------5 hours
204 ---- x
340x = 204 *5 Divide both sides by 340
x=3
So it will take more 3 hours so that Nolan can finish his trip.
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.
Write an equation in slope-intercept form of the line that passes through the point (5,2) and is parallel to 2y+4x=5
• We are given 2y +4x = 5
This can be rewritten as :
2y = -4x +5
y = -4/2x +5/2
y = -2x +5/2
• A line parallel to this line will also have the exact, same slope
Therefore m = -2
in order to find the equation , we will use the following formula
y = mx +c , where m = -2 :
y = -2x + c , at point (5;2)
2 = -2(5) +c
2 +10 = c
Therefore c = 12
finally;
y = -2x +12 is our equation .
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]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]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+121) Compare the following numbers. Choose the correct inequality symbol 10 pointsto go in the circle. *Remember the inequality symbol “eats” the biggernumber!√8 + 3 ? 8 + √3
√8 + 3 ? 8 + √3
√8 is between √4 (= 2) and √9 (= 3), then
√8 + 3 < 3 + 3 = 6
Therefore,
√8 + 3 < 8 + √3
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]ZA and ZB are supplementary angles. If mZAZB = (7x – 26)°, then find the measure of ZA.
the sum of two supplementary angles is 180 degrees
[tex]m\angle A+m\angle B=180[/tex]7x+10+7x-26 = 180
14x = 180 + 16
x = 196/14
x = 14
so the value of m7x+10
= 7(14) + 10
= 98 + 10
= 108
m
(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
1. 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.
To know more about meter per second,
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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
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 -1/2what percentage of college graduates believe their education was useful for helping them grow personally and intellectually, but not useful for helping them develop specific skills and knowledge for the workplace?Write your answer as a percentage
We get the following from the given table.
The percentage of college graduates who believes their education was helping them grow personally and intellectually =62 % + 31 %= 93 %
The percentage of college graduates who believes their education was useful for helping them develop specific skills and knowledge for the workplace = 49%+25%= 84 %
The percentage of college graduates who does not believe their education was useful for helping them develop specific skills and knowledge for the workplace=100-84=16%
The percentage of college graduates believes their education was helping them grow personally and intellectually and does not believe useful for helping them develop specific skills and knowledge for the workplace=the least value of 93 and 16 is 16 %.
Hence the required percentage is 16%.
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]The perpendicular bisectors of a triangle are congruent. Their common point is the:
Given
The perpendicular bisector of the triangle are concurrent. Their common point is the .........
Find
Complete the statement
Explanation
The three angle bisector of triangel are concurrent in a point equidistant from the sides of the triangle.
The point of concurrency of the angle bisectors of a triangle is known as
circumcenter.
Final Answer
Hence , the correct option is C
Complete the table and answer the questions below.a) without graphing, which equation from above has the steepest line? How do you know?b) without graphing, which equation describes a decreasing line? How do you know?
The values on the table are:
[tex]\begin{gathered} y=x-3 \\ \Rightarrow slope\colon m=1 \\ \Rightarrow y-axis\colon b=-3 \\ y=\frac{1}{5}x+2 \\ \Rightarrow slope\colon m=\frac{1}{5} \\ \Rightarrow y-axis\colon b=2 \\ y=-2x \\ \Rightarrow slope\colon m=-2 \\ \Rightarrow y-axis\colon b=0 \end{gathered}[/tex]a) the steepest slope is m=-2 (from the third option). We can see this because in the first option, the rate of change is 1 and in the second option is 1/5. Then for each increase of x, the value of y will be modified but not as much as in the equation y=-2x.
b)the equation y=-2x represents a decreasing line, since the slope is negative.
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.]
Every quadrilateral with opposite angles supplementary can be inscribed in a circle.TrueFalseIf a triangle is inscribed in a circle, the center of the circle is called the circumcenter.TrueFalse
Explanation
The Inscribed Quadrilateral Theorem states that a quadrilateral can be inscribed in a circle if and only if the opposite angles of the quadrilateral are supplementary
Answer 1: True
Also, Given a triangle, the circumscribed circle is the circle that passes through all three vertices of the triangle. The center of the circumscribed circle is the circumcenter of the triangle, the point where the perpendicular bisectors of the sides meet.
Answer 2: True
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]