The area of a circle is given by:
[tex]A=\pi r^2[/tex]Since the radius is half the diameter we have that r=6. Then the area is:
[tex]A=\pi(6)^2=36\pi[/tex]Therefore, the answer is the first one.
Jason predicted that 227 students would attend the school dance.
The actual number was 250. What is the percent error of Jason's prediction?
.
1. What is the difference between the predicted value and the
actual value?
2. Complete the equation:__=p • ___
3. Solve the equation for p.
(I already did number one I just need help with 2 and 3)
Question 2
[tex]23=p \cdot 250[/tex]
The difference is 23.The actual value is 250.Question 3
[tex]p=\frac{23}{250}=0.092[/tex]
There are 130 people in a sport centre.
76 people use the gym
60 people use the swimming pool.
32 people use the track.
23 people use the gym and the pool.
8 people use the pool and the track.
20 people use the gym and the track.
6 people use all three facilities.
Given that a randomly selected person
uses the gym and the track, what is
the probability they do not use the
swimming pool?
The probability is 0.57
What is meant by probability?
Probability is a discipline of mathematics that deals with appropriate units of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number ranging from zero and 1, where 0 denotes the event's feasibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur. Tossing a fair (unbiased) coin is a basic example. Because the coin is fair, the two possibilities ("heads" and "tails") are equally likely; the chance of "heads" equals the probability of "tails," and because no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.
Probability of using the pool = 97/225 = 0.43
Probability that they do not use the swimming pool = 1 - 0.43 = 0.57
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Find the slope and the equation of the line having the points (0, 2) and (5, 5)
Answer:
The slope is 3/5 and the equation is:
[tex]y=\frac{3}{5}x+2[/tex]Explanation:
Given the points (0,2) and (5, 5)
The slope of a line is the ratio of the difference between the y coordinates to the x coordinates. The x coordinates are 0 and 5, the y coordinates are 2 and 5.
[tex]\begin{gathered} m=\frac{5-2}{5-0} \\ \\ =\frac{3}{5} \end{gathered}[/tex]The equation of a straight line is given as:
y = mx + b
Where m is the slope and b is the y-intercept
Using any of the given points, we can find b
Use (0, 2), with x = 0, y = 2
2 = (3/5)(0) + b
b = 2
Now the equation is:
[tex]y=\frac{3}{5}x+2[/tex]A package of 8-count AA batteries costs $6.16. A package of 20-count AA batteries costs $15.60. Which statement about the unit prices
is true?
The 8-count pack of AA batteries has a lower unit price of $0.77 per battery.
The 20-count pack of AA batteries has a lower unit price of $0.77 per battery.
The 20-count pack of AA batteries has a lower unit price of $0.78 per battery.
Answer:
it would be within the range of $0.77 <x< $0.78
Advantage Cellular offers a monthly plan of $25 for 500 minutes. What is the cost per minute? Round to the nearest hundredths place.
The cost per minute is $0.05 and it is round off to the nearest hundredths place.
Round off:
Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.
Given,
Advantage Cellular offers a monthly plan of $25 for 500 minutes.
Here we need to find the cost per minute and we have also need to round off the result to the nearest hundredth place.
We know that,
500 minutes cost = $25
So, to calculate the price for one minute, then we have to divide the cost by the total number of minutes.
So, it can be written as,
=> 25 ÷ 500
So, the cost for one minute is.
=> 0.050
When we rounded to the nearest hundredths place.
The 5 in the hundredths place rounds down to 5, or stays the same, because the digit to the right in the thousandths place is 0.
Therefore, the cost per minute is $0.05.
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6. If you start with 200 MNM's and eat 15 every minute and your friend starts with300 MnM's but eats 25 every minute. When will you have the same number asyour friend? How much longer will it take you to finish your MnM's? At 10minutes you both will have 50 left. You will finish 1 min and 20 seconds after yourfriend.
Given:
The initial number of MNMs I have, x=200.
The number of MNM's eat by me every minute, p=15.
The initial number of MNMs my friend have, y=300.
The number of MNM's eat by friend every minute, q=25.
Let n be the number of minutes after which both will have the same number of MNM. Then, the amount of MNM remaining with me after n minutes is,
[tex]x-pn[/tex]The amount of MNM remaining with my friend after n minutes is,
[tex]y-qn[/tex]Equate the above expressions and substitute the values to find the number of minutes n.
[tex]\begin{gathered} x-pn=y-qn \\ 200-15n=300-25n \\ 25n-15n=300-200 \\ 10n=100 \\ n=\frac{100}{10} \\ n=10 \end{gathered}[/tex]Therefore, I will have the same number as my friend after 10 minutes.
The number of minutes taken by me to finish 200 MNM's is,
[tex]\begin{gathered} m=\frac{x}{p} \\ =\frac{200}{15} \\ =13\frac{5}{15} \\ =13\frac{1}{3}\text{minutes} \\ =13\text{minute}+\frac{1}{3}\min utes\times\frac{60\text{ seconds}}{1\text{ minute}} \\ =13\text{ minutes +20 seconds} \end{gathered}[/tex]So, I will take 13 minutes 20 seconds to finish the MNM's.
The number of minutes taken by my friend to finish 300 MNM's is,
[tex]\begin{gathered} k=\frac{y}{q} \\ =\frac{300}{25} \\ =12\text{ minutes} \end{gathered}[/tex]So, the friend will take 12 minutes to finish the MNM's.
So, I will finish
Can yoy help me with number 3? I do not understand the question.
The law of sines states that:
[tex]\frac{\sin\alpha}{a}=\frac{\sin\beta}{b}=\frac{\sin \gamma}{c}[/tex]where alpha is the opposite angle to side a, beta is the opposite angle to side b and gamma is the opposite angle to side c.
For the triangle given we notice that:
Angle x is opposite to side 2.5.
Angle 28° is opposite to side 3.
Therefore the expression to find x is:
[tex]\frac{\sin x}{2.5}=\frac{\sin 28}{3}[/tex]What is the value of the expression 4x−y2y+x when x = 3 and y = 3? −31918
7 ( 1 + 3 )
Solve the sum inside the parentheses ( 1 + 3 = 4 )
7 ( 4 )
multiply
7*4 = 28
Since the sum must equal 28
7 + 21 = 28
Correct option = 7+21
Give. ∆ABC Angle B = 42°, Angle C = 71° and BC = 22. Find AB and round your answer to nearest integer.
Let's make a diagram to visualize the problem.
First, let's find angle A.
[tex]\begin{gathered} A+B+C=180 \\ A+42+71=180 \\ A=180-71-42 \\ A=67 \end{gathered}[/tex]Then, we use the law of sines to find AB.
[tex]\begin{gathered} \frac{AB}{\sin71}=\frac{BC}{\sin A} \\ \frac{AB}{\sin71}=\frac{22}{\sin 67} \\ AB=\frac{22\cdot\sin 71}{\sin 67} \\ AB\approx23 \end{gathered}[/tex]Therefore, AB is 23 units long, approximately.the digits 1through 6 are used for a set of locker codes. suppose the digits cannot repeat. find the number of possible two digit codes and three digit codes. describe any pattern and use it to predict the number of possible five digit codes
SOLUTION
This is a permutation problem.
a) To find the number of possible two digits codes
[tex]^6P_2[/tex][tex]^6P_2=\frac{6!}{(6-2)!}[/tex][tex]\begin{gathered} =\frac{6!}{4!} \\ =\frac{720}{24} \\ =30\text{ ways} \end{gathered}[/tex]There are 30 possible two-digit codes pattern.
b) To find the number of three digits codes
[tex]\begin{gathered} ^6P_3=\text{ }\frac{6!}{(6-3)!} \\ \text{ =}\frac{6!}{3!} \\ \text{ =}\frac{720}{6} \\ \text{ = 120 ways} \end{gathered}[/tex]There are 120 possible three-digit codes pattern.
Any other pattern can be calculated using
[tex]\begin{gathered} ^6P_r \\ \text{where r is the number of digits code (1,2,3,4,5,6)} \end{gathered}[/tex]So to predict the number of possible five-digit codes will be:
[tex]^6P_5[/tex][tex]\begin{gathered} =\frac{6!}{(6-5)!} \\ =\frac{6!}{1!} \\ =720\text{ways} \end{gathered}[/tex]There are 720 different possible five-digit codes
the answer of this question is 720 ways
find the first second and third derivatives of the function
Given the function
[tex]f(x)=\frac{8}{5}x-9[/tex]Finding the derivative we have
[tex]f^{^{\prime}}(x)=\frac{8}{5}[/tex]Also
[tex]f^{\doubleprime}(x)=0^{}[/tex]Finally
[tex]f^{^{\doubleprime}^{\prime}}(x)=0[/tex]Assume the random variablex is normally distributed with mean p=85 and standard deviation o=5. Find the indicated probabiliP73
Remember that
z =(x - μ)/σ
we have
μ=85
σ=5
For x=73
Find out the value of Z1
z1=(73-85)/5
z1=-2.4
For x=76
Find out the value of Z2
z2=(76-85)/5
z2=-1.8
using a z-scores table values
we have that
P(73Which ordered pair is a solution set for the linear equation, x + 16 = 6y? A (16,4) B (2, 3) C (-4,-2) D (-10,-1)
Explanation
to figure out if a pair is a solution, just replace x and y values and check if the equation is true,then
Step 1
[tex]\begin{gathered} x+16=6y \\ A)(16,4)\rightarrow when\text{ x=16 and y =4} \\ \text{replace} \\ 16+16=6\cdot4 \\ 32=24\rightarrow False,then\text{ A is not a solution} \end{gathered}[/tex]Step 2
[tex]\begin{gathered} B)(2,3)\rightarrow whenx=\text{ 2 and y=3} \\ x+16=6y \\ \text{replace} \\ 2+16=6\cdot3 \\ 18=18\rightarrow true \\ so\text{ B is a solution} \end{gathered}[/tex]Step 3
[tex]undefined[/tex]which statement is true of the system of equations shown below
3x + 7y= 14
3x+7y= 10
Subtract the second equation to the first.
3x +7y= 14
-
3x + 7y= 10
_________
0x +0y = 4
0 = 4
0 is no
Identify each pair of angles as corresponding, alternate interior, alternate exterior, consecutiveinterior, vertical, or adjacent.
SOLUTION
Given the image on the answer tab;
Explanation;
The two angles are said to be adjacent angles when they share the common vertex and side.
Considering our question;
Which is an example of a survey?A- collecting the cholesterol readings of a group of elderly people in a small townB- interviewing college students to find what percentage expect a job immediately after graduationC- testing the effectiveness of a hair product by allowing one group to use it and comparing results against a control groupD- testing the effectiveness of a mouthwash by allowing one group to use it and comparing results with those of a group that doesn't use ot
Answer: B- interviewing college students to find what percentage expect a job immediately after graduation
Surveys are meant to collect data that can be used to analyze a population as ahwole. This option analyzes the perspective of college students as a whole, whereas option A only focuses on a minority group of elderly. Additionally, options C and D are moreso experiments and not surveys that can be applied on a larger scale.
An athlete runs at a speed of 9 miles per hour. If one lap is 349 yards, how many laps does he run in 22 minutes
An athlete run in 22 minutes is 19.232 laps
Given,
An athlete runs at a speed of 9 miles per hour.
and, If one lap is 349 yards.
To find the how many laps does he run in 22 minutes?
Now, According to the question:
Firstly, Convert the mph into yard per minute,
Remember that:
I mile = 1,760 yard
1hour = 60 minute
Convert the speed in miles/hour to yards/minute
9 [tex]\frac{miles}{hour}[/tex] = 9[tex]\frac{1760}{60}[/tex] = 264 yard/ min
We know that
The speed is equal to divide the distance by the time
Let
s → the speed
d → the distance in yards
t → the time in minutes
Using the formula :
Speed = distance/ time
Solve the distance:
d = speed x time
Speed = 264 yard/ minute
Time = 22 minute
Therefore,
Distance = 264 x 22
Distance = 5,808 yards
Divide the distance by 302 yards to find out the number of laps
= 5,808/ 302 = 19.232 laps
Hence, An athlete run in 22 minutes is 19.232 laps
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Rigid Transformations: Question 3A military compound is located in a city where the streetsare arranged in a grid. The compound is going to be movedto a new location in the same city. The new compound willbe exactly the same as the old one and in the sameorientation. The existing location is represented on thecoordinate grid shown, where each unit represents one cityblock. Which of the following best describes the situation?14B1210CDD'C6 4AB2-14 12 10 86226 8 10 12 142D4С6 8N10Wm12s141
In this question, we are given two locations of a military compound.
Let's take the coordinates of point A from the graph,
A = (-3, 2)
The new coordinates of A' = (5, 13)
translation in x-axis = 5 - (-3) = 5 + 3 = 8
translation in y-axis = 13 - 2 = 11
hence, each point of the figure will be translated to 8 units on the x-axis and 11 units on the y-axis.
A classic car is now selling for $2000 more than two times its original price. If the selling price is now $12,000, what was the car's original price?
brainliest will be given to whoever has the correct answer
The CLOSEST correct answer regarding "x" is the first one (answer A), since x is 79. The correct answer is: X measures 79 because it is an alternate external angle between parallel lines to the one labeled 79 in the picture.
6. Suppose that wedding costs in the Caribbean are normally distributed with a mean of $6000 and a standard deviation of $735. Estimate the percentage of Caribbean weddings that cost (a) between $5265 and $6735. % (b) above $6735. % (c) below $4530. % (d) between $5265 and $7470. %
To solve this problem, the first thing we must do is find the Z-Score of the given costs: $5265 , $6735 , $4530 ,and $7470
Then we proceed to find the percentages for each interval based on the graph
z-score for $5265 )
[tex]Z_{5265}=\frac{5265-6000}{735}=-1[/tex]z-score for $6735 )
[tex]Z_{6735}=\frac{6735-6000}{735}=1[/tex]z-score for $4530 )
[tex]Z_{4530}=\frac{4530-6000}{735}=-2[/tex]z-score $7470 )
[tex]Z_{7470}=\frac{7470-6000}{735}=2_{}[/tex]now, let's analyze the intervals
a ) between $5265 and $6735
This interval goes from (μ-σ) to (μ+σ)
if we look at the graph we find that this corresponds to a percentage of 68%
b) above $6735
This corresponds to what is to the right of (μ+σ)
This is a percentage of 16%
[tex]\frac{100-68}{2}=\frac{32}{2}=16[/tex]c ) below $4530
This corresponds to what is to the left of (μ-2σ)
This is a percentage of 2.5%
[tex]\frac{100-95}{2}=\frac{5}{2}=2.5[/tex]d ) between $5265 and $7470
This interval goes from (μ-σ) to (μ+2σ)
This is a percentage of 81.5%
[tex]\begin{gathered} 100-\frac{100-68}{2}-\frac{100-95}{2} \\ =100-16-2.5 \\ =81.5 \end{gathered}[/tex]50 points.
Daisy is a botanist who works for a garden that many tourists visit. The function f(s) = 3s + 30 represents the number of flowers that bloomed, where s is the number of seeds she planted. The function s(w) = 12w represents the number of seeds she plants per week, where w represents the number of weeks.
Part A: Write a composite function that represents how many flowers Daisy can expect to bloom over a certain number of weeks.
Part B: What are the units of measurement for the composite function in Part A?
Part C: Evaluate the composite function in Part A for 36 weeks.
From the situation described in this problem, it is found that:
A. The composite function is: f(s(w)) = 36w + 30.
B. The unit of measurement of the composite function is: flowers.
C. After 36 weeks, Daisy can expect to bloom 1326 flowers.
Composite functionFor a composite function, the output of the inner function serves as the input of the outer function.
In the context of this problem, the functions are given as follows:
f(s) = 3s + 30.s(w) = 12w.Hence the composite function that represents how many flowers Daisy can expect to bloom over a certain number of weeks is:
f(s(w)) = f(12w) = 3(12w) + 30 = 36w + 30.
The unit of measurement of the composite function is the unit of the outer function, which is flowers.
After 36 weeks, the number of flowers that Daisy can expect to bloom is given as follows:
f(s(36)) = 36(36) + 30 = 1326 flowers.
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This not a test btw ! But can you please help me with this !
Using elimination:
[tex]\begin{gathered} (A)-3(B)\colon \\ 6x+12x-3y+3y=-4-15 \\ 18x=-19 \end{gathered}[/tex]Therefore, the answer is:
B) Multiply A by 1 and B by -3
The lengths of two sides of the right triangle ABC shown in the illustration givena=12 cm and c= 20cm
In the right triangle of sides a, b, and c
[tex]a^2+b^2=c^2[/tex]Since a = 12 and c = 20
Substitute them in the given rule
[tex]\begin{gathered} (12)^2+b^2=(20)^2 \\ 144+b^2=400 \end{gathered}[/tex]Subtract 144 from both sides
[tex]\begin{gathered} 144-144+b^2=400-144 \\ b^2=256 \end{gathered}[/tex]Take a square root for both sides
[tex]\begin{gathered} \sqrt[]{b^2}=\sqrt[]{256} \\ b=16 \end{gathered}[/tex]The answer is b = 16
the question is on the sheet .The shaded region is the area within the figure but not the corner squares
Based on the information given in the exercise, you know that the shaded region has this area:
[tex]6x^2-2xy+3y^2[/tex]And the area of each square region in the corners is:
[tex]4x^2[/tex]Since there are four square regions, you can multiply that the area of any of them by 4, in order to find the total area of them:
[tex]4(4x^2)=16x^2[/tex]Then, in order to find the total area of the figure, you must add the area of the shaded region and the total area of the square regions:
[tex](6x^2-2xy+3y^2)+(16x^2)=22x^2^{}-2xy+3y^2[/tex]Therefore, the total of the figure is:
[tex]22x^2-2xy+3y^2[/tex]A college conducted a survey of randomly selected freshmen about their choice of major. The table shows the results of the survey. KS
ONLY F is correct;
Here, we want to select the correct inference from the data presented
f) We want to comapre the number of English freshmen and the undecided
Both have a count of 50; we can see that these values are equal and thus, we conclude that these two are equal
This makes the inference correct
g) Here, we want to compare Education freshmen to science freshmen or others
From the question, the number of education freshmen is 60
The number of science or others is (30+25) = 55
The number for education is greater and not less
This makes this option or inference incorrect
h) Here, we want to comapre Business/Education and Science/Engineering
Business OR Education is = 45 + 60 = 105
Science OR Engineering is = 35 + 40 = 75
Business/Education is greater and this makes this option or inference wrong
j) Here, we want to compare Business and English
Business is 45
English is 50
We can see that English is greater and this makes the inference/option wrong
Nov 28,Quadrilateral ABCD is dilated by a scale factor of to form quadrilateral A'B'C'D'.What is the measure of side DA?Dal1515301B2162А
The quadrilateral ABCD was dilated by a scale factor of 3/4 to form the quadrilateral A'B'C'D'
This means that each side of the quadrilateral was multiplied by 3/4 to make the dilation.
You know that the scale factor is 3/4 and the length of D'A' is equal to 30 units, then:
[tex]\begin{gathered} D^{\prime}A^{\prime}=\frac{3}{4}DA \\ 30=\frac{3}{4}DA \end{gathered}[/tex]Multiply both sides by the reciprocal of 3/4
[tex]\begin{gathered} 30\cdot\frac{4}{3}=(\frac{4}{3}\cdot\frac{3}{4})DA \\ 40=DA \end{gathered}[/tex]The length of side DA is 40 units.
What is the day supply for 30 tablets if the direction is a half tabletsFor 7 days then 1 once daily
Answer:
33 days
Explanation:
If you use a half tablet for 7 days, you will consume:
0.5 x 7 days = 3.5 tablets.
So, at the end of the 7th day, you will consume 3.5 tablets and you will have 26.5 tablets left because:
30 tablets - 3.5 tablet = 26.5 tablets.
Then, you will consume 1 tablet daily, so if you have 26.5 tablets, you will have a tablet daily for 26 days.
Therefore, the day supply for 30 tablets will be the sum of the initial 7 days and the 26 days, so:
7 days + 26 days = 33 days.
Therefore, the answer is 33 days
Ashlee was born on 09/08/1981. How many eight digit codes could she make using the digits in her birthday
Ashlee could make 2520 eight digit codes using the digits in her birthday .
In the question
it is given that
the birthdate of Ashlee is 09/08/1981.
So, the number of digits are 0,0,1,1,8,8,9,9 .
number of digits = 8
So, 8 digits can be arranged in 8! ways
8! = 8*7*6*5*4*3*2*1 = 40320
Repeating digits are
0 repeated 2 times = 2! = 2
1 repeated 2 times = 2! = 2
8 repeated 2 times = 2! = 2
9 repeated 2 times = 2! =2
So, the number of 8 digits codes is = 8!/(2!*2!*2!*2!)
= 8!/(2*2*2*2)
= 40320/16
= 2520
Therefore , Ashlee could make 2520 eight digit codes using the digits in her birthday .
The given question is incomplete , the complete question is
Ashlee was born on 09/08/1981. How many eight digit codes could she make using the digits in her birthday ?
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the square root of 31 is closer to which number? 6 or 5.
Answer:
6
Explanation:
First, we find the squares of 5 and 6.
[tex]\begin{gathered} 5^2=25 \\ 31-25=6 \end{gathered}[/tex][tex]\begin{gathered} 6^2=36 \\ 36-31=5 \end{gathered}[/tex]We conclude therefore that the square root of 31 is closer to 6 since it has a smaller difference.