Answer:
Remember that the area of a circle of radius R is given by:
A = pi*R^2
pi = 3.14
We know that:
Personal Pizza: radius = 10cm
price = $5
The area of pizza that you are getting is:
A = 3.14*(10cm)^2 = 314 cm^2
In the other case, we have a pizza with radius of 30 cm, cutted into 8 slices, such that each slice costs $5.
Then, if yo pay $5, the area of pizza that you get is an eight of the area of a circle of radius 30cm
This is:
A' = (1/8)*(3.14*(30cm)^2) = 353.25 cm^2
We can see that in the second case the area is larger, then the second option is the better deal, as you are getting a larger pizza area for the same price.
In a clothing store, 65% of the customers buy a shirt, 30% of the customers
buy a pair of pants, and 20% of the customers buy both a shirt and a pair of
pants.
If a customer is chosen at random, what is the probability that he or she buys
a shirt or a pair of pants?
Answer:
75%
Step-by-step explanation:
List out known probabilities
[tex]\Pr(shirt) = 0.65 = \frac{65}{100} = \frac{13}{20}\\ \Pr(pants) = 0.40 = \frac{30}{100} = \frac{6}{20}\\\Pr(shirt \cap pants) = 0.20 = \frac{20}{100}=\frac{1}{5}[/tex]
recall equation
[tex]\Pr(A \cup B)=\Pr(A)+\Pr(B)-\Pr(A \cap B)[/tex]
Plug in values
[tex]\Pr(shirt \cup pants)=\frac{13}{20}+\frac{6}{20}-\frac{1}{5}\\\\therefore \Pr(shirt \cup pants) = \frac{15}{20} =\frac{3}{4} = 75\%[/tex]
si el radio de un circulo es de 3 pulgadas. cual es el area del circulo?
Answer:
I don’t know
Step-by-step explanation:
What is filtration??
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
[tex]\pmb{\qquad{\qquad{\qquad{\underline{\purple{\underline{\sf{Filtration}}}}}}}}[/tex]
Filtration is a physical or chemical separation process that separates solid matter and flu.id from a mixture using a filter medium that has a complex structure through which only the flu.id can pa.ss.
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
Write the trigonometric ratio as a fraction. Find the missing angles.
sin D = cosF=m
Answer/Step-by-step explanation:
Recall: SOH CAH TOA
✔️Sin D = Opp/Hyp
Opposite = 7
Hypotenuse = 25
Substitute:
Sin D = 7/25
[tex] D = sin^{-1}(\frac{7}{25}) [/tex]
m<D = 16.3°
✔️Cos F = Adj/Hyp
Adjacent = 7
Hypotenuse = 25
Substitute:
Cos F = 7/25
[tex] F = cos^{-1}(\frac{7}{25}) [/tex]
m<D = 73.7°
A sample of 25 undergraduates reported the following dollar amounts of entertainment expenses last year:
734 769 687 689 759 752 739 694 736 700 768 693 713
732 712 700 707 730 711 700 703 710 682 753 706
a. Find the mean, median and mode of this information. (Round your answers to 2 decimal places.)
Mean $
Median $
Mode (Click to select)$700$712$694
b. What are the range and standard deviation? (Round your answers to 2 decimal places.)
Range $
Standard deviation $
c. Use the Empirical Rule to establish an interval which includes about 95 percent of the observations. (Round your answers to 2 decimal places.)
The interval is from $ up to $ .
Expense
734
769
687
689
759
752
739
694
736
700
768
693
713
732
712
700
707
730
711
700
703
710
682
753
706
Answer:
a) The mean μ = 719,16
The median is the middle number m = 711
The mode is the number that occurs more often
md = 700
b) The range r = 67
The standard deviation σ = 25.63
I ( 95 % ) = ( 667.90 ; 770.42)
Step-by-step explanation:
We order the set of numbers in ascending order
682 687 689 693 694 700 700 700 703 706 707 710 711 712 713 730 732 734 736 739 752 753 759 768 769
The mean μ = Σ xi/n
μ = 719,16
The median is the middle number
m = 711
The mode is the number which occurs more often
md = 700
The range is r = 769 - 682 r = 67
c) Interval with 95 % of observations is ( μ + 2σ ; μ- 2σ )
I = ( 719.16 - 2*25.63 ; 719.16 + 2*25.63)
I ( 95 % ) = ( 667.90 ; 770.42)
Jessica has 3 cards in a bag, each marked with a letter. The letters are X, Y , and
Z. Without looking, she reaches into the bag, pulls out a card, and then puts the card
back in the bag. If Jessica does this 3 times, what is the probability she pulls out the
X card first, then the Y card, and then the Z card?
1/27
Step-by-step explanation:
get one card is 1/3 so you do 1/3x1/3x1/3
X-9=13 what should be done to solve the following equation
Answer:
X=22
Step-by-step explanation:
add 9 to both sides
X-9+9=13+9
X=22
what's the prime factorization of 78
Answer:
2,3 &13
Step-by-step explanation:
78=2times39=3times13
therefore the prime factors of 78=2,3,13
Alex and Thomas share 52 sweets. They divide them in the ratio 7:6. How many sweets does
Thomas have?
Answer:
24
Step-by-step explanation:
[tex]52 \times (6 \div (6 + 7)) = 4 \times 6 = 24[/tex]
Step-by-step explanation:
you first add the ratios 6+7= 13 then you divide the number of sweets by the total number of the ratio 52÷13=4 then you multiply the first ratio by the 4 you found 7×4=28 for Alex then by the second ratio 6×4=24
At-home medical test kits have increased in popularity in recent years. This year, 380 million test kits are expected to be sold. This represents a 114% increase from the number of kits that were sold last year. How many medical test kits were sold last year?
Answer:
326.8 million
Step-by-step explanation:
You just get 14% of 380 million and subtract it from 380 million
Divide. Write the quotient in the lowest terms.
Answer:
[tex]12/1\frac{1}{5}[/tex] [tex]= 10[/tex]
Answer:
10
Step-by-step explanation:
The 18 students in Ms. Sara's class picked 660 strawberries at a strawberry patch during their field trip. If they share them equally, how many whole strawberries can each student have
Answer:
36
Step-by-step explanation:
Since there are 18 students in the class and they picked 660 strawberries, you divided 660 by 18, giving you a quotient of 36.6666667. Since the question asks for how many whole strawberries each student can have, the answer is 36.
Answer:
36
Step-by-step explanation:
Find the volume of the cylinder
Answer:
C. 1,620 in^3
Step-by-step explanation:
Thank you!
Please help guys for these 2 questions
Answer:
question 11 ans = $2.2
question 12 ans = 4
How many solutions exist for the system of equations graphed below?
none
one
two
infinitely many
Answer:
no solutions
Step-by-step explanation:
The lines are parallel and never intersect. The solutions occur when the lines intersect, so there are no solutions
The system of equations which is graphed have no solution.
What is system of linear equations?A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.
A system of linear equation has only one solution when the graphs intersect at a point.A system of linear equation has no solution when the graph are parallel.A system of linear equation has infinite solutions when the graph are the exact same.According to the given question.
We have a graph.
In the given graph the two lines are drawn, which are parallel to each other. So, they don't have a common point.
Therefore, the system of equations which is graphed have no solution.
Find out more information about system of equations here:
https://brainly.com/question/12895249
#SPJ2
A window is being built and the bottom is a rectangle and the top is a semicircle. If the perimeter is 12 meters, what dimensions of the window would let in the most light
Answer:
x = 0,41 m or x = 41 cm
r = 2,18 m
Step-by-step explanation:
Window which allow most light is that with maximum area
The perimeter of the window is the perimeter of the semicircle (psc ) plus the perimeter of the three sides of the rectangle, sides of the rectangle are 2*x and 2*r then:
pt = 12 = psc + pr
psc = π*r pr = 2*x + 2*r
pt = π*r + 2*x + 2*r
pt = 12 = π*r + 2*x + 2*r (1)
The area of the window is:
A(w) = area of the semicircle ( π*r²/2 ) + area of the rectangle (x*2*r)
A(w) = ( π*r²/2 ) + 2*x*r
Using (1) we get: 12 = r* ( π + 2 ) + 2*x
r = ( 12 - 2*x ) / ( π + 2 )
Plugging that value in A(w) we find total area A(w) as a function of x
A(x) = π* [ (12 - 2*x ) / ( π + 2 )]²/ 2 + 2*x*( 12 - 2*x ) / ( π + 2 )
A(x) = π* [ 144 + 4*x² - 48*x/ ( π + 2 )² + 24*x + 4*x²/ ( π + 2 )
A(x) = [ π*/ ( π + 2 )² ] * (144 + 4*x² - 48*x ) + 24*x + 4*x²/ ( π + 2 )
Tacking derivatives on both sides of the equation:
A´(x) = [ π*/ ( π + 2 )² ]* 8*x - 48 + ( 24 + 8*x )/ ( π + 2 )
A´(x) = 0 [ π*/ ( π + 2 )² ]* 8*x - 48 + ( 24 + 8*x )/ ( π + 2 ) = 0
π* (8*x - 48) / ( π + 2 ) + 24 + 8*x = 0
8*π*x - 48*π + ( 24 + 8*x ) *( π + 2 ) = 0
8*π*x - 48*π + 24*π + 48 + 8*π*x + 16*x = 0
16*π*x - 24*π + 16*x + 48 = 0
x ( 16*π + 16 ) - 24*π + 48 = 0
66,24 * x = 75,36 - 48
x = 27,36 / 66,24 m
x = 0,41 m or x = 41 cm
r = ( 12 - 2*x ) / ( π + 2 )
r = 12 - 2* 0,41 / 3,14 + 2
r = 11,18 / 5,14
r = 2,18 m
find the slope of the line between (1,4) and ( 3 , 10 )
Answer:
3
Step-by-step explanation:
slope of line = gradient of line
= [tex]\frac{10-4}{3-1}[/tex]
= 3
Can someone answer this question please
Answer:
Round off the decimal to the nearest tenths.
0.82
The answer is 0.80
Step-by-step explanation:
When I learned rounding, we would round to the place value behind it then if its less than 5 than my answer would be what its rounded to. If I round 92 to the nearest tenth, it would be 90 because 2 is not greater than 5 so it would round to 90 because its the nearest tenth. If it was 95 it would be rounded to 100, any number that is 5 to 9 would be rounded to the greater tenth closer to it. So 0.82 is less than 5 nor 5 so it would round up to 0.80
A regular hexagon of side 8 cm is given. the hexagon is devided into 6 congruent triangles . calculate the area of the hexagonal
Answer:
96√3 cm^2
Step-by-step explanation:
half base = 4 cm
height of each triangle = 4√3 cm
Area of each triangle
(8 * 4√3)/2 = 16√3 cm^2
area of the hexagonal = 16√3 * 6 = 96√3 cm^2
Finding a final amount in a word problem on exponential growt...
An amount of $25,000 is borrowed for 15 years at 5.5% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be
paid back?
9514 1404 393
Answer:
$55,811.91
Step-by-step explanation:
The amount with interest is given by the formula ...
A = P(1 +r)^t
where r is the annual interest rate and t is the number of years.
A = $25000(1.055^15) ≈ $55,811.91
The amount due at the end of 15 years will be $55,811.91.
Math Lab Review Work
1. Macy's is having their family and friends' sale. They are having 80% off everything. Janyla says
that she can find the sale price of an item that has a regular price of p by evaluating the
expression 0:20p. Nalia says that she can find the sale price for the same item by evaluating the
expression p-0.80p. Who is correct? (Hint: Substitute a value for p. Use the same number for
both expressions to see if you get the same answer
1 Pt
A) Neither
B) Both
C) Janyla
D) Nalia
A
B
0
D
E
Answer:
I think it C because I know that Nalia isn't correct so it's not D or B.
You are solving a system of two linear equations in two variables, and you discover that there are no solutions to the system.
Which of the following graphs could describe the system of equations?
A
Green
B
Purple
C
Blue
D
Pink
Answer:
D. Pink
Step-by-step explanation:
Two equation with no solutions means the lines are parallel
In your own words, explain why the ratios 3:2, 6:4 and 9:6 are all equivalent
ratios.
Answer:
because in lowest term it's ratio is same
Step-by-step explanation:
hope you understand
Answer:
The ratios of 3:2, 6:4, and 9:6 are all equivalent because when you divide the numerator over the denominator, you get the same result for all of them. This means that if we took 3/2 and got 1.5, and took 6/4 and got 1.5 as an answer, and took 9/6 and got 1.5 as an answer as well, we would have the same answer for all of them. This is why (in my own words) the ratios are all equivalent.
Think of 5 positive integers that have a mode of 4, a median of 8, a mean of 9 and a range of 12 what are the 5 integers
Answer:
{4, 4, 8, 13, 16}
Step-by-step explanation:
If we have a set of N numbers in order:
{x₁, x₂, ..., xₙ}
The median is the middle number of the set.
The mode is the value that is repeated more times in the set
The mean is computed as:
[tex]M = \frac{x_1 + x_2 + ... + x_n}{N}[/tex]
And the range is the difference between the largest value and the smallest value.
Here we want 5 positive integers, so we have something like:
{x₁, x₂, x₃, x₄, x₅}
We know that the median is 8.
Then the middle value, x₃, is equal to 8.
We also know that the mode is 4, then we can have the number 4 repeated two times, and because 4 is smaller than 8 and this must be in order, then we can have:
x₁ = x₂ = 4
Replacing these in the set we have:
{4, 4, 8, x₄, x₅}
Now we know that the range is 12, and this was the difference between the largest and smallest value.
We know that the smallest value is 4, and the largest value is x₅, then we will have:
x₅ - 4 = 12
x₅ = 12 + 4 = 16
Then our set is:
{4, 4, 8, x₄, 16}
Finally, we know that the mean is 9.
Remember that the equation for the mean is:
[tex]M = \frac{4 + 4 + 8 + x_4 + 16}{5}[/tex]
Then we need to solve:
[tex]9 = \frac{4 + 4 + 8 + x_4 + 16}{5}[/tex]
[tex]9*5 = 4 + 4 + 8 + x_4 + 16}[/tex]
[tex]45 = 32 + x_4[/tex]
[tex]45 - 32 = x_4 = 13[/tex]
Then the set of five positive integers is:
{4, 4, 8, 13, 16}
A ______ is a graph of data based on quartiles showing a rectangle with lines extending from both its ends.
Another alternative answer is "box-and-whisker plot"
The box portion consists of data between Q1 and Q3, with the median somewhere in between. The whiskers represent stuff below Q1 and above Q3. The tip of each whisker represents the min and max, assuming there are no outliers. If there are outliers, then you'll have island points disconnected from the main boxplot.
fill in the blank so that the ordered pair is a solution of the equation . please help with this question i will mark you brainliest !
Answer:
2.
Step-by-step explanation:
You don't have to mark me brainliest but, 4=22-9x. -18=-9x. 9x=18. x=2
2.
What is the result of subtracting the second equation from the first?
-4x-2y=-2
x-2y=9
Please tell me if I should answer with the point (10, 5) or some way else.
Please help asap
I might give brainliest
Answer:
5x = 11.
Step-by-step explanation:
-4x - 2y = -2
x - 2y = 9
Subtracting:
-4x - x - 2y - (-2y) = -2 - 9
-5x - 2y + 2y = -11
-5x = -11
5x = 11.
4x+y>9 Select all the correct answers. (1, 6) (2, 2) (3, −4) (5, 0) (−1, 13)
Answer: 1,6 2,2 5,0 These are the correct answers.
Step-by-step explanation:
Researchers would like to know the mean body temperature of runners at the completion of a marathon. They plan to take a random sample of 100 runners who complete a marathon and record their temperatures. Which of the following will the researchers know after they have taken the sample? Explain your answer in each part.a. The value of the mean of the sampling distribution of the sample mean.b. The approximate shape of the sampling distribution of the sample mean.c. The standard deviation of the sampling distribution of the sample mean.
Answer:
They would know a and b.
a. The mean of this distribution, by the Central Limit Theorem, is the sample mean, and thus, the researches would know this after they took the sample.
b. Sample size is 100 > 30, and thus, by the Central Limit Theorem, they would know that the shape of the distribution is approximately normal.
c. To know the standard deviation of the sampling distribution of the sample mean, the researchers would have to know the population's standard deviation, which they can't get for the sample. So they would not know the standard deviation of the sampling distribution of the sample mean after they took the sample.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
a. The value of the mean of the sampling distribution of the sample mean.
The mean of this distribution, by the Central Limit Theorem, is the sample mean, and thus, the researches would know this after they took the sample.
b. The approximate shape of the sampling distribution of the sample mean.
Sample size is 100 > 30, and thus, by the Central Limit Theorem, they would know that the shape of the distribution is approximately normal.
c. The standard deviation of the sampling distribution of the sample mean.
To know the standard deviation of the sampling distribution of the sample mean, the researchers would have to know the population's standard deviation, which they can't get for the sample. So they would not know the standard deviation of the sampling distribution of the sample mean after they took the sample.
Sqrt 15(3+5) = Sqrt3+ sqrt 5
Answer:
False
Step-by-step explanation:
Assuming a and b are 2 different terms,
Sqrt a + Sqrt b is not equal to Sqrt (a * b).
The only way to obtain Sqrt (a * b) is by doing the following:
Sqrt (a * b) = Sqrt (a) * Sqrt (b)