An exercise teacher wants each student in her class to have at least 48 square feet of space on the floor. What is the largest number of students she will allow in a classroom with a student exercise area of this size? A. 20 students B. 24 students C. 40 students D. 50 students
Answers
Answer:
D. 50 students
Step-by-step explanation:
First we find the area of the classroom which is worked out below and it is the shape of a rectangle;
Area of a rectangle = Length * Breadth
= 60 ft * 40 ft
= 2400 ft²
Now to find the number of students that she will allow in the classroom, we have to divide the area of the classroom which is 2400 ft²by the amount of space allocated to each student which will be;
= [tex]\frac{2400}{48}[/tex]
= 50
This means she will allow 50 students into her class.
Answer:
50
Step-by-step explanation:
Related Questions
The U.S. Department of Agriculture (USDA) uses sample surveys to obtain important economic estimates. One USDA pilot study estimated the price received by farmers for corn sold in January from a sample of 20 farms. The mean price was reported as $3.64 per bushel with a standard deviation of $0.0835 per bushel. Give a 95% confidence interval for the mean price received by farmers for corn sold in January.
Answers
Answer:
{$3.60; $3.68}
Step-by-step explanation:
The confidence interval for a sample of size 'n', with mean price 'X' and standard deviation 's' is determined by:
[tex]X\pm z*\frac{s}{\sqrt n}[/tex]
The z-score for a 95% confidence interval is 1.96.
Applying the given data, the lower and upper bounds of the confidence interval are:
[tex]3.64\pm 1.96*\frac{0.0835}{\sqrt 20} \\L=\$3.60\\U=\$3.68[/tex]
The confidence interval for the mean price received by farmers for corn sold in January is:
CI : {$3.60; $3.68}
According to a report from the Center for Studying Health System Change, 20% of Americans delay or go without medical care because of concerns about cost (The wall street journal, June 26, 2008). Suppose eight individuals are randomly selected.
The probability no one delays or goes without medical care is ____________ ;
The probability only one person delays or goes without medical care is ____________.
Please keep three decimals.
Answers
Answer:
The probability no one delays or goes without medical care is 0.168;
The probability only one person delays or goes without medical care is 0.336.
Step-by-step explanation:
This problem can be modeled with a binomial random variable, with sample size n=8 and probability of success p=0.2.
The probability that exactly k Americans delay or go without medical care because of concerns about cost within the sample of eight individuals can be calculated as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{8}{k} 0.2^{k} 0.8^{8-k}\\\\\\[/tex]
The probability no one delays or goes without medical care (x=0) is:
[tex]P(x=0) = \dbinom{8}{0} p^{0}(1-p)^{8}=1*1*0.168=0.168\\\\\\[/tex]
The probability only one person delays or goes without medical care (x=1) is
[tex]P(x=1) = \dbinom{8}{1} p^{1}(1-p)^{7}=8*0.2*0.21=0.336\\\\\\[/tex]
Please answer this question now in two minutes
Answers
Answer:
the slope equation is y2 - y1 divided by x2 - x1
Step-by-step explanation:
so the answer would be 3 over 2 because of this method
Answer:
3/2
Step-by-step explanation:
Use the easy rise over run method.
start at the point (50,20) then go up 3 units and 2 units to the right to get the next point.
3/2 should be the slope.
Hope I helped you!
Define f(0,0) in a way that extends f(x,y)=x^2 - y^2/x^2 + y^2 to be continuous at the origin.
Answers
Answer:
It cannot be extended.
Step-by-step explanation:
Consider the function [tex]f(x,y) = \frac{x^2-y^2}{x^2+y^2}[/tex]. To extend this functions so it is continous at (0,0) we must define [tex] f(0,0) = \lim_{(x,y)\to(0,0)\frac{x^2-y^2}{x^2+y^2}[/tex]. However, this implies that the limit exists. So, we should find if the limit exists or not.
In this case, consider the case in which y =0. When y=0 then
[tex]\lim_{(x,y)\to(0,0) \frac{x^2-0^2}{x^2+0^2} = \lim_{x\to 0}\frac{x^2}{x^2}= 1[/tex]
But, when x=0, we get
[tex]\lim_{(x,y)\to(0,0) \frac{0^2-y^2}{0^2+y^2} = \lim_{y\to 0}\frac{-y^2}{y^2}=-1[/tex].
So, since the limit depends on how we approach to the point (0,0) the limit does not exist. So we can't extend f(x,y) so it is continous.
Jaleel and Lisa are simplifying the expression 2 (x minus 2) + 2 as shown. Jaleel’s Method 2 (x minus 2) + 2 = 2 x minus 4 + 2 = 2 x minus 2 Lisa’s Method 2 (x minus 2) + 2 = 2 x minus 2 + 2 = 2 x Whose method is correct and why? Lisa’s method is correct because 2 (x minus 2) equals 2 x minus 2. Lisa’s method is correct because 2 (x minus 2) equals 2 x. Jaleel is correct because 2 (x minus 2) equals 2 x minus 2. Jaleel is correct because 2 (x minus 2) equals 2 x minus 4.
Answers
Answer:
(D)Jaleel's method is correct because 2(x-2)=2x-4.
Step-by-step explanation:
Jaleel and Lisa are simplifying the expression 2(x-2)+2 as shown.
[tex]J$aleel's Method: \left\{\begin{array}{ccc}2 (x -2) + 2 \\= 2 x - 4 + 2 \\= 2 x - 2\end{array}\right[/tex]
[tex]L$isa's Method: \left\{\begin{array}{ccc}2 (x-2) + 2 \\= 2 x -2 + 2 \\= 2 x\end{array}\right[/tex]
We can see that Jaleel's method is correct because:
2(x-2)=2x-4.
When you expand, you must multiply the term outside by all the terms inside the bracket.
The correct option is D.
Answer:
Jaleel is correct because 2 (x minus 2) equals 2 x minus 4.
D is correct
Step-by-step explanation:
i just took the quiz.
Please find the missing side of the triangle and round the answer to the nearest tenth. Thanks.
Answers
Answer:
x = 74.3
Step-by-step explanation:
Using the trigonometric ratio formula, the missing side, x, of the right angled triangle, can be found as follows:
Ѳ = 22°,
adjacent side length = x
Opposite side length = 30
Thus, we would apply the formula:
tan Ѳ = opposite length/adjacent length
[tex] tan 22 = \frac{30}{x} [/tex]
Multiply both sides by x
[tex] tan 22*x = \frac{30}{x}*x [/tex]
[tex] tan 22*x = 30 [/tex]
[tex] 0.4040*x = 30 [/tex]
Divide both sides by 0.4040 to make x the subject of the formula
[tex] \frac{0.4040*x}{0.4040} = \frac{30}{0.4040} [/tex]
[tex] x = \frac{30}{0.4040} [/tex]
[tex] x = 74.26 [/tex]
x ≈ 74.3 (to the nearest tenth)
What is the value of p?
Answers
Answer:
Step-by-step explanation:
The angle next to 90 degrees is also 90 degrees and it's supplementary
the angle next to 133 degrees is 47 degrees and it's also supplementary
p + 90 + 47 = 180
p + 137 = 180
p = 43 degrees
the solution is d
The population of a town is 9,000, and it grows at a rate of 7% per year. What will the population be in 6 years?
Answers
Answer:
12,780
Step-by-step explanation:
Initial population = 9000
grows 7% of 9000= 630 people in a year
after 6 yrs, number of added people = 630× 6=3780 ...... totally, population = 9000+ 3780
= 12,780
The population of the town after 6 years will be 13506.
Concept:As the population grows at r% per year and if the Current population is P, then After 'x' years, the population will be [tex]P_x = P(1 + \frac{r}{100} )^x[/tex]How to solve the given question?Initial Population, P = 9000Rate of increase in population, r = 7% per yearPeriod , x = 6 years∴ The population after 6 years,[tex]P_x = P(1 + \frac{r}{100} )^x[/tex]∴ [tex]P_6 = 9000(1 + \frac{7}{100})^6\\[/tex]
∴[tex]P_6 = 13506 \ peoples[/tex]
Thus, the population of the town after 6 years will be 13506.
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Does anyone know the slope of this line?
Answers
Answer:
3/4
Step-by-step explanation:
Use [tex]\frac{rise}{run}[/tex]. From the bottom red point, you have to go up 3 and left 4 to get to the top point. That's your answer.
A smart phone manufacturer is interested in constructing a 99% confidence interval for the proportion of smart phones that break before the warranty expires. 97 of the 1750 randomly selected smart phones broke before the warranty expired. Round your answers to three decimal places. A. With 99% confidence the proportion of all smart phones that break before the warranty expires is between and .
Answers
Answer:
With 99% confidence the proportion of all smart phones that break before the warranty expires is between 0.041 and 0.069.
Step-by-step explanation:
We have to calculate a 99% confidence interval for the proportion.
The sample proportion is p=0.055.
[tex]p=X/n=97/1750=0.055[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.055*0.945}{1750}}\\\\\\ \sigma_p=\sqrt{0.00003}=0.005[/tex]
The critical z-value for a 99% confidence interval is z=2.576.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=2.576 \cdot 0.005=0.014[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.055-0.014=0.041\\\\UL=p+z \cdot \sigma_p = 0.055+0.014=0.069[/tex]
The 99% confidence interval for the population proportion is (0.041, 0.069).
A large mixing tank initially contains 1000 gallons of water in which 30 pounds of salt have been dissolved. Another brine solution is pumped into the tank at the rate of 4 gallons per minute, and the resulting mixture is pumped out at the same rate. The concentration of the incoming brine solution is 2 pounds of salt per gallon. If represents the amount of salt in the tank at time t, the correct differential equation for A is:__________.A.) dA/dt = 4 - .08AB.) dA/dt = 8 -.04AC.) dA/dt = 4-.04AD.) dA/dt = 2-.04AE.) dA/dt = 8-.02A
Answers
Answer:
(B)[tex]\dfrac{dA}{dt}=8-0.004A[/tex]
Step-by-step explanation:
Volume of fluid in the tank =1000 gallons
Initial Amount of Salt in the tank, A(0)= 30 pounds
Incoming brine solution of concentration 2 pounds of salt per gallon is pumped in at a rate of 4 gallons per minute.
Rate In=(concentration of salt in inflow)(input rate of brine)
[tex]=(2\frac{lbs}{gal})( 4\frac{gal}{min})=8\frac{lbs}{min}[/tex]
The resulting mixture is pumped out at the same rate, therefore:
Rate Out =(concentration of salt in outflow)(output rate of brine)
[tex]=(\frac{A(t)}{1000})( 4\frac{gal}{min})=\frac{A}{250}[/tex]
Therefore:
The rate of change of amount of salt in the tank,
[tex]\dfrac{dA}{dt}=$Rate In-Rate out\\\dfrac{dA}{dt}=8-\dfrac{A}{250}\\\dfrac{dA}{dt}=8-0.004A[/tex]
The decay constant for 14C is 0.00012. A 4050-year-old wooden chest is found by archaeologists. What percentage of the original 14C would you expect to find in the wooden chest? (Express your answer as a percentage rounded to one decimal place.)
Answers
Answer:
The radioactive decay constant or k = ln (.5) / Half-Life
Half-Life = -.693147 / .00012
Half-Life = -5,776.225 years
We'll call beginning amount as 100%
Ending Amount = Beginning Amount / 2^n (where n = # of half-lives)
n = 4,050 / 5,776.225 = 0.7011499725
Ending Amount = 100% / 2^0.7011499725
Ending Amount = 100% / 1.625800202
Ending Amount = 61.5081729452%
Ending Amount = 61.5 % (rounded)
Step-by-step explanation:
Two planes travel toward each other from cities that are about 1725 km apart at rates of 360 km/hr and 330 kr/hr. They started at the same time. In how many hours
will they meet?
hours.
The two planes will meet after
(Simplify your answer.)
Answers
Answer: 2 1/2 or 2.5 hours
Step-by-step explanation:
Add 360 and 330
360 + 330 = 690
Divide 1,725 by 690
1,725 / 690 = 2.5
The two planes will meet in 2.5 hours
The speed is the distance covered by an object at a particular time. The time it will take for the two planes to meet is 2.5 hours.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Given that the speed of the two planes is 360 km/hr and 330 km/hr. Therefore, the relative speed of the two planes with respect to each other is,
Relative speed = 360 km/hr + 330 km/hr
= 690 km/hr
Now, since the total distance between the two cities is 1725 km. Therefore, the time it will take for two planes to meet is,
Time = Distance /Speed
= 1725 km / 690 km/hr
= 2.5 hour
Hence, the time it will take for the two planes to meet is 2.5 hours.
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What is the solution to the system of equations?
y = 3x - 10
h
2x + y = 4
04-8. 6)
O (-6, 16)
O (6.-8)
O (16.-6)
Answers
Answer:
The answer is option C
y = 1/3x - 10 ........ 1
2x + y = 4 .......... 2
Substitute the first equation into the second one
That's
2x + 1/3x - 10 = 4
7/3x = 14
Multiply through by 3
That's
7x = 42
Divide both sides by 7
x = 6
Substitute x = 6 into any of the Equations
y = 1/3x - 10
y = 1/3(6) - 10
y = 2 - 10
y = - 8
Therefore
x = 6 y = - 8
Hope this helps
2x+y=4
=y=-2x+4
New equations:
y=1/3x-10
y=-2x+4
14=7/3x
x=6
y=-8
Make sure it’s correct:
-8=-2(6)+4
-8=-8
The manager of a computer retail store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.5 years and a standard deviation of 0.4 years. He then randomly selects records on 45 laptops sold in the past and finds that the mean replacement time is 4.4 years. Assuming that the laptop replacment times have a mean of 4.5 years and a standard deviation of 0.4 years, find the probability that 45 randomly selected laptops will have a mean replacment time of 4.4 years or less.
Answers
Answer:
The probability that 45 randomly selected laptops will have a mean replacment time of 4.4 years or less is P(M<4.4)=0.0468.
Step-by-step explanation:
We have a population normally distributed with mean 4.5 years and standard deviation of 0.4 years.
Samples of size n=45 are selected from this population.
We have to calculate the probability that a sample mean is 4.4 years or less.
Then, we calculate the z-score for the sample mean M=4.4 and then calculate the probability using the standard normal distribution:
[tex]z=\dfrac{M-\mu}{\sigma/\sqrt{n}}=\dfrac{4.4-4.5}{0.4/\sqrt{45}}=\dfrac{-0.1}{0.06}=-1.677\\\\\\P(M<4.4)=P(z<-1.677)=0.0468[/tex]
The probability that 45 randomly selected laptops will have a mean replacment time of 4.4 years or less is P(M<4.4)=0.0468.
Identify the statement as true or false.
New Jersey is a state if and only if Florida is not a state.
Is the statement true or false?
O true
O false
Answers
Both Florida and New Jersey are states today and they have been for over one hundred years
NEED UGANT HELP really stuck xx
Answers
Answer:
0.6
Step-by-step explanation:
3+2=5
P (white) = 3/5 = 0.6
(Hopefully this works, if not, on hearty maths you can go back to your assigned tasks page and go back onto the task to get a new question if that makes sense)
What is the answer? ACB ~ EFD
Answers
Answer:
z = 60°
Step-by-step explanation:
In ΔABC
Sum of all angles of triangle = 180
65 + 55 +∠A = 180
120 +∠A = 180
∠A = 180 - 120
∠A = 60
In similar triangles, corresponding angles are congruent
z = ∠A
z = 60°
what is the slope of a line of duty hat is parallel to the line whose equation is 5y+2x=12
Answers
Answer:
-2/5
Step-by-step explanation:
The slope of two parallel lines will be the same.
Here, our equation is 5y + 2x = 12. Let's find the slope by isolating y:
5y + 2x = 12
5y = -2x + 12
y = (-2/5)x + 12/5
So, the slope is -2/5.
Thus, the slope of the line parallel to the given one will be -2/5.
~ an aesthetics lover
Answer:
-2/5
Step-by-step explanation:
5y+2x=12
Solve for y
Subtract 2x
5y = -2x+12
Divide by 5
5y/5 = -2/5 x +12/5
y = -2/5x +12/5
The slope is -2/5
Parallel lines have the same slope
What is the value of x?
O 40
O 70
O 140
O 160
Answers
what is the question? if u give the question , I might help and edit this :)
Answer:
i think it's 70
Step-by-step explanation:
sorry if its wrong let me know plz
Give a recursive definition of each of these sets of ordered pairs of positive integers. (Hint: plot the points in the set in the plane and look for lines containing points in the set. 1. S={(a, b) I a E Z+, b Ñ Z+ , and a | b}2. S={(a, b) I a E Z+, b Ñ Z+ , and 3 | a + b} 3. S={(a, b) | a Ñ Z+ , b Ñ Z+ , and a + b is odd) a) (1,2) S, (2, 1) E S and if (a, b) S then (a + 2, b) E S, (a, b + 2) E S and (a + 1, b + 1) E S b) (1,2) es, (2, 1) Ñ Sand if (a, b) Ñ S then (a + 3, b) Ñ s, (a, b + 3) Ñ s, (a+1, b + 2) ES and (a + 2, b + 1) Ñ s c) (1,1) Ñ Sand if (a, a) Ñ Sthen (a + 1, a + 1) Ñ S and if (a, b) Ñ S, then (a, b + a) Ñ s
Answers
Answer:
1. s=gfcgj sdgc
gzgixxhcxc
vxtuixzdfhvxxgjknn
jfhujhgcxvjkmvcghj
mvhuiknbb5542698755
8423675369
8823
REALLY NEED HELP PLS
CAN U HELP Xx
Answers
Answer:
0
Step-by-step explanation:
There are no green counters in the bag.
slope of line passes through (7/20, 8/3) and (3/8, 7/9)
Answers
Answer:
[tex]slope = \dfrac{-680}{9}[/tex]
Step-by-step explanation:
We are given coordinates of two points:
Let the points be A and B respectively:
[tex]A(\dfrac{7}{20}, \dfrac{8}{3})\\B(\dfrac{3}{8}, \dfrac{7}{9})[/tex]
To find the slope of line AB.
Formula for slope of a line passing through two points with coordinates [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:
[tex]m = \dfrac{y_2- y_1}{x_2- x_1}[/tex]
Here, we have:
[tex]x_2 = \dfrac{3}{8}\\x_1 = \dfrac{7}{20}\\y_2 = \dfrac{7}{9}\\y_1 = \dfrac{8}{3}\\[/tex]
Putting the values in formula:
[tex]m = \dfrac{\dfrac{7}{9}- \dfrac{8}{3}}{\dfrac{3}{8}- \dfrac{7}{20}}\\\Rightarrow m = \dfrac{\dfrac{7-24}{9}}{\dfrac{15-14}{40}}\\\Rightarrow m = \dfrac{\dfrac{-17}{9}}{\dfrac{1}{40}}\\\Rightarrow m = \dfrac{-17\times 40}{9}\\\Rightarrow m = \dfrac{-680}{9}[/tex]
So, the slope of line AB passing through the given coordinates is:
[tex]m = \dfrac{-680}{9}[/tex]
Determine the absolute maximum and minimum of f(x)= 2 cosx+ sin 2x
Answers
Answer:
2.598 and -2.598.
Step-by-step explanation:
f(x) = 2 cos x + sin 2x
f'(x) = -2 sin x + 2 cos 2x = 0 for turning points.
cos 2x = 1 - 2 sin^2 x so we have
-2 sin x + 2 - 4 sin^2 x = 0
4sin^2 x + 2 sin x - 2 = 0
2(2 sin^2 x + sin x - 1) = 0
2(2sinx - 1)(sinx + 1) = 0
sin x = 0.5, -1 when f(x) is at a turning point.
x = π/6, -π/2, 5pi/6
The second derivative is 2 cos x + 2 * -2 sin 2x
= 2 cos x - 4 sin 2x
When x = π/6, this is negative , when x = -π/2 it is positive
so x = π/6 gives a maximum f(x) and x = -π/2 gives 0 so this is a point of inflection
When x = π/6 , f(x) = 2.598
When x = 5pi/6, f(x) = -2.598.
5x + 7y = -29 y = x + 1
Answers
Answer:
(x, y) = (-3, -2)
Step-by-step explanation:
Perhaps this is a system of equations you want the solution for.
Since you have an expression for y, substitution is a viable approach.
5x +7(x+1) = -29 . . . . . . substitute for y
12x = -36 . . . . . . subtract 7 and simplify
x = -3 . . . . . . . . . divide by 12
y = (-3) +1 = -2 . . . use the expression for y
The solution is (x, y) = (-3, -2).
6th term in the sequence -1,4,-16,64
Answers
6th term in the sequence is 1024
Answer:
1024
Step-by-step explanation:
I hope this helps!
A composition of reflections over parallel lines is the same as a __________. A. translation B. rotation C. glide reflection D. double rotation
Answers
Answer: A
Step-by-step explanation:
Answer: A.
Step-by-step explanation:
A composition of reflections over two parallel lines is equivalent to a translation.
empt 1
Find the equation in slope-intercept form of a line with slope - 2 and y-intercept 4.
a) y = -2x
Ob) y - 2x-4
c) y = -2x+4
d) y - 4x -2
Question 12 (5 points)
Answers
Answer:
y = -2x +4
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = -2x +4
g python Suppose the instructor of the course is convinced that the mean engagement of students who become knowledgeable in the material (i.e., the eng1 population) is 0.75. Formulate null and alternative hypotheses for a statistical test that seeks to challenge this belief. What are the null and alternative hypotheses, and what type of test can be used
Answers
Answer:
Step-by-step explanation:
The null and alternative hypothesis that would seek to challenge this belief would be
Null hypothesis: u = 0.75
Alternative hypothesis: u =/ 0.75
The type of test to be used would be a one sample z test where one sample is drawn from the population and the mean engagement of students who become knowledgeable in the material is measured and tested in an experiment against the null hypothesis.
A sequence starts 1, 4, 9, 16 ... The nth term is n^2. Use this fact to find the nth term of the following sequences: a) 2, 5, 10, 17 b) 2, 8, 28, 32
Answers
Answer:
n²+1
2n²
Step-by-step explanation:
We can see that 2, 5, 10, and 17 becomes 1, 4, 9, and 16 when we subtract 1.
So it adds 1. The nth will be n² + 1.
2, 8, 18, and 32 is the double of n². 1, 4, 9, and 16 are their half.
So the nth term becomes 2n².
The value of the equation is
a) The nth term of the equation is Aₙ = n² + 1
b) The nth term of the equation is Bₙ = 2n²
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
a)
Let the nth term of the equation be represented as Aₙ
Now , the sequence is
P = { 2 , 5 , 10 , 17 , .. }
when n = 1 , P₁ = 2
when n = 2 , P₂ = 5
So , the equation for the nth term is Aₙ = n² + 1
b)
Let the nth term of the equation be represented as Bₙ
Now , the sequence is
Q = { 2 , 8 , 18 , 32 , .. }
when n = 1 , P₁ = 2
when n = 2 , P₂ = 8
So , the equation for the nth term is Bₙ = 2n²
Hence , the equations are solved
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