Answer:
52+n=m
Step-by-step explanation:
Answer:
6.5 /52 m = n
Step-by-step explanation:
The rate is 6.5 miles / 52 minutes
We are going to run m miles in n minutes
m = 6.5 / 52 * n
We want to solve for n
Multiply each side by 52/ 6.5
6.5 /52 m = 6.5 / 52 * n * 6.5 / 52
6.5 /52 m = n
The average length of "short hospital stays" for men is slightly longer than that for women, 5.6 days versus 4.5 days. A random sample of recent hospital stays for both me and women revealed the following.
1. The goal of the study is to determine if there is sufficient evidence to conclude, at α = 0.01, that the average hospital stay for men is longer than the average hospital stay for women?
Men Women
Sample size 37 35
Sample mean 5.6 days 4.5 days
Population standard deviation 1.2 days 1.6 days
2. What would be the critical value(s)?
A) +_2.58
B) 2.58
C) 2.33
D) +_2.33
Answer:
1) There is enough evidence to support the claim that the average hospital stay for men is longer than the average hospital stay for women. (P-value = 0.00051).
2) zc=2.33
Step-by-step explanation:
1) This is a hypothesis test for the difference between populations means.
The claim is that the average hospital stay for men is longer than the average hospital stay for women.
Then, the null and alternative hypothesis are:
H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0
The significance level is 0.01.
The sample 1, of size n1=37 has a mean of 5.6 and a standard deviation of 1.2.
The sample 2, of size n2=35 has a mean of 4.5 and a standard deviation of 1.6.
The difference between sample means is Md=1.1.
[tex]M_d=M_1-M_2=5.6-4.5=1.1[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{1.2^2}{37}+\dfrac{1.6^2}{35}}\\\\\\s_{M_d}=\sqrt{0.039+0.073}=\sqrt{0.112}=0.335[/tex]
Then, as we know the population standard deviation of both, we can calculate the z-statistic as:
[tex]z=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{1.1-0}{0.335}=\dfrac{1.1}{0.335}=3.29[/tex]
This test is a right-tailed test, with z=3.29, so the P-value for this test is calculated as:
[tex]P-value=P(z>3.29)=0.00051[/tex]
As the P-value (0.00051) is smaller than the significance level (0.01), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the average hospital stay for men is longer than the average hospital stay for women.
2. The critical values for this right tail test are calculated from the z-table and the significance level (α=0.01)
[tex]P(z>z_c)=0.01[/tex]
This happens for zc=2.33:
[tex]P(z>2.33)=0.01[/tex]
Tristen is building 3 trophies using Legos. He needs 324 total Legos. Tristen uses 220 Legos for the largest trophy and 135 Legos for the smallest trophy. How many Legos will he use to build the final trophy
Answer:
166 legos are required
Step-by-step explanation:
In this case, let's analyze the data. We need 3 trophies, using at most 324 legos in total. The big trophy requires 220 legos, the smallest requires 135, so we need to know how much will be used in the medium trophy. This number should be 135 < X < 220
Now, if we know that the total legos to be used are 324, then, we can make a difference and sum for all the legos, and then, calculate the number of legos used.
Total legos = A + B + C
324 = 220 + 135 + C
324 = 355 + C
C = -31
This means that there is difference of 31 legos between the smallest and biggest trophy, therefore, this difference should be used and added to the smallest trophy and see how much Tristen use in the final trophy:
135 + 31
= 166 legos
So we need to use 166 legos to build the final trophy.
Answer:
he already used 355 so 166
Step-by-step explanation:
A bag contains 5 blue balls, 4 red balls, and 3 orange balls. If a ball is picked from the bag at random, what is the probability that it is a blue ball?
Answers have been rounded to the tenths place.
A
0.5
B.
0.4
O C.
0.3
OD. 0.2
Answer:
[tex] p =\frac{Possible}{Total}[/tex]
Where possible represent the possible cases on this case 5 since we have 5 balls and the total is the size of the sample space on this case 12. And replacing we got:
[tex] p =\frac{5}{12}= 0.417[/tex]
And rounded to the tenths place we got:
[tex] p=0.4[/tex]
And the best answer is:
B. 0.4
Step-by-step explanation:
For this case the size of the sampel space is 5+4+3= 12 representing the total of balls used.
We select a random ball from the total and we want to find the probability of selecting a blue ball. And for this case the can use the empirical definition of probability from Laplace given by:
[tex] p =\frac{Possible}{Total}[/tex]
Where possible represent the possible cases on this case 5 since we have 5 balls and the total is the size of the sample space on this case 12. And replacing we got:
[tex] p =\frac{5}{12}= 0.417[/tex]
And rounded to the tenths place we got:
[tex] p=0.4[/tex]
And the best answer is:
B. 0.4
If it takes a planet 1.2 years to orbit the Sun, how long (in years) will it take the planet to go all the way around our sky once?
Answer:
about 225-250 million years:
What is the solution to the equation 4x - 6 =
10x - 3?
а
x = 1/2
b
x = -2
C
x = 2
d
x = -1/2
Answer:
d
Step-by-step explanation:
did da math
If Tim draws two cards at random from a standard deck of cards without replacement, which expression represents the probability that Tim draws two aces?
1. 4/52 * 4/52
2. 4/52 * 4/51
3. 4/52 * 3/51
4. 4/52 * 3/52
Answer: B) 4/52 * 3/51
Step-by-step explanation:
the probability of drawing the first ace is 4/52 bc there are 4 aces and 52 cards. the probability of drawing the second ace is 3/51 bc there are now three aces ( bc we removed one in the first step) and there are now 51 cards (bc we removed a card in the first step and there is no replacement). combine the probabilities with multiplication because it’s a multistage event
The expression is equivalent to? Please?
Answer: The expression 2√2 + √50 is equivalent to 7√2.
Step-by-step explanation: When 2√2 + √50 is added together, the result if 7√2.
Kim's softball team was playing in the championship game. When there were 4 innings left, the team was losing by a score of 17 to 6 points. In the last 4 innings, her team scored the same number of points per inning, and the other team did not score any more points. Kim's team won with the most points.
Find the minimum whole number of points per inning Kim's team could have scored.
Answer: I think the answer is 3.
Step-by-step explanation:
Kim's team scored the same number of innings to win the game and Kim's team already had 6 points so four times a number has to be greater than 17.
4* 3 + 6= 18
which means the minimum number can't be less than three so they may have scored three or more points in each of the four innings that was left.
Using the letter x for any unknown number. i think of a number i add one and then double it
Answer:
2(x+1) or 2x+2
1/3x + 3/10x = -17 + 17
Answer:
x = 0
Step-by-step explanation:
[tex]\frac{1}{3} x+\frac{3}{10}x=0[/tex]
x = 0
The radius of a sphere is multiplied by . What effect does this have on the volume of the sphere? A. The volume of the sphere is multiplied by 1/343. B. The volume of the sphere is multiplied by 1/49. C. The volume of the sphere is multiplied by 1/7 . D. The volume of the sphere is multiplied by 1/21 . E. The effect on the volume of the sphere cannot be determined.
Answer:
Option A. The volume of the sphere is multiplied by 1/343.
Step-by-step explanation:
The volume of a sphere can be obtained by the following formula:
V = 4/3πr^3
Let the initial volume (V1) of the sphere be:
V1 = 4/3πr^3 = (4πr^3)/3
Now, if we multiply the radius by 1/7, then the new volume (V2) of the sphere will be:
V2 = 4/3 x π x (1/7r)^3
V2 = 4/3 x π x 1/343r^3
V2 = (4πr^3)/1029
Now we determine the ratio of V2 : V1 as shown below:
V2/V1 = (4πr^3)/1029 ÷ (4πr^3)/3
V2/V1 = (4πr^3)/1029 × 3/(4πr^3)
V2/V1 = 3/1029
V2/V1 = 1/343
V2 = 1/343 x V1
Therefore, the volume of the sphere is multiplied by 1/343.
the hiking club plans to go camping In a state park where the probability of rain on any given day is 0.7. which expression can be used to find the probability that it will rain on exactly 3 of the seven days they are there
Answer:
[tex]P(X = 3) = C_{7,3}.(0.7)^{3}.(0.3)^{4} = 0.0972[/tex]
Step-by-step explanation:
For each day there are only two possible outcomes. Either it rains, or it does not. The probability of rain on a day is independent of any other day. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In a state park where the probability of rain on any given day is 0.7.
This means that [tex]p = 0.7[/tex]
Which expression can be used to find the probability that it will rain on exactly 3 of the seven days they are there
We have to find [tex]P(X = 3)[/tex] when [tex]n = 7[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{7,3}.(0.7)^{3}.(0.3)^{4} = 0.0972[/tex]
Suppose that a college student is taking three courses: a two-credit course, a three-credit course, and a four-credit course. The expected grade in the two-credit course is 3.5, while the expected grade in the three- and four-credit courses is 3.0. What is the expected overall grade point average for the semester?
Answer:
The overall expected grade point average for the semester is 3.16/3.1 or 3.2 if you round it up.
Step-by-step explanation:
To get the average, you need to add up all the numbers then divide the sum by how many numbers you added.
3.5 + 3.0 + 3.0 = 9.5
9.5 / 3 = 3.16
Given Information:
expected grade in two-credit course = 3.5
expected grade in three-credit course = 3.0
expected grade in four-credit course = 3.0
Required Information:
Expected overall grade point average = ?
Answer:
The expected overall grade point average of this college student is 3.11
Step-by-step explanation:
The overall expected grade point average is given by
E(X) = Sum of grades/Total number of credit hours
Sum of grades = ∑ weightage*expected grades
Sum of grades = 2*3.50 + 3*3.0 + 4*3.0 = 28
Total number of credit hours = 2 + 3 + 4 = 9
E(X) = Sum of grades/Total number of credit hours
E(X) = 28/9
E(X) = 3.11
Therefore, the expected overall grade point average of this college student is 3.11 .
Indicate the general rule for this sequence. Find a1 and the common difference. a4 = 18 a7 = 9
Answer:
[tex]a_{n} = 27 - 3(n-1)[/tex]
Step-by-step explanation:
Arithmetic sequences concepts:
The general rule of an arithmetic sequence is the following:[tex]a_{n+1} = a_{n} + d[/tex]
In which d is the common diference between each term.
We can expand the general equation to find the nth term from the first, by the following equation:
[tex]a_{n} = a_{1} + (n-1)*d[/tex]
And also:
[tex]a_{n} = a_{m} + (n-m)*d[/tex]
In this question:
[tex]a_{4} = 18, a_{7} = 9[/tex]
Finding the common ratio:
[tex]a_{n} = a_{m} + (n-m)*d[/tex]
[tex]a_{7} = a_{4} + (7-4)*d[/tex]
[tex]9 = 18 + 3d[/tex]
[tex]3d = -9[/tex]
[tex]d = \frac{-9}{3}[/tex]
[tex]d = -3[/tex]
Finding the first term:
[tex]a_{4} = a_{1} + (4-1)*d[/tex]
[tex]18 = a_{1} + 3*(-3)[/tex]
[tex]a_{1} = 27[/tex]
General rule:
[tex]a_{n} = a_{1} + (n-1)*d[/tex]
[tex]a_{n} = 27 - 3(n-1)[/tex]
A game consists of randomly choosing a bag (labelled 1, 2 or 3) out of a choice
of 100, and then again randomly, picking a ball (red or black) from it.
Each bag has the same total number of balls (10).
Bag options
Ball options
a) Complete the tree diagram.
0.6 Red
b) Work out the probability that a player
will select a red ball.
0.4 Black
0.35
0.44
0.2
Red
0.45
2
0.8
Black
c) The same player is going to play the
game 200 times consecutively.
How many black balls should he
expect to pick?
0.2
0.7
Red
3
I
+
0.3
Black
Two men start at the same place walk rate of 5 km / hr and 5.6 km / hr respectively. What time will they take to be 3 km apart, the same direction as they walk?
A ) 3hrs B ) 4hrs C ) 5hrs D ) 6hrs
Answer:
5 hours
Step-by-step explanation:
5.6 all you have to use is .6 times 5hours to make 3kmapart
Please help ASAP!! Will get brainliest
Answer:
x=7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
12 bars --- 2 boxes
42 bars --- x boxes
x = 42*2/12 = 7
What is 192837288-19929
Step-by-step explanation:
The answer is to your question is 192817359
What is the correct order to represent 92,232
the fire hydrant sits 72 feet from the base of a 125-foot buiding. Find the ANGLE OF ELEVATION from the fire hydrant to the top of the building. *
Answer:
60°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between angles and sides in a right triangle. Here, we're given the side Adjacent and the side Opposite the angle of interest. This makes it appropriate to choose the relation ...
Tan = Opposite/Adjacent
For our angle of elevation α, this means ...
tan(α) = 125/72
α = arctan(125/72) = 60.058°
α ≈ 60°
The angle of elevation is about 60°.
The difference of two supplementary angles is 24 degrees. Find the measure of the angles.
Answer:
102, 78
Step-by-step explanation:
angle 1= x
angle 2= x-24
x+x-24=180
x=102
x-24=78
102+78=180
The measure of the angles are 102 and 78 degrees
Let one of the angles be xLet the other angle be y.If the difference of two supplementary angles is 24 degrees, then;
x - y = 24
y = x - 24
Taking the sum of the angles and equating to 180 degrees since they are supplementary
x + y = 180
x + x - 24 = 180
2x = 180 + 24
2x = 204
x = 102
Since y = 180 - x
y = 180 - 102
y = 78 degrees
Hence the measure of the angles are 102 and 78 degrees
Learn more on supplementary angles here: https://brainly.com/question/404323
given a soda can with a volume of 15 and a diameter of 2 what is the volume of a cone that fits perfectly inside the can
Answer:
[tex]5cm^{3}[/tex]
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, cone an cylinder.from the formula of cylinder and cone we can see that the volume of a cone is 3 times smaller than that of a cylinder
[tex]volume=\pi r^{2} h[/tex]....................cylinder
[tex]volume= \frac{1}{3} \pi r^{2}h[/tex].................cone
assuming all units in (cm)
Given data.
Volume of cylinder = [tex]15cm^{3}[/tex]
Diameter d= [tex]2cm[/tex]
Radius r = [tex]\frac{d}{2}[/tex][tex]= \frac{2}{2} = 1cm[/tex]
Height h= ??
we know that the expression for the volume of a cylinder is
[tex]volume=\pi r^{2} h[/tex]
we can substitute our given data to find the height h
[tex]15= 3.142*1^{2}*h\\15= 3.142h[/tex]
divide both side by 3.142 we have
[tex]h= \frac{15}{3.142}\\ h= 4.77cm[/tex]
We can now use this height[tex]4.77cm[/tex] and radius [tex]1cm[/tex] to find the equivalent volume of a cone.
the expression for the volume of a cone is
[tex]volume= \frac{1}{3} \pi r^{2}h[/tex]
substituting our data into the expression we have
[tex]volume= \frac{3.142*1^{2*} 4.77}{3} \\volume= \frac{15}{3} \\voulume = 5cm^{3} \\[/tex]
Which decimal is equivalent to 2680?
Answer:
0.5361
Step-by-step explanation:
Hope this helps :)
Answer:
0.325
Step-by-step explanation:
Divide 26 by 80
the drama club is holding auditions for 5 different parts in a one-act play. if 9 people audition, how many ways can the roles be assigned?
Answer:
The roles can be assigned in 15120 ways.
Step-by-step explanation:
The parts, which means that the order in which the people are selected is important. So we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
5 people chosen from a set of 9. So
[tex]P_{(9,5)} = \frac{9!}{(9-5)!} = 15120[/tex]
The roles can be assigned in 15120 ways.
Seth has a triangle that measures 20 inches by 20 inches
by 35 inches. What type of triangle does he have?
Answer:
Isosceles
Step-by-step explanation:
An isosceles triangle is a triangle in which the length of at least two sides are same.
The triangle which Seth has two sides of same length that is 20 inches.
Third side is different.
Hence. the triangle which Seth has is isosceles.
Find the midpoint of the line segment with end coordinates of: ( 0 , 2 ) and ( 8 , 8 )
Answer:
(4,5)
Step-by-step explanation:
To find the x coordinates of the midpoint, add the x coordinates together and divide by 2
(x1+x2)/2 = (0+8)/2 = 8/2 = 4
To find the y coordinates of the midpoint, add the y coordinates together and divide by 2
(y1+y2)/2 = (2+8)/2 = 10/2 = 5
The midpoint is (4,5)
Answer:
(4,5)
Step-by-step explanation:
Midpoint: (0+8)/2, (2+8)/2
8/2, 10/2
4,5
Choose the best option.
1.(101), in base 10 is equal to:
a)10
b)1
c)2
d)5
Answer:5
Step-by-step explanation:(1×2^2)+(0×2^1)+(1×2^0)=
1×4+0×2+1×1=
4+1=
5
A company wants to decrease their energy use by 10%. If their electric bill is currently $1,500 a month, what will their bill be if they are successful? Give your answer accurate to at least the nearest dollar.
Answer:
$1350
Step-by-step explanation:
Apparently, we're to assume that the bill is proportional to the energy usage. Then reducing energy by 10% would reduce the bill by 10%.
10% of the bill is 0.1 × $1500 = $150.
If the bill is reduced by $150, it becomes ...
$1500 -150 = $1350
If they are successful, their bill will be $1350.
_____
In general, utility bills have a number of fixed charges or fees that are not proportional to the quantity of utility used. Too, they can have graduated rates that make them non-proportional.
Figuring 90% of some arbitrary number might be an interesting math exercise, but it has no relation to the world of utility billing for a 10% change in usage.
A) Find the difference between3y minutes and 25y second,giving your answer in second.
B) find the sum of 50(3z- 2) minutes and4(z+1) hour,giving your answer in second.
Pls tell answers of both question
Answer:
a. 3 mintes = 180 seconds
Answer:
155ysec ; 23400z+ 8400 secs
Step-by-step explanation:
3y mins = 3* 60=180y sec
3y mins - 25y sec= 180y sec - 25y= 155y sec
155ysec
From B
50(3z-2)min = 50 * 60 (3z-2) sec
= 3000(3z-2)=9000z-6000
4 (z + 1) hours =4*3600(z+1) =14400z + 14400z
Adding both expression we have;
9000z+14400z-6000+14400=23400z+ 8400 secs
23400z+ 8400 secs
What is the approximate area of a circle with a radius of 11 m?
O A. 190 m2
O B. 69 m2
O C. 34.5 m2
O D. 380 m2
Hello!
Answer:[tex]\boxed{ \bf The~approximate~area~of~the~circle~is~D.~380~m^2}[/tex]
___________________________________________
Explanation:We must use a certain formula to find the area of a circle.
A = πr²
Let's plug in the radius.
A = π × 11²
A = π × 121
A = 380