Answer:
the speed of the plane when there is no wind is 212.25 mi/hr
Step-by-step explanation:
Let v represent the speed of the plane without wind.
Wind speed = 20.1 mi/hr
The resultant speed with wind is;
v + 20.1 mi/hr
The resultant speed against wind is;
v - 20.1 mi/hr
Let t represent the time for the travel.
With wind;
(v+20.1)t = 630 ......1
Against wind;
(v-20.1)t = 521 ......2
Divide equation 1 by 2
(v+20.1)/(v-20.1) = 630/521
Cross multiply;
521(v+20.1) = 630(v-20.1)
Collecting like terms;
v(630-521) = 20.1(630+521)
v = 20.1(1151)/109
v = 212.25 mi/hr
the speed of the plane when there is no wind is 212.25 mi/hr
£ represents 29 students in class
B represents students who have a brother
S represents students who have a sister
a) One student from the class is chosen at random. What is the probability that the student has a sister?
b)One of the students who has a brother is chosen at random. What is the probability that this student has a sister?
Answer:
a) One student from the class is chosen at random. What is the probability that the student has a sister?
S/£
b)One of the students who has a brother is chosen at random. What is the probability that this student has a sister?
BS/£²
Step-by-step explanation:
In the question, we are given the following values:
£ represents 29 students in class = Total number of students in the class.
B represents students who have a brother
S represents students who have a sister
The formula for probability = Number of events ÷ Number of possible outcomes.
a) One student from the class is chosen at random. What is the probability that the student has a sister?
Number of events = Number of students that have a sister = S
Number of possible outcomes = £ represents 29 students in class
The probability that the student has a sister = S/£
b)One of the students who has a brother is chosen at random. What is the probability that this student has a sister?
This is calculated as
The Probability of Students that have a brother and a sister = Probability of students that have a brother × Probability of student that have a sister.
Number of students that have a brother = B
Number of students that have a sister = S
The Probability of Students that have a brother and a sister = B/£ × S/£
= BS/£²
Answer:
a) 14/29
b) 4/11
Step-by-step explanation:
You forgot to add the Venn diagram
7+4+2x+X+3 =29
14 +3x= 29
3x = 15
X = 5
2*5=10
10+4=14
5+3=8
14/29
I hope this helps you :D
Have a good day
6. David leaves the house to go to school He walks 200 m west and 125 m
north. Calculate how far he is from the sting point.
Answer:
~235.8
Step-by-step explanation:
200^2 +125^2= distance traveled^2
55625= distance traveled^2
235.849528301
A group of students recorded how much money they earned per week for allowance to the nearest dollar. The students created the following histogram.
Which data set below was used to create this histogram?
A
$1, $2, $2, $3, $3, $3, $4, $4, $4, $4
Answered Incorrectly
B
$2, $3, $4, $5, $6, $7, $8, $10, $14, $15
C
$2, $4, $5, $7, $7, $9, $10, $14, $15, $20
D
$3, $4, $6, $7, $7, $8, $11, $14, $16, $17
Answer:
C
Step-by-step explanation
Answer:
c
Step-by-step explanation:
4.16×10^−5 divided by 8.0×10^−4 in scientific notation
Answer: 13/250 or 0.052
Step-by-step explanation:
4.16 (1/100000)/ 8 (10^-4)
Then keep doing order of operations and dividing down.
Answer:
5.2*10^-2
Step-by-step explanation:
8. Is this relation a function?
{(1, 1)(2, 2)(3, 3)(4,4)}
a) Yes
b) No
Answer:
Yes
Step-by-step explanation:
The inputs in a function should have only one output. In other words, each x value should only be assigned to one y value.
For example, (−2, −1),(1, 0),(1, 5),(2, 0) would not be a function because x value 1 is assigned to both number 0 and number 5.
In (1, 1)(2, 2)(3, 3)(4,4), non of the X values repeat themselves, so it IS a function.
every natural number is a whole number why?
Answer:
Step-by-step explanation:
0 is whole number and 1 is natural number they both end in infinity. So there is only 0 in whole number but not in natural number.thats why every natural number is whole number
Natural numbers are the counting
numbers and they are always positive.
The set of natural numbers begin at 1 and go on indefinitely.
The natural numbers look like {1, 2, 3, 4, 5, ...}.
When we include 0 in the set of natural numbers, the new set,
{0, 1, 2, 3, 4, ...} is called the set of whole numbers.
Notice that all natural numbers are
included within the set of whole numbers.
We can represent the relationship between these
two sets of numbers using a diagram.
The bigger circle below represents the set of whole numbers
and all natural numbers will appear within the set of whole numbers.
In summary, natural numbers are the same as whole numbers except for the fact that whole numbers include 0.
4/7 of the students in a classroom are boys. If there are twelve girls in the class, how many total students are there?
Answer:
28 students total.
Step-by-step explanation:
Let's use a ratio:
boys : girls
4 : 3
16 : 12
To find the total, we need to add 16 and 12 which equals 28
Answer:
28 students
Step-by-step explanation:
If 4/7 of the students are boys,
then 1- 4/7 = girls
7/7 -4/7 = 3/7
total students *3/7 = girls
total students * 3/7 = 12
Multiply each side by 7/3
total students * 3/7 *7/3 = 12*7/3
total students = 28
QUESTION 1 What is the median of the data set? 23 19 13 11 17 19 18 12 17 19
Answer:
17.5
Step-by-step explanation:
First you need to put those numbers in order from least to greatest
second go from each side and count till you get to the middle 17 and 18
third add 17 + 18 = 35
fourth divid by 2 35/2 = 17.5
Hope this helps
Stir-fry is tony's favorite food to cook, but it always makes a lot of smoke! Tony needs to know the volume of his kitchen so he can buy a fan that is the right size. Tony's kitchen has a floor area of 85 square feet. The height of the ceiling is 8 feet. What is the volume of tony's kitchen?
Answer:
Volume = 680 ft³
Step-by-step explanation:
Given
Floor Area = 85 ft²
Height = 8 ft
Required
Volume of the Kitchen
To solve this, it'll be assumed that Tony's kitchen has a regular shape.
Having said that, the volume of Tony's kitchen is calculated as thus.
Volume = Floor Area * Height.
Substitute the values of floor area and height
Volume = 85ft² * 8ft
Volume = 680 ft³
Hence, the volume of Tony's kitchen is 680ft³
The volume of an oblique pyramid with a square base is V units3 and the height is h units.
An oblique pyramid with a square base has a volume of V units cubed and a height of h units.
Which expression represents the area of the base of the pyramid?
StartFraction 3 V Over h EndFraction units2
(3V – h) units2
(V – 3h) units2
StartFraction V Over 3 h EndFraction units2
Answer:
StartFraction 3 V Over h EndFraction units2Step-by-step explanation:
volume of an oblique square pyramid V = 1/3 * b * H where;
b is the base area of the pyramid
H is the height of the pyramid
To determine the expression that represents area of the base of the pyramid, we will make the variable 'b' the subject of the formula from
V = 1/3 bH
[tex]V=\frac{bH}{3}[/tex]
Cross multiplying we have;
[tex]3V = bH\\[/tex]
Dividing both sides by H we have;
[tex]\frac{3V}{H} = \frac{bH}{H} \\b = \frac{3V}{H}units^{2}[/tex]
This gives the correct expression for the base area of the pyramid
Answer:
A.
Step-by-step explanation:
135 = 2x + 25
solve for x
Answer:is 55
Step-by-step explanation:
135-25=2x
110/2=55
Answer:
x = 55
Step-by-step explanation:
First you start with your equation, which is: [tex]135=2x+25[/tex]
Subtract 25 from both sides. Once you do that, you get: [tex]110=2x[/tex]
Then after that, you divide both sides by 2. Then you get your answer, which is: [tex]x=55[/tex]
✌Hope I helped ya✌
Angela works 18 hours a week for 12 weeks in the summer at the local swimming pool as a life guard. she earns $13 per hour. her employer takes 15 percent out of her check for federal income tax withholding and 6.2 percent for social security and 1.45 percent for medicare. she will receive 12 paychecks, one for each week she works. calculate angela’s weekly gross pay: calculate the amount taken out of angela’s check for federal income tax withholding: calculate the amount taken out of angela’s check for social security taxes: calculate the amount taken out of angela’s check for medicare taxes: calculate angela’s net paycheck using the calculations above: calculate angela’s total gross pay for all 12 weeks: calculate angela’s total net pay for all 12 weeks:
Answer:
Gross pay per week = $234
Federal income tax = $421.2
Social security = $174.96
Medicare =$40.71
net pay per week = $181
Total gross pay = $2,808
Total net pay = $2172
Step-by-step explanation:
Hi, to answer this question, first, we have to calculate Angela gross income per week:
18 hours per week x $13 per hour = $234 per week (gross)
234 x 12 =2,808
Amount taken ; multiply weekly gross pay by each percentage discount in decimal form (divided by 100)
Federal income tax = 234 x (15/100) = $35.1 (in 12 weeks = 35.1 x 12 = $421.2)
Social security = 234 x (6.2/100)= $14.508 (in 12 weeks = 14.5 x 12 = $174.96)
Medicare = 234 x (1.45/100)=$3.393 (in 12 weeks = 3.39x 12 = $40.71)
Total amount taken (per week)= 35.1+14.508+3.393=$53.001
Net pay per week = 234-53 = $181
For the total gross pay we have to multiply the weekly gross pay by the number of weeks (12)
Total gross pay = 234 x 12 =$2,808
Total net pay = 181 x 12 = 181 per week x 12 = $2172
Question 3 (1 point)
Which best describes the range of the function f(x)=2(3)^3?
Answer:
(0, ∞ )
Step-by-step explanation:
Basic exponential functions always take on values ranging from (but not touching) 0 upward.
Thus, the range of this particular exponential function is (0, ∞ )
The National Center for Education Statistics surveyed 4400 college graduates about the lengths of time required to earn their bachelor's degrees. The mean was 5.15 years and the standard deviation was 1.68 years. Based on the above information, find the margin of error for a 98% confidence level. Round your answer to the nearest hundredth.
Answer:
The margin of error for a 98% confidence level is of 0.06 years.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.98}{2} = 0.01[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.01 = 0.99[/tex], so [tex]z = 2.327[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this question:
[tex]\sigma = 1.68, n = 4400[/tex]
So
[tex]M = 2.327*\frac{1.68}{\sqrt{4400}}[/tex]
[tex]M = 0.06[/tex]
The margin of error for a 98% confidence level is of 0.06 years.
How many solutions does this equation have?
–6 − 8r = 8 − r
Answer:
1
Step-by-step explanation:
–6 − 8r = 8 − r
− 8r - r = 8 + 6
-9r = 14
r = -14/9
Answer:
r =-2
Step-by-step explanation:
–6 − 8r = 8 − r
Add r to each side
–6 − 8r+r = 8 − r+r
-6 -7r = 8
Add 6 to each side
-6+6 -7r = 8+6
-7r = 14
Divide each side by -7
-7r/-7 = 14/-7
r =-2
Order the following expressions by their values from least to greatest.
b-a
a -0.5
a
Answer:
a
a -0.5
b -a
i believe that is the order but i could be wrong
Answer:
hi there !!
the correct answer should be: a - 0.5, a, b - a
Step-by-step explanation:
first let's show -0.5 on the number line.
now let's show b - a on the number line.
the given expressions are ordered by their values below.
Find the area of the semicircle? Helpppp
Answer:
14.135
Step-by-step explanation:
6 divided by 2 (half) = 3, π·32≈28.27433 dived by 2 (half) equals 14.135
Answer:
14.13 units ^2
Step-by-step explanation:
A= 3.14 (3)^2 (area of a circle)
A= 28.26 / 2 (divide to find half of the circle)
A=14.13 units ^2
The total number of subsets of a set A is 120 more than the total number of subsets of set B. The number of elements in the two sets respectively are
(A) 3, 7 (B) 4, 8 (C) 8, 4 (D) 7, 3
Answer:
(D) 7, 3
Step-by-step explanation:
If a set has 'n' elements, the total number of subsets is (2^n) - 1
So if set A has more subsets than set B, it needs to have more elements, so option (A) and (B) can't be correct.
So, checking option (C), we have:
Set A: number of subsets = 2^8 - 1 = 255
Set A: number of subsets = 2^4 - 1 = 15
Difference: 255 - 15 = 240
The difference is not 120, so this is not the correct option
Option (D):
Set A: number of subsets = 2^7 - 1 = 127
Set A: number of subsets = 2^3 - 1 = 7
Difference: 127 - 7 = 120
Correct option: (D)
Plz, help me plz!!!!!!
Which triangles are congruent?
Image below
Answer:
B. Triangles A and C
Step-by-step explanation:
Let's find the missing angle of all Triangles:
Triangle A: 180-110-30=40°
Triangle B: 180-30-45=105°
Triangle C: 180-110-40=30°
All triangle angles in numerical order:
ΔA: 30, 40, 110
ΔB: 30, 45, 105
ΔC: 30, 40, 110
We see that only ΔA and ΔC are congruent with the same angle sizes.
Which of theses numbers are prime
7,42,65,87,95
Answer:
7
Step-by-step explanation:
7 is a prime number. hope this helps!! moo!
Find the area of the shape
(shown in image)
Answer:
A = 108 units^2
Step-by-step explanation:
A = (1/2)(1 + 8)(24)
A = (1/2)(9)(24)
A = (9)(12)
A = 108
Answer:
108
Step-by-step explanation:
If it's a whole rectangle, the are would be 192
The piece that's missing is a right triangle.
The area of the right triangle = 1/2 base x height = (1/2)(7)(24) = 84
A = 192 - 84
A = 108
A 4-foot long steel pipe consists of two concentric cylinders, with the inner cylinder hollowed out. The radius of the outside of the pipe is 6 inches and the radius of the inside of the pipe is 5.75 inches.
A. Determine the volume of metal used to build the pipe
B. If the pipe is to be powder-coated on the inside and outside surfaces, what is the total surface area to be powder-coated?
Answer:
Step-by-step explanation:
The radius of the outside of the pipe is 6 inches and the radius of the inside of the pipe
is 5.75 inches
Determine the volume of metal used to build the pipe.
135 apples are to be packed into boxes.each box can take only 12 apples.find the number of boxes that will be fully packed and the number of boxes that will remain.
Answer:
11 boxes will be fully packed and .25 will be remaining
Our total amount of apples is 135 apples, and the amount that each box can hold is 12.
So, that means we can make an equation for this.
The equation would be 135 = 12x.
Then, to find x we can divide both sides by 12.
135/12 = 11.25
Next, we take 11 and multiply it by 12 to see how many apples it is.
11 x 12 = 132
So, 135-132 equals 3.
3 is 1/4 of 12.
That means 11 boxes will be fully packed and 1/4 of a box will be filled.
1. Express as a unit rate
a) Serena walks 4 km in 1 h.
Answer:
Step-by-step explanation:
Serena walks 4 km in 1 h.
That means:
1) She walks 4 km per hour.
2) She spends 1/4 = 0.25 hour per mile.
Have a good day.
We can write this as:
4 kilometers/1 hour
The unit rate is already simplified so there is nothing else to do.
Answer: 4km/1hr
Best of Luck!
A factory uses 3/4 of a barrel of raisins in each batch of granola bars. Yesterday, the factory
used 1 1/2 barrels of raisins. How many batches of granola bars did the factory make
yesterday?
Answer:
Step-by-step explanation:
3/4 * 2 = 1 1/2
The factory made two batches of granola bars.
???????????????????????
Answer:
1
Step-by-step explanation:
[tex]10-\frac{54}{6}[/tex]
10-9
1
y - 4x = 5
8x - 2y = 16
Solve using system of equations
Answer:
No solution
Step-by-step explanation:
Let's solve this system using elimination through addition/subtraction. Multiply the second equation by (1/2), which results in the system
y - 4x = 5
4x - y = 8
--------------
0x + 0y = 13. This is NEVER true. This system of equation has NO SOLUTION.
Need help ASAP. WILL MARK BRAINLIEST.
Answer:
Circumference = 2 x 3.14 x radius = 27 (in)
=> radius = 27/(2 x 3.14) = 4.3 (in)
=> Area = 3.14 x radius^2 = 3.14 x 4.3^2 = 58.1 (in2)
Answer:
58 inches^2
Step-by-step explanation:
The formula for the area of a circle is [tex]\pi *radius^{2}[/tex]
To work out the area of this circle you would first need to divide the circumference of 27 by pi, this gives you 8.594. This is because the formula for the circumference is: [tex]\pi *diameter\\[/tex] and so by dividing the circumference by pi we are isolating the value of the diameter.
Then now that we have worked out the diameter we can now begin to work out the area, however in order to work out the area we must work out the radius. You can do this by dividing the diameter by 2, which gives you 4.297.
Then to work out the area you would multiply pi by the radius of 4.297 squared, this gives you 58.01 [tex]inches^{2}[/tex].
The next step is to round it to the nearest whole number, this gives you 58.
1) Divide 27 by pi.
[tex]27/\pi =8.594[/tex]
2) Divide 8.594 by 2.
[tex]8.594/2=4.297[/tex]
3) Multiply pi by 4.297 squared.
[tex]\pi *4.297^{2} =58.01[/tex]
4) Round to the nearest whole number.
58 square inches
Rao's Finance claims that less than 50% of adults in Suva have a will. A will is a legal document that sets forth your wishes regarding the distribution of your property and the care of any minor children. If you die without a will, those wishes may not be carried out. To substantiate the claim, a random sample of 1000 adults showed that 450 of them have a will. A. At the 5% significance level, can you conclude that the percentage of people who have a will is less than 50%? B. What is the Type I error in part A? What is the probability of making this error? C. What would your decision be in part A if the probability of making a Type I error were zero? Explain.
Answer:
See the explanation below.
Step-by-step explanation:
n = sample size = 1000
X = proportion of adults that a will = 450 / 1,000 = 0.45
P-value = 0.5
a = level of significance = 5%, or 0.05
A. At the 5% significance level, can you conclude that the percentage of people who have a will is less than 50%?
Our hypotheses are:
Null hypothesis: u ≥ 0.5
Alternate hypothesis: u < 0.5
Since this indicates a left tailed test, the decision rule is to reject null hypothesis if p-value is less than the level of significance.
[tex]Z = test statistic = \frac{0.45 - 0.5}{0.5/\sqrt{1,000} }[/tex]
Z = - 0.05 / 0.0158113883008419 = - 3.1623
Using the excel function NORMSDIST(-3.1623), we have:
P- value = 0.000782701129001276, approximately 0.0008
Therefore, null hypothesis is rejected at 5% level of significance since the p-value 0.0008 is less than 5%, or 0.05.
Therefore, there is an enough reason to reject null hypothesis.
B. What is the Type I error in part A? What is the probability of making this error?
Since the probability is greater than 50%, the Type I error is therefore the statement in the question that less than 50% of adults have a will.
Also, the probability of making this Type I error is the 5% level of significance.
C. What would your decision be in part A if the probability of making a Type I error were zero?
The null hypothesis will be rejected if the probability of making a Type I error were zero in part A.
The sale price of ground beef at a local grocery store is $1.49 for the first pound and $1.09 for each additional pound. Which function rule shows how the cost of ground beef, y depends on the number of pounds, x?
Answer:
y=1.09x+0.4
Step-by-step explanation:
Let's assume that the price of beef stays the same for every pound of beef (the first pound is also $1.09)
Then, the equation would be, it y was the cost, and x was pounds:
y=1.09x
But, the price of beef is not the same for the first pound.
The first pound costs an extra 1.49-1.09=0.4 dollars a pound, so we will add that to the equation.
y=1.09x+0.4
