Answer: the speed of the plane in still air is 101.2 mph
Step-by-step explanation:
Let x represent the speed of the plane in still air.
The pilot flew his single-engine airplane 60 miles with the wind from City A to above City B. If the wind was a constant 30 miles per hour, it means that the total speed at which he flew the plane while going is (x + 30) mph.
Time = distance/speed
Time spent while going is
60/(x + 30)
He then turned around and flew back to City A against the wind. it means that the total speed at which he flew the plane while returning is (x - 30) mph.
Time spent while returning is
60/(x - 30)
If the total time going and returning was 1.31.3 hours, it means that
60/(x + 30) + 60/(x - 30) = 1.3
Cross multiplying, it becomes
60(x - 30) + 60(x + 30) = 1.3(x - 30)(x + 30)
60x - 1800 + 60x + 1800 = 1.3(x² + 30x - 30x - 900)
120x = 1.3x² - 1170
1.3x² - 120x - 1170 = 0
The general formula for solving quadratic equations is expressed as
x = [- b ± √(b² - 4ac)]/2a
From the equation given,
a = 1.3
b = - 120
c = - 1170
Therefore,
x = [- - 120 ± √(- 120² - 4 × 1.3 × - 1170)]/2 × 1.3
x = [120 ± √(14400 + 6080)]/2.6
x = [120 ± √20480]/2.6
x = (120 + 143.1)/2.6 or x = (120 - 143.1)/2.6
x = 101.2 or x = - 8.9
Since the speed cannot be negative, then x = 101.2 mph
Students were surveyed about their preference between dogs and cats. The following two-way table displays
data for the sample of students who responded to the survey.
Approximately what percent of students in the sample prefer cats?
Round your answer to the nearest percent.
X
D
Male
Female
TOTAL
Preference
Prefers dogs
N
Prefers cats
No preference
TOTAL
2
The 36% of the students in the sample prefer cats. Hence, 36% is correct answer.
The step-by-step calculation to determine what percent of students in sample prefer cats:
1) Find the total number of students who prefer cats:
Add the number of male students who prefer cats (10) to the number of female students who prefer cats (26). 10 + 26 = 36
2) Find the total number of students surveyed:
Add the number of students who prefer dogs (36 + 20), the number of students who prefer cats (36), and the number of students with no preference (2 + 6). 36 + 20 + 36 + 2 + 6 = 100
3) Calculate the percentage of students who prefer cats:
Divide number of students who prefer cats (36) by the total number of students surveyed (100) and multiply by 100%. 36 / 100 * 100% = 36%
4) Round the answer to the nearest percent:
36% rounded to nearest percent is 36%.
Complete and correct question is in the image:
According to the given sample, 36% of students in the sample prefer cats.
To find the percentage of students in the sample who prefer cats, we need to sum up the number of students who prefer cats, which is 26 for females and 10 for males.
Total number of students who prefer cats = 26 (females) + 10 (males) = 36.
Now, let's find the total number of students in the sample:
Total number of students = 36 (males who prefer dogs) + 20 (females who prefer dogs) + 10 (males who prefer cats) + 26 (females who prefer cats) + 2 (males with no preference) + 6 (females with no preference)
= 36 + 20 + 10 + 26 + 2 + 6
= 100.
Now, we can calculate the percentage of students who prefer cats:
Percentage of students who prefer cats = [tex]\frac{Number \ of \ students \ who \ prefer \ cats}{Total \ number \ of \ students}[/tex] × 100
= ([tex]\frac{36}{100}[/tex]) × 100 = 36%.
So, approximately 36% of students in the sample prefer cats.
The question is:
Students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey.
Preference Male Female
Prefers dogs 36 20
Prefers cats 10 26
No preference 2 6
Approximately what per cent of students in the sample prefer cats?
What is the surface area of the triangular prism?
a
2,001 square feet
b
2,376 square feet
c
2,592 square feet
d
4,320 square feet
Answer:
BStep-by-step explanation:
2376
Paige rolls a number cube sixty-four times. The number 4 comes up fourteen times. The number 3 comes up six times
Rounded to the nearest whole percent, what is the experimental probability of rolling a 3 or 4?
====================================================
Explanation:
The number 4 shows up 14 times
The number 3 shows up 6 times
This is a total of 14+6 = 20 times we get a 3 or a 4 on the dice
This is out of 64 total rolls
Use a calculator to find that 20/64 = 0.3125
Move the decimal point over 2 spots to the right to get 31.25%
Lastly, round this to the nearest whole number percent to get 31%
Keep in mind that this only works for experimental probability. Theoretical probability is going to be different.
Answer:
31 percent on edgunity
Step-by-step explanation:
PLZZ HELP WILL GIVE BRAINLIST!! SOMEONE HURRY!! PLZZ WILL GIVE LOTS OF POINTS!!
Heidi drove to visit her friend one summer. The miles she traveled are shown on the graph below.
What is the unit rate of miles driven per hour?
A.
50 miles per hour
B.
25 miles per hour
C.
75 miles per hour
D.
100 miles per hour
Answer: A. 50 miles per hour
Step-by-step explanation:
in between the lines if you look at the number it goes 25,50,75,100 etc.
Tomas bought 3 software apps and 2 e-books for a total of $21. The two e-books cost $12. If s represents the cost of each app, the total cost of all 5 items is represented by 3 s + 12 = 21. Which statement about verifying the solution for s is true?
The solution is given by s = 6 because it makes the value of 3 s + 12 equal to 21.
The solution is given by s = 3 because it makes the value of 3 s + 12 equal to 21.
The solution is given by s = 9 because it makes the value of 3 s + 12 equal to 21.
The solution is given by s = 12 because it makes the value of 3 s + 12 equal to 21.
Answer:
The solution is given by s=9 because it makes the value of 3s+12 equal to 21.
Step-by-step explanation:
If you replace s with 9 you will get 21
Answer:
b. The solution is given by s = 3 because it makes the value of 3 s + 12 equal to 21.
Explanation:
I took the test and got it right.
Step 1: Substitute s for 3. You get 3(3) + 12 = 21.
Step 2: 3(3) + 12 = 21 is converted to 9 + 12 = 21.
Step 3: 9 + 12 equals 21.
A state park charges a $6.00 entry fee plus $7.50 per night of camping. Write an algebraic expression for the cost in dollars of entering the park and camping for n nights.
The algebraic expression for the cost of entering a state park and camping for n nights, with an entry fee of $6.00 and a nightly fee of $7.50, is Cost = $6.00 + ($7.50 times n).
The algebraic expression to represent the cost in dollars of entering a state park and camping for n nights, when the state park charges a $6.00 entry fee plus $7.50 per night of camping, is calculated as follows:
Cost = Entry fee + (Cost per night times Number of nights)
Here, the entry fee is $6.00, and the cost per night is $7.50. Therefore, the expression becomes:
Cost = $6.00 + ($7.50 times n)
Where n represents the number of nights spent camping.
Hector invests $800 in an account that earns 6.96% annual interest compounded semiannually. Rebecca invests $1,000 in an account that earns 5.44% annual interest compounded monthly. Find when the value of Rebecca's investment equals the value of Hector's investment and find the common value of the investments at that time. If necessary, enter the year to the nearest tenth and the value to the nearest cent. The value of Rebecca's investment equals the value of Hector's investment after approximately ________ years to the nearest tenth. The common value of the investments is approximately $_________ .
Answer:
The value of Rebecca's investment equals the value of Hector's investment after approximately 15.8 years to the nearest tenth
The common value of the investments is approximately $2358.05
Step-by-step explanation:
The formula of the compound interest including the principal is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where
A is the future value of the investment/loan, including interestP is the principal investment amountr is the annual interest rate (decimal)n is the number of times that interest is compounded per unit tt is the time the money is invested or borrowed forHector invests $800 in an account that earns 6.96% annual interest compounded semiannually
∵ P = 800
∵ r = 6.96 = [tex]\frac{6.96}{100}[/tex] = 0.0696
∵ n = 2 ⇒ semiannually
- Substitute all these values in the formula to find future value
∴ [tex]A=800(1+\frac{0.0696}{2})^{2t}[/tex]
∴ [tex]A=800(1.0348)^{2t}[/tex]
Rebecca invests $1,000 in an account that earns 5.44% annual interest compounded monthly
∵ P = 1,000
∵ r = 5.44 = [tex]\frac{5.44}{100}[/tex] = 0.0544
∵ n = 12 ⇒ monthly
- Substitute all these values in the formula to find future value
∴ [tex]A=1000(1+\frac{0.0544}{12})^{12t}[/tex]
∴ [tex]A=1000(1.004533333)^{12t}[/tex]
∵ Rebecca's investment equals the value of Hector's investment
- Equate the two equations
∵ [tex]1000(1.004533333)^{12t}[/tex] = [tex]800(1.0348)^{2t}[/tex]
- Insert ㏑ in both sides and remember ㏑(ab) = ㏑(a) + ㏑(b)
∴ ㏑( [tex]1000(1.004533333)^{12t}[/tex] ) = ㏑( [tex]800(1.0348)^{2t}[/tex] )
∴ ㏑(1000) + ㏑( [tex](1.004533333)^{12t}[/tex] ) = ㏑(800) + ㏑( [tex](1.0348)^{2t}[/tex] )
- Remember [tex]ln(a)^{n}[/tex] = n ㏑(a)
∴ ㏑(1000) + 12t [㏑(1.004533333)] = ㏑(800) + 2t [㏑(1.0348)]
- Subtract ㏑(800) and 12t [㏑(1.004533333)] from both sides
∴ ㏑(1000) - ㏑(800) = 2t [㏑(1.0348)] - 12t [㏑(1.004533333)]
- Take t as a common factor from the right hand side
∴ ㏑(1000) - ㏑(800) = t(2[㏑(1.0348)] - 12[㏑(1.004533333)])
- Divide both sides by (2[㏑(1.0348)] - 12[㏑(1.004533333)])
∴ 15.8 = t
The value of Rebecca's investment equals the value of Hector's investment after approximately 15.8 years to the nearest tenth
Let us find this value using Hector or Rebecca equations
∵ [tex]A=800(1.0348)^{2t}[/tex]
- Substitute t by 15.8
∴ [tex]A=800(1.0348)^{2(15.8)}[/tex]
∴ A = 2358.05
The common value of the investments is approximately $2358.05
29x + 92 = 29x - 11 solution
In the equation, 29x + 92 = 29x - 11, subtracting 29x from both sides cancels out the variable and leaves 92 = -11, which is a contradiction. Therefore, the equation has no solution.
Explanation:In the given equation, 29x + 92 = 29x - 11, you can see that the variable x is on both sides. The first step in solving this equation is by canceling out same terms on both sides.
When you subtract 29x from both sides, the equation will become 92 = -11 since the 29x cancels out on both sides. This equation doesn't make sense because 92 is not equal to -11. Therefore, the equation has no solution. This situation is known as a contradiction, because the variable cancels out and leaves us with a false statement.
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The heights of 6 randomly selected students in a classroom are 64 inches, 73 inches, 67 inches, 70 inches, 69 inches, and 65 inches. What is the mean of the students' heights?
Answer:
68
Step-by-step explanation:
if you have 2 cookies and split them between 3 friends including you how much cookie will each person get?
Answer:
[tex]\frac{2}{3}[/tex] or [tex].666666666[/tex] or [tex]\%66.66[/tex]
Step-by-step explanation:
Answer:
Each person would get 2/3
Step-by-step explanation:
Split the two circles and each person gets one portion of it.
Using the Zero Product Property, solve for the x-values given (x-2)(x+3)=0.
x=2 x=-3
x=-2 x=3
x=-2 x=-3
x=2 x=3
What is x 35x+10=190
Answer:
Step-by-step explanation:
35x + 10 = 190
35x = 190 - 10
35x = 180
x = 180 / 35
Therefore x = 5.14
Answer:
x=5 1/7 or 5.14
Step-by-step explanation:
35x+10=190
35x=190-10
35x=180
x= 180÷35
x=5 1/7 or 5.14
Urgent! Can someone answer these questions for me as I’m not in the right state of mind atm
Answer:
300 g. of chocolate.
75 g. of flour
3 people.
Step-by-step explanation:
These are proportion problems. I'll just give you the first formula.
[tex]\frac{200}{4} =\frac{x}{6} \\\\(200)(6)=4x\\1200=4x\\x=300[/tex]
Can you do the rest? I'll be waiting in the comments.
:)
Jorge watches cars that pass in front of his house. He counts 25 red cars and 40 cars that are not red. What is the approximate probability that the next car Jorge sees is red?
A) 62.5 %
B) 8/5
C) 0.33
D) 5/13
Step-by-step explanation:
firstly you will add
the red cars and non red cars together and which is 65
probability of the red car = 25/65
to the lowest form is the 5/13(D)
Answer:
its D
Step-by-step explanation:
A travel mug of 87∘C coffee is left on the roof of a parked car on a cold winter day. The temperature of the coffee after t minutes is given by H=87(2)−t/14. After how many minutes will the coffee be only lukewarm (30∘C)?
Answer:
After 21.28 minutes will the coffee be only lukewarm (30∘C)
Step-by-step explanation:
Given -
A travel mug of 87∘C coffee is left on the roof of a parked car on a cold winter day . The temperature of the coffee after t minutes is given by
[tex]H = 87(2)^{\frac{-t}{14}}[/tex]
Let after [tex]t_{1}[/tex] time H will be [tex]$30^\circ$[/tex]C
put t = [tex]t_{1}[/tex] , H = [tex]$30^\circ$[/tex]C
[tex]30 = 87(2)^{\frac{-t_{1}}{14}}[/tex]
[tex]\frac{30}{87} = (2)^{\frac{-t_{1}}{14}}[/tex]
.3448275 = [tex](2)^{\frac{-t_{1}}{14}}[/tex]
Taking logarithm both side
[ [tex]log(2^{x}) = xlog2[/tex] ]
log.3448275 = [tex]{\frac{-t_{1}}{14}}[/tex] log 2
-.4581 = [tex]{\frac{-t_{1}}{14}} \times.3010[/tex]
[tex]{\frac{-t_{1}}{14}}[/tex] = -1.52
[tex]t_{1}[/tex] = 21.28 minutes
To find the time it will take for the coffee to cool to 30 degrees Celsius, we need to solve the equation 30=87(2)−t/14 for the variable 't', which represents time.
Explanation:The subject of this problem is a mathematical application of heat transfer. To answer this question thoroughly, we need to solve the given equation H=87(2)−t/14 for 't' when H (the temperature of the coffee) is 30 degrees Celsius.
When we set H equal to 30, we can rearrange the equation to solve for 't':
Set H=30. The new equation becomes 30=87(2)−t/14. By simplifying the equation, we find t=(87(2)-30)*14.The solution of 't' will give the time it will take the coffee to reach 30 degrees Celsius.While this equation primarily pertains to heat transfer, it is also fundamentally about solving algebraic expressions, the core focus of high school Mathematics.
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Lukas plotted these points on the number line. Point A: −12 3 Point B: −2 3 Point C: −11 3 Point D: −22 3 Which point did he plot incorrectly? Point
Answer:
The answer is A.
Answer: The Answer is A
Step-by-step explanation:
A circle has its center at the origin and has a diameter of 24 units.
What is the standard equation of the circle?
Question 2 options:
x2+y2=242
x2−y2=122
x2−y2=242
x2+y2=122
Answer:
x² + y² = 144
Step-by-step explanation:
The general equation of a circle is given as
(x - a)² + (y-b)² = r²
where a and b are the center of the circle along the x and y axis respectively and r is the radius of the circle.
Hence a circle that has its center at the origin and has a diameter of 24 units, we can deduce that the values of a,b are 0,0. Also,
radius = diameter/2
= 24/2
= 12 units
Hence the standard equation of the circle
(x - 0)² + (y - 0)² = 12²
x² + y² = 144
If there are 192 students in 4 buses, then how many students are in each bus
Answer:
48 in each bus
Step-by-step explanation:
divide 192 by 4
Answer: 48
Step-by-step explanation:
If there are 4 buses and 192 students you divide 192 by 4 and get 48
According to the diagram, which way is the magnetic
field pointing?
O into the screen
O out of the screen
O left
Oright
Answer:
The answer is left
Step-by-step explanation:
Answer:
Left
Step-by-step explanation:
Took it on edg
what is the diameter of a circle if the radius is 1 inch
Answer:
2 inch
Step-by-step explanation:
The radius is the fixed distance from the center of a circle to any point on its circumference. The radius of a circle always equals half of its diameter, so to find the diameter, multiply the radius by two. ( 1 x 2= 2 inch)
The radius of a circle is 1/2 inch with a diameter of 1 inch.
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r and the radius of a circle is half if the diameter which is r.
Given, A circle has a diameter of 1 inch.
As we know the radius of a circle is half of the diameter,
∴ A circle with a diameter of 1 inch will have a radius of 1/2 inch.
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What is the answer and how you solved it plz I need help
Answer:
3/6
Step-by-step explanation:
there are 3 white slice, two grey slice and 1 black slice. in total there are six slices. so the answer is 3/6.
hope it helps
ABC is translated onto A’B’C’. The coordinates of point A are (3, 7) and the coordinates of
point A’ are (1, 12). If the coordinates of point B are (7, 2), what are the coordinates of point
B’?
The horizontal shift from point A to point A’ is _______. The vertical shift from point A to
point A’ is _______. Since in a translation all points shift the same distance, the coordinates of
point B’ are ( ____, ____ ).
Answer:
The horizontal shift from point A to point A’ is -2. The vertical shift from point A to point A’ is 5. Since in a translation all points shift the same distance, the coordinates of point B’ are (5, 7 ).
Step-by-step explanation:
A moved two units to the left.
1 - 3 = -2
A also moved 5 units up.
12 - 7 = 5
The translation rule is: [tex](x,y) -> (x - 2, y + 5)[/tex]
Apply the translation rule to point B.
[tex](7 -2, 2+5) = (5,7)[/tex]
B' should be (5,7).
Answers and Step-by-step explanations:
1. The horizontal shift from point A to point A' will simply be the difference in the x-coordinates. The x-coordinate of A is 3 and the x-coordinate of A' is 1. So, we take 1 - 3 = -2. The horizontal shift is 2 units to the left.
2. The vertical shift is the difference in the y-coordinates. The y-coordinate of A is 7 and the y-coordinate of A' is 12. So, we take 12 - 7 = 5. The vertical shift is 5 units up.
3. Basically, we want to move the coordinates of B 2 units to the left and 5 units up. B is currently (7, 2). When we move 2 units to the left, we subtract 2 from the x-coordinate 7, and when we move 5 units up, we add 5 to the y-coordinate 2: B' = (7 - 2, 2 + 5) = (5, 7)
Hope this helps!
It's believed that as many as 24% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group. What sample size would allow us to increase our confidence level to 95% while reducing the margin of error to only 4%?
Answer:
n=438
Step-by-step explanation:
-Given the sample proportion [tex]\hat p=0.24[/tex] and the confidence level is 95%.
-The sample size can be calculated using the formula;
[tex]ME=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
#Substitute parameters in the formula and make n the subject of the formula;
[tex]ME=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=z_{0.025}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\n=(\frac{z_{0.025}}{ME})^2\hat p(1-\hat p)\\\\\\=(\frac{1.96}{0.04})^2\times 0.24\times 0.76\\\\=437.94\approx 438[/tex]
Hence, the desired sample size is n=438
choose a symbol that makes the statement true 8_l-8l <, =, >
I need help please???
Answer:
i think it is E
Step-by-step explanation:
Activity
Patricia and her brother Ian help themselves to a pitcher of lemonade on the kitchen counter. Patricia takes a glass and fills it with p ounces of lemonade. Ian takes a bigger glass and pours himself 20% more lemonade than Patricia poured in her glass. Write an expression to represent the quantity of lemonade (in ounces) in Ian’s glass in terms of the quantity in Patricia’s glass (p).
Complete the steps below to solve the problem.
Part A
Write an expression in terms of p that shows how many more ounces Ian poured in his glass than Patricia poured in hers.
a = (1+0.2)p
This equation is used to calculate the quantity of lemonade.
Step-by-step explanation:
Let the quality of lemonade in lans glass be 'a'
Quantity of lemonade in patricias glass = p ounces
Lan pours 20% more than Patricia
a = (1+0.2)p
This equation is used to calculate the quantity of lemonade
Answer:
Patricia poured P ounces of lemonade in her glass. Ian poured 20% more than P ounces in his glass; that is, he poured 0.20p or .2p ounces more than Patricia.
ANSWER: 0.20p
Step-by-step explanation:
Please help! Will give good rating.
Dot Plot Data:
20, 21, 21, 25, 20, 23, 27, 23, 24, 25, 26, 24, 23, 22, 24
Which measure of center would best describe a typical
value of the data set? Why?
_______would be best,
because the data distribution is ______.
fill in the blank options:
1) The mean, Neither the mean nor median
2) Nearly symmetrical, neither symmetrical nor skewed
Convert the unit mass . Enter your answer in the box
6.75 kg = _____ g
Answer:
6750
Step-by-step explanation:
There are 1000g in a single kilogram. Therefore, [tex]\frac{6.75kg}{1}\cdot \frac{1000}{1kg}=6750g[/tex]. Hope this helps!
Answer:
6750
Step-by-step explanation:
A Weather Forecaster, predicts that there is a 30% chance of rain on Saturday and a 40% chance of rain on Sunday. If these probabilities are correct, what is the probability that it will rain both days?
35%
10%
12%
70%
"The correct answer is C. The statement If these probabilities are correct, 12%is the probability that it will rain both days
To find the probability that it will rain both days, we need to multiply the probability of rain on Saturday by the probability of rain on Sunday, assuming that the events are independent.
The probability of rain on Saturday is 30%, which can be expressed as 0.30 or[tex]\(\frac{30}{100}\)[/tex].
The probability of rain on Sunday is 40%, which can be expressed as 0.40 or[tex]\(\frac{40}{100}\)[/tex].
Now, we multiply these two probabilities to find the probability of both events occurring:
[tex]\[ P(\text{Rain on Saturday}) \times P(\text{Rain on Sunday}) = \frac{30}{100} \times \frac{40}{100} \][/tex]
[tex]\[ \frac{30}{100} \times \frac{40}{100} = \frac{30 \times 40}{100 \times 100} \] \[ \frac{30 \times 40}{100 \times 100} = \frac{1200}{10000} \] \[ \frac{1200}{10000} = \frac{12}{100} \] \[ \frac{12}{100} = 0.12 \][/tex]
Converting this decimal to a percentage, we get 12%.
Therefore, the probability that it will rain both days is 12%."
A tissue box has a volume of 105 cm³. If the length of the box is 7 cm and the width is 5 cm, what is the surface area of the box? *
142 cm²
35 cm²
735 cm²
365 cm²
FInd the height of the box by dividing the volume by 7 x 5 ( length x width)
Height = 105 / 35
Height = 3cm
There are 6 sides to a box.
Surface area = 2 x length x width + 2 x length x height + 2 times height x width
SA = 2*7*5 + 2*7*3 + 2*5*3
SA = 70 + 42 + 30
SA = 142 cm^2