A boat heads south at 1,200 mph while a steamer heads east at 500 mph. If they started from the same dock and at the same time, when will the distance between them be 1,300 mi?
Answers
(1200 m/h)^2 + (500 m/h)^2 = (1300 m)^2
Time is 1 Hour
So the distance between the boat heads and steamer heads if they started the same time and be 1300 mi is 1 hour.
Answer: After t=1 hour the distance between the boat and the steamer be 1300 mi.
Step-by-step explanation:
Given the speed of boat = 1200 mph
the speed of steamer =500 mph
Distance traveled by boat in time "t"=[tex]\frac{distance}{time}=\frac{1200}{t}[/tex]
Distance traveled by steamer in time time "t"=[tex]\frac{500}{t}[/tex]
As boat head south and steamer heads east ∴ they will make a right angle triangle with hypotenuse=shortest distance between them =1300mi(given)
By Pythagoras theorem
[tex](Perpendicular)^2+(Base)^2=(Hypotenuse)^2\\\\\Rightarrow(\frac{1200}{t})^2+(\frac{500}{t})^2=(1300)^2\\\\\Rightarrow\frac{1440000}{t^2}+\frac{250000}{t^2}=1690000\\\\\Rightarrow\frac{1690000}{t^2}=1690000\\\\\Rightarrow\ t^2=\frac{1690000}{1690000}=1[/tex]
⇒t=1 hour
Thus, after t= 1 hour the distance between them be 1300 mi.
Related Questions
Parks spent 1/3 of his money on a sweater. He spent 3/5 of the remainder on a pair of jeans. If he has $36 left, how much did the sweater cost?
Answers
1/3x + 6/15x = x - 36
11/15x = x - 36
4/15x = 36
x = 135
sweater costs 1/3x = 45
hope that helps, God bless!
How many radians are in one degree, accurate to three decimal places?
Answers
[tex]\bf \begin{array}{ccll} de grees&radians\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 180&\pi \\ 1&r \end{array}\implies \cfrac{180}{1}=\cfrac{\pi }{r}\implies r=\cfrac{1\cdot \pi }{180}[/tex]
One radian is approximately 0.0175 degrees. To convert from radians to degrees, multiply the radians value by 57.3°. This conversion is commonly used in mathematics and physics.
Explanation:One radian is equal to approximately 0.0175 degrees. To convert from radians to degrees, you can use the conversion factor of 1 radian = 57.3°. So, to convert an angle from degrees to radians, you can multiply the degrees value by 0.0175. This conversion can be used when working with angular measurements in mathematics and physics.
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A reconnaissance airplane P, flying at 19,000 feet above a point R on the surface of the water, spots a submarine S at an angle of depression of β = 21° and a tanker T at an angle of depression of α = 33°, as shown in the figure. In addition, ∠SPT is found to be γ = 119°. Approximate the distance between the submarine and the tanker.
Answers
The solution for the problem is:
Tan 33(degrees) = opposite/adjacent
Starting off with the submarine, find how far it is from
point R.
Tan 21 = 19,000/x
or
19,000/Tan 21= x
x = 49496.69 feet the submarine is from point R.
Now, find how far the tanker is from point R.
Tan 33= 19,000/x
or
19,000/Tan 33 = x
x = 29257.43 feet the tanker is from point R.
Now subtract and the difference would be the answer
= 49496.69 - 29257.43
The tanker and sub are 20239.26 feet away from each other.
An oil spill spreads 25 square meters every 16
hour. How much area does the oil spill cover after 2 hours?
Answers
rounding to estimate the difference of 18.14 - 9.88
Answers
Answer:
18.14 rounds to 18 because you look at the 1 and (0, 1, 2, 3, 4) tell you to round down. That means 18.14 rounds down to 18
9.88 rounds to 10 because you look at the first 8 and (5, 6, 7, 8, 9) tell you to round up. That means 9.88 rounds up to 10.
Now it's just simple math. 18-10 = 8
Step-by-step explanation:
Answer:
18.14 rounds to 18 because you look at the 1 and (0, 1, 2, 3, 4) tell you to round down. That means 18.14 rounds down to 18
9.88 rounds to 10 because you look at the first 8 and (5, 6, 7, 8, 9) tell you to round up. That means 9.88 rounds up to 10.
18-10=8.
Determine which numbers could not be used to represent the probability of an event. select all that apply.
a. minus−1.5, because probability values cannot be less than 0.
b. 0.0002, because probability values must be rounded to two decimal places.
c. startfraction 64 over 25 endfraction 64 25, because probability values cannot be greater than 1.
d. 33.3%, this is because probability values cannot be greater than 1.
e. startfraction 320 over 1058 endfraction 320 1058, because probability values cannot be in fraction form. f. 0, because probability values must be greater than 0.
Answers
So, the range of probability is [0, 1]
Here,
a. minus−1.5, because probability values cannot be less than 0. CORRECT
b. 0.0002, because probability values must be rounded to two decimal places. WRONG 0.0002 is greater than 0 & less than 1
c. startfraction 64 over 25 endfraction 64 25, because probability values cannot be greater than 1. CORRECT
d. 33.3%, this is because probability values cannot be greater than 1. WRONG 33.3 % is less than 1 & greater than 0.
e. startfraction 320 over 1058 endfraction 320 1058, because probability values cannot be in fraction form. f. 0, because probability values must be greater than 0.WRONG 33.3 % Probability values can be written in fraction, But it's decimal value of fraction should be greater than 0 & less than 1.
a. minus− 1.5, because probability values cannot be less than 0.
c. startfraction 64 over 25 endfraction 64 25 , because probability values cannot be greater than 1.
Probability would be in a range of 0-1. There won't be minus probability since the lowest possible will be 0. If the number using percent like 33.3%, then the maximal probability is 100%. If you calculate 64/25 you will got 2.56 which was higher than 1.
What does the y intercept represent in distance vs time squared?
Answers
Another tip, when you see the title, such as distance vs time squared. The first term in the title always goes for the y axis and the second goes for the x axis.
I hope this answers your question!
stacey has 18 bracelets after she organizes the bracelets by color she has 3 equal groups how many bracelets are in each group
Answers
write the fraction in simplest form 8/10
Answers
divide by 2 each
\frac{4}{y 5} is the simplest form
The simplest form of 8/10 is 4/5.
Given,
8/10
We need to write it in the simplest form.
What is the simplest form of a given fraction?It means that there is no common factor between the numerator and the denominator other than 1.
Example:
4/8
4 = Numerator
8 = Denominator
4 = 4 x 1
8 = 4 x 2
= 4 x 1 / 4 x 2
Cancel the common factor 4.
= 1/2 is the simplest form of 4/8
Find the simplest form of 8/10.
= 8/10
Look for a common factor.
= 2 x 4 / 2 x 5
Cancel the common factor 2.
= 4 / 5
Now we do not see any common factor.
= 4/5
Thus the simplest form of 8/10 is 4/5.
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How are the variables on the graph related?
Answer choices:
A. As speed decreases, height stays constant.
B. As speed decreases, height increases.
C. As speed increases, height decreases.
D. As speed increases, height increases.
Answers
The graph demonstrates a uniform relationship between speed and height, indicating that as speed increases, height also increases. Therefore, the correct answer is:
D. As speed increases, height increases.
The Graph indicates a uniform relationship between speed and height. To interpret this in the context of the answer choices:
D. As speed increases, height increases.
This is the most appropriate choice based on the information provided. In a uniform relationship, as speed increases, the corresponding height also increases. Therefore, Option D accurately captures the relationship depicted on the graph.
Table tennis the path of a table-tennis ball after being hit and hitting the surface of the table can be modeled by the function h=-4.9t(t-0.42) where h is the height in meters above the table and t is the time in seconds. how long does it take the ball to hit the table?
Answers
the ball hits the table, when it hits "the ground" or goes all the way back down, at that point, the height of the ball is 0, thus h = 0.
[tex]\bf 0=-4.9t(t-0.42)\implies t= \begin{cases} 0=-4.9t\\ 0=t\\ ------\\ 0=t-0.42\\ \boxed{0.42=t} \end{cases}[/tex]
If there were to be 9 boys and 6 girls at a party and the host wanted each to be given the same number of candies that could be bought in packages containing 12 candies, what is the fewest number of packages that could be bought? I got 36. But i'm not sure.
Answers
Using the least common factor of 15 and 12, it is found that the fewest number of packages that could be bought is of 5.
How to find the least common factor of two amounts?To find the lcm(least common multiple), we factor the numbers by prime factors, and then multiply these factors.
In this problem, packages of 12 candies will be used to give candies for 9 + 6 = 15 people, hence the least number of candies is lcm(12,15).
Then:
12 - 15|2
6 - 15|2
3 - 15|3
1 - 5|5
1 - 1
Hence lcm(12,15) = 2 x 2 x 3 x 5 = 60.
Since 60 candies are needed, and each package has 12 candies, the number of packages is given by:
n = 60/12 = 5.
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How many integers between 100 and 999 have all distinct digits (i.e., no two digits the same)?
Answers
-----------------------------------------------------
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Explanation:
We have this set of digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
From that set, we can only pick three items. We cannot select the same digit twice.
Consider a blank three digit number such that it is composed of slot A, slot B, slot C.
Since the number must be larger than 100, this means that we cannot select 0 as the first digit. We go from a pool of 10 digits to 10-1 = 9 digits for our first selection.
In other words, we have this subset to select from
{1, 2, 3, 4, 5, 6, 7, 8, 9}
So we have 9 choices for slot A.
For slot B, we also have 9 choices since 0 is now included. For instance, if we selected the digit '4' then we have this subset of choices left over: {0, 1, 2, 3, 5, 6, 7, 8, 9} which is exactly 9 items.
For slot C, we have 9-1 = 8 items left to choose from. For example: If we choose '4' for slot A, and '2' for slot B, then we have this subset to choose from: {0, 1, 3, 5, 6, 7, 8, 9} exactly 8 items
In summary so far, we have...
9 choices for slot A
9 choices for slot B
8 choices for slot C
Giving a total of 9*9*8=81*8=648 different three digit numbers. You'll notice that I'm using the counting principle which allows for the multiplication to happen. Think of a probability tree.
Final answer:
To determine how many integers between 100 and 999 have distinct digits, we calculate the possibilities for each position, giving us 9 options for the first digit, 9 for the second, and 8 for the third, resulting in a total of 648 integers.
Explanation:
The question is about finding the number of integers between 100 and 999 with distinct digits. To find this, we calculate the possibilities for each digit separately. The first digit can be anything from 1 to 9 (excluding 0 because the number cannot be less than 100), so there are 9 possibilities for the first digit. For the second digit, since it cannot be the same as the first, there are 9 possibilities (0 can now be included). Finally, for the third digit, we subtract the choices we've already used, so there are 8 possible digits left.
Calculating the total, we multiply the possibilities for each digit: 9 (first digit) × 9 (second digit) × 8 (third digit) = 648. Therefore, there are 648 integers between 100 and 999 that have all distinct digits.
To do linear regression, there must be paired scores on two variables.
Answers
List the sample space in the experiment "roll two dice - a red die and a white die." (hint: use a table)
Answers
A bar of soap weighs as much as 3/4 of an identical bar plus 3/4 of a pound. How much does the bar of soap weigh?
Answers
Since 3/4 (of the bar) + 1/4 (of the bar) equals a whole bar (1), and 3/4 (of the bar) + 0.75 equals the whole weight of the bar, 0.75 is 1/4 of the bar. 1/4 times 4 equals 1, and 0.75 times 4 equals 3, so the bar of soap weighs 3 pounds.
The weight of the bar of soap can be found by setting up the equation [tex]w = \(\frac{3}{4}w + \frac{3}{4}\)[/tex] and solving for 'w', which results in the soap weighing 3 pounds.
To find the weight of the bar of soap, we can set up an equation based on the given information. Let's define the weight of the soap as 'w'. According to the problem, the weight of the soap is equal to [tex]\frac{3}{4}[/tex] of itself plus [tex]\frac{3}{4}[/tex] of a pound, which can be written as:
[tex]w = \(\frac{3}{4}w + \frac{3}{4}\)[/tex]
Now, to solve for 'w', we need to isolate it on one side of the equation. We can do this by subtracting [tex]\(\frac{3}{4}w\)[/tex] from both sides:
[tex]w - \(\frac{3}{4}w\) = \(\frac{3}{4}\)[/tex]
This simplifies to [tex]\(\frac{1}{4}w\) = \(\frac{3}{4}\)[/tex], so when we multiply both sides by 4 to solve for 'w', we get:
w = 3 pounds
Therefore, the bar of soap weighs 3 pounds.
Sarah cut 6 yards of ribbon from a spool. How much did she cut in inches?
Answers
Answer: 216
How far will a cyclist travel in 1/4hour if he cycles at 18km per hour?
Answers
The length of a rectangle is 5 less than twice the width. If the perimeter of the rectangle is 146 centimeters, find the dimensions of the rectangle.
Answers
Perimeter = 146 cm
Equations we will use...
w = width
(2w - 5) = length (l)
perimeter (p) = 2(l + w)
Substitute equation for length into equation for perimeter
p = 2(l + w)
146 = 2((2w - 5) + w) [use distributive prop.]
146 = 4w - 10 + 2w [combine like terms]
146 = 6w -10 [solve for w]
156 = 6w
w = 26 cm
Now substitute width back into the equation for length...
l = 2w - 5
l = 2(26) - 5
l = 47
Double check to make sure values added up to 146 cm
w + w + l + l = 146
26 + 26 + 47 + 47 = 146
146 = 146
Therefore, the width is 26 cm and the length is 47 cm.
The dimension of the rectangle should be 47cm and 26 cm respectively.
Given that,
The perimeter of the rectangle is 146 cm.And, the length is 5 less than twice the width. Here we assume the length be x and the width be y.Based on the above information,
We know that
The perimeter of the rectangle = 2(l + w)
w = width
(2w - 5) = length
So,
146 = 2(2w - 5 + w)
146 = 4w - 10 + 2w
156 = 6w
w = 26 cm
And, the length is
= 2(26) - 5
= 47 cm
Therefore we can conclude that the dimension of the rectangle should be 47cm and 26 cm respectively.
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Which equation is an identity?
7m – 5 = 8m + 7 – m
3w + 8 – w = 4w – 2(w – 4)
9 – (2v + 3) = –2v – 6
–3y + 3 = –3y – 6
Please explain your answer.
Answers
3w + 8 – w = 4w – 2(w – 4). w = 8
Answer:
The correct option is 2.
Step-by-step explanation:
The equations that are true for any value of the variable, no matter what value is plugged in for the variable, then they are called Identity equations.
The first equation is
[tex]7m-5=8m+7-m[/tex]
[tex]7m-5=7m+7[/tex]
Subtract 7m from both the sides.
[tex]-5=7[/tex]
This statement is false for any value of m. Therefore this is not an Identity equation.
The second equation is
[tex]3w+8-w=4w-2(w-4)[/tex]
Using distributive property,
[tex]2w+8=4w-2w+8[/tex]
[tex]2w+8=2w+8[/tex]
[tex]0=0[/tex]
This statement is true for any value of w. Therefore this is an Identity equation.
The third equation is
[tex]9-(2v+3)=-2v-6[/tex]
[tex]9-2v-3=-2v-6[/tex]
[tex]-2v+6=-2v-6[/tex]
[tex]6=-6[/tex]
This statement is false for any value of v. Therefore this is not an Identity equation.
The fourth equation is
[tex]-3y+3=-3y-6[/tex]
Add 3y on both the sides.
[tex]3=-6[/tex]
This statement is false for any value of y. Therefore this is not an Identity equation.
Hence the correct option is 2.
2 out of 10 people have an allergic reaction to a new medicine. What is the probability that exactly 4 out of 10 people given the medicine experience an allergic reaction?
Answers
The probability that exactly 4 out of 10 people given the medicine experience an allergic reaction is approximately 0.087 or 8.7%.
To find the probability that exactly 4 out of 10 people experience an allergic reaction to the new medicine, we use the binomial probability formula:
[tex]\[ P(X = k) = \binom{n}{k} \times p^k \times (1 - p)^{n - k} \][/tex]
Where:
( n ) is the number of trials (in this case, 10 people)
( k ) is the number of successes (in this case, 4 people)
( p ) is the probability of success on each trial (in this case, the probability of having an allergic reaction, which is 2 out of 10, or 0.2)
Now let's calculate:
[tex]\[ P(X = 4) = \binom{10}{4} \times 0.2^4 \times (1 - 0.2)^{10 - 4} \][/tex]
[tex]\[ P(X = 4) = \frac{10!}{4!(10-4)!} \times 0.2^4 \times 0.8^6 \][/tex]
[tex]\[ P(X = 4) = \frac{10!}{4! \times 6!} \times 0.2^4 \times 0.8^6 \][/tex]
[tex]\[ P(X = 4) = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} \times 0.2^4 \times 0.8^6 \][/tex]
[tex]\[ P(X = 4) = 210 \times 0.2^4 \times 0.8^6 \][/tex]
[tex]\[ P(X = 4) = 210 \times 0.0016 \times 0.262144 \][/tex]
[tex]\[ P(X = 4) = 0.08704 \][/tex]
So, the probability that exactly 4 out of 10 people given the medicine experience an allergic reaction is approximately 0.087 or 8.7%.
The standard deviation of the sampling distribution of x overbarx, denoted sigma subscript x overbarσx, is called the
Answers
This is called as the standard error of the mean. Standard error is a numerical term that calculates the accurateness with which a sampling embodies a populace or population. In statistics, a sample mean moves away from the real mean of a population; this deviancy is the standard error.
Find the value of x so that the function has the given value.
j(x)=−4/5x+7; j(x)=−5
Answers
-5=(4/5x)+7
Add 7 to both sides
2=4/5x
Muliply both sides times 5x
10x=4
Divide both sides by 10
X=4/10
Simplify
X=2/5
What is the maximum percentage of net spendable income that should be set aside for housing?
Answers
The maximum percentage of net spendable income that you should spend on a house is 36%.
Answer:
The maximum percentage of net Spendable income that should be set aside for housing is given by [tex]\frac{28}{36}[/tex] rule,which states that ,if your total gross income after deduction is $ x, then you should use 28% of your income for housing finances and 36 % of your income for debt Purpose.
So, Maximum percentage of net spendable income that should be set aside for housing=28% of total gross income
Use the formula for Interest:
P = 100
r = 7.2%
Y = 5
A = ?
Answers
Which of the following statements are equivalent to the statement "price increased by 1/2 "?
Choose all correct answers.
(A) The price doubled
(B) The price is 150% of the price before
(C) The price was reduced by a quarter
(D) The price became a half of what it was before
(E) The price is now 1.5 of what it was before
(F) The price now is 66 2 3 % of what it was before
(G) The price now is 200% of what it was before
(H) The price is 75% of what it was before
Answers
Correct answers to the statement that the price increased by 1/2 are: (B) The price is 150% of the price before and (E) The price is now 1.5 of what it was before. All other options either imply the price doubled, decreased, or was halved, which are not equivalent to an increase by half.
When it is stated that the price increased by 1/2, it means that the new price is the original price plus half of the original price. This is equivalent to multiplying the original price by 1.5. Let's evaluate the provided options:
(A) The price doubled - This would mean the new price is twice the original price, or the original price multiplied by 2, which is incorrect.(B) The price is 150% of the price before - This is correct because 150% implies the original price plus 50% of the original price, which matches our initial statement.(C) The price was reduced by a quarter - This would mean the new price is 75% of the original price, which is incorrect.(D) The price became a half of what it was before - This means the new price is half the original price, which is incorrect.(E) The price is now 1.5 of what it was before - This is correct, as it directly states that the new price is 1.5 times the original price.(F) The price now is 66 2/3% of what it was before - This would imply a decrease in price, which is incorrect.(G) The price now is 200% of what it was before - This implies the price doubled, which is not the case.(H) The price is 75% of what it was before - This would mean the price decreased, which is incorrect.Therefore, the correct answers to the statement "price increased by 1/2" are (B) The price is 150% of the price before and (E) The price is now 1.5 of what it was before.
The equivalent statements are (B) "The price is 150% of the price before" and (E) "The price is now 1.5 of what it was before".
To determine which statements are equivalent to the statement "price increased by 1/2", let's analyze each option:
(A) The price doubled:
This statement is not equivalent because doubling the price means multiplying it by 2, which is an increase of 100%.
(B) The price is 150% of the price before:
This statement is equivalent. Increasing by 1/2 is equivalent to increasing by 50%, which makes the new price 150% of the original price.
(C) The price was reduced by a quarter:
This statement is not equivalent because reducing by a quarter means subtracting 25%, not adding 50%.
(D) The price became a half of what it was before:
This statement is not equivalent because it implies a decrease to half, whereas the original statement implies an increase by half.
(E) The price is now 1.5 of what it was before:
This statement is equivalent. If the price is increased by 1/2, it becomes 1 + 1/2 = 1.5 times the original price.
(F) The price now is 66 2/3 % of what it was before:
This statement is not equivalent. 66 2/3 % represents a decrease, not an increase.
(G) The price now is 200% of what it was before:
This statement is not equivalent because 200% represents a doubling, not an increase of 1/2.
(H) The price is 75% of what it was before:
This statement is not equivalent because 75% represents a decrease, not an increase.
So, the equivalent statements are (B) and (E).
List two actions a person can take to minimize the fees paid to a bank.
ANSWER:
1. Keep good records to avoid overdraft fees.
2. Be sure to check banks carefully. Look at the services to see if the bank charges fees for those services. Compare multiple banks before settling with one.
Answers
Answer:
First, keep good records to avoid overdraft fees. Second, be sure to check banks out carefully. Look at the services you will most likely need and see whether the bank charges fees for those services. Compare several different banks before opening an account in one of them.
Step-by-step explanation:
Plato answer
there are 24 students in science class. mr james will give each pair of students 3 magnets . so far ,mr James has given 9 pairs of students their magnets . how many magnets doses mr james need sp that each pair of students has exactly 3 magnes?
Answers
24/2 = 12 pairs of students
if he gave 9 pairs of students magnets there are 12-9 = 3 pairs left
3 magnets per pair
3*3 = 9 more magnets are needed
Answer:
the answer is d
Step-by-step explanation:
Determine the number of solutions for the system y-3x=2 and 2y-6x=2
Answers
Equation 2) 2y - 6x = 2
Rearrange both equations so that it is standard form (Ax+Bx=C)
1) -3x + y = 2
2) -6x + 2y = 2
Then, multiply ALL of equation 1 by two.
1) 2(-3x + y = 2)
Simplify.
1) -6x + 2y = 4
2) -6x + 2y = 2
Subtract equations from one another.
0 = 2
Therefore there are no solutions for this system of equations.
~Hope I helped!~
△EFG≅△JKL . What is m∠K ?
Answers
The two triangles are congruent, so the corresponding angles are the same, K is the mid-late phase of JKL, so K is the same as the mid-late phase of EFG. Therefore K = F = 62°.
What is compromise?
If a geometric shape can be placed on top of another so that all its points coincide, the geometry is said to be congruent or harmonious. >
Now that K is JKL, K will be similar to EFG's mid and late game.
Middle and late phase of EFG = F
M∠F = 62°
Therefore m∠K = m∠F = 62°
So "The two triangles are congruent, so the corresponding angles will be the same. K is at the end of JKL, so K will be the same as the end of EFG. So, K = F = 62°."
The probable question maybe:
In a triangle EFG and LJK, we are given angle G = 53 degree and angle F is 62 degree. △EFG≅△JKL. find the value of m∠K ?