Final answer:
The constant of proportionality when y = 18 and x = 60 is calculated by dividing y by x, which results in a constant of 0.3.
Explanation:
To find the constant of proportionality when y = 18 and x = 60, we must assume that the relationship between y and x is directly proportional. This means that as x increases, y increases at a constant rate, and vice versa. If the relationship is directly proportional, we can write y = kx, where k is the constant of proportionality.
To calculate k, we simply divide y by x. So we have:
k = y / x
k = 18 / 60
k = 0.3
Therefore, the constant of proportionality is 0.3.
Quadrilateral ABCD is the result of a translation of quadrilateral EFGH. Segment EF is parallel to segment HG in the pre-image.
Select from the drop-down menus to correctly complete the statement.
Segment EF is parallel to segment HG in the pre-image.
The corresponding segments are what
Answer: Segment BC of image is parallel to segment AD of image.
Step-by-step explanation:
Given: Quadrilateral ABCD is the result of a translation of quadrilateral EFGH.
Segment EF is parallel to segment HG in the pre-image.
Since translation is a rigid transformation which preserves the side-lengths and angles of the original figures.
Therefore, all the segments of the image figure are parallel to correspondent segments of the original figure.
Segment AD of image is parallel to segment HG in the pre-image.
Segment BC of image is parallel to segment EF in the pre-image.
Hence, if Segment EF is parallel to segment HG in the pre-image.
⇒ Segment BC of image is parallel to segment AD in image.
A basket contains 12 apples, of which two are rotten. a sample of three apples is selected at random. in how many ways can two rotten apples be chosen
Using the concept of combinations, there are 10 ways to choose three apples from a basket, where two are rotten and one is not.
Explanation:The question is asking about the number of ways two rotten apples can be chosen from a basket, given the total apples and the number of rotten ones. This is a problem based on probability and combinations.
The total number of apples in the basket is 12, two of them are rotten. The number of ways of choosing 2 rotten apples from 2 is simply 1 way, because there are only 2 and you're choosing each one of them.
But, the student is asked to select three apples, so the last apple would be one of the other 10 (remaining good ones). The number of ways you can choose that is 10 C 1.
From combinations rules, we know nCr=n!/[r!(n-r)!], where n is the total items, r is the number chosen, and '!' refers to factorial.
So to find the number of ways to choose 1 apple from 10, we find 10! / [1!(10-1)!]. This calculates as 10! / [1!9!] = 10. So, there are 10 ways to choose three apples with two of them being rotten.
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There are 10 different ways to choose a sample of three apples from the basket such that exactly two of them are rotten.
To determine the number of ways to choose two rotten apples from a basket containing 12 apples (2 of which are rotten) when a sample of three apples is selected.
We can use combinatorics.
Step-by-Step Solution:
1. Identify the total number of apples and the rotten apples:
Total apples: [tex]\( 12 \)[/tex]
Rotten apples: [tex]\( 2 \)[/tex]
2. Determine the possible cases for choosing two rotten apples in the sample of three:
We need to choose 2 out of the 2 rotten apples.
We need to choose the remaining 1 out of the 10 good apples.
3. Calculate the number of ways to choose 2 rotten apples out of 2:
[tex]\[ \binom{2}{2} = 1 \][/tex]
4. Calculate the number of ways to choose 1 good apple out of 10:
[tex]\[ \binom{10}{1} = 10 \][/tex]
5. Multiply the results from the above steps to get the total number of ways to choose two rotten apples and one good apple:
[tex]\[ \text{Total ways} = \binom{2}{2} \times \binom{10}{1} = 1 \times 10 = 10 \][/tex].
A train leaves Los Angeles at 2 p.m. heading north at 50 mph. If the next train leaves three hours later and also heads north at 60 mph, at what time will the second train catch up with the first?
The Second train will catch up with the first train after 15 hours which is 8a.m the following morning.
First train :
Departure time = 2 pm
Speed = 50 mph
Second train :
Departure time = 2 pm + 3 hours = 5 pm
Speed = 60 mph
Distance = speed × time
Distance already covered by first train before the departure of the second = 50 mph × 3 hpird = 150 miles
The number of hours needed for second train to catch up will be h;
(60 × h) = (50 × h) + 150
60h = 50h + 150
60h - 50h = 150
10h = 150
h = 150/ 10
h = 15
Second train will catch up after 15 hours :
Hence, time will be : (5pm + 15 hours) = 8 a.m the following morning.
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Answer: 8:00 am
Step-by-step explanation:
(5pm + 15 hours) = 8 a.m the following morning.
60h = 50h + 150
60h - 50h = 150
10h = 150
h = 150/ 10
h = 15
The amount left when you subtract last month's payment from last month's balance on a credit card statement is the
A. APR.
B. unpaid balance.
C new balance.
D. minimum payment.
The percentage charged each month on purchases charged to the credit card account is called the
A. periodic rate
B. new balance
C. unpaid balance
D. minimum payment
Answer:
Question 1)
Option: B
( unpaid balance)
Question 2)
Option: D
( Minimum payment )
Step-by-step explanation:
Question 1)
UNPAID BALANCE:
unpaid balance is the remaining balance of a loan, cash advance or credit that has not been paid.
Hence, The amount left when you subtract last month's payment from last month's balance on a credit card statement is the:
unpaid balance.
Question 2)
Minimum payments are typically calculated as percentage of your outstanding balance plus any fees that have been added to your balance.
Hence, The percentage charged each month on purchases charged to the credit card account is called the:
Minimum payment.
order 56.2 56.32 56.321 from greatest you least
What are the values of the 7 in the number 17,372
how many 1/4 cup servings of oatmeal are in 3/5 of a cup of oatmeal?
what is five divided by 2835
Solve the equation
5(-3x - 2) - (x - 3) = -4(4x + 5) + 13
Edmundo used a number line to show the solution for the inequality |2x-6|<4 Which number line shows the solution? HURRY PLEASE
To solve the inequality |2x-6|<4, we break it down into two inequalities and solve for the range of values. Then, we can plot the solution on a number line.
Explanation:The given inequality is |2x-6|<4. To solve this inequality, we need to break it down into two separate inequalities:
2x-6<4-(2x-6)<4Solving these inequalities will give us the range of values that satisfy the original inequality. Once we have the solution, we can plot it on a number line.
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Answer:
Step-by-step explanation:
an absolute value has two solutions, one negative and one positive.
so 2x-6<-4
2x<2
x<1
and
2x-6<4
2x<10
x<5
1>x<5
Option A is correct
F(x, y) = x2 i + y2 j c is the arc of the parabola y = 2x2 from (1, 2) to (2, 8) (a) find a function f such that f = ∇f.
Suppose Q and R are independent events. Find P(Q and R) if P(Q) = 0.27 and P(R) = 0.03.
Answer:
Value of [tex]P(Q \cap R)[/tex] is, 0.0081
Step-by-step explanation:
For an independent events A and B is given by:
[tex]P(A \cap B) =P(A) \cdot P(B)[/tex]
As per the statement:
Suppose Q and R are independent events.
P(Q) = 0.27 and P(R) = 0.03.
We have to find [tex]P(Q \cap R)[/tex]
By definition we have;
[tex]P(Q \cap R) =P(Q) \cdot P(R)[/tex]
Substitute the given values we have;
[tex]P(Q \cap R) =0.27 \cdot 0.03[/tex]
⇒[tex]P(Q \cap R)=0.0081[/tex]
therefore, the value of [tex]P(Q \cap R)[/tex] is, 0.0081
Express each ratio as a unit rate. 325.4 miles on 17.3 gallons
having trouble :/
To express the given ratio as a unit rate, divide the miles by the gallons to obtain 18.8 miles per gallon.
Explanation:To express the given ratio as a unit rate, divide the miles by the gallons. So, the unit rate would be:
325.4 miles ÷ 17.3 gallons = 18.8 miles per gallon
Therefore, the unit rate for the given ratio is 18.8 miles per gallon.
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A runner can jog at a rate of 4 miles per hour uphill. Downhill, he can run 3 miles in the same time it takes him to run 2 miles uphill. How long would it take to run 2 miles uphill and then 3 miles downhill?
what is the most important variable?
To calculate the total time it takes to run 2 miles uphill at 4 mph and then 3 miles downhill at a speed that takes the same time as running 2 miles uphill, we find that the time for each is 0.5 hours, or 30 minutes, totaling 1 hour
The main question asks how long it would take for the runner to run 2 miles uphill and then 3 miles downhill, knowing that he jogs at a rate of 4 miles per hour uphill, and he can run 3 miles downhill in the same time it takes to run 2 miles uphill
First, let's find the time it takes to run 2 miles uphill. Since he runs at 4 miles per hour uphill, the time for 2 miles uphill is 2 miles divided by 4 miles per hour, which equals 0.5 hours or 30 minutes. Now, since it takes the same time to run 3 miles downhill, we know the downhill time is also 30 minutes
The total time taken for 2 miles uphill and 3 miles downhill is the sum of both, which is 30 minutes + 30 minutes = 60 minutes, or 1 hour. Thus, the answer to the student's question is 1 hour
A client is instructed to take
1 1/2 teaspoons of a cough syrup 3 times a day. How many teaspoons of cough syrup will the client take each day?
A rectangle is divided into 8 equal parts. Two parts are shaded. Which fraction is equivalent to the shaded area of the rectangle?
Kathy runs a 26.2- mile marathon at an average pace of 6.2 minutes per mile how long will it take her to finish
Kathy will complete the 26.2-mile marathon in approximately 2 hours and 42 minutes by multiplying the marathon distance by her average pace and converting the result from minutes to hours and minutes.
To calculate the time it will take for Kathy to finish a 26.2-mile marathon at an average pace of 6.2 minutes per mile, we simply multiply the distance of the marathon by her average pace per mile. This is a basic mathematics problem involving multiplication to determine the total time.
Here is the calculation:
Total marathon distance = 26.2 miles
Average pace = 6.2 minutes per mile
Total time = Total marathon distance x Average pace
Total time = 26.2 miles x 6.2 minutes per mile = 162.44 minutes
To convert minutes into hours and minutes, we know that there are 60 minutes in an hour. Therefore:
Hours = Total time / 60
Hours = 162.44 minutes / 60 ≈ 2.707 hours
Since we want hours and the remaining minutes, we can take the decimal part and multiply it by 60:
Remaining minutes = 0.707 x 60 ≈ 42.42 minutes
Hence, Kathy will complete the marathon in approximately 2 hours and 42 minutes.
A diver begins at 150 feet below sea level, descends at a steady rate of 5 feet per minute for 3.5 minutes, and then ascends 122.2 feet. What is the diver’s current depth? Explain how to write a numerical expression to find the answer.
You diver begin at -150 feet and then descend at 5 feet/minute for 3.5 minutes, which could be represented by (-5)(3.5). you then go up 122.2 feet. The expression is -150 + (-5)(3.5) + 122.2. You then get that the diver’s depth is 45.3 feet below sea level, or -45.3.
what is the 13th term in the arithmetic sequence described by this explicit formula an=84+(n-1)(-6)
Answer:
12
Step-by-step explanation:
The formula given is [tex]a_n=84+(n-1)(-6)[/tex]
Where [tex]a_n[/tex] gives the nth term
Since we want 13th term, we can say we want [tex]a_{13}[/tex] and we plug in 13 in [tex]n[/tex] into the formula. So we get:
[tex]a_n=84+(n-1)(-6)\\a_{13}=84+(13-1)(-6)\\a_{13}=84+(12)(-6)\\a_{13}=84-72\\a_{13}=12[/tex]
So, the 13th term of the sequence is 12
Results for 'Tanisha's office is on the ninth floor of an office building.she products your car in the underground parking garage for floors below ground level but how many floors are between Tanisha's Office and her car? '
In the diagram, polygon ABCD is flipped over a line of reflection to form a polygon with its vertices at A′, B′, C′, and D′. Points A′, B′, and D′ are shown, but the line of reflection and point C′ are not. The line of reflection is , and the coordinates of C′ are . NextReset
Find the value of a so that the differential equation y ' − xy − 6x = 0 has a solution of the form y(x) = a + bex2/2 for any constant
b.
Answer:
a = -6
Step-by-step explanation:
Which statements about the graph of the function f(x) = –x2 – 4x + 2 are true? Check all that apply.
The domain is {x|x ≤ –2}.
The range is {y|y ≤ 6}.
The function is increasing over the interval (–∞ , –2).
The function is decreasing over the interval (−4, ∞).
The function has a positive y-intercept.
write the equation then solve to find the number:seventy four less than a number is 98
what is the quotient a-3/7÷3-a/21
The quotient of the expression [tex]\(\frac{a-3}{7} \div \frac{3-a}{21}\)[/tex] is -3.
To find the quotient of the expression [tex]\(\frac{a-3}{7} \div \frac{3-a}{21}\)[/tex], we follow the rules of division for fractions, which involves multiplying the first fraction by the reciprocal of the second fraction.
The expression can be rewritten as:
[tex]\[\frac{a-3}{7} \times \frac{21}{3-a}\][/tex]
Now, we can simplify the expression by canceling out common factors. Notice that [tex]\(a-3\)[/tex] and [tex]\(3-a\)[/tex] are negatives of each other, and [tex]\(7\)[/tex] is a factor of [tex]\(21\)[/tex].
First, we can cancel [tex]\(a-3\)[/tex] with [tex]\(3-a\)[/tex], keeping in mind that a negative sign will be introduced since [tex]\(a-3 = -(3-a)\)[/tex]:
[tex]\[\frac{-1}{7} \times \frac{21}{-1}\][/tex]
Next, we simplify [tex]\(21\)[/tex] divided by [tex]\(7\)[/tex], which is [tex]\(3\)[/tex]:
[tex]\[-1 \times 3\] = -3[/tex]
What is the thickness t of the thin film of diamond? express your answer in nanometers using three significant figures?
The thickness of a thin film of diamond can be calculated using the formula t = (m * λ) / (2 * n), where m is the number of fringes, λ is the wavelength of light used, and n is the refractive index of diamond.
Explanation:The thickness of a thin film of diamond can be determined using the formula:
t = (m * λ) / (2 * n)
where t is the thickness, m is the number of fringes, λ is the wavelength of light used, and n is the refractive index of diamond.
In this case, the number of fringes is given as 14 per centimeter, which can be converted to 140 per meter. The wavelength of the light used is not provided, so we cannot determine the thickness without that information.
There are 10 less trumpet and saxophone players number of saxophone players three times the number of trumpet players how many trumpet players are there?
There are 3 trumpet players.
We have,
Let's assume the number of trumpet players is represented by "x".
According to the given information, the number of saxophone players is three times the number of trumpet players, so the number of saxophone players would be 3x.
It is also stated that there are 10 less saxophone players than the total number of trumpet and saxophone players.
So, the number of saxophone players would be (x + 3x) - 10, which simplifies to 4x - 10.
Since the number of saxophone players is equal to 4x - 10, we can set up an expression to solve for x:
4x - 10 = x
To isolate x, subtract x from both sides of the expression:
4x - x - 10 = x - x
This simplifies to:
3x - 10 = 0
Next, add 10 to both sides:
3x - 10 + 10 = 0 + 10
This yields:
3x = 10
Finally, divide both sides by 3:
(3x) / 3 = 10 / 3
The solution is:
x = 10/3 or approximately 3.33
Therefore,
There are approximately 3.33 trumpet players.
Since you cannot have a fraction of a player, we can conclude that there are 3 trumpet players.
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Are the fractions equivalent? 12/15 and 20/25
What is the value of the underlined digit 5,678.321
The value of the underlined digit is 600.
What is the place value strategy?The place value strategies are defined as math strategies that use to assist you in resolving your elementary math problems, use your places values, such as tens and hundreds. It is possible to employ enlarged notation or compensation. Using regrouping techniques, you can make the problem easier by compensating for addition.
We must determine the values of each integer in order to calculate the value of the underlined digit (6) in the equation.
In 5,678.321, the first digit, 5, is 1,000 in the thousands of places.
The second digit, 6, is in the hundreds (100) place.
So the value is 600.
Hence, the value of the underlined digit is 600.
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Your question is incomplete, probably the complete question is:
What is the value of the underlined digit 5,678.321, the underlined digit (6)
Can you plz solve 336.752 divided by 31 in long division form. This would help a whole bunch:)