Two clocks are turned on at the same time.One clock chimes every 15 minutes.The other clock chimes every 25 minutes.In how many minutes will they chime together
Answer:
The two clock will chime together in 75 minutes
Step-by-step explanation:
- Two clocks are turned on at the same time
- One clock chimes every 15 minutes
- The other clock chimes every 25 minutes
- We need to know in how many minutes they will chime together
- The two clock will chime together in the multiples of 15 and 25
- Lets find the first common multiple of 15 and 25
∵ 15 = 5 × 3
∴ The prime factors of 15 are 3 and 5
∵ 25 = 5 × 5
∴ The prime factor of 25 is 5
∴ The lowest common multiple of 15 and 25 = 5 × 3 × 5 = 75
∴ The two clocks will chime together every 75 minutes
The two clock will chime together in 75 minutes
You are given 1000 one dollar bills and 10 envelopes. Put the bills into the envelopes in such a way that someone can ask you for any amount of money from $1 to $1000 (examples - $532, $619, $88, etc.) and you can give it to them through a combination of the envelopes.
Answer:
We can do it with envelopes with amounts $1,$2,$4,$8,$16,$32,$64,$128,$256 and $489
Step-by-step explanation:
Observe that, in binary system, 1023=1111111111. That is, with 10 digits we can express up to number 1023.This give us the idea to put in each envelope an amount of money equal to the positional value of each digit in the representation of 1023. That is, we will put the bills in envelopes with amounts of money equal to $1,$2,$4,$8,$16,$32,$64,$128,$256 and $512.
However, a little modification must be done, since we do not have $1023, only $1,000. To solve this, the last envelope should have $489 instead of 512.
Observe that:
1+2+4+8+16+32+64+128+256+489=1000Since each one of the first 9 envelopes represents a position in a binary system, we can represent every natural number from zero up to 511. If we want to give an amount "x" which is greater than $511, we can use our $489 envelope. Then we would just need to combine the other 9 to obtain x-489 dollars. Since [tex]x-489\leq511[/tex], by 2) we know that this would be possible.f(x) = x(2x/2)/x(x+5)(x+6)^2
Find the vertical asymptotes?
Answer:
x = -5, x = -6
Step-by-step explanation:
After canceling common terms from numerator and denominator, there are two factors remaining in the denominator that can become zero. The vertical asymptotes are at those values of x.
[tex]\displaystyle F(x)=\frac{x\frac{2x}{2}}{x(x+5)(x+6)}=\frac{x}{(x+5)(x+6)}[/tex]
The denominator will be zero when ...
x + 5 = 0 . . . . at x = -5
x + 6 = 0 . . . . at x = -6
The exact number of kilometers in m miles is f(m), where f is the function defined by f(m) = 1.609344m. (a) find a formula for f−1(k). (b) what is the meaning of f−1(k)?
Answer:
f⁻¹(k) = k/1.609344f⁻¹(k) is the exact number of miles in k kilometersStep-by-step explanation:
(a) If we let k = f(m), we can solve for m to find f⁻¹(k).
k = 1.609344m
k/1.609344 = m = f⁻¹(k)
__
(b) Since k is the number of kilometers in m miles, m is the number of miles in k kilometers.
__
In summary ...
(a) f⁻¹(k) = k/1.609344
(b) f⁻¹(k) is the exact number of miles in k kilometers
In the past year, Ann watched 27 movies that she thought were very good. She watched 90 movies over the whole year. Of the movies she watched, what percentage did she think were very good?
Answer:
30%
Step-by-step explanation:
27 over 90 is equal to 0.3 in decimal form, turn that into percentage by multiplying by 100, and you get 30%
Addison painted her room. She had 505050 square meters to paint, and she painted at a constant rate. After 222 hours of painting, she had 353535 square meters left. Let yyy represent the area (in square meters) left to paint after xxx hours. Complete the equation for the relationship between the area and number of hours.
Answer:
y = 50 - 7.5x
Step-by-step explanation:
Given,
The original area for painting = 50 m²,
Let c meter per hour be the constant rate of painting,
So, after 2 hours, the area painted = 2c m²,
Thus, the area left to paint = 50 - 2c
According to the question,
50 - 2c = 35
2c = 15
⇒ c = 7.5
i.e. the constant rate of painting is 7.5 meters per hour,
Hence, the area left after x hours = 50 - 7.5x
If y represents the area left to paint after x hours,
Then,
y = 50 - 7.5x
Which is the required equation.
A company had 15 employees whose salaries are shown below.
Answer:
14,740
Step-by-step explanation:
The mean of a set of data is another way of saying the average
To find the average you find the sum of all the numbers/amount of numbers
In this case it would be 221,100/15
Can someone help me with number 10? Thank you.
Answer:
east 95 kmsouth 89 kmStep-by-step explanation:
SOH CAH TOA can remind you of the relationships between triangle measures. The distance east is the side of the right triangle that is opposite the angle, so is related to the hypotenuse (ship's travel distance) by the sine function.
sin(43°) = (travel distance)/(distance east)
So, ...
(distance east) = (travel distance)·sin(43°)
Likewise, the cosine function can be used to find the distance south.
Then we have ...
east = (130 km)sin(43°) ≈ 95 km
south = (130 km)cos(43°) ≈ 89 km
Two angles are complementary. One angle measures 20 degrees more than the other angle. Find the measure of the LARGER angle. Just type in the answer. Do not type in a variable or the degree symbol.
Two complementary angles equal 90 degrees.
If one is 20, the larger one would be 90 - 20 = 70 degrees.
I don’t get this question, please help.
Answer:
A = 7
B = 2
Step-by-step explanation:
The question is asking for the simplified form of √(-98). You are expected to know that √-1 = i, and you are expected to be able to factor the number 98.
[tex]\sqrt{-98}=\sqrt{(-1)(7^2)(2)}=7i\sqrt{2}[/tex]
Matching parts of the simplified expression to the form you are given, you see that ...
A = 7
B = 2
Consider this bag of marbles.
Answer:
p(green) = 0.5odds in favor of green: 1 : 1Step-by-step explanation:
There are 5 green marbles among the 10 in the bag, so the probability of drawing one at random is 5/10 = 0.50.
The odds in favor of drawing a green marble will be the ratio of the number of green marbles to the number that are not green: 5 : 5. Usually, the odds are expressed using integers with no common factors, so they would be written as 1 : 1.
What is the end behavior of the polynomial function?
Answer:
see below
Step-by-step explanation:
Ordinarily a graph like this will have arrowheads on the ends of the curve, indicating the curve continues on in the same direction. Here, we have to assume the existence of such arrowheads in order to choose a sensible answer.
As x goes to -∞, the curve continues to increase toward +∞. This is not an answer choice.
As x goes to +∞, the curve continues to decrease toward -∞. This matches the third answer choice.
Answer:
As [tex]x[/tex] tend to ∞, tehn [tex]y[/tex] tend to -∞.Step-by-step explanation:
In the graph you can observe the beahaviour of each variable.
Observe, as [tex]x[/tex] tend to ∞, then [tex]y[/tex] tend to -∞. This beahaviour is located in the IV quadrant.
So, in the options, the best answer is "as [tex]x[/tex] tend to ∞, tehn [tex]y[/tex] tend to -∞", because is true.
Other options are just false, for example, as [tex]x[/tex] tend to -∞, [tex]y[/tex] doesn't tendo to -∞.
As [tex]x[/tex] tend to -∞ [tex]y[/tex] doesn't tendo to 0.
Therefore, the right answer is the third choice.
Rewrite the expression 225 divided by 5/8 as 225 x 8/5. So, the quotient says a sloth may move 360 feet in 1 hour. Rewrite 90 minutes as 1 1/2 hour. Multiply by 1 1/2 to get feet in 90 minutes.
Answer:
540 feet
Step-by-step explanation:
225x(8/5)
360 feet in 1 hour
6 feet in 1 minute
540 feet in 90 minutes
The equivalent expressions of the given expressions is 540 feet in 90 minutes.
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.
The expression of 225 divided by 5/8 as 225 x 8/5.
225 x (8/5)
So, the quotient says a sloth may move 360 feet in 1 hour.
360 feet in 1 hour
Then, 6 feet in 1 minute
90 minutes as 1 1/2 hour.
Multiply by 1 1/2 to get feet in 90 minutes.
540 feet in 90 minutes
The equivalent expressions of the given expressions is 540 feet in 90 minutes.
Learn more about expression here;
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The function f(x) = (x − 4)(x − 2) is shown. On a coordinate plane, a parabola opens up. It goes through (2, 0), has a vertex at (3, negative 1), and goes through (4, 0). What is the range of the function? All real numbers less than or equal to 3 all real numbers less than or equal to −1 all real numbers greater than or equal to 3 all real numbers greater than or equal to −1
Answer: all real numbers greater than it equal to negative one.
Step-by-step explanation: if you graph this equation you see that the vertex is at (3,-1). We know that Range is all possible Y values.so, By looking at their graph we can see that the lowest point it touches is at -1. The rest of the graph goes off into positive and negative infinity.
Range= Y is greater than it equal to -1.
Answer:
All real numbers greater than or equal to −1
Step-by-step explanation:
Here, the given parabola,
[tex]f(x) = (x-4)(x-2)[/tex]
[tex]f(x) = x^2-4x-2x + 8[/tex]
[tex]f(x) = x^2 - 6x+8[/tex]
∵ Leading term = positive
So, the parabola is upward.
We know that an upward parabola is minimum at its vertex
Or it gives minimum output value at its vertex.
for instance, If (h, k) is the vertex of an upward parabola,
then its range = { x : x ≥ k, x ∈ R }
Note : Range = set of all possible output values
We have given,
Vertex = (3, -1)
Hence, Range = all real numbers greater than or equal to −1
LAST option is correct.
I am so confused and lost!! Please Help!!!
Answer:
x = 2.4
Step-by-step explanation:
To find the value when f(x) = x, you just have to replace f(x) for x
[tex]f(x) =-\frac{1}{4}x +3 \\x = - \frac{1}{4}x +3 \\x +\frac{1}{4}x=3 \\\frac{5}{4} x= 3 \\ x = 3*\frac{4}{5} \\x = 2.4[/tex]
Two boats leave port at the same time. One goes west and the other south. The speed of the southbound boat is 5 mph more than the westbound boat. After 3 hours the boats are 27 miles apart. Find the speed of the southbound boat. Round to the nearest tenth of a mile per hour.
Westbound boats speed = X
Southbound boats speed = X + 5
In 3 hours they are 27 miles apart:
3X + 3(x+5) = 27
Simplify:
3x + 3x +15 = 27
Combine like terms:
6x + 15 = 27
Subtract 15 from both sides:
6x = 12
Divide both sides by 6:
x = 12/6
x = 2
Westbound was 2 miles per hour
Southbound was 2 +5 = 7 miles per hour
Check:
2 miles per hour x 3 hours = 6 miles
7 miles per hour x 3 hours = 21 miles
21 + 6 = 27 miles
The population of ages at inauguration of all U.S. Presidents who had professions in the military is 62, 46, 68, 64, 57. Why does it not make sense to construct a histogram for this data set?
Answer: You only have 5 samples, always when you want to do statistics, you need a large sample size.
let's suppose you throw a dice 5 times, the results that it shows are 1,4,2,1,4. If you make statistics whit that numbers, you will think that the 1 and 4 have a bigger possibility than the other numbers, but that can't be, if you throw the dice enough times you will se that all numbers have the same possibility.
Matching: write in the correct letter.
line segment AB
Ray AB
The length of line segment AB
Line AB
answer options
a) AB
b) AB with a line above it.
c) AB with a line above it going only left.
d) AB with a line with both arrows on either side.
Line segment AB - b) AB with a line above it.
Ray AB - c) AB with a line above it going only left.
The length of line segment AB - a) AB
Line AB - d) AB with a line with both arrows on either side.
To match the given terms with the correct letter options, let's define each term and find its corresponding notation:
Line segment AB: A line segment is a part of a line that is bounded by two distinct end points.Ray AB: A ray starts at one point and extends infinitely in one direction. The length of line segment AB: This refers to the numerical length or distance between points A and B. Line AB: A line extends infinitely in both directions.These notations are crucial in geometry to clearly communicate different types of lines and measurements.
Kenya plans to make a down payment plus monthly payments in order to buy a motorcycle. At one dealer she would pay $2,350 down and $175 each month. At another dealer, she would pay $2,850 down and $150 each month. After how many months would the total amount paid be the same for both dealers? What would that amount be?
Answer:
20 months
Step-by-step explanation:
Let x be the number of months. The cost equation for each dealer is the total of the down payment and the total monthly contribution. Thus,
Deal 1 cost = $2,350 + $175x
Dealer 2 cost =$2,850 + $150x
The number of months after which the costs from both dealers are equal is calculated by equating the costs for both dealers. Therefore,
$2,350 + $175x = $2,850 + $150x
$175x -$150x =$2,850 -$2,350
$25x =$500
x= $500/$25
x = 20 months
Selena is driving to visit her grandmother who lives 325 miles away from Selena home. she travels an average of 60 miles per hour. Determine the independent and dependent quantities in each scenario. Be sure to include the appropriate units of measure for each quantity
Answer:
Step-by-step explanation:
independent quantity=60 m/h
dependent =time taken=t
60 t=325
t=325/60=65/12=5 5/12 hours
find the value of x, question and choices attached above
Answer:
E. 22Step-by-step explanation:
Look at the picture.
The lines l and m are parallel, therefore alternate interior angles are congruent.
Therefore [tex]\beta=50^o[/tex]
Supplementary angles add up to 180°.
Therefore
[tex](5x-16)+\theta=180[/tex] add 16 to both sides
[tex]5x+\theta=196[/tex] subtract 5x from both sides
[tex]\theta=196-5x[/tex]
We know: the sum of the triangle angle measures is 180°.
Therefore we have the equation:
[tex]50+2x+196-5x=180\\\\-3x+246=180\qquad\text{subtract 246 from both sides}\\\\-3x=-66\qquad\text{divide both sides by (-3)}\\\\x=22[/tex]
A ball is thrown in the air from a ledge. It's height in feet represented by f(x)=16(x^2-6x-7), where x is the number of seconds since the ball has been thrown. The height of the ball is 0 feet when it hits the ground. How many seconds does it take the ball to reach the ground?
Answer:
Step-by-step explanation:
Since we know that the height is 0, we can figure out how long it took the ball to reach the ground by setting [tex]f(x) = 0[/tex] and solving for [tex]x[/tex]:
[tex]f(x) = 16(x^{2} - 6x - 7)[/tex]
[tex]0 = 16(x^{2} - 6x - 7)[/tex]
[tex]0 = x^{2} - 6x - 7[/tex]
[tex]0 = (x - 7)(x + 1)[/tex]
[tex]x = -1, 7[/tex]
Because time can only be positive, the answer is 7 seconds.
Answer:
7 seconds.
Step-by-step explanation:
height h = 16(x^2-6x-7) = 0
x^2 - 6x - 7 = 0
(x - 7)(x + 1) = 0
x = 7 seconds (we ignore the negative).
If you eat one quarter of a pizza and your dog eats one eighth of it, what percent is left over?
Answer:
5/8 after subtraction :)
Step-by-step explanation:
Answer: The answer is: 62.5 % (left over).
______________________________________________
Step-by-step explanation:
______________________________________________
[tex]\frac{1}{4} + \frac{1}{8} = ?[/tex] ;
Change "(1/4)" to: "(?/8)" ;
What is "(?)" ? ;
→ (1/4) = (?/8) ;
notice the denominators;
(1/4) = (?/8) ; In the first fraction, how does the "denominator", "4" ; turn to "8" ? Specifically, since we dealing with "fractions", what number do we multiply "4" by, to get: "8" ??? ;
→ " 4 * ? = 8 " ?? ;
→ " 8 ÷ 4 = ? " ;
= 2 ;
______________________________________________
so " 1/4 = ?/8 " ;
Since we multiply the denominator, "4" ; by "2" , to get:
"8" (the denominator in the other fraction);
we multiply the numerator, "1" ; by "2" ; to get:
"2" (the denominator in the other fraction):
______________________________________________
→ " [tex]\frac{1}{4} = \frac{(1*2)}{(4*2)} = \frac{2}{8}[/tex] ;
______________________________________________
Now, the amount of the pizza that "you" ate is: "(2/8)" ;
The amount of the pizza eaten by "your dog" is: "(1/8)" ;
Let's add up the amount of pizza eaten:
[tex]\frac{2}{8} + \frac{1}{8} = \frac{(2+1)}{8} = \frac{3}{8}[/tex] .
The total amount of the pizza would be: " [tex]\frac{8}{8}[/tex] " .
Note: " [tex]\frac{8}{8}[/tex] = 8 ÷ 8 = 1 whole [pizza].
To find the amount left over, subtract the amount eaten; "(3/8)" ; from the whole pizza; "(8/8)" ; as follows:
______________________________________________
→ [tex]\frac{8}{8} - \frac{3}{8} = \frac{(8-3)}{8} = \frac{5}{8}[/tex] .
______________________________________________
Now, the question asks, what percent is left over? ;
So, we convert "(5/8)" into a percentage;
Change "(5/8)" to: "(?/100)" ;
→ Notice the denominators;
(5/8) = (?/100) ; In the first fraction, how does the "denominator", "8" ; turn to "100" ? Specifically, since we dealing with "fractions", what number do we multiply "8" by, to get: "100" ??? ;
→ " 8 * ? = 100 " ?? ;
→ " 100 ÷ 8 = ? " ;
= 12.5 ;
______________________________________________
so " 5/8 = ?/100 " ;
Since we multiply the denominator, "8" ; by "12.5" , to get:
"100" (the denominator in the other fraction);
we multiply the numerator, "5" ; by "12.5" ; to get:
"2" (the denominator in the other fraction):
______________________________________________
→ " [tex]\frac{5}{8} = \frac{(5*12.5)}{(100*12.5)} = \frac{62.5}{100}[/tex] ;
______________________________________________
→ [tex]\frac{62.5}{100} = 62.5 % .
______________________________________________
Hope this helpful to you!
Wishing you the best!
______________________________________________
Given that Ray B A bisects ∠DBC, which statement must be true? m∠ABD = m∠ABC AB ≅ BC B is the midpoint of DC. m∠DBC = 90°
Answer:
A.[tex]m\angle ABD=m\angle ABC[/tex]
Step-by-step explanation:
We are given that a ray BA bisects angle DBC.
We have to find true statement .
Angle bisector property:When a ray bisect any angle then the angles made by bisection of angle are equal.
When ray BA bisects angle DBC
Then, [tex]m\angle ABD=m\angle ABC[/tex]
By angle bisector property.
Therefore, option A is true.
Answer:A.[tex]m\angle ABD=m\angle ABC[/tex]
Answer:
A
Step-by-step explanation:
Because I said this was the answer. I know all.
PLZ HURRY IT'S URGENT!!
Which shows the phrase "the difference between a number and 10" as a variable expression?
x−10
10x−10
x + 10
−10x
Answer: x-10
Since you're finding the difference of a number, x, and 10, you would do x-10.
Final answer:
The variable expression for "the difference between a number and 10" is represented by x − 10, which implies the subtraction of 10 from a variable x.
Explanation:
The phrase "the difference between a number and 10" as a variable expression is represented by x − 10. When we discuss 'the difference' in mathematical terms, we are referring to the result of subtracting one number from another. Here, whatever the unknown number (represented by the variable x) is, we are subtracting 10 from it.
Anyone know the answer to this geometry problem?
Answer:
540°
Step-by-step explanation:
The sum of the interior angles of a polygon is:
(n-2)*180
where n = number of sides
Here you have :
(5 - 2)*180 = 540°
El costo por kilo de queso chihuahua, es de 78. el total de queso comprado el dia anterior fue de 195. que fraccion del total de queso chihuahua queda
Answer: [tex]\frac{3}{8}\ kg[/tex]
Step-by-step explanation:
The table attached is part of the exercise (Without the table the question was incomplete).
We know that the cost of 1 kilogram of Chihuahua cheese is 78 and the Chihuhua cheese bought the day before cost 195.
The first step is to calculate the amount of cheese bought with 195:
[tex]\frac{195}{78}=\frac{5}{2}\ kg[/tex]
Now, we need to add the fractions provided in the table (This table shows the amount of cheese that was used in that day). Then:
[tex]\frac{1}{2}\ kg+\frac{7}{8}\ kg+\frac{3}{4}\ kg=\frac{17}{8}\ kg[/tex]
Finally, in order to find what fraction of Chihuahua cheese is left, we must subtract [tex]\frac{5}{2}\ kg[/tex] and [tex]\frac{17}{8}\ kg[/tex]:
[tex]\frac{5}{2}\ kg-\frac{17}{8}\ kg=\frac{3}{8}\ kg[/tex]
A company had the following direct materials cost information:
Standard costs assigned: Direct materials standard cost (405,000 units @ $2/unit) $810,000
Actual costs: Direct Materials costs incurred (403,750 units @ $2.20/unit) $888,250
What was the cost variance?
a) $2,500 Favorable.
b) $78,250 Favorable
c) $78.250 Unfavorable
d) $80,750 Favorable.
e) $80,750 Unfavorable.
Answer:
Option c) $78,250 unfavorable
Step-by-step explanation:
The given information in the question :
Standard cost = $810,000
Actual cost = $888,250
Cost variance can be calculated as using the following formula :
Cost variance = standard cost - actual cost
= 810,000 - 888,250
= ($78,250) unfavorable
Favorable indicates how much under budget the project.
unfavorable indicates how much over budget the project.
Therefore, Option c) 78,250 unfavorable is the answer.
Wayne is hanging a string of lights 58 feet long around the three sides of his patio, which is adjacent to his house. The length of his patio, the side along the house, is 6 feet longer than twice its width. Find the length and width of the patio.
Answer:
The length of the patio is 32 ft and the width is 13 ft
Step-by-step explanation:
see the attached figure to better understand the problem
Let
L ----> the length of his patio
W ---> the width of his patio
we know that
[tex]L+2W=58[/tex] ----> equation A
[tex]L=2W+6[/tex] ----> equation B
substitute equation B in equation A and solve for W
[tex]2W+6+2W=58[/tex]
[tex]4W+6=58[/tex]
[tex]4W=58-6[/tex]
[tex]4W=52[/tex]
[tex]W=13\ ft[/tex]
Find the value of L
[tex]L=2W+6[/tex] ----> [tex]L=2(13)+6=32\ ft[/tex]
therefore
The length of the patio is 32 ft and the width is 13 ft
The required patio length(L) = 32 and width(w) = 13.
Given that,
Wayne is hanging a string of lights 58 feet long,
And the side along the house, is 6 feet long.
We have to find,
The length and width of the patio.
According to the question,
Let, the length of his patio be L and width w,
Wayne is hanging a string of lights 58 feet long around the three sides of his patio, which is adjacent to his house.
L + 2W = 58
And The length of his patio, the side along the house, is 6 feet longer than twice its width.
L = 2W + 6
Solving the equation putting the of L from equation 2 in equation 1,
= 2W + 6 + 2W = 58
= 4W = 58 - 6
= 4W = 52
= W = [tex]\frac{52}{4}[/tex]
= W = 13
And L = 2(13) + 6 = 32
Patio length(L) = 32 And width(w) = 13.
Hence , The required patio length(L) = 32 And width(w) = 13.
For the more information about Measurement click the link given below.
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For a certain commodity the supply equation is given by S = 2p + 5 At a price of $1, there is a demand for 19 units of the commodity. If the demand equation is linear and the market price is $3, find the demand equation.
Answer:
The demand equation is: D=-4p+23
Step-by-step explanation:
To get started, we should keep in mind that the market price (p=3) occurs when supply equals demand ,therefore when p=3
S=2(3)+5=11
Thus, when p=3 D=11 and, according to the problem when p=1 D=19.
We already know two points on the demand curve. Great!
The demand equation is linear, so it has form D=bp+c.
The variable b is the slope of the demand linear equation . It can be computed through the formula
[tex]b=\frac{y2-y1}{x2-x1}[/tex]. equation 1
Substituting the two points (3,11) and (1,19) on equation 1.
[tex]b=\frac{19-11}{1-3} =\frac{8}{-2}[/tex]
b=-4
Now we can find the value of intercept of the demand equation c trough point-slope form y-y1=b(x-x1).
We can use any of the points. Let's take (3,11) and write in point-slope :
y-11=-4(x-3)
y=-4x+11+12
y=-4x+23
Rewrite the linear equation according our variables D and p
D=-4P+23
Finally we found the demand equation !