1:00 a.m. (and 3:00 a.m., and 5:00 a.m.)
Step-by-step explanation:The problem is to find the least common multiple (LCM) of the barking intervals. One way to find the LCM is to find the product of the factors of the numbers.
... 5 = 5 . . . . a prime number
... 8 = 2³
... 12 = 2²×3
The factor 2³ is a multiple of the factor 2², so we only need 2³ in our final product.
The LCM is then ...
... 2³×3×5 = 120 . . . . minutes
The dogs will all bark together every 120 minutes (2 hours).
2 hours after 11 p.m. is 1 a.m.
_____
The problem statement doesn't say whether Ms. Li was awakened multiple times. The dogs will bark together again at 3 a.m., 5 a.m. and (possibly) 7 a.m.
The time when Ms. Li was awakened by the dogs Lola, Patch and Lady barking together was calculated using the concept of least common multiple (LCM). The LCM of the intervals the dogs bark (5, 8, and 12 minutes) is 120 minutes or 2 hours. Therefore, Ms. Li was awakened at 1:00 am.
Explanation:This problem is a least common multiple (LCM) problem in Mathematics. The dogs Lola, Patch, and Lady started barking together at 11:00 pm. Lola barked every 5 minutes, Patch every 8 minutes, and Lady every 12 minutes. The number that is divisible by all of 5, 8, and 12 is their LCM.
To find the LCM of 5, 8, and 12, list the multiples of each number. The LCM is the smallest number that occurs in each list. In this case, the LCM is 120.
So they all barked together 120 minutes, or 2 hours, after 11:00 pm. Therefore, Ms. Li was awakened at 1:00 am.
Learn more about Least Common Multiple here:https://brainly.com/question/30060162
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on a road map of pennsylvania, the distance from philaephia to washington d.c. is 6.8 centimeters. whatis the actual distance between the cities if the mape scale is 2 centimeters = 40 miles.
Answer:
136 miles
Step-by-step explanation:
The map distance is 3.4 times 2 cm, so the road distance will be 3.4 times 40 miles, or 136 miles.
Re-arrange the BMI formula for h, height.
Answer:
[tex]Height=\sqrt{\frac{weight}{\text{body mass index}}}[/tex]
Step-by-step explanation:
We have BMI formula that is body mass index formula which is:
[tex]\text{Body mass index}=\frac{weight}{height^2}[/tex]
Now, we have to arrange the formula for height:
we will rearrange the terms and derive the formula for height in terms of weight and height.
[tex]Height^2=\frac{weight}{\text{body mass index}}[/tex]
Hence, the required result is:
[tex]Height=\sqrt{\frac{weight}{\text{body mass index}}}[/tex]
Identify the equivalent trigonometric values. A sin 17°, cos 17° B cos 29°, sin 61° C sin 78°, cos 102° D cos 83°, cos 7°
Option B (cos 29° and sin 61°) contains equivalent trigonometric values, as the angles are complementary and adhere to the identity sin(90° - x) = cos(x).
The question asks us to identify equivalent trigonometric values out of the given pairs. The equivalent values will have the same numerical value if their angles are complementary (i.e., they add up to 90°) because of the identity sin(90° - x) = cos(x). Considering this, let's evaluate the provided pairs:
A: sin 17° and cos 17° are not complementary, so they are not equivalent.
B: cos 29° and sin 61° are complementary (29° + 61° = 90°), hence equivalent.
C: sin 78° and cos 102° are not complementary, and 102° is greater than 90°, so they are not equivalent.
D: cos 83° and cos 7° are not complementary, but they are both cosines of different angles, so they are not equivalent.
Thus, the pair with equivalent trigonometric values is B: cos 29° and sin 61°.
For someone who is clinically underweight and has been encouraged by their doctor to gain a few pounds, how many calories per day should someone consume to gain 2 pounds in two weeks assuming they burn 2000 calories per day?
Answer:
2500 total calories per day.
Step-by-step explanation:
Assuming that 3500 excess calories produces 1 pound gain, 7000 excess calories required for 2 pound gain
to be accomplished in 14 days
7000/14 = 500 excess calories per day
2000 required calories per day
2500 total calories per day.
The cost of an office chair is $159 and the markup rate is 24% of the cost. What is A. the dollar markup and B. the selling price?
A. The dollar amout of the markup is found by multiplying the markup rate by the dollar cost. "24% of cost" means "24% × cost". Of course, you know that 24% = 24/100 = 0.24.
... markup = 0.24 × cost = 0.24 × $159 = $38.16
B. The markup is the amount added to the cost to get the selling price. It is the amount by which the cost is marked up.
... selling price = cost + markup = $159.00 +38.16 = $197.16
What numbers are on the nnumber line starting with the number 1 then it has 10 spaces then 1.01 then 10 spaces then 1.02 then 10 spaces then 1.03 then 10 spaces then 1.04.
You are referring to the thousandths spot.
1.00(0)000001
So, between any given number n to n.01 there are 10 numbers.
n.001, n.002, n.003, ..., n.01
In the △PQR, PQ = 39 in, PR = 17 in, and the altitude PN = 15 in. Find QR.
Final answer:
To find the length of QR, we used the Pythagorean theorem on triangle PNQ to find NQ, then added it to PR, resulting in QR measuring 53 inches.
Explanation:
To find the length of side QR in △PQR, we can apply the Pythagorean theorem to one of the right triangles formed by the altitude PN. The triangle we'll use is △PNQ, where NQ is part of QR, and PN is given as 15 in.
Firstly, we can calculate NQ using the Pythagorean theorem:
PN² + NQ² = PQ²
15² + NQ² = 39²
NQ² = 39² - 15²
NQ² = 1521 - 225
NQ² = 1296
NQ = √1296
NQ = 36 in
Since PR = 17 in, we can conclude that NR is the difference between PR and NQ:
NR = PR - NQ
NR = 17 - 36
NR = -19 in
The negative value indicates a mistake since lengths cannot be negative. Therefore, we should use the entire length of PQ instead:
QR = NQ + NR
QR = 36 + 17
QR = 53 in
Thus, side QR measures 53 inches.
What is the maximum Number of different sizes of faces that a rectangular Prism can have.
Answer:
3
Step-by-step explanation:
For a rectangular prism of dimensions L × W × H, pairs of opposite faces will have dimensions ...
L × WW × HH × LThese will be three different sets of dimensions if L, W, and H are all different lengths.
you pay $2.76 for 6 bagels. what is the unit price?
a) $0.46 per bagel
b)$0.48 per bagel
c)$0.52 per bagel
d)$0.44 per bagel
Answer:
a) $0.46 per bagel
Step-by-step explanation:
When you are looking for a unit price, you have to divide the price in this instance by the amount of items that you have. For example, here you just have to divide $2.76 by 6 to get $0.46.
Hope I could help! :)
If (x-y)^2=100 and xy=20. what's the value of x^2+y^2?
Answer: The value of [tex]x^2+y^2[/tex] is 140
Step-by-step explanation:
We are given an expression:
[tex](x-y)^2=100[/tex]
And,
xy = 20
Using the identity:
[tex](a-b)^2=a^2+b^2-2ab[/tex]
Solving the expression:
[tex]x^2+y^2-2xy=100[/tex]
Putting the value of 'xy' in above equation, we get:
[tex]x^2+y^2-2(20)=100\\\\x^2+y^2=100+40\\\\x^2+y^2=140[/tex]
Hence, the value of [tex]x^2+y^2[/tex] is 140
The cost of a laptop computer in 2007 was $1,250. In 2009, the price decreased to $1,100.
A.) Find the percent decrease in the price of the laptop from 2007 to 2009.
B.) Find the percent decrease in the price of the laptop from 2009 to 2010 if the price decreased by $165 in 2010.
Given : The Cost of Laptop in 2007 is $1250
Given : The Cost of Laptop in 2009 is $1100
Decrease in Price of Laptop from 2007 to 2009 : (1250 - 1100) = $150
A) Percent Decrease in the Price of the Laptop from 2007 to 2009 is :
[tex]\mathsf{\implies \frac{Decrease\;in\;Price\;of\;Laptop\;from\;2007\;to\;2009}{Price\;of\;Laptop\;in\;2007} \times 100}[/tex]
[tex]\mathsf{\implies \frac{150}{1250} \times 100}[/tex]
[tex]\mathsf{\implies 12\%}[/tex]
Given : Decrease in Price of Laptop from 2009 to 2010 = $165
B) Percent Decrease in the Price of the Laptop from 2009 to 2010 is :
[tex]\mathsf{\implies \frac{Decrease\;in\;Price\;of\;Laptop\;from\;2009\;to\;2010}{Price\;of\;Laptop\;in\;2009} \times 100}[/tex]
[tex]\mathsf{\implies \frac{165}{1100} \times 100}[/tex]
[tex]\mathsf{\implies 15\%}[/tex]
The percent decrease in laptop prices, use the formula ((Original Price - New Price) / Original Price) x 100%. The percent decrease from 2007 to 2009 is 12%, and from 2009 to 2010 is 15% with a $165 decrease.
The cost of a laptop computer in 2007 was $1,250. In 2009, the price decreased to $1,100.
A.) To find the percent decrease from 2007 to 2009, you use the formula: Percent decrease = ((Original Price - New Price) / Original Price) x 100%
Substitute the values: ((1250 - 1100) / 1250) x 100% = 12%
Therefore, the percent decrease in the price of the laptop from 2007 to 2009 is 12%.
B.) To find the percent decrease from 2009 to 2010 with a $165 decrease, you apply the same formula: Percent decrease = ((Price in 2009 - Price in 2010) / Price in 2009) x 100%.
Substitute the values: ((1100 - (1100 - 165)) / 1100) x 100% = 15%
Therefore, the percent decrease in the price of the laptop from 2009 to 2010 is 15%.
Which graph represents f(x)=1/2x^2 ?
Answer:
See below.
Step-by-step explanation:
The one that looks like the attachment.
It is vertically shortened from f(x) = x^2, so appears wider than f(x) = x^2 does. The vertex is still at (0, 0), it still opens upward, and it remains symmetrical about the y-axis.
[tex]f(x)=\dfrac{1}{2}x^2\\\\for\ x=0\to f(0)=\dfrac{1}{2}(0)=0\to(0,\ 0)\\\\for\ x=\pm1\to f(\pm1)=\dfrac{1}{2}(\pm1)^2=\dfrac{1}{2}(1)=\dfrac{1}{2}\to\left(-1,\ \dfrac{1}{2}\right);\ \left(1;\ \dfrac{1}{2}\right)\\\\for\ x=\pm2\to f(\pm2)=\dfrac{1}{2}(\pm2)^2=\dfrac{1}{2}(4)=2\to(-2,\ 2);\ (2,\ 2)\\\\for\ x=\pm4\to f(\pm4)=\dfrac{1}{2}(\pm4)=\dfraC{1}{2}(16)=8\to(-4,\ 8);\ (4,\ 8)[/tex]
Find the value of the polynomial:
6a^3–a^10+4a^3+a^10–8a^3+a for a=−3
-57
Step-by-step explanation:We can collect terms to simplify the arithmetic.
... = a^3(6 +4 -8) +a^10(-1 +1) +a
... = 2a^3 +a
... = a(2a^2 +1)
For a = -3, this is
... -3(2(-3)² +1) = -3(2·9 +1)
... = -3·19 = -57
The graph shows how far a snail traveled over time. What information can you draw from the point (3,18) on the graph?
The point (3, 18) on the graph means the snail's position when the time is 3 units of time from the time reference is 18 units of distance from the the reference point for distance.
_____
We cannot conclude anything else. We don't know if the snail is moving (or has moved), or if there are any other points on the graph.
Answer: B) The snail traveled 18 ft in 3 h.
Step-by-step explanation: If you look at the graph they graphed (3, 18) the left side says distance (ft) and the dot is to the right of the 18 so it traveled 18 feet. At the bottom it says time (h) and the dot above the 3 so it took to travel 8 feet.
Hope This Helped ^_^
!!!!!!!!!!!! Helppppppp !!!!!!!!!!!!
Which of the following points lie in the solution set to the following system of inequalities?
y ≤ x − 5
y ≥ −x − 4
A. (−5, 2)
B. (5, −2)
C. (−5, −2)
D. (5, 2)
Answer:
B. (5,-2)
Step-by-step explanation:
Plug in X and Y, verify accuracy
Six friends go out to lunch and decide to split the bill evenly. The bill comes to $61.56. How much does each person owe?
Answer:
each person owe $10.26
Step-by-step explanation:
Six friends go out to lunch and decide to split the bill evenly. The bill comes to $61.56.
Total bill for 6 friends = $61.56
To find bill cost for 1 person we divide the total cost by 6
Bill for each person = [tex]\frac{61.56}{6}= $10.26[/tex]
So each person owe $10.26
In a parallelogram ABCD point K belongs to diagonal BD so that BK:DK=1:4. If the extension of AK meets BC at point E, what is the ratio of BE:EC?
Answer:
BE:EC= 1/3
Step-by-step explanation:
Given ABCD is a parallelogram, Point K is such that it belongs to diagonal BD so that BK:DK=1:4.
If we make an extension of AK which meets BS at point E, then using ΔDKA and ΔEKB, we have
∠DKA=∠EKB (Vertically opposite angles)
∠KDA=∠KBE (Alternate interior angles)
∠DAK=∠BEK (Alternate interior angles)
Thus by AAA similarity,ΔDKA≅ΔEKB
⇒[tex]\frac{AD}{BE}[/tex]= [tex]\frac{DK}{BK}[/tex],
Since, AD= BC,therefore
[tex]\frac{AD}{BE}[/tex]= [tex]\frac{BC}{BE}[/tex]= [tex]\frac{4}{1}[/tex]
Now, BC= BE+EC, ⇒[tex]\frac{BE+EC}{BE}[/tex]= [tex]\frac{4}{1}[/tex]
⇒1+[tex]\frac{EC}{BE} = \frac{4}{1}[/tex]
⇒[tex]\frac{EC}{BE}= 3[/tex]
Reciprocating on both the sides, we get
[tex]\frac{BE}{BC} = \frac{1}{3}[/tex]
What is the area of the rectangle shown on the coordinate plane? Enter your answer in the blank. Do not round at any steps.
12 units²
Step-by-step explanation:Counting half-squares around the perimeter of the rectangle, we find there are 10. Counting full squares inside the rectangle, we find there are 7. Then the total area is
... (1/2)·10 +7 = 12 square units
_____
Alternate calculation
The long side is the hypotenuse of a right triangle with legs 3, so has length 3√2. The short side is the hypotenuse of a right triangle with legs 2, so has length 2√2. The area is the product of these lengths, so is ...
.. area = (3√2)(2√2) = 6(√2)² = 6·2 = 12 . . . square units
Answer:
21
Step-by-step explanation:
PLZ HELP ME ASAP. I DONT UNDERSTAND
AND PLZ PLZ PLZ SHOW YOUR WORK
To find the rate of change, find the difference of people at the park at each given hour and divide that by the total number of hours in the given time frame.
Early Time interval:
Hour 1 there was 55 people.
Hour 3 there was 135 people.
The rate of change is 135 - 55 / 3-1 = 80/2 = 40 people per hour.
Late time interval:
Hour 3 had 135 people.
Hour 5 had 175 people.
The rate of change is 175 - 135 / 5-3 = 40/2 = 20 people per hour
20 is less than 40, so the late time interval had the smallest rate change.
help please? i would really appreciate it.
Answer:
The answer is option C i.e; y=0.9x-45
Step-by-step explanation:
When you substitute the values of x you have to get same values as given in the table
For example: substitute x=50 in the equation y=0.9x-45
Y= 0.9(50)-45
Y= 45-45
Y=0
Sophia puts $250 in the bank with a 2.5% annual interest rate compounded monthly. If Sophia does not touch his money, how much money will she have after four years? A) $260.00 B) $275.00 C) $275.95 D) $276.26
Answer:
D) $276.26Step-by-step explanation:
Deposited amount initially (P) = $250.
Rate of interest(r) = 2.5% compounded monthly = 0.025
Number of years (t) = 4.
Number of months in an year (n) = 12.
Formula for compound interest:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex].
Plugging values in formula, we get
[tex]A= 250(1+\frac{0.025}{12})^{12\times 4}[/tex]
[tex]A= 250(1.00208)^{48}[/tex]
[tex]A= 250\times \:1.10506[/tex]
A=276.26.
Therefore, correct option is D) $276.26.These prisms are similar. Find the volume of the larger prism in decimal form. Ratio 5:7. Volume of smaller Prism is 50 m3
Answer:
137.2 m³
Step-by-step explanation:
The ratio of volumes is the cube of the ratio of linear dimensions. The larger volume is ...
... V = (7/5)³ × 50 m³ = 2.744 × 50 m³
... V = 137.2 m³
pls help!!!
in which line is a mistake first made when solving the following system of equations by substitution? 2x - y =-4 3x + y = -9
line 1: 2x -y = -4
y= 3x-9
line 2: 2x-(3x-9)=-4
line 3: 2x-3x+9=-4
line 4: -1x + 9 = -4
line 5: -1x = -13
line 6: x = 13
Answer:
The very first line has an error.
Step-by-step explanation:
When you are solving the second system of equations for y, you need to subtract 3x from both sides and therefore it should be negative.
3x + y = -9
y = -3x - 9
Since the 3x isn't negative in the first line, there is an error.
Proportional Relationships Please help :3
Worth 25 per answer (i think cause i put 50 points)
Answer:
6
Step-by-step explanation:
Since the relationship is proportional, when y is increased by a factor of 3 from 7 to 21, so is x—from 2 to 2×3 = 6.
3. A family is tracking its spending habits. Over the past year, the grocery bill has ranged from $110 to $170. Suppose you were going to plot these points on a coordinate grid. (a) What is a good scale to use for the y-axis? Explain your reasoning. (b) What is a good interval to use for the y-axis? Explain your reasoning. Answer:
The best way to plot them is by month.
170 - 110 = $60.
We are supposed to plot in months and the above calculation is in year, convert it into months
60/5 = $5 each month
So, the coordinates would be 0, 110 1, 115 2, 120 3, 125
The month will be in the x axis and your money will be the Y axis
A suitable y-axis scale to plot spending habits ranging from $110 to $170 would start at $100 and go up to $180, while a good interval for the y-axis would be $10 to allow for clear plotting of values in whole dollars.
To answer the student's question about how to plot spending habits on a coordinate grid:
A good scale for the y-axis when plotting the family's grocery bills that range from $110 to $170 would be one that fits the entire range of values without being too cramped or too spread out. For instance, a scale that starts at $100 and goes up to $180 would allow all points to be plotted clearly. Since these are monetary values, maintaining a scale that reflects currency would be logical.A good interval for the y-axis could be multiples of $10 since this allows for clear and precise plotting of bills that are likely to be in whole dollars, making the graph easier to read while still being detailed enough to discern differences of $10.Permutations and Combinations!
how many 5 digit numbers can be formed that do not contain the digits 0 or 8?
Answer:
9×9×8×7×6= 27,216
Step-by-step explanation:
Your answer is :- 9×9×8×7×6= 27,216
Why did i multiply 9×9×8×7×6 ⤵️
Because we can fill each place of a five digit number with ten digits (0,1,2,3,4,5,6,7,8,9).
Now, let us assume the five digit number is abcde, where each alphabet represent a digit.
so according to our question a cannot be equal to 0 ( a≠0), because if a will be equal to zero then our number will be a four digit number. So a can be equal to 9 digits.
b digit can also be equal to 9 numbers. why??because we can place zero on the position of b and only one number will not be repeated which is a.
Now for c, d, e :- accordingly no number will be repeated so on the place of c, there can be 8 digits. On the place of d, there can be 7 digits. And on the place of e there can be 6 digits.
Therefore,
a×b×c×d×e=9×9×8×7×6=27,216
The graph of the function, f(x) = 3x^2 + x + 2, opens down/up and has a maximum/minimum value.
If the function has a ∪ shape (opens up), then it only goes so low—has a minimum value.
Any even-degree function with a positive leading coefficient will open up, so have a minimum. Your function is degree 2 (even) and has a leading coefficient of 3 (positive).
_____
Comment on other polynomial functions
If the leading coefficient of an even-degree function is negative, it will have an inverted-U shape (∩), so will have a maximum.
Any odd-degree function will have a generally rising (/) or generally falling (\) shape, depending on the sign of its leading coefficient. If positive, then rising; if negative, then falling.
Help please #10 if you can
Answer:
200,000 m
Step-by-step explanation:
We will multiply the length of the ant by the number of ants to find out how long the line is.
10 million is 10 with 6 zeros
20 * 10 ^-3 move the decimal 3 places to the left
20. * 10 ^-3 = .02
.02 * 10000000
200000
There are 12 apples in a basket. 5 of these apples are green. The rest of them are red. (a) What is the ratio of red apples to all apples in the basket? (b) What is the ratio of red apples to green apples?