Answer:
70
Step-by-step explanation:
the least common multiple of 10 and 14 will be the answer
the prime factorization of 10 is 2 and 5
the prime factorization of 14 is 2 and 7
so you can multiply the number in common, 2, by the ones not common, 5 and 7
2 x 5 x 7 = 70
The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a. M. H = 0. 5 cosine (StartFraction pi Over 12 EndFraction t) 9. 5 h = 0. 5 cosine (StartFraction pi Over 6 EndFraction t) 9. 5 h = cosine (StartFraction pi Over 12 EndFraction t) 9 h = cosine (StartFraction pi Over 6 EndFraction t) 9.
The motion of the hour hand of a clock is a periodic motion that repeats every 12 hours.
The equation that can be used to models the height as a function of time, based on the given options, is presented as follows; [tex]\displaystyle \underline{ H = 0.5 \cdot cos \left(\frac{\pi}{6} \cdot t \right) + 9.5}[/tex]Reasons:
The given parameters are;
The variation of the height of the tip of the hour hand = 9 feet to 10 feet
At t = 0, the time = 12.00 a.m.
Required: The equation that can be used to model the height as a function of time.
Solution:
The general form of the cosine function is presented as follows;
y = a·cos(b·x - c) + d
The amplitude = a
[tex]\displaystyle a = \mathbf{ \frac{Maximum \ value -Minimum \ value}{2}}[/tex]
Therefore;
[tex]\displaystyle a = \frac{10 -9}{2} = 0.5[/tex]
b = The cycle speed
The period, T, is given as follows;
[tex]\displaystyle T = \mathbf{ \frac{2 \cdot \pi}{b}}[/tex]
The period of a block, T = 12 hours
Therefore;
[tex]\displaystyle b = \frac{2 \cdot \pi}{T}[/tex]
[tex]\displaystyle b = \frac{2 \cdot \pi}{12} = \mathbf{ \frac{ \pi}{6}}[/tex]
[tex]\displaystyle d = \mathbf{ \frac{Maximum \ value +Minimum \ value}{2} = \frac{10 + 9 }{2}} = 9.5[/tex]
At t = 0, H = The highest point = 10 ft.
Which gives;
[tex]\displaystyle H = \mathbf{0.5 \cdot cos \left(\frac{\pi}{6} \times 0 -c\right) + 9.5} = 10[/tex]
[tex]\displaystyle cos \left( -c\right) = \frac{0.5}{0.5} = 1[/tex]
-c = arcos(1) = 0
-c = 0
c = 0
The equation is therefore;
[tex]\displaystyle H = \mathbf{0.5 \cdot cos \left(\frac{\pi}{6} \cdot t \right) + 9.5}[/tex]
The above equation is the same as; H = 0.5cosine (StartFraction pi Over 6 EndFraction t) + 9.5
Learn more about the cosine function here:
https://brainly.com/question/4458343
https://brainly.com/question/24368105
Simplify the expression. Explain each step 7(4y)
Answer: 28 y
Step-by-step explanation: All you really have to do is multiply 7 by 4y. 7(4y) 28y
Please guys the surface area of the pyramid... I will mark you brainliest
Answer:
I can answer this but all you have to do is get the length, weight, and height and multiply it. I was going to do it but I could it find the height, and width.
If the slope of a line is 2/3 and one point is (1, 1), what could be another point?
Answer:
(3,4)
Step-by-step explanation:
My old teacher taught me a trick for this. Treat the first number like the y and the second like the x. Count Accordingly from there.
Highlighter pens cost $3. 86 per set at an office supply store. Which equation can be used to determine the price, P, of n sets of these pens? n = 3. 86P P equals 3. 86 over n n equals 3. 86 over P P = 3. 86n.
Answer:
Total = ($3.86)n, but it ids not among the answer options.
Step-by-step explanation:
P would be equal to the price per pen set ($3.86) times the number of pen sets sold, n.
Total, P = ($3.86)n
I translated the paragraph into these options:
n = 3. 86P No, n = P/3.86
P = 3. 86/n No, P = 3.86n
n = 3. 86/P No, n = P/3,86
P = 3. 86n.
Reed compró 1.8 libras de frijoles. Los frijoles cuestan
$1.27 por libra. ¿Cuál fue el precio total de los frijoles que compro Reed?
Answer:
1.27? :v
Step-by-step explanation:
porque la libra cuesta 1.27 y el solo compro 1.8? la verdad no tiene sentido esta pregunta o quizas abra que hacer una ecuacion...en fin suerte.
PLEASE PLEASE HELP
ME!!!
Write a two-column proof.
I WILL GIVE BRAINLIEST TO BEST ANSWER! PLS HELP!
refer to images for question
MUST WRITE FULL PROOF
Proof:-
In ∆TOP and ∆ZAP
[tex]\because\sf\begin{cases}\sf <O\cong <A(Given)\\ \sf TO\cong AZ(Given)\\ \sf <TPO\cong <ZPA(Opposite angles)\end{cases}[/tex]
Hence
∆TOP[tex]\cong[/tex]∆ZPA(Side-Angle-Side)
Step-by-step explanation:
Statement Reason
∠O ≅ ∠A Given
TO ≅ AZ Given
∠OPT and ∠ZPA are vertical angles Vertical angles theorem
∠OPT ≅ ∠ZPA Definition of vertical angles
ΔTOP ≅ ΔZAP Angle - angle -side AAS postulate
= 82.2×3.6 Show your working out
3-(-5)=3+?
Not sure what this was
Answer:
5
Step-by-step explanation:
3 - ( - 5 )
= 3 + 5
3 + ? = 3 + 5
? = 5
Three men can build a wall in 8 days. How long will it take them if they have the help of 2 boys? Assume that each boy works half as fast as each man.
(with explanation pls)
Answer:
6 days
Step-by-step explanation:
2 boys that each work half as fast as the men is equivalent to having one extra man. So instead of 3 men we have 4. 4/3 the manpower means 3/4 the time. 3/4 of 8 is 6.
Answer:
6 days.
Step-by-step explanation:
The 3 men can build 1/8 of a wall in 1 day.
So 1 man can build 1/24 wall in 1 day.
So 1 boy can build 1/48 in 1 day and 2 boys can build 1/24 wall in 1 day.
So we have the equivalent of 4 men working and they can build 4 * 1/24
= 1/6 of a wall per day
So the answer is 6 days.
Evaluate the equation:
4z = 10
z =
Answer:
z = 2.5
Step-by-step explanation:
4z = 10
---- -----
4 4
z = 2.5
hope this helps! :D
have a miraculous day, and brainliest is immensely appreciated!! <3
Her Packet.pdf + 127% 7. Approximately 4% of the population has blonde hair, and 10% of the population has blue eyes. If 75% of people with blonde hair have blue eyes, what percent of the population has blue eyes without blonde hair? Show your work.
Using proportions, it is found that 7% of the population has blue eyes without blonde hair.
10% of the population has blue eyes. These 10% are composed by:
75% of 4%(have blonde hair).x% of 96%(do not have blonde hair)Hence, the relation according to the proportion of 10% is:
[tex]0.75(0.04) + 0.96x = 0.1[/tex]
[tex]x = \frac{0.1 - 0.75(0.04)}{0.96}[/tex]
[tex]x = 0.0729[/tex]
Out of the entire population:
0.0729(0.96) = 0.07
7% of the population has blue eyes without blonde hair.
You can learn more about proportions at https://brainly.com/question/24372153
estimate the area hurry.
Answer:
32.5 and 30
Step-by-step explanation:
I counted the unit squares one by one.
Hope this helped! :)
4. Does the scatterplot have positive correlation, negative correlation, or no correlation?
Negative correlation
Positive correlation
No correlation
Answer:
Negative Correlation
Step-by-step explanation:
The plot looks like it's going downwards. If it was an equation, it'd be something with y = -x +b.
A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 3 inches. A random sample of 41 fish is taken from the tank. Let x be the mean sample length of these fish. What is the probability that x is within 0.5 inch of the claimed population mean? (Round your answer to four decimal places.)
Answer:
0.5160
Step-by-step explanation:
Let us assume that the length of fishes in the tank is normally distributed. Thus, x is the random variable representing the length of fishes in the tank. Since the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = standard deviation
number of samples
From the information given,
µ = 15
σ = 4
n = 31
We want to find the probability that x is between (15 - 0.5) inches and (15 + 0.5) inches. The probability is expressed as
P(14.5 ≤ x ≤ 15.5)
For x = 14.5
z = (14.5 - 15)/(4/√31) = - 0.7
Looking at the normal distribution table, the probability corresponding to the z score is 0.2420
For x = 15.5
z = (15.5 - 15)/(4/√31) = 0.7
Looking at the normal distribution table, the probability corresponding to the z score is 0.7580
Therefore,
P(14.5 ≤ x ≤ 15.5) = 0.7580 - 0.2420 = 0.5160
The expression 2,500(1.095)x represents the value of an investment after x years. What is the meaning of the 2,500?
Answer:
The value of the investment
Step-by-step explanation:
PLEASE HELPPPP! ANYTHING U CAN ANSWER WOULD BE SOOO GREAT :) (AND NO ITS NOT A VIRUS)
Answer:
but what if it is a virus?
Step-by-step explanation:
Answer:
isnt oit iron pick
Step-by-step explanation:
HELP!!!
‐6x – 1 = 23
Please do not just post the answer please explain how you got the answer. Whoever explains best gets brainliest!
Answer:
-4
Step-by-step explanation:
23+1=24
24/-6=-4
Help help help help help math
Answer:
8
Step-by-step explanation:
2. The graph represents the amount
of water, y, left in a 13.5-gallon tub
after x minutes. What is the slope of
the line? What does the slope mean
in this context?
Answer:
Slope: -3/2
With the question, we can determine that the slope with two points: (0,13.5) and (9,0). To calculate use the equation [tex]\frac{y2-y1}{x2-x1}[/tex] and get [tex]\frac{0-13.5}{9-0} =\frac{-13.5}{9} =\frac{-3}{2}[/tex]
This slope means that the water is decreasing at a rate of 3/2 gallons per minute.
How to expand Expand 7n-3+1-2n
Answer:
5n-2
Step-by-step explanation:
collect like terms
-> (7n-2n)+(-3+1)
simplify
=> 5n-2
Solve the following system of equations using the substitution method.
x = 2y
2x + 5y = 9
From the given system of equation x = 2y and 2x + 5y = 9, using the substitution method we get the value of y = 1.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
We have given system of equation
x = 2y
2x + 5y = 9
Using the substitution method
2(2y) + 5y = 9
4y + 5y = 9
9y = 9
y = 1
Learn more about solving equations here:
https://brainly.com/question/18015090
#SPJ2
Match the vocabulary word with the correct definition,
1. coefficient
a number, a variable, or the product
of a number and variable(s)
a letter used to represent an
unknown number
The number in front of a variable in
2. constant
3. term
a term
a single term, multiple terms
connected by an addition or subtraction
sign
a number, a term containing no
4. variable
5. expression
variables
TURNITIN
NEXT QUESTION
READ NEXT SECTION
ASK FOR HELP
Answer:
Definitions matched below with vocabulary wordsStep-by-step explanation:
A number, a variable, or the product of a number and variable(s)
→ 3. termA letter used to represent an unknown number
→ 4. variableThe number in front of a variable in a term
→ 1. coefficientA single term, multiple terms connected by an addition or subtraction sign
→ 5. expressionA number, a term containing no variables
→ 2. constantHelp me Please no bots I need help
Answer:
y = 2/3x + 3/2
Step-by-step explanation:
18 inches is 3/2 feet. 8 inches is 2/3 feet.
The equation will have a slope of 2/3 ft per year, and an initial value of 3/2 ft.
y = 2/3x + 3/2
please help me asap plz
Unit rate is the conversion of one unit to another unit with its standard conversion.
The width of the gymnasium in the blueprint is 4.75 inches.
What is unit conversion?Unit rate is the conversion of one unit to another unit with its standard conversion.
Example:
1 minute = 60 seconds
1 km = 100 m
1 m = 100 cm
1 feet = 12 inches
We have,
Gymnasium:
Length = 88 feet
Width = 76 feet ____(1)
Blueprint:
Gymnasium:
Length = 5.5 inches
This means,
88 feet = 5.5 inches
Divide both sides by 88.
1 feet = 0.0625 inches ____(2
The width of the gymnasium on the blueprint.
From (1) and (2)
76 feet
= 76 x 1 feet
= 76 x 0.0625 inches
= 4.75 inches.
Thus,
The width of the gymnasium in the blueprint is 4.75 inches.
Learn more about unit conversion here:
https://brainly.com/question/13899873
#SPJ2
What’s
9 times 13 1/2
Answer:
answer is 121.5
Step-by-step explanation:
Answer:
121.5
Step-by-step explanation:
first make 13 1/2 into a mixed fraction which is 27/2 then multiply by 9/1 you should get 243/2 and once you divide, you should have 121.5
What is 13/12 as a percentage?
Serious help needed what is the domain and range
Answer:
domain: all real numbersrange: -1 ≤ y ≤ 5 or -1 ≤ y < ∞Step-by-step explanation:
The arrows on the ends of the graph mean the graph extends indefinitely left and right. The domain is the horizontal extent of the graph, so it extends from -∞ to +∞, all real numbers.
__
The upward slant of the graph at the ends is ambiguous regarding the vertical extent of the graph. It could mean either of ...
the graph oscillates indefinitely between the values -1 and +5, orthe graph continues upward toward +∞We expect the latter case would be drawn with the ends of the arrows above the peak value shown. However, oscillation tends to involve a certain symmetry, and the graph has no symmetry about the local minimum points. In short the usual clues to the vertical extent are missing. Your guess is as good as mine.
The range could be [-1, 5], or it could be [-1, ∞). We cannot tell from this graph.
_____
Additional comment
The shape of the graph does not seem to match that of a 4th-degree polynomial, so we're not at all certain what sort of function is being plotted here. (A 4th-degree polynomial gets steeper beyond the outside zeros, rather than flatter, as shown here.) A couple of different functions with the approximate characteristics shown are graphed in the attachment.
Ned had 76 boxes. together the boxes weighed 723 kilograms. About how much did each box weigh
Answer: ~9.51 kilograms each.
Step-by-step explanation: 723/76=9.5131