The possible formula for the depth of water in tank is , D = 2.8 + 8 sin(π t/4) where t is time in hours.
Sinusoidally function, is defined as one of triagnometric function with a smooth, repetitive oscillation. "Sinusoidal" comes from "sine", function. We can write its equation in the following form y = A·sin(B(x - C)) + D
where, A --> amplitude
B--> period in form of pi
C--> phase or horizontal shift
D --> vertical shift
We have, the depth of water in a tank oscillates sinusoidally.
The smallest depth of water in tank = 6.6 feet
The largest depth of water in tank = 9.4 feet
We have to determine the formula of depth of water in tank as a function of time in hours .
For sinusoidal function,
Amplitude , A = average depth
= ( largest depth + smallest depth)/2
= (6.6 + 9.4)/2
= 16.0/2 = 8
Now, The period of 8 hours so, B = 2π/8
=> B = 45° = π/4
Also, upward shift , D is 9.4 - 6.6 = 2.8
Horizontal shift, C = 0
So, required function is D = 2.8 + 8 sin(π t/4) .
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if pam makes 250 dollars from making 15 pots, what is her piece rate?
Pam's piece rate is $16.67 for every pot she produces.
What is the rate?A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.
Pam's piece rate is the amount of money she earns for each pot she makes. In this case, she earned $250 for making 15 pots, so her piece rate is:
$250 ÷ 15 pots = $16.67 per pot
Therefore, Pam earns $16.67 for each pot she makes. This is a way of calculating her pay based on the number of units she produces, rather than by the hour.
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Rene makes $38,000 per year and pays about 35% of
his gross monthly income in federal and state taxes.
He wants to find an apartment to rent. Estimate how
much he can afford to pay for rent each month. Then
determine how much money he will have after taxes
and rent are paid.
PLEASE HELP
After the taxes and rent, the remaining amount in his gross pay is $5,700
The term gross income is defined as also known as gross pay when it’s on a paycheck is an individual’s total earnings before taxes or other deductions.
Here we have given that Rene makes $38,000 per year and pays about 35% of his gross monthly income in federal and state taxes.
And as we all know that If you live in a metropolitan city, your HRA is equivalent to 50% of your basic salary.
Therefore, the remaining amount in his hand is calculated as,
=> $38000 - [35% of income + 50% of income]
Here the 35% of income is
=> 38000 x 35/100
=> 380 x 35
=> 13300
Similarly, the 50 percent of the income is
=> 38000 x 50/100
=> 380 x 50
=> 19000
Then the remaining amount is calculated by apply the values on it, then we get,
=> $38000 - [$13300 + $19000]
=> $3800 - $32300
=> $5700
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How many dollars will Ms. Davis have saved after 30 weeks?
Ms. Davis has $54. 50 saved
• She will save $33. 25 each week for the next 30 weeks
• She will not spend any of the money
Enter your response here:
$1052 is the total saving og Ms. Davis after 30 weeks from the given point .
Given that:
Inital saving of Ms. Davis = $54.50
Ms. Davis has already saved $54.50 and plans to save an additional $33.25 each week for the next 30 weeks. This means that she will be adding a total of $33.25 x 30 = $997.50 to her savings over the next 30 weeks.
If she does not spend any of the money she has saved, her total savings will be :
sum of Initial saving and saving after 30 weeks
$54.50 + $997.50 = $1,052.00.
so the total saving is $1052.
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The three largest categories of motor vehicles are sedan, SUV, and minivan. Suppose
hat of the buyers in a particular community who now own a minivan, 18% will change to
an SUV and 20% will change to a sedan. Of the buyers who now own a sedan, 35% will
hange to a minivan and 20% will change to an SUV, and of those who now own an
SUV, 12% will buy a minivan and 32% will buy a sedan.
Draw a transition diagram that displays these changes.
On solving the provided question, we can say that - here in the percentage obtained = 40 => so, 40/100X100 = 40%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
here,
total is = 100
obtained = 40
so, 40/100X100 = 40%
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A sequence is represented by the explicit formula
The value of a₂₆ in the arithmetic sequence aₙ= 14 + 9n is 248.
The correct option is D.
What is an arithmetic sequence?A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
An arithmetic sequence,
aₙ= 14 + 9n
We have to find the value of a₂₆.
That means, n = 26.
Substitute the value of n = 26 to the sequence,
a₂₆ = 14 + 9(26)
a₂₆ = 14 + 234
a₂₆ = 248
Therefore, the value of a₂₆ is 248.
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Use the diagram to find.. (Trigonometry)
Answer:
Step-by-step explanation:
b and f
Determine whether the geometric series is convergent or divergent. 10 – 8 + 6.4 – 5.12 +... A. convergent B. divergent If it is convergent, find its sum. (If the quantity diverges, leave this blank.) _____
The given series is convergent and the sum S∞ is 5.555
Think about 10 - 8 - 6.4 - 5.12
If the common ratio of the series is between -1 and 1, then a geometric progression will be convergent.
the average ratio,
r = -8/10
⇒ r = -0.8
This equals 1 - 0.8 - 1.
The presented series is hence convergent.
Sum of series = S∞ = a/(1 - r)
Here, first term(a) = 10,
common ratio(r) = -0.8,
S∞ = a/(1 - r)
⇒ S∞ = 10/(1 - (-0.8))
⇒ S∞ = 10/(1 + 0.8)
⇒ S∞ = 10/1.8
⇒ S∞ = 5.555
Therefore, the given series is convergent and the sum S∞ is 5.555
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PLS HELP ASAP 50 POINTS!!!
Identify or mark the missing side or angle that would make triangle ABC congruent to triangle PDF by AAS
The angles that would make triangle ABC congruent to triangle PDF by AAS are ∠ ACB and ∠ PFD i.e. ∠ ACB = ∠ PFD.
What is triangle?Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.
Given:
The triangle ABC and PDF are concurrent by AAS,
The AAS concurrency required two angles and one side to be equal,
Here,
AB = PD,
∠ ABC = ∠ PDF
Now one more angle is required to be equal,
∠ ACB = ∠ PFD
Thus, the missing angle is ∠ ACB and ∠ PFD.
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F(x) = 3x -4 find each value of F(0)
Answer:
Step-by-step explanation:
Rewrite the function as an equation.
y
=
3
x
−
4
Use the slope-intercept form to find the slope and y-intercept.
Tap for fewer steps...
The slope-intercept form is
y
=
m
x
+
b
, where
m
is the slope and
b
is the y-intercept.
y
=
m
x
+
b
Find the values of
m
and
b
using the form
y
=
m
x
+
b
.
m
=
3
b
=
−
4
The slope of the line is the value of
m
, and the y-intercept is the value of
b
.
Slope:
3
y-intercept:
(
0
,
−
4
)
these ar the numbers and i need the ratio
thank you!
help me please its due tomorrow !!!!!!!!!!
help please
ill get in trouble!!!!
Answer:
1:3
Step-by-step explanation:
There are 260 eighth grade students at South Whitenardh middle school. All right grade students are required to enroll in either a music class or an art class. No students take both art and music classes. The number of students taking music classes is 14 more than twice the number taking art classes. Write an equation to represent the total number of eight grade students
178 students taking a music class and 82 students taking an art class
There was no clear question, but I'm assuming you want to know how many students are enrolled in music and painting classes.
Let x= the number of children enrolled in art classes.
number of children enrolled in music classes: 2x + 14
The overall number of children will be 260, including all of these children.
x+2x+14 = 260
3x=246 x=82 pupils attend an art lesson.
To find people taking music classes, enter x to 2x+14.
2(82)+14 = 178
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The complete question would be;
There are 260 eighth-grade students at South Whitemarsh Middle School. All eighth-grade students are required to enroll in either a music class or an art class. No students take both art and music classes. The number of students taking music classes is 14 more than twice the number taking art classes.
1
Which line is pointing to the cell body?
A. 1
B. 2
C. 4
D. 5
2
3
4
5
Image by Dhp 1080
The line 2 is pointing towards the body of the cell, in the given image of a neuron.
What is cell body?The soma, or cell body, is the spherical part of the neuron that houses the nucleus. The cell body is linked to the dendrites, which transport information to the neuron, and the axon, which sends information to other neurons.
When one neuron receives information from another, the dendrites send it to the cell body. Depending on the signal strength, the cell body may then send the information to the axon.
The cell body's role is to regulate all of the cell's functions. It has several important organelles that aid in this process. Organelles are tiny organelles found within cells that each perform a specific function. The nucleus is the most important organelle within the cell body.
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what part of 3$ is the sum of 7 dimes, 1 nickel and 3 pennies?
Answer:
7/60
Step-by-step explanation:
First, we would need to add up all of the coins and know their values.
1 dime (d) = 10¢
1 nickel (n) = 5¢
1 penny (p) = 1¢
An equation we can use will look something like this:
(d × 7) + (n × 1) + (p × 3) =?
Now just add the numbers and solve.
(10 × 7) + (5 × 1) + (1 × 3) = 78
Therefore, the total amount is 78¢.
Now to figure out how much 78¢ is out of $3, we can use an equation that looks something like this:
3 ÷ 0.78 = 3.84615385 or 7/60
So, this means that with 7 dimes, 1 nickel and 3 pennies it is 7/60 of $3.
The difference between the two groups compared will have more significance as the p-value becomes __________. The difference between the two groups compared will have more significance as the t-value becomes __________.
The significance of the difference between the two groups under comparison will increase as the p-value decreases. The significance of the difference between the two groups under comparison will increase as the t-value rises.
If there is a significant difference between two groups, what does that mean?A difference that is "statistically significant" does not necessarily have to be "large, important, or significant in terms of the utility of the finding"; it simply means that there is statistical evidence that there is a difference.
When the p-value exceeds the significance level, what does that mean?In general, when the null hypothesis H0 is true, our sample results could have happened by random chance alone when the p-value is "high" (i.e. greater than or equal to the significance level).
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Evaluating Linear Functions
The value of linear equations are f(x) = -17 and f(x) = -73 .
What is linear equation ?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).
Equation with two variables of degree one is referred to as a linear equation with two variables. Formal expression: ax+by+c=0, where a, b, c R & a, b 0.
A)
f(x) = -2x + 7 when x = -12f (x) = -2*12 + 7
= -24 + 7
= -17
f(x) = 5x - 13 when x = -14f(x) = 5*-14 - 13
= -60 -13
= -73
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Which variation is represented by this situation:
Martha earns $375 when she works 5 hours. How much will she earn
if she works 12 hours? Is it direct variation or inverse variation?
Direct variation is represented by this situation and she earn $900
if she works 12 hours.
What are direct variation and indirect variation?Direct variation describes a relationship whereby one measure directly affects the other when the first one changes. This is completely opposed by inverse variation. Learn the definitions of direct and inverse variations in this article, along with some instances that have been solved.
How do inverse and direct variations differ from one another?When x is not equal to 0, y = kx is the equation that describes the linear function known as direct variation. An equation of the form xy = k, where x is not equal to zero and k is a nonzero real number constant, describes the nonlinear function known as inverse variation.
5 hours = earns $ 375
1 hours = 375/5 = earns $ 75
12 hours = 75 12 = earns $ 900
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a sample of a radioactive isotope had an inital mass of 130 mg in the year 2010 and decays exponentially over time. a measurmentin the year 2012 found that the samples masshad decayed to 80 mgwjat would be the expected mass of the sample in the year 2021 to the nearest whole number
The expected mass of the sample in the year of 2021 is given as follows:
9 mg.
How to define the exponential function?An exponential function is defined as follows:
y = a(b)^x.
For which the parameters are given as follows:
a is the initial value.b is the rate of change.The initial mass was of 130 mg, hence the parameter a is given as follows:
a = 130.
In two years, the mass decayed to 80 grams, hence the parameter b can be obtained as follows:
b² = 80/130
b = square root(80/130)
b = 0.78446454055.
This means that the exponential function for the mass of the sample in x years after 2010 is given as follows:
y = 130(0.78446454055)^x.
2021 is 11 years after 2010, hence the expected mass is obtained as follows:
y = 130(0.78446454055)^11
y = 9 mg.
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Is y 2x 3 in slope intercept form?
Answer:
y=2x+3
Step-by-step explanation:
y=mx+b
y=2x+3
Simplify the following polynomial, then evaluate for x = -2
2x2 - 4x + 3x2 + x - 7
Answer:
[tex]5x^2-3x-7,\,\,f(-2)=19[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2-4x+3x^2+x-7\\f(x)=5x^2-3x-7\\f(-2)=5(-2)^2-3(-2)-7\\f(-2)=5(4)+6-7\\f(-2)=20-1\\f(-2)=19[/tex]
cant find the anwer help
Answer:
Wouldn't it be 68,844? Because 12 divided by 3 = 4 and 17,211 x 4 is 68,844. I could be wrong but im sure that im right?
Answer in explanation:
I went over it and your answer seems correct, but the problem says 'how much money, in dollars'
There are 12 months in a year
3 x 4 = 12
17,211 x 4 = 68,844
you wrote 67.844 so possibly changing to a comma would help!
I hope this helps!
What is the measure of m?
n
m
28
7
m = [? ] V
Give your answer in simplest form.
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
[tex]\cfrac{35}{m}=\cfrac{m}{7}\implies 245=m^2\implies \sqrt{245}=m\implies \sqrt{7^2\cdot 5}=m\implies 7\sqrt{5}=m[/tex]
Can you help me with this
30PTS 30PTS don’t explain just answer (it’s not 90)
Answer:
20
Step-by-step explanation:
110 -70 = 40 40/2= 20
Answer:
[tex] \sf \: x = {20}^{o} [/tex]
Step-by-step explanation:
Let's take the value of y as,
→ y = 90°
(Because, it is a right angle)
Forming the equation,
→ x + y + 70° = 180°
Now the value of x will be,
→ x + y + 70° = 180°
→ x + 90° + 70° = 180°
→ x + 160° = 180°
→ x = 180° - 160°
→ [ x = 20° ]
Hence, the value of x is 20°.
Andy and Trevor share 40 sweets in a ratio 11: 9
How many more sweets does Andy receive than Trevor does?
Answer:
Step-by-step explanation:
no
Answer:
22:18
Step-by-step explanation:
In this case, firstly you have to add 11 and 9 together, which makes 20.
Then, 40 ( number of sweets ), divided by 20 gives us 2.
This means that every piece, or block, of our ratio will be 2.
Therefore, the last step is multiplying 11x2 and 9x2.
So, Andy has 22 sweets an Trevor has 18.
n \triangle NOP,△NOP, \overline{PN}\cong \overline{OP}
PN
≅
OP
and \text{m}\angle P = 50^{\circ}.m∠P=50
∘
. Find \text{m}\angle O.m∠O.
The value of the measure of ∠O in the given triangle will be 65°
What is triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In ΔNOP;
PN ≅ OP
So, ∠O = ∠N
And, Measure of ∠P = 50°
Now,
In the ΔNOP;
The sum of all the three angles are 180°.
The value of the measure of ∠O = x
We get;
∠O + ∠N + ∠P = 180°
Substitute ∠P = 50° and ∠O = ∠N = x we get;
x + x + 50 = 180
2x + 50 = 180
2x = 180 - 50
2x = 130
x = 65
Thus, The value of the measure of ∠O will be 65°.
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Write and solve an equation to find what fraction of the student f voted for fruit juice or water
If [tex]\frac{1}{4}[/tex] of fruit punch is pineapple juice. About [tex]\frac{1}{6}[/tex] of the fruit punch is orange juice, then fraction of punch that is pineapple juice or orange juice is [tex]\frac{5}{12}[/tex] .
The fraction of pineapple juice in fruit punch is = [tex]\frac{1}{4}[/tex] ;
the fraction of orange juice in fruit punch is = [tex]\frac{1}{6}[/tex] ;
the equation that can be used to find the fraction of fruit punch that is pineapple juice or orange juice is
⇒ [tex]Frcation Of (Pinapple Juice +Orange Juice)[/tex]
substituting the values ,
we get the equation as ;
⇒ [tex]\frac{1}{4} +\frac{1}{6}[/tex]
taking LCM as 4 and 6 as 12 and solving further ,
we get ;
⇒ [tex]\frac{3}{12} +\frac{2}{12}[/tex] ; = [tex]\frac{5}{12}[/tex] .
Therefore , the fraction of fruit punch that is pineapple juice or orange juice is [tex]\frac{5}{12}[/tex] .
The given question is incomplete , the complete question is
About 1/4 of fruit punch is pineapple juice. About 1/6 of the fruit punch is orange juice. Write and solve an equation to find the fraction of the punch that is pineapple juice or orange juice .
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-8 5/9 = 4 2/3w
.............................
Answer:
w = -11/6
Step-by-step explanation:
-8 5/9 = 4 2/3w
-8 5/9 = -77/9
4 2/3 = 14/3
So, our equation is
-77/9 = 14/3w
Divided both sides by 14/3
w = -11/6
Pleaseeee help asapppppp
Simplifying
0.75x + 1.2 = 0
Reorder the terms:
1.2 + 0.75x = 0
Solving
1.2 + 0.75x = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-1.2' to each side of the equation.
1.2 + -1.2 + 0.75x = 0 + -1.2
Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 0.75x = 0 + -1.2
0.75x = 0 + -1.2
Combine like terms: 0 + -1.2 = -1.2
0.75x = -1.2
Divide each side by '0.75'.
x = -1.6
One of the roots of the equation x^2-5x+q=0 is 2. Find the other root and the value of the coefficient q.
The value of q in the given equation x²- 5x + q = 0 will be 4.
What is a polynomial?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.
given an equation x²- 5x + q = 0 and the question states that it has a root that is equal to 2
Since 2 is the root of this quadratic equation it will satisfy the equation
Substituting the values in the equation
4 - 5*2 + q = 0
q = 6
Equation will be
x²- 5x + 6 = 0
The root of the given equation using the fraction method
x²- 3x - 2x + 6= 0
(x -2)(x - 3) = 0
The root of the given equation are 2 and 3
Therefore, In the given equation x²- 5x + q = 0 the value of q will be 4.
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How do you graph 3 4 on a number line?
By drawing a number line and then marking it as 0 and 1, and by dividing the distance in 8 equal parts we can graph 3/4 on the number line, where 3/4 = 6/8, which will be equal to the sixth part from the left end.
A number line is a diagram of a graded straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present.
For drawing 3/4 on a number line, we will follow the following steps:
We will first draw a line and mark 0 and 1 on it.
In between 0 and 1, we will divide the total distance into 8 equal parts, where one part will represent (1/8)th portion.
As 3/4 can be written as 6/8 which will be equal to 6 parts out of those 8 parts.
Hence. by marking there we can locate 3/4 on the number line.
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The correct question should be like:
How do you plot 3/4 on number line