The depth of water in a tank oscillates sinusoidally once every

8 hours. If the smallest depth is 6. 6 feet and the largest

depth is 9. 4 feet, find a possible formula for the depth in terms

of time t in hours. Assume that at t=0 the water level is at

the average of the depth and is rising.
.

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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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

)

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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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) = -2*12 + 7

          = -24 + 7

          = -17

       f(x) = 5*-14 - 13

             = -60 -13

             = -73

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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°.

Answer:

y=2x+3

Step-by-step explanation:

y=mx+b

y=2x+3

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!

The value of a₂₆ in the  arithmetic sequence aₙ=  14 + 9n is 248.

The correct option is D.

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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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.

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

The value of q in the given equation x²- 5x + q = 0 will be 4.

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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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

On solving the provided question, we can say that - here in the percentage obtained = 40 => so, 40/100X100 = 40%

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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The angles that would make triangle ABC congruent to triangle PDF by AAS are ∠ ACB and ∠ PFD i.e. ∠ ACB = ∠ PFD.

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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Answer:

Step-by-step explanation:

b and f

Direct variation is represented by this situation and she earn $900

if she works 12 hours.

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.

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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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]

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]

Pam's piece rate is $16.67 for every pot she produces.

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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The line 2 is pointing towards the body of the cell, in the given image of a neuron.

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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$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 value of the measure of ∠O in the given triangle will be 65°

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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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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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.

Answer:

1:3

Step-by-step explanation:

The expected mass of the sample in the year of 2021 is given as follows:

9 mg.

An exponential function is defined as follows:

y = a(b)^x.

For which the parameters are given as follows:

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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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.

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.

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.

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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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