find the tangent of the cycloid x = r(t-sin t), y = r(1-cos t) at the point where t = pi/3.

ANSWER

She worked 13 hours in Job A and 12 hours in Job B.

EXPLANATION

Eleanor works two part-time jobs.

Both jobs take a total of 25 hours a week.

Let the number of hours worked in Job A be x.

Let the number of hours worked in Job B be y.

This means that:

x + y = 25 _____(1)

Job A pays $6.00 per hour and Job B pays $6.80 per hour.

The total she made that week was $159.60.

This means that:

6 ^ x + 6.8 * y = 159.60

=> 6x + 6.8y = 159.6 _____ (2)

We have two simultaneous equations:

x + y = 25 _____ (1)

6x + 6.8y = 159.6 ___(2)

From (1), we have that:

x = 25 - y

Put that in (2):

6(25 - y) + 6.8y = 159.6

150 - 6y + 6.8y = 159.6

150 + 0.8y = 159.6

Collect like terms:

0.8y = 159.6 - 150 = 9.6

y = 9.6 / 0.8

y = 12 hours

Recall that:

x = 25 - y

=> x = 25 - 12

x = 13 hours

Therefore, she worked 13 hours in Job A and 12 hours in Job B.

Answer:

The answer is B

Step-by-step explanation:

the ans has to be 36 or more. so A and D can't B the answer. amongst B and C the lowest possible value is B - 36. so 36 is the answer

Answer:

I believe the answer would be -4 1/2.

The probability of a student playing a sport but not playing an instrument is around 0.4286.

The likelihood of a student not playing an instrument, provided they play a sport, is:
\(Probability=\dfrac{Number\ of\ students\ who\ play\ a\ sport\ but\ do\ not\ play\ an\ instrument​}{Number of \students\ who\ play\ a\ sport}\)

It is known that 14 students participate in a sport, while 8 students do not engage in either a musical instrument or a sport. Thus, the number of students who play a sport but do not play an instrument is:

Number of students who play a sport but do not play an instrument = 14- 6
                                                                                                                 = 6
Now, let's calculate the probability:

Probability = 6/14
                  = 0.4286

Rounded to four decimal places, the likelihood of a student playing a sport but not playing an instrument is approximately 0.4286.

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​

Based on the calculation below, the amount he should pay altogether is RM15x – y.

Let C represent the entrance fee for a child and A represents the entrance fee for an adult, we therefore have:

C = RM(3x-y)

A = RM(3x-y) + RM2y = RM3x – RMy + RM2y = RM(3x – y + 2y) = RM(3x + y)

Since Mr. Kamal and his wife bring their three children to the circus, this implies that we have 2 adults and 3 children.

The amount he should pay altogether (T) can therefore be calculated by collecting the like terms as follows:

T = 3C + 2A = 3RM(3x – y) + 2RM(3x + y)

T = RM9x – 3y + RM6x + 2y

T = RM9x + RM6x – 3y + 2y

T = RM15x – y

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Answer:

53 + 26

therefore m angle 4 is 79

Answer:

(-1, 1)

Step-by-step explanation:

I used a graphing tool to graph the two lines. When graphed, the lines intercept at point (-1,1). Therefore, it is the solution to the system of equations.

Hope this helps.

Para resolver este problema, llamemos a los dos números "a" y "b".

Dada la razón geométrica de los números, podemos establecer la siguiente relación:

b/a = 8/13 --> b = (8/13)a

Dada la razón aritmética de los números, podemos establecer la siguiente relación:

(a + b)/2 = 60

Sustituyendo el valor de "b" en términos de "a" en la segunda ecuación, obtenemos:

(a + (8/13)a)/2 = 60

(21/13)a/2 = 60

(21/13)a = 120

a = (13/21) * 120

a ≈ 76.19

Sustituyendo el valor de "a" en la relación b = (8/13)a, obtenemos:

b = (8/13) * 76.19

b ≈ 46.81

La suma de los dos numerous es:

a + b ≈ 76.19 + 46.81 ≈ 123

Por lo tanto, la sumac de los dos numerous es aproximadamente 123.

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The missing side of the triangle is known as the hypotenuse. The length of the missing side is 13.

What is a right triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.

A right triangle has two legs and one hypotenuse.

The length of the legs is 5 and 12.

The sum of the square of the legs is equal to the square of the hypotenuse.

Therefore,

Hypotenuse² = 5²+ 12²

Hypotenuse² = 25+ 144

Hypotenuse² = 169

Hypotenuse = 13

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Answer:

Step-by-step explanation:

the graph of g(x) is shifted 7 units to the right and 3 units below the graph of f(x).

The graph of g(x) is shifted 7 units to the left and 3 units below the graph of f(x).

The graph of g(x) is shifted

7 units to the right and 3 units above the graph of f(x).

The graph of g(x) is shifted 7 units to the left and 3 units above the graph of f(x)

Time independent variable situatiοn is,

A researcher wants tο investigate the effect οf different exercise regimes οn heart rate. The researcher randοmly assigns participants tο different exercise grοups and measures their heart rate after a fixed amοunt οf time, say 30 minutes.

Time dependent variable situatiοn is,

A researcher wants tο investigate the relatiοnship between the amοunt οf sleep a persοn gets and their reactiοn time. The researcher measures the amοunt οf sleep a persοn gets each night fοr a week and measures their reactiοn time each day using a standardized test.

An independent variable is a variable that is manipulated οr cοntrοlled in an experiment tο οbserve its effect οn the dependent variable.

The dependent variable is the variable being οbserved οr measured in respοnse tο changes in the independent variable. The dependent variable depends οn the independent variable, while the independent variable is nοt affected by the dependent variable.

Situatiοn 1: Time, t, as an independent variable

Suppοse a researcher wants tο investigate the effect οf different exercise regimes οn heart rate. The researcher randοmly assigns participants tο different exercise grοups and measures their heart rate after a fixed amοunt οf time, say 30 minutes. In this case, time (t) is an independent variable because it is cοntrοlled and varied by the researcher tο investigate its effect οn heart rate.

Situatiοn 2: Time, t, as a dependent variable

Suppοse a researcher wants tο investigate the relatiοnship between the amοunt οf sleep a persοn gets and their reactiοn time. The researcher measures the amοunt οf sleep a persοn gets each night fοr a week and measures their reactiοn time each day using a standardized test. In this case, time (t) is a dependent variable because it is being measured as a functiοn οf the amοunt οf sleep a persοn gets. The amοunt οf sleep a persοn gets is the independent variable in this situatiοn.

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Answer:

m<x=100

Step-by-step explanation:

the left side <100 what's near to here is 80 100+80=180

so x and what's near to hear "up" needs to be 180 what's near to hear was 80 so x+80=180 180-80=x x=100

Answer:

False

Step-by-step explanation:

An integer is any whole number

Answer:

I believe the answer is true

Step-by-step explanation:

Answer:

94

Step-by-step explanation:

Add the three distances.

23 + 42 + 29 = 94

94 miles

\(\text{We need to get the total miles Milicent cycled}\\\\\text{To do this, we would add up all the distances she travelled}\\\\\text{Add:}\\\\23+42+29=94\\\\\boxed{\text{94 miles}}\)

Answers:

one small box = 30 pounds

one large box = 40 pounds

==========================================================

Work Shown:

S+L = 70 since the two boxes combine to 70 pounds.

70S = weight of 70 small boxes

50L = weight of 50 large boxes

70S+50L = weight of 70 small and 50 large

70S+50L = 4100

The system of equations is

\(\begin{cases}S+L = 70\\70S+50L = 4100\end{cases}\)

There are a few ways to solve this system. I'll use substitution.

I'm going to isolate L in the first equation like so

S+L = 70

L = 70-S

Which I'll then plug into the other equation to solve for S

70S+50L = 4100

70S+50(70-S) = 4100

70S+3500-50S = 4100

20S+3500 = 4100

20S = 4100-3500

20S = 600

S = 600/20

S = 30

Each small box is 30 pounds.

Use this value of S to find L

L = 70-S

L = 70-30

L = 40

Each large box is 40 pounds.

Like we expect, each large box weighs more compared to any given small box.

------------------

Check:

Both equations are true for the ordered pair (S,L) = (30,40). Therefore, the answers have been confirmed.

a. the linear approximating polynomial L(x) is 1+x

b. the quadratic approximating polynomial Q(x) is 1 + x + x^2

a. The linear approximating polynomial for a function f(x) centered at the point a can be found using the formula:

L(x) = f(a) + f'(a)(x - a)

where f'(a) is the derivative of the function evaluated at the point a.

b. The quadratic approximating polynomial for a function f(x) centered at the point a can be found using the formula:

Q(x) = f(a) + f'(a)(x - a) + (1/2)f''(a)(x - a)^2

where f''(a) is the second derivative of the function evaluated at the point a.

c. To approximate the quantity 1/(1-x) using the linear and quadratic approximating polynomials obtained in parts a. and b., we need to first find the values of f(a), f'(a), f''(a) at the given point a.

Let's assume a = 0 for simplicity.

a. Linear Approximation:
To find the linear approximating polynomial, we need to evaluate f(0) and f'(0).

f(x) = 1/(1-x)

f(0) = 1/(1-0) = 1

To find f'(0), we need to take the derivative of f(x) and evaluate it at x = 0.

f'(x) = 1/(1-x)^2

f'(0) = 1/(1-0)^2 = 1

Using the linear approximation formula, we can now find the linear approximating polynomial L(x):

L(x) = f(0) + f'(0)(x - 0) = 1 + 1(x - 0) = 1 + x

b. Quadratic Approximation:
To find the quadratic approximating polynomial, we need to evaluate f''(0).

f''(x) = 2/(1-x)^3

f''(0) = 2/(1-0)^3 = 2

Using the quadratic approximation formula, we can now find the quadratic approximating polynomial Q(x):

Q(x) = f(0) + f'(0)(x - 0) + (1/2)f''(0)(x - 0)^2 = 1 + 1(x - 0) + (1/2)2(x - 0)^2 = 1 + x + x^2

Now, we can use these linear and quadratic approximating polynomials to approximate the given quantity 1/(1-x). For example, if we want to approximate the value of 1/(1-x) at x = 0.1, we can substitute x = 0.1 into both L(x) and Q(x) to get the approximate values.

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Answer:0

. 5 + 2 = 7 . 5

1 2 + 2 = 7 . 5

Step-by-step explanation:

Answer:

m = 11

Step-by-step explanation:

0.5m + 2 = 7.5

0.5m + 2 - 2 = 7.5 - 2

0.5m = 5.5

0.5m ÷ 0.5 = 5.5 ÷ 0.5

m = 11

The total cost of repayment over 5 years is $23,300.

A loan repayment refers to the act of paying back money previously borrowed from a lender.

To get total cost of repayment, we must principal amount, the interest rate and the duration of the loan.

The formula to get total cost of repayment is given by \(Total Cost of Repayment = Principal + Interest\)

Interest = Principal * Interest Rate * Time

Given:

Principal amount is $20,000

Interest rate is 3.3%

Duration is 5 years.

Interest = $20,000 * 0.033 * 5

Interest = $3,300

Total Cost of Repayment = Principal + Interest

= $20,000 + $3,300

= $23,300.

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A cucumber seed needs to be planted 1 inch deep for optimal growth. the plant grows an average of 3 inches every 2 weeks. then the slope in the situation is 2

How do you find the slope of a line?

We need to find the ratio of the difference between the y-coordinates and x-coordinates of the two points, that form the line. The resulted value is the slope of the line. It shows the rise of the line along the y-axis over the run along x-axis.

since seed planted 1 inch deep then y1 = -1 and initial x1 =0

the plant grow an average of 3 inches every 2 weeks then y2 =3 and x2=2

putting in the formula

slope= y2 -y1 /x2 -x1

       = 3-(-1)/2-0

      = 4/2

      =2

thus the slope in this situation is 2

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The scatterplot with the least squares line provides insights into the relationship between average annual global surface temperature and the years from 2000 to 2015, allowing us to assess trends, strength of correlation, and make predictions within certain limitations.

The scatterplot represents the relationship between the average annual global surface temperature, in degrees Celsius, and the corresponding years from 2000 to 2015. The line drawn on the plot is the least squares line, which is the best fit line that minimizes the overall distance between the observed data points and the line.

The least squares line is determined using a statistical method called linear regression. It calculates the equation of a straight line that represents the trend in the data. This line serves as a mathematical model to estimate the average temperature based on the year.

By analyzing the scatterplot and the least squares line, we can make several observations. Firstly, we can see whether the temperature has been increasing, decreasing, or remaining relatively stable over the given years. If the slope of the line is positive, it indicates a positive correlation, implying that the temperature has been increasing. Conversely, a negative slope suggests a decreasing trend.

Additionally, we can evaluate the strength of the relationship between temperature and time by examining how closely the data points cluster around the line. If the points are closely grouped around the line, it suggests a strong correlation, indicating that the line is a good representation of the data. On the other hand, if the points are more scattered, the correlation may be weaker.

Furthermore, the line can be used to predict the average annual global surface temperature for future years beyond the data range of 2000 to 2015. However, it's important to note that such predictions should be made with caution and considering other factors that may affect global temperatures, such as climate change and natural variability.

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Question

The given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.

Answer:

125

Step-by-step explanation:

By using normal division method,

3125÷25 goes as 125

Answer:

C

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 3, - 1) and (x₂, y₂ ) = (5, 1) ← 2 points on the line

m = \(\frac{5-(-3)}{1-(-1)}\) = \(\frac{5+3}{1+1}\) = \(\frac{8}{2}\) = 4 → C

Mila will receive 68 EUROS of money after the exchange of 80 US dollar.

USD is the official money currency of united states of America.. its symbol of representation is $., also value of 1 US$ =82 rupee.

Unit of money used in other countries of European union is known as euro, also value of 1 EURO=87 rupee.

According to the given data in the question,

1 USD =0.85 EURO

80 USD = 0.85*80 EURO

80 USD= 68 EURO

Hence 80USD will be converted to 68 EUROS

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The vertex of the parabola y = f(x + 1) is (1, -1).

To find the vertex of the parabola given by the equation y = f(x + 1), we need to determine the effect of the transformation on the vertex coordinates.

The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) represents the vertex coordinates.

In the given equation, y = f(x + 1), we can see that the transformation is a horizontal shift of 1 unit to the left. This means that the new vertex will be located 1 unit to the left of the original vertex.

Given that the original vertex is (2, -1), shifting 1 unit to the left would result in a new x-coordinate of 2 - 1 = 1. The y-coordinate remains the same.

Therefore, the vertex of the parabola y = f(x + 1) is (1, -1).

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The value of Erica's investment after 6 years is approximately $4,939.05.

To find the value of Erica's investment after 6 years, we can use the compound interest formula. The formula for compound interest is given as:

A = P\((1 + r/n)^(nt)\)

Where:

A is the final amount or value of the investment.

P is the initial principal or investment amount.

r is the annual interest rate (as a decimal).

n is the number of times the interest is compounded per year.

t is the number of years.

In this case, Erica's initial investment is $4000, the annual interest rate is 4% (or 0.04 as a decimal), and the investment is growing annually. Therefore, we have:

P = $4000

r = 0.04

n = 1 (since the interest is compounded annually)

t = 6 years

Plugging these values into the compound interest formula, we can calculate the final value of the investment:

A = $4000(1 + \(0.04/1)^(1*6)\)

A = $4000(1 + 0.04)^6

A = $4000(1.04)^6

Evaluating this expression, we find:

A ≈ $4,939.05

Therefore, the value of Erica's investment after 6 years is approximately $4,939.05.

This calculation assumes that no additional investments or withdrawals were made during the 6-year period and that the interest rate remains constant at 4% per year.

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The simplified form of the given expression is \(\frac{3}{2} x-3.5+2y\).

The given expression is \((\frac{7}{4} x-5)+(2y-3.5)+(-\frac{1}{4} x+5)\).

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression can be solved as follows:

\((\frac{7}{4} x-5)+(2y-3.5)+(-\frac{1}{4} x+5)\)

Group the like terms and simplify.

That is, \(\frac{7}{4} x-5+2y-3.5-\frac{1}{4} x+5\)

\(=(\frac{7}{4} x-\frac{1}{4} x)-5-3.5+5+2y\)

\(=\frac{6}{4} x-3.5+2y\)

\(=\frac{3}{2} x-3.5+2y\)

Therefore, the simplified form of the given expression is \(\frac{3}{2} x-3.5+2y\).

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Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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The time that it will take for the balance to be of $1360 is given as follows:

8 years.

The balance of an account after t years, using continuous compounding, is  modeled by the equation presented as follows:

A(t) = A(0)e^(kt).

In which:

The parameters for this problem are given as follows:

A(t) = 1360, A(0) = 500, k = 0.125.

Hence the time is obtained as follows:

500e^(0.125t) = 1360

e^(0.125t) = 1360/500

0.125t = ln(1360/500)

t = ln(1360/500)/0.125

t = 8 years.

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The description that accurately explains how a fair decision can be made in this situation is : IF a ball with number 4 and 5 are picked you order the largest size, if a ball with number 4 and another with number 4 is picked you order the medium size, but if the balls picked are that of number 2 and 4, then you order a small size. The probability of each result occurring is a fair one.

Probability is the degree of occurrence of an event. it can also be said to be the chance for an event to occur.

Probability helps us know the chance an event has to occur. The closer it gets to zero(0) the less chance it has to occur. The closer it gets to one(1) the more chance it has to occur.

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