X
y
13
45° I need this

Answer:

\(-\frac{28}{3}\)

Step-by-step explanation:

\(\frac{-3-(-1/5)}{(1/10)-(-1/5)}=-\frac{28}{3}\)

Answer:

54

Step-by-step explanation:

The monthly payments for this add on interest loan are of $164.71.

Given Information and Formula Used

It is given that for an add on interest loan,

Principal Amount, p = $8,276.17

Annual Interest Rate, r = 5.7%

Term of the loan, T = 5.5 years

The formula for simple interest is given as follows,

I = (p)(r)(t)/100 ............... (1)

The formula for total amount of add on interest is given by,

A = p + I ....................... (2)

Computing the Interest

Substitute the given values of p, r, and t in the formula (1) of interest to get,

I = (8276.17)(5.7)(5.5)/100

I = 259457.9295/100

I = $2,594.58

Computing the Monthly Payment for Add-on Interest Loan

Substituting the values of p and I in the formula (2), we obtain the total amount as,

A = $ (8276.17 + 2594.58)

A = $ 10,870.75

Monthly payment for the add on interest loan = A/t(in months)

=  $ (10,870.75/66)

= $164.71

Therefore, monthly payments of $164.71 are to be made for the add on interest loan.

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Answer:

A) 50 km : 45 km : 65 km

B) 18:45:3

Step-by-step explanation:

A) 160 km in the ratio 10:9:13

10:9:3 ⇔ 50 km : 45 km : 65 km

B) 66 in the ratio 6:15:1

6:15:1  ⇔ 18:45:3

Answer:

D. 78°

Step-by-step explanation:

50°+28°= 78°

_______

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

Answer:

what we have to find or to prove.

The amount of hot chocolate served daily is inversely correlated with the temperature of the city, with more cups being sold once the temperature is between 40 and 50 F.

When two variables change in tandem, the relationship is said to be direct. The variable y increases as the variable x increases. A linear relationship denoted by the equation y = kx is directly proportional.

There is a direct correlation between a circle's radius and area, meaning that when the radius is increased or decreased, the area correspondingly changes. If one variable increases while the other declines or vice versa, the relationship between the two variables is inverse.

For given question-

Jordan created the graph below to illustrate the correlation between a city's temperature and the daily sales of hot chocolate.

As we can see that - when the temperature increases the demand for the ice cream also increases which is the direct relation.

Thus, the amount of hot chocolate served daily is inversely correlated with the temperature of the city, with more cups being sold once the temperature is between 40 and 50 F.

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The diagram for the question is attached:

Answer: 21+3x

Step-by-step explanation: simply distribute the three into the parentheses

Hope this helps

Answer:

21+3x

Step-by-step explanation:

you multiply 3 by 7 and then you sum it with 3 multiplied by x hope i helped

Point G is on line segment FH. Given FG = 7 and GH = 2, the length of line segment FH is 9 units.

The length of line segment FH can be determined by adding the lengths of its two parts, FG and GH.

This is based on the property that the whole length of a line segment is equal to the sum of its parts.

Given that FG = 7 and GH = 2,

we can find the length of FH as follows:

FH = FG + GH

FH = 7 + 2

FH = 9

So, the length of line segment FH is 9 units.

This is a basic principle in geometry where the total length of a segment can be calculated by adding the lengths of its individual parts.

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Step-by-step explanation:

(7m - 3)² = 49m² - 42m + 9

play it through and do the actual multiplication behind the square :

(7m - 3)² = (7m - 3)(7m - 3) =

= 7m×7m + 7m×(-3) + (-3)×7m + (-3)(-3) =

= 49m² - 2×21m + 9 = 49m² - 42m + 9

Answer:

-263

Step-by-step explanation:

replace x by -9

This question is incomplete, the complete question is;

The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.

What proportion of the students scored at least 23 points on this test, rounded to five decimal places?

Answer:

proportion of the students that scored at least 23 points on this test is 0.30850

Step-by-step explanation:

Given the data in the question;

mean μ = 22

standard deviation σ = 2

since test closely followed a Normal Distribution

let

Z = x-μ / σ      { standard normal random variable ]

Now, proportion of the students that scored at least 23 points on this test.

P( x ≥ 23 ) = P( (x-μ / σ) ≥  ( 23-22 / 2 )

= P( Z ≥ 1/2 )

= P( Z ≥ 0.5 )

= 1 - P( Z < 0.5 )

Now, from z table

{ we have P( Z < 0.5 ) = 0.6915 }

= 1 - P( Z < 0.5 ) = 1 - 0.6915 = 0.30850

P( x ≥ 23 ) = 0.30850

Therefore, proportion of the students that scored at least 23 points on this test is 0.30850

According to the information we can infer that in the Mayan numeral system, the year 2010 is represented as follows: snail, point, snail, point, point, point, point, point

The number 2010 is broken down into Mayan units, using the symbols corresponding to the different positional values. In the Maya system, three main symbols are used:

To represent the number 2010 in Maya, the combination of these symbols is used as follows:

Two shells represent the value of 2000. One point represents the value of 10. So, the representation of the year 2010 in Mayan numbers would be:

snail, point

Remember that the Mayan number system is positional, similar to the decimal system, so the value and position of each symbol are important to determine the complete number.

Note: The question in English is: How to represent 2010 in Mayan numbers?

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Answer:

h = 14.5 in

Step-by-step explanation:

Data

radius = 5 in

Volume = 725 π in³

height = ?

Formula

              Volume = 2πr²h

Substitution

                    725 π in³ = 2πr² h

                   h = 725π / 2πr²

                   h = 725 / 2(5)²

                   h = 725 / 50

                   h = 14.5 in

Answer:

Molly has four choices for which shirt to wear on the first day, and one of those choices is the black shirt. So the probability that she will wear the black shirt on the first day is 1/4. Therefore, the answer is 1/4.

Step-by-step explanation:

Answer:

? = 92°

Step-by-step explanation:

the chord- chord angle ? is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

? = \(\frac{1}{2}\) (LM + AK) = \(\frac{1}{2}\) (120 + 64)° = \(\frac{1}{2}\) × 184° = 92°

Answer:

Here's an interesting project idea for mathematics that can relate three different topics:

Topic 1: Fractals

Topic 2: Chaos Theory

Topic 3: Differential Equations

Research Question: Can fractals be used to model chaotic systems described by differential equations?

In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.

Your research paper can cover the following areas:

Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.

Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.

Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.

Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.

Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.

Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.

Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.

Step-by-step explanation:

Answer:

Slope=− 1.083/1.083 =−0.542

x−intercept= 144/13 =11.07692

y−intercept= 144/24 =6.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Intercepts of a Line

The x-intercept of a given line is the point where the line crosses the x-axis and the y-intercept of a given line is the point where the line crosses the y-axis.

We are given the following line:

-12x + 18y = 108

To find the x-intercept, we set y=0 and solve for x:

-12x + 18*0 = 108

-12x = 108

x = 108 / (-12) = -9

The x-intercept is the point (-9,0)

To find the y-intercept, we set x=0 and solve for y:

-12*0 + 18y = 108

18y = 108

y = 108 / 18 = 6

The y-intercept is the point (0,6)

Answer:

a=81.0

there ya go

Descent  = 10 feet

Time required = 2 1/2 minutes.

The rate of descent = (10 feet)/(2.5 mn) = 4 ft/min

In 6 minutes, the descent will be

(4 ft/min)*(6 min) = 24 ft

Answer:

(a) 4 feet/minute

(b) 24 feet

Answer:

With ignoring the last sentence the answer is 920.

Step-by-step explanation:

115/46=2.5

2.5*368=920

The exact value of sin(5π/12) is (√6 + √2)/4

From the question, we have the following parameters that can be used in our computation:

sin 5pi/12

Express properly

So, we have

sin(5π/12)

Convert the angle to degrees

This gives

sin(5π/12) = sin(5/12 * 180)

Evaluate

sin(5π/12) = sin(75)

The actual value of sin(75) is (√6 + √2)/4

This means that

sin(5π/12) = (√6 + √2)/4

Hence, the exact value of sin(5π/12) is (√6 + √2)/4

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The exact value of sin 5π/12 is (√6 + √2)/4

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Angle in trigonometry can be measured in either degree or radian.

π is a measurement in radian which is equivalent to 180° in degrees.

Therefore:

5π/12 = 5 × 180/12

= 75°

Therefore sin5π/12 = sin75°

sin75 = sin( 45+30) = sin45cos30+ cos 45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= √3/2√2 + 1/2√2

= (√3+1)/2√2

rationalizing;

(2√6 + 2√2)/8

dividing through by 2

=(√6 + √2)/4

therefore tan75 =(√6 + √2)/4

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The coefficients a, b, and c in the 12th term of the expanded form are 312, 64, and 11, respectively.

The 12th term is 312(64x^3)(y^11) or 19968x^3y^11.

We would use the binomial theorem formula

Σ [n! / (k!(n - k)!) * a^(n - k) * b^k] for k = 0 to n.

For our calculation, we have affirmed that n equals 14 whereas a and b are equivalent to 4x and y respectively.

Our objective parameter is set to the twelfth term where k holds the value of 11 (as k begins counting from zero).

Thus substituting these values in the binomial equation, it follows:

(4x + y)^14 = Σ [14! / (k!(14 - k)!) * (4x)^(14 - k) * y^k] from k= 0 to 14.

From this derivation, the number we had sought becomes calculable by assigning value k equals 11:

Term_12 = 14! / (11!(14 - 11)!) * (4x)^(14 - 11) * y^11.

The above simplifies after that further leading to:

Term_12 = 14!/(11! × 3!) × (4x)^3×y^11\

Term_12=(14 × 13 × 12)/(3 × 2 × 1) × (4x)^3 × y^11

which leads to, after computation:

Term_12= 2 ×13 × 12×64x^3y^11

Immediately from our results, the constant values a, b, and c have become clear:

a = 2 × 13 × 12 which reduces to 312

b = 64

c = 11

Thus note that for term 12: 'a' is equal to 312; 'b' is represented by 64 while 'c' stands for 11.

Simplification of this value would lead to expressing the twelfth term as 19968 x^3 y^11.

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Given the expression (4x + y)^14, find the coefficients a, b, and c in the 12th term of the expanded form

Answer:

y

a= ——

(r + 1 )t

Step-by-step explanation:

divide both sides

The 95th percentile of the actual losses that exceed the deductible is given as follows:

$1,198.

The exponential probability distribution, with mean m, is described by the following equation:

\(f(x) = \mu e^{-\mu x}\)

In which \(\mu = \frac{1}{m}\) is the decay parameter.

The probability of obtaining a value lower than x is given as follows:

\(P(X \leq x) = 1 - e^{-\mu x}\)

Losses incurred follow an exponential distribution with a mean of $396, hence the decay parameter is of:

\(\mu = \frac{1}{396}\)

\(\mu = 0.0025\)

The 95th percentile is x for which P(X < x) = 0.95, hence:

0.95 = 1 - e^(-0.0025x)

e^(-0.0025x) = 0.05

x = -ln(0.05)/0.0025

x = $1,198.

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The pattern is empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

Given that, there are 6 pails in a row. The first 3 pails are filled with water.

The easiest way to solve this problem is to empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty. This will create the desired pattern of full, empty, full, empty, full, empty.

Therefore, empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

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