5 quarters plus 4 dimes plus 4 nickels plus 10 pennies equals

ANSWER:

tan(30⁰)=√3/3

cos(30⁰)=√3/2

sin(x) /√3/2 =√3/3

3·sin(x) /√3/2 =3·√3/3

2√3 sin (x) =√3

2√3 sin (x) / 2√3 = √3 / 2√3

sin (x)= 1/2

The rate of interest is given by the equation R = 3.5 %

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the rate of interest be represented as R

Now , the simple interest I = $ 175

The principal amount invested P = $ 2,500

The time period T = 2 years

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Rate of Interest = (Simple Interest x 100 ) / Principal Amount x Time Period )

Substituting the values in the equation , we get

Rate of Interest R = ( 175 x 100 ) / ( 2500 x 2 )

Rate of Interest R = 17500 / 5000

Rate of Interest R = 3.5 %

Hence , the interest rate is 3.5 %

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The teacher can thus use social sciences as a vehicle to develop mathematical skills by facilitating the development of skills such as data interpretation and analysis.

As an instructor, I would use social sciences to develop mathematical skills in the following manner:Consider a social science topic like demography. In this case, a teacher could use mathematics to assist students in interpreting population statistics.

Teachers might guide students to gather information about population size, growth rate, and geographical distribution from various countries and then use statistics to analyze the data.

For example, a teacher could give students graphs or charts to help them understand population growth rates. They can be asked to make comparisons and identify trends.

In this way, students' understanding of the population is improved, as is their mathematical reasoning.Aside from using mathematics to interpret population statistics,

the teacher can also incorporate mathematical skills development in social sciences by using methods that involve understanding and analysis of data. In other words, students learn how to use data to reach conclusions and make decisions.

They learn how to interpret data and how to extract information from it.This method of teaching creates opportunities for the use of the same skills in different contexts and areas of learning.

It enables students to see connections between subjects and fosters an integrated approach to learning.

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To determine the inverse of the function we need to follow these steps:

1 - Replace f(x) by y;

2 - Switch the places of x and y on the expression;

3 - Solve the expression for y;

4 - Replace y by f^-1(x).

Let's apply them to the given expression.

The inverse of the function is "3x - 6".

Answer:

the correct answer is 100

Answer:

1. isosceles and acute

2. Scalene and acute

3. Equilateral and equiangular

4. Right (and isosceles ?)

(not sure ab isosceles for the last one but everything else is fine)

:)

Es importante recordar que la velocidad final será negativa, ya que la pelota se está moviendo en dirección contraria al vector de gravedad cuando toca el suelo vel = 0.9 cm/mil*2 * t

La ecuación de velocidad final de los cuerpos en caída libre es:

vel = g x t

Donde "g" es la aceleración debido a la gravedad (en la Tierra, g = -9.8 m/s^2) y "t" es el tiempo que tarda en caer la pelota. Si conocemos la altura "h" desde la que se deja caer la pelota, podemos utilizar la ecuación de cinemática:

h = 1/2 x g x t^2

Despejando "t" de esta ecuación obtenemos:

t = sqrt(2h/g)

Ahora podemos calcular el tiempo que tarda la pelota en caer al suelo:

t = sqrt(2 x altura / (0.0098 km/s^2))

Y utilizando la ecuación de velocidad final de los cuerpos en caída libre, podemos calcular la velocidad final que alcanza la pelota al tocar el piso:

vel = 0.9 cm/mil*2 * t

Es importante recordar que la velocidad final será negativa, ya que la pelota se está moviendo en dirección contraria al vector de gravedad cuando toca el suelo. Espero que esto ayude.

vel = 0.9 cm/mil*2 * t

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The graph's function limit at x=4 is 6.

In mathematics, the limit of a function is the value that the function approaches as the input approaches a certain value or as the input approaches infinity or negative infinity. A function may or may not have a limit at a given point or as the input goes to infinity or negative infinity.

The formal definition of the limit of a function f(x) as x approaches a value a is as follows:

For every positive number ε (epsilon), there exists a corresponding positive number δ (delta) such that if 0 < |x-a| < δ, then |f(x)-L| < ε.

Limit f(x) at x tend to 4⁺ =6.

Limit f(x) at x tend to 4⁻ =6

Hence, the graph's function limit at x=4 is 6.

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Answer:

green line or "b"

Step-by-step explanation:

we can set this up into the slope intercept form

y=mx+b

where m is the slope and b is y intercept

12=3x+4y

-3x -3x

-3x+12=4y

/4.  /4.  /4

-3/4x+3=y

we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"

hopes this helps please mark rainliest

Step-by-step explanation:

it says here "college".

well ...

X + X + X + Y = 4.2

3X + Y = 4.2

X + X + Y = 3.0

2X + Y = 3.0

what is the difference ?

one X (from 3X to 2X) on the left, and 1.2 (from 4.2 to 3.0) on the right.

so, X = 1.2

therefore,

X + Y = 1.8

why ?

because another X (= 1.2) was removed.

and 3.0 - 1.2 = 1.8

Answer: The square root of 16 is 4

Step-by-step explanation:

Answer:

B and D

Step-by-step explanation: I got it right

Peter invested $138 in the 12% account and $288 in the 13% account.

Let x be the amount invested in the 12% account and y be the amount invested in the 13% account.

We know that the total amount invested is the sum of the two accounts, so: x + y = total amount invested

We also know that Peter has $150 more in the 13% account, so:

y = x + 150

The total interest earned is $54, which can be expressed as:

0.12x + 0.13y = 54

Substituting y with x + 150, we get:

0.12x + 0.13(x + 150) = 54

Simplifying and solving for x, we get:

0.12x + 0.13x + 19.5 = 54

0.25x = 34.5

x = 138

Therefore, Peter invested $138 in the 12% account and $288 in the 13% account.

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Answer:

the picture quality is not good

Step-by-step explanation:

so I am unable to give the answer of this question

I am really sorry

Answer:

5,560

Step-by-step explanation:

Answer:

Step-by-step answer should

be 5560 because if you divide 94,520 by 17 you can use calculator and the answere should be 5,560

Answer:

angle is 30 because when the light surface hits the water it perfectly make an refracted angel which will be 30

I know this question is already answered but I have doubts about the answer sooo yeah. Anyways,

to find refraction angle we need to use snell's law, which is

\(\frac{sin\alpha }{sin\beta } = \frac{n_{2} }{n_{1} }\)

Here n1 is refractive index of air, n2 is refractive index of water, α is incident angle & β is angle of refraction.

The 3 sets of data with the same median but different mean are given as follows:

The mean of a data-set is calculated as the sum of all values in the data-set divided by the number of values in the data-set.

The median of a data-set is the middle value of the data-set, the value which 50% of the data-set is less than and 50% of the data-set is more than.

Hence, for a data-set of five elements, which is an odd cardinality, the median is the third element of the ordered data-set.

Then the three data-sets can be constructed with five elements, in which the third element is the same but the sum of the five elements is different.

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Answer:

b

Step-by-step explanation:

integer because is a negative number

Hello !

you made a typo with the c^-2 because otherwise it does not make a round result

\(a^{2} *b^{2} *c^{2} \\\\= 1^{2} *2^{2}* (-3)^{2} \\\\= 1*4*9\\\\\boxed{= 36}\)

Answer:

y = -2/3x + 1/3

Step-by-step explanation:

Do you mean passing through point (-7,5)?

Slope-intercept: y = mx + b

m = -2/3

using (-7,5)

5 = -2/3(-7) + b

5 = 14/3 + b

b = 5 - 14/3 = 15/3 - 14/3 = 1/3

then y = -2/3x + 1/3

Angle x and angle BOC are supplementary. We know that Supplementary angles add up to 180 degrees

180 = x + 156

Subtract 156 from both sides.

24 = x

Answer:

(a) Independent variable:  b (number of bags sold)

    Dependent variable:  p(b)  (profit)

(b) 25

(c) 84700

(d) 70

(e) b < 25

Step-by-step explanation:

(a) Independent variable:  b (number of bags sold)

    Dependent variable:  p(b)  (profit)

(b) To break even, set p(b) to zero and solve for b:

⇒ 350b - 8750 = 0

⇒ 350b = 8750

⇒ b = 8750 ÷ 350

⇒ b = 25

(c) Substitute b = 267 into equation and solve for p(b):

⇒ 350(267) - 8750 = 84700

(d) Set p(b) to 15750 and solve for b:

⇒ 350b - 8750 = 15750

⇒ 350b = 15750 + 8750

⇒ 350b = 24500

⇒ b = 24500 ÷ 350

⇒ b = 70

(e) If she breaks even when she sells 25 bags, if she sells less than 25 bags she will have a negative profit. So b < 25

Three options which are used to calculate the volume of a right triangular prism, with triangular base whose base = 8meters , height = 14meters and height of the prism = 7meters are as follow:

                                               = 56 squared meters

                                                = 392 meters cubed.

As given in the question,

To calculate the volume of the right triangular prism, with triangular base Measures of the triangular base are :

Base = 8meters

Height = 14meters

Height of the prism = 7meters

Three valid options from the given options are as follow:

1. To calculate the area of the base:

Area of the base of triangular prism = 1/2 ( base ) ( height)

Correct option.

2. To calculate the area of the base:

Area of the base of triangular prism = ( base ) ( height)

Incorrect option.

3. To calculate the area of the base:

Area of the base of triangular prism = 1/2 ( 7 ) ( 8)

Height of the base is 14 meters.

Incorrect option.

4. To calculate the area of the base:

Area of the base of triangular prism = 1/2 ( 8 ) ( 14)

                                                            = 56 meters squared

Correct option.

5. Volume of the right triangular prism = (56 ) (7)

                                                                = 392 meters cubed

Correct option.

Therefore, Three options which are used to calculate the volume of a right triangular prism, with triangular base whose base = 8meters , height = 14meters and height of the prism = 7meters are as follow:

                                               = 56 squared meters

                                                = 392 meters cubed.

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Answer:

The formula used for the average growth rate over time method is to divide the present value by the past value, multiply to the 1/N power and then subtract one. "N" in this formula represents the number of years.

Step-by-step explanation:

Hello!

To find the equation of the line that passes through the points (0, -8) and (4, -3), we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

First, we can find the slope of the line by using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (0, -8) and (x2, y2) = (4, -3). Substituting these values, we get:

m = (-3 - (-8)) / (4 - 0) = 5/4

So the slope of the line is 5/4. Now we can use the point-slope form of the equation with either of the given points. Let's use the point (0, -8):

y - (-8) = 5/4(x - 0)

Simplifying this equation, we get:

y + 8 = 5/4x

Subtracting 8 from both sides, we get the final equation:

y = 5/4x - 8

So the equation of the line that passes through the points (0, -8) and (4, -3) is y = 5/4x - 8.

Answer:

x = 15.

Step-by-step explanation:

3/5 = x/25

5x = 75

x = 15.

Answer:20%

Step-by-step explanation:

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.).

The length of side AB is about 5.87 units.

The triangle ABC is a right angle triangle. A right angle triangle is a triangle that has one of its angles as 90 degrees.

Therefore, let's find the length AB in the right triangle.

Using trigonometric ratios,

cos 33 = adjacent / hypotenuse

Therefore,

Adjacent side = AB

hypotenuse side = 7 units

cos 33° = AB / 7

cross multiply

AB = 7 cos 33

AB = 7 × 0.83867056794

AB = 5.87069397562

AB = 5.87 units

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