A ringtoss toy is composed of a rectangular prism on top of a cylinder. The rectangular prism is completely filled with water. The dimensions of the rectangular prism are shown in the diagram.



What is the volume of the rectangular prism in cubic centimeters?

If $4400 is placed in account at 8.25% for 22 years , then the final amount received after 22 years will be $26480.08  .  

We use the formula for compound interest to find the final amount  :

that is ⇒  A = P(1 + r)ˣ  ;

where:  A = the amount of money in the account after "x years"  ;

P(initial amount) = $4400 ;   r (interest rate) = 0.0825  ;

⇒ x(time) = 22 years

we get ;

⇒ A = 4400×(1 + 0.0825)²²  ;

⇒ A =  4400×(1.0825)²²  ;

⇒ A =  4400×6.018028  ;

⇒ A = 26480.08  ;

Therefore , the amount in the account after 22 years is $26480.08  .

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Answer:

b.  53.1°

c.  126.9⁰

Step-by-step explanation:

These are SSA triangles;  use Law of Sines to find the unknown angle:

b)  sin30/15 = sinA/24

sinA(15) = sin30(24)

sinA = sin30(24)/15 = 0.80

m∠A = sin⁻1(0.80) = 53.1°

c)  m∠A = 180 - 53.1 = 126.9⁰

Answer:

∠ BAC = 53.13° , ∠ BAC = 126.87°

Step-by-step explanation:

using the Sine rule in Δ ABC

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex]

where a is the side opposite ∠ A and c is the side opposite ∠ C

here a = BC = 24 and c = AB = 15 , then

[tex]\frac{24}{sinA}[/tex] = [tex]\frac{15}{sin30}[/tex] ( cross- multiply )

15 sinA = 24 sin30° ( divide both sides by 15 )

sin A = [tex]\frac{24sin30}{15}[/tex] , then

A = [tex]sin^{-1}[/tex] ( [tex]\frac{24sin30}{15}[/tex] ) = 53.13°

(b)

acute angle BAC = 53.13°

(c)

the sine of an angle is positive in both the first and second quadrant , so

obtuse angle BAC = 180° - 53.13° = 126.87°

Answer: x=8

Step-by-step explanation: since we know 2 sides of both quadrilaterals and they are similar,

just put 32/40 = 24/3x+6 ,

cross multiply ( 32 x 3x+6   and 40 x 24),

they become 96x +192 = 960.

move 192 to the other side and divide both sides by 96

Answer:

A(t) = 9000(1 + 0.036/12)^12t

[Function formula for the compound interest]

A = 9000(1 + 0.036/12)^12t

[General formula for the compound interest]

A(1) ≈ 9329.40 $

[Compound interest over 1 year]

Step-by-step explanation:

Compound interest formula:

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

P is the principal or starting amount.

r is the interest rate.

n is the number of times compounded per year.

t is the period of time.

Given P is 9000, r is 3.6% or 0.036, n is 12 or monthly, and t is variable.

The following function represents the relationship over time:

A(t) = 9000(1 + 0.036/12)^12t

The statement that is true is: The equation 4 √2x + 4 √x + 3 = 0 has one solution, which is x = -1/2.

To determine which statement about 4 √2x + 4 √x + 3 = 0 is true, we need to solve the equation.

However, it is not possible to solve the equation exactly because it contains square roots. We can simplify the equation by multiplying both sides by the conjugates of the square roots, which eliminates the square roots.

Multiplying both sides by (2x + x + 3) / (2x + x + 3), we get:

(4 √2x + 4 √x + 3) * (2x + x + 3) / (2x + x + 3) = 0 * (2x + x + 3) / (2x + x + 3)

Expanding the left-hand side, we get:

12x + 6 = 0

Solving for x, we get:

x = -1/2

So, the statement that is true is: The equation 4 √2x + 4 √x + 3 = 0 has one solution, which is x = -1/2.

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The mentioned  scenario can be calculated using the distance equation, the number of seconds in which explosion would occur is 1.125 seconds.

The distance covered by the object is equal to the  product of the speed of object and the time required for it.

Distance = Time x speed

Firework A :

D = 360xt - - - (1)

Firework B:

D = 280x(0.25) + 280xt

D= 70 + 280xt - - - (2)

Equate equation (1) and (2) :

360t = 280t + 70

Collect like terms

360t - 280t = 70

80t = 70

t = 70/80

t = 0.875 seconds

0.875 + 0.25 = 1.125 seconds

Hence, the fireworks will explode after 1.125 seconds of launching Firework B.

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Answer: approx 13.54 (full decimal : 13.416666667)

Step-by-step explanation:

Area = Base Area x Height   OR    Length x Width x Height

5/3 x 13/4 x 5/2

5 x 13 x 5 = 325

3 x 4 x 2 = 24

325/24 = approx 13.54

The expression for the number of different samples is: C(3, 2) x C(47, 4) = 3 x C(47, 4) = 3 x

(47! / (4! x 43!)).

The number of different samples of size 6 that contain exactly 2 defective parts can be calculated using the binomial coefficient formula:

C(3, 2) x C(47, 4)

where C(n, k) represents the number of ways to choose k objects from a set of n objects.

In this case, we first choose 2 defective parts from the 3 defective parts in the bin, which can be done in C(3, 2) ways. Then we choose 4 nondefective parts from the 47 nondefective parts in

the bin, which can be done in C(47, 4) ways. We multiply these two quantities together to obtain the total number of different samples of size 6 that contain exactly 2 defective parts.

Therefore, the expression for the number of different samples of size 6 that contain exactly 2 defective parts is:

C(3, 2) x C(47, 4) = 3 x C(47, 4) = 3 x (47! / (4! x 43!))

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3 minutes is the cost of the call that is same for both plans

Two or more expressions with an Equal sign is called as Equation.

Let's assume the call duration in minutes is represented by x.

For David, the cost of the call can be represented by the equation: C(d) = 4 + x

For Alec, the cost of the call can be represented by the equation: C(a) = 1 + 2x

Since the cost of the call is the same for both plans, we can set the two equations equal to each other and solve for x:

4 + x = 1 + 2x

Solve for x.

3 = x

Hence, the call duration that costs the same on both plans is 3 minutes.

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We can simplify the expression to get:

[tex]\sqrt[4]{x^3}[/tex]

Here we want to simplify the following expression:

[tex]\sqrt[]{x} *\sqrt[4]{x}[/tex]

Remember that a square root is equivalent to a power of 1/2, and the fourth root is equivalent to a power of 1/4.

Then we can write:

[tex]\sqrt[]{x} *\sqrt[4]{x} = x^{1/2}*x^{1/4}[/tex]

Now in the product we just add the exponents:

[tex]\sqrt[]{x} *\sqrt[4]{x} = x^{1/2}*x^{1/4} = x^{1/2 + 1/4} = x^{3/4} = \sqrt[4]{x^3}[/tex]

That is the expression si,plified.

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If 18% of middle school student voted in a school election and number of students who voted is 213 , then the total students in the middle school is approximately 1184 students .

Let "x" be = total number of middle school students.

We know that 18 percent  of the students voted = 0.18x, and is equal to 213  ;

that means , ⇒ 0.18x = 213 ;

Now we need to solve for x,

We divide both sides by 0.18 ;

⇒ x = 213/0.18  ;

Simplifying, we get:

⇒ x = 1183.33

Since the number of students cannot be in decimal ,

So ,  the actual number of students must be greater than or equal to 1183.33.

Therefore, the middle school has approximately 1184 students.

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Mae Ling make $590 in a work week if she sold $4,500 worth of merchandise.

The given is:

We need to find how much she would earns in a work week

Mae Ling earns a weekly salary of $320

She earns a 6.0% commission on sales

She sold by $4,500 in that week

Add $320 to the product of 6.0% and $4,500

She made = 320 + (6.0% × 4,500)

6.0% = 6.0 ÷ 100 = 0.06

She made = 320 + (0.06 × 4,500)

She made = 320 + 270

She made = 590

She would make $590 in a work if she sold $4,500 worth of merchandise.

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The measure of the length of the shortest side will be 15 units.

If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. How frequently one value contains or is contained within another is shown by the numerical connection between the two values.

Given that the perimeter of the triangle is 100 and the ratio of the sides of the triangle is 3:5:12.

The length of the shortest side will be calculated as:-

3x + 5x + 12x = 100

20x = 100

x = 20

Length = 3x

Length = 3 x 5 = 15 units

Hence, the shortest side will be 15 units.

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Answer:

Step-by-step explanation:

He is now 14 years old because if you minus 21 and 7, it will be 14

Answer:

If your friend says that he will be 21 years old in seven years, then he is currently 21 - 7 = 14 years old.

Step-by-step explanation:

The best description of the transformation for the image being projected on the retina is A. A dilation with a scale factor between 0 and - 1 and center at the nodal point.

An mage is inverted and reversed as it passes through the lens of the eye, and is then projected upside down and reversed onto the retina. The process of transforming the image is called "rectification."

In mathematical terms, a dilation would have taken place because the object was shrunken by the eyes at the nodal point. When an object shrinks , then the scale factor is between 0 and 1 but because this image is inverted, the scale factor is between 0 and - 1.

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The probability that the department store will get at most 3 calls in a 55 minute period is 0.066

The Poisson distribution is a discrete probability function that means the variable can only take specific values in a given list of numbers, probably infinite. A Poisson distribution measures how many times an event is likely to occur within “x” period of time.

It is given that a department store gets an average of 16 calls in a 2 hour or 161055 = 223 calls per minute

Find the probability by Poisson distribution with parameter

λ = 223

P(X = x) = λˣе - λx!

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

   = (223)⁰е - 223(0!) +(223)¹е - 223(1!) +(223)²е - 223(2!) +(223)³е - 223(3!)

  = 0.0006 + 0.004 + 0.018 + 0.043

P(X ≤ 3) ≈ 0.066

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The solutions of the given absolute value equation |4/3 x + 2| - 6 = 0 are x = 3 and x = -6.

Absolute value equations are kind of equations which includes the absolute value symbol in the expression.

For example : |x - 5| = 4 is an absolute value equation.

The given absolute value equation is,

four thirds times x plus 2 end quantity minus 6 equals 0.

|4/3 x + 2| - 6 = 0

Isolating the absolute value quantity on one side,

|4/3 x + 2| - 6 + 6 = 0 + 6

|4/3 x + 2| = 6

This can be written as,

4/3 x + 2 = 6 and 4/3 x + 2 = -6

Solving each of these,

4/3 x + 2 = 6

4/3 x = 4

x = 3

4/3 x + 2 = -6

4/3 x = -8

x = -6

Hence the value of x are 3 and -6.

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Daniella and her friends collected a total of 44 shells.

What is linear equation ?

Linear equation can be defined as equation in which highest degree is one.

Given ,

Daniella and her 10 friends are collecting shells on the beach to make crafts.

After they have collected the shells and put them in a pile, they split them evenly among the group. Each person gets 4 shells.

The correct equation for this problem is:

s = 11 x 4

where s is the total number of shells collected.

Simplifying this equation, we have:

s = 44

Therefore, they collected a total of 44 shells.

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The value of z   is -1.09.

The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a given data collection.

Given: P(Z<z)=0.14

To find the value of z such that 0.14 of the area lies to the left of z.

We will use z-score table to get the value of z here.

IN z-score table, we have

For P(Z<-1.09)=0.14

Hence, the value of z is -1.09.

Its approximate value is -1.09

So the final answer is z=-1.09.

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The total cost of the item would be [tex]$115[/tex].The original price of oranges purchased by Mr. S Ralph can be calculated by subtracting the sales tax from the total cost.

Sales tax is calculated as a percentage of the original price. In this case, the sales tax is 15%, meaning that the original price can be found by dividing the total cost (which includes the sales tax) by 1.15.To calculate the original price of the oranges, divide the total cost of $165.31 by 1.15. This gives us a total of $143.87. Thus, the original price of the oranges purchased by Mr. S Ralph is $143.87 without the sales tax included.Sales tax is a form of taxation imposed by governments on goods and services. Generally, for the majority of goods and services, the sales tax is calculated as a percentage of the original price. This means that the total cost of the goods or services can be calculated by adding the percentage of sales tax to the original price.For example, if an item costs $100, and the sales tax rate is 15%, the total cost of the item would be calculated by multiplying the original price by 1.15 (100% + 15% = 115%). The total cost of the item would be [tex]$115[/tex].

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An estimated Rs. 1863.40 will be needed to cement the route.

Diameter of park [tex]$=7 \mathrm{~m}$[/tex]

so, radius of park [tex]$=\mathrm{r}_1=3.5 \mathrm{~m}$[/tex]

Width of park [tex]$=0.7 \mathrm{~m}$[/tex]

Bigger radius of park [tex]$=\mathrm{r}_2=0.7+3.4=4.2 \mathrm{~m}$[/tex]

Now, Area of path = area of bigger circle -area of smaller circle

[tex]$=\pi r_2^2-\pi r_1^2=$ $\pi\left(r_2^2-\mathrm{r}_1^2\right)=\frac{22}{7}\left(4.2^2-3.5^2\right)=\frac{22}{7}(17.64-12.25)=16.94 \mathrm{~m}^2$[/tex]

Also, Cost of expenditure = rate [tex]$\times$[/tex] area [tex]$=110 \times 16.94=1863.40$[/tex]

Cost of Expenditure of cementing the path is Rs. 1863.40.

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Answer:

The length of one lap around the path is 2π x 350 m, which is equal to 2200 m.

Jimmy jogs 2200 m x 3 laps x 5 days, which is equal to 33000 m or 33 km.

Step-by-step explanation:

Answer:

8 < f

8 must be strictly lesser than f, not greater than or equals to.

Answer:

Rs 3520 is divided in the ratio 11:12:17 as rs 968, rs 1056, and rs 1469

Step-by-step explanation:

According to the question, we have to divide rs 3520 in the ratio 11:12:17

let the common ratio be x

so, total share= (11+12+17)x = 40 x

for the first person, share would be (11x/40x)*(Rs 3520)

=Rs 968

for the second person, share would be (12x/40x)*(Rs 3520)

=Rs 1056

for the third person, share would be (17x/40x)*(Rs 3520)

=Rs 1496

The shares are Rs 968, Rs 1056, and Rs 1469

hope this helps :)

The number of people who become aware of the product at time t is [tex]p(t) = 5(1 - 0.9^{\frac{t}{10} })[/tex]

The advertising company wants to introduce a new product to a population of 5 million people. They assume that no one was aware of the product at the beginning of the campaign. They also know that after 10 days of advertising, 10% of the people became aware of the product. To find out how many people become aware of the product at time t, they use a function called p(t).

The function p(t) represents the number of people (in millions) who become aware of the product by time t. The company assumes that the rate at which p increases is proportional to the number of people still unaware of the product. This means that the more people who are unaware of the product, the faster the number of people who become aware of it will increase.

To express the proportionality mathematically, we can use the equation:

p'(t) = k [5 - p(t)]

Where p'(t) is the rate of change of p with respect to time t, and k is the proportionality constant that determines the speed of the increase. The quantity (5 - p(t)) represents the number of people who are still unaware of the product at time t. This means that as p(t) gets closer to 5 million, the rate of increase of p(t) will slow down.

To solve this equation, we need to use calculus. Integrating both sides of the equation, we get:

ln|5 - p(t)| = kt + C

Where C is the constant of integration. To determine the value of C, we use the initial condition that p(0) = 0. This means that at the beginning of the campaign, no one was aware of the product. Substituting this into the equation, we get:

ln|5 - 0| = k(0) + C

Simplifying, we get:

C = ln(5)

Substituting this value into the equation, we get:

ln|5 - p(t)| = kt + ln(5)

To find the value of p(t) at a specific time t, we can solve for p(t) by taking the exponential of both sides of the equation:

[tex]|5 - p(t)| = e^{kt+ln(5)}[/tex]

Simplifying, we get:

[tex]5 - p(t) = 5e^{kt}[/tex]

Or:

[tex]p(t) = 5(1 - e^{kt})[/tex]

To find the value of k, we can use the fact that 10% of the people were aware of the product after 10 days of advertising. This means that:

p(10) = 0.1(5) = 0.5

Substituting this into the equation, we get:

[tex]0.5 = 5(1 - e^{10k})[/tex]

Solving for k, we get:

k = -0.1 ln(0.9)

Substituting this value into the equation for p(t), we get:

[tex]p(t) = 5(1 - e^{-0.1ln(0.9)t})[/tex]

Simplifying, we get:

[tex]p(t) = 5(1 - 0.9^{\frac{t}{10} })[/tex]

This is the formula that tells us how many people will become aware of the product at time t.

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(a) Potential on the opposite sides of the positive and negative plates is 8475 V and -8475 V, respectively. (b). 772 m/s is the speed at which the positive plate will be struck.

A more technical or sophisticated phrase, velocity, is occasionally used interchangeably with speed to refer to extremely high rates of linear or circular speed, such as the velocity of a bullet.

a). Positivplate should be on the right and negativeplate should be on the left.

Potential equals zero at the center of the plates.

Electric field between it plates: 30e⁻⁶/8.85e⁻¹² (338 V/m) = sigma/e0

Potential is equal to 3389830x, where x is the distance in meters from the center of the plates.

Where x is the distance in meters from the center of the plates, the potential to the left of either the middle point equals -3389830x.

Potential outside of the positive plate is equal to 3389830*0.005/2, or 8475 V.

The potential is -8475 V on the contrary side of the negative plate.

Potential between it plates is equal to -8474 + 3389830x, where x is the distance in meters from the negative plates.

b). Electron energy at the positive plate is equal to [8475 - -8475]. eV = 2*8475*1.6e⁻¹⁹ = 2.712*10⁻¹⁵ J

Speed = sqrt(2E/m) = sqrt(2*2.712e-15/9.1e⁻³¹) = 772 meters per second.

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A polygon with a sum of interior angles of 3960 has 22 sides.

The sum of the interior angles of a polygon can be calculated using the formula:

(n-2) * 180

where n is the number of sides of the polygon. This formula is derived from the fact that the total degree measure of a polygon is equal to the sum of the degree measures of its interior angles. In a polygon with n sides, there are n angles, each measuring 180 degrees. So the total degree measure of a polygon with n sides is n * 180.

Now, if we subtract the degree measures of two angles, we are left with the sum of the degree measures of the remaining n-2 angles. This is why the formula for the sum of the interior angles of a polygon is given as (n-2) * 180.

To find the number of sides of a polygon given its sum of interior angles, we can rearrange the formula as follows:

n = (Sum of interior angles / 180) + 2

So, if the sum of the interior angles is given as 3960, we can plug that into the formula:

n = (3960 / 180) + 2

n = 22

Therefore, a polygon with a sum of interior angles of 3960 has 22 sides.

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How many sides does a polygon have if the sum of the interior angles is 3960?

Answer:

y – 7 = 3(x – 5)

Step-by-step explanation:

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 3}(x-\stackrel{x_1}{5}) \\\\\\ y-7=3x-15\implies {\Large \begin{array}{llll} y=3x-8 \end{array}}[/tex]

Answer: 5/12

Step-by-step explanation:

- For the ease of the problem, turn them into improper fractions, so it would be:

13/3 divided by 14/5 divided by 26/7

- Next, let's turn the equation from division to multiplication. This can be done by flipping the fractions of everything being divided, so:

13/3 times 5/14 times 7/26

- We can cross out some parts of the fraction, like 13 and 26, 14 and 7, which simplifies our equation to:

1/3 times 5/2 times 1/2 = 5/12

Answer:

[tex]\dfrac{5}{12}[/tex]

Step-by-step explanation:

Given equation:

[tex]4 \frac{1}{3} \div 2 \frac{4}{5} \div 3 \frac{5}{7}[/tex]

Convert the mixed numbers into improper fractions:

[tex]\dfrac{4 \times 3+1}{3} \div \dfrac{2 \times 5+4}{5} \div \dfrac{3 \times 7+5}{7}[/tex]

[tex]\dfrac{13}{3} \div \dfrac{14}{5} \div \dfrac{26}{7}[/tex]

[tex]\textsf{Apply the fraction rule:} \quad \dfrac{a}{c}\div\dfrac{b}{d}=\dfrac{a}{c}\times \dfrac{d}{b}[/tex]

[tex]\dfrac{13}{3} \times \dfrac{5}{14} \times \dfrac{7}{26}[/tex]

Multiply the fractions:

[tex]\dfrac{13\times5\times7}{3 \times14 \times 26}[/tex]

[tex]\dfrac{455}{1092}[/tex]

The greatest common factor of 455 and 1092 is 91.

Therefore, divide the numerator and denominator by the GCF:

[tex]\dfrac{455 \div 91}{1092\div 91}=\dfrac{5}{12}[/tex]