A toddler is playing with his toys in the bathtub. He is using a toy shaped like a rectangular prism, filling it with water to the top, and filling his other toys to overflowing.

Rectangular prism toy:


a. What is the volume of the rectangular prism toy?


b. What formula did you use to calculate your answer?


C. What formula did you use to calculate the volume of the cylindrical toy?


help

Answer:

y = - [tex]\frac{5}{6}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 5 ) and (x₂, y₂ ) = (6, 0 )

m = [tex]\frac{0-5}{6-0}[/tex] = [tex]\frac{-5}{6}[/tex] = - [tex]\frac{5}{6}[/tex]

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = - [tex]\frac{5}{6}[/tex] x + 5 ← equation of line

Answer:

y= -x+3

Step-by-step explanation:

We can see that our given equation is in slope-intercept form

, where m represents slope of line and b represents the ­y-intercept.

Upon looking at our given equation, we can see that the slope of our given line is 1

and the ­y-intercept is at point

.0,3

Upon graphing our given equation, we will get our required graph as shown below:

The digits in the hundreds place is 2.

The digits in the hundredths place is 9.

The digits in the ten thousandths place is 1.

A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:

Based on the numerical data (number) provided above 248.7961, we can reasonably infer and logically deduce that the place value of one (1) is ten thousandths, nine (9) is hundredths, and two (2) represent hundreds.

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To maximize profit, the manufacturer should produce 22 thousand units of each brand, and the maximum profit is:

Profit = (39 × 22) + (49 × 22) - (61 - 39)×(71 - 49) = $256 thousand.

Profit is a term used in business and economics to refer to the amount of money or value that is gained after deducting the cost of production or acquisition from the revenue earned.

Mathematically, profit can be calculated as follows:

Profit = Revenue - Cost

To maximize profit, we need to determine the optimal values of P1 and P2. We can do this by setting up the profit function as follows:

Profit = Total Revenue - Total Cost

Profit = (P1 × x) + (P2 × y) - C

Profit = (P1 × (61 - P1)) + (P2 × (71 - P2)) - (61 - P1)×(71 - P2)

Taking the derivative of the profit function with respect to P1 and P2 and setting it equal to zero will give us the optimal values of P1 and P2 that maximize profit:

∂Profit/∂P1 = 61 - 2P1 + P2 = 0

∂Profit/∂P2 = 71 - 2P2 + P1 = 0

Solving these equations simultaneously, we get P1 = 39 and P2 = 49.

To find the quantities of each brand that should be produced, we can substitute P1 and P2 into the demand functions for x and y:

x = 61 - P1 = 22 thousand units of brand 1

y = 71 - P2 = 22 thousand units of brand 2

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The value of the side QR labelled x is equal to 2√3 using the trigonometric ratio of tan 45° for the right triangle QRT.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

using the trigonometric ratio of tan 45°

{recall that tan 45° = 1}

tan 45° = QR/RT {opposite/adjacent}

tan 45° = x/2√3

x = tan 45 × 2√3 {cross multiplication}

x = 1 × 2√3

x = 2√3

Therefore, the value of the side QR labelled x is equal to 2√3 using the trigonometric ratio of tan 45° for the right triangle QRT.

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The image that results from the dilation transformation is as shown in the attached file with coordinates as:

G'(0, -8)

H'(8, 0)

I'(-8, 4)

A dilation is defined as a transformation that produces an image that is the same shape as the original, but is a different size.

The coordinates of the given triangle are:

G(0, -2)

H(2, 0)

I(-2, 1)

Now, when an object with coordinates is dilated by a factor about the origin, what we will do is to multiply each coordinate by that factor . The factor of dilation is 4 and as such we have:

G(0, -2) * 4 = G'(0, -8)

H(2, 0) * 4 = H'(8, 0)

I(-2, 1) * 4 = I'(-8, 4)

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Thus, the simplification of the polynomial in standard form for (x − 7)² is subtracted from 6x is found as: : (- x² + 20x - 49)

A degree two polynomial is a quadratic polynomial. The formula for a  quadratic polynomial is f(x)=ax2 + bx + c.

A quadratic equation is one that contains a quadratic polynomial. For the answers of any arbitrary quadratic problem, there is a closed-form solution described as the quadratic formula.

standard form of quadratic polynomial:

ax²  + bx + c

The given quadratic polynomial:

= (x − 7)²

On expansion:

= x² + 7² - 2*7*x

= x² + 49 - 14x

Now, (x − 7)² is subtracted from 6x.

=  6x - (x − 7)²

=  6x - (x² + 49 - 14x)

=   6x - x² - 49 + 14x

= - x²  + 20x - 49

Thus, the simplification of the polynomial  in standard form for (x − 7)² is subtracted from 6x is found as: (- x²  + 20x - 49).

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Answer:

The equation would be y = 3x - 7

Step-by-step explanation:

The equation of the trend line given the two coordinates is: y = -6x - 4

How to find the equation of a line?

The formula to find the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

The formula to find the equation of a line between two coordinates is:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

From the given two coordinates, we can say that:

(y - 8)/(x + 2) = (-10 - 8)/(1 + 2)

(y - 8)/(x + 2) = -6

y - 8 = -6x - 12

y = -6x - 4

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Step-by-step explanation:

common multiples are numbers that can be divided without remainder by both numbers.

12. 3 and 5

3 and 5 are both prime numbers, so their common multiple are multiples of their product (3×5 = 15).

so,

1×15 = 15

2×15 = 30

3×15 = 45

13. 4 and 6

the prime factors of 4 are

2×2

the prime factors of 6 are

2×3

the last common multiple is the product of the longest chains of prime factors of the numbers :

2×2 × 3 = 12

6 has only one 2 factor, 4 has two 2 factors, so that is the longest chain. and 6 has one 3 factor, which makes it the longest chain for that.

the multiples for 4 and 6 and now the multiples of 12 :

1×12 = 12

2×12 = 24

3×12 = 36

4×12 = 48

14. 3 and 7

they are both again prime numbers, so we are looking for multiples of their product (3×7 = 21).

1×21 = 21

2×21 = 42

15.

what do we need to do to change the denominator by keep the overall value of the fraction ?

we need to multiply numerator and denominator by the same value (e.g. by 2/2, 3/3, 4/4, ...)

3/4 = 6/8 = 9/12 = 12/16

16.

as before.

2/3 = 4/6 = 6/9 = 8/12

17.

as before

4/5 = 8/10 = 12/15 = 16/20

18.

now we need to find the largest n/n factor hidden in the fraction. by eliminating that we get the core (simplified) value of the fraction.

4/12 = 1/3 × 4/4

so,

1/3 is the simplified fraction.

19.

as before

6/10 = 3/5 × 2/2

3/5 is the simplified fraction.

20.

as before

4/8 = 1/2 × 4/4

1/2 is the simplified fraction.

Answer:

32

Step-by-step explanation:

add the exponents

2 + 3 = 5

2⁵ = 32

Every [tex]2.75[/tex] kilometres in an elevated coaxial cable, the energy decreases by a factor of 10. This indicates that the transmit strength drops with one (0.1) of its original value after every [tex]2.75[/tex] kilometres.

Let's write "d" to represent the signal's maximum range before it loses strength and dips to [tex]37.5 W[/tex]. The following formula can be used to determine the distance [tex]d:  P(d) = P(0) / 10^(d / L)[/tex]

[tex]P(d)[/tex] is the signal's power after travelling a distance of d,[tex]P(0)[/tex] is the signal's initial strength,[tex]L[/tex] is indeed the attenuation length in this instance ([tex]2.75 km[/tex]), and "([tex]37.5 W[/tex])" stands for "to the power of d/L".

Inputting the values provided yields: [tex]37.5 μW = 0.375 W / 10^(d / 2.75 km)[/tex]0  The result of dividing both sides with [tex]0.375 W is: .0 /001 = 1 10^(d / 2.75 km)[/tex]The result is: when we take the logarithmic (based 10) of both sides. [tex]-4 = -(d / 2.75 km)[/tex]By dividing all sides by [tex]2.75[/tex] kilometres, we arrive at:[tex]11 km = d[/tex]

As a result, the signal may travel 11 kilometres before losing power and becoming weaker [tex](37.5W) .[/tex]

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We can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.

A functiοn frοm a set X tο a set Y is an assignment οf an element οf Y tο each element οf X. The set X is called the dοmain οf the functiοn and the set Y is called the cοdοmain οf the functiοn.

A functiοn, its dοmain, and its cοdοmain, are declared by the nοtatiοn f: X→Y, and the value οf a functiοn f at an element x οf X, denοted by f(x), is called the image οf x under f, οr the value οf f applied tο the argument x.

Functiοns are alsο called maps οr mappings, thοugh sοme authοrs make sοme distinctiοn between "maps" and "functiοns" (see § Other terms).

Tο plοt twο pοints οn the line fοr the functiοn p(x) = 1 - 12x, we can chοοse any twο values οf x and find the cοrrespοnding values οf p(x).

Fοr example, if we chοοse x = 0, then p(0) = 1 - 12(0) = 1, sο the pοint (0,1) is οn the line.

If we chοοse x = 1, then p(1) = 1 - 12(1) = -11, sο the pοint (1,-11) is οn the line.

Therefοre, we can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.

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Answer:

Translate 3 right and 1 up.

Step-by-step explanation:

Looking at the picture and count the movement.

Answer:

Step-by-step explanation:

3 units right.

1 unit up.

Each of the letters is moved by these amounts to create the new image.

Answer:

u rock tgu hjgr yyihh yihgg

The explicit formula for the geometric sequence is  [tex]a_n=25(\frac{1}{5})^{n-1}[/tex].

What is explicit formula for geometric series?

The explicit formula for geometric sequence is [tex]a_n=a_1(r)^{n-1}[/tex] where r is common ratio.

Here the given sequence is 25,5,[tex]\frac{1}{2}[/tex]...

Here first term [tex]a_1=25[/tex]  

Common ratio  = [tex]$ \frac{a_2}{a_1}=\frac{5}{25}=\frac{1}{5}[/tex]

Now, Explicit formula [tex]$ a_n=a_1(r)^{n-1}[/tex]

=> [tex]$ a_n=25(\frac{1}{5})^{n-1}[/tex]

Hence the explicit formula of geometric series is  [tex]$ a_n=25(\frac{1}{5})^{n-1}[/tex].

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Answer:

There is no solution

Step-by-step explanation:

Answer:

x+1

Step-by-step explanation:

For the first part of the expression, factor into (x+2)(x+1).

(x+2)(x+1)/(x+2)

The x+2 cancels out, so the answer is x+1

Answer:

C . False, a soundscape can only be written out in words.

Step-by-step explanation:

Because :

False, a soundscape cannot be written by using a table and diagrams.

Explanation:

A soundscape is the acoustic environment as perceived by humans, in context. The term was originally coined by Michael Southworth, and popularised by R. Murray Schafer. There is a varied history of the use of soundscape depending on discipline, ranging from urban design to wildlife ecology to computer science.

Answer:

2400

Step-by-step explanation:

before anything got taken away they added 200 wich means before they added that they had 2200 and if 700 pounds were removed twice that would mean the mound lost 1400 pounds and so if you add 1000 to the 1400 that they took you can find the amount that was there before.l

Answer:

C.  136

Step-by-step explanation:

Add up the surface areas of each individual section. Area is length times width.

Lets start by figuring out the area of the 2 by 6 rectangle on the bottom. 2cm*6cm=12 sq cm. The rectangle on the top right also has an area of 2cm*6cm. So it also has an area of 12 sq cm. lets figure out the area of the smaller rectangle on the right side. 7cm times 2 cm equals 14 cm squared. There is also a 7cm by 2cm box in the middle of the pattern. so 14 + 14 = 28, + 12 + 12= 52. so all of the tiny rectangles added up equal 52. Finally, lets figure out the area of the two 6*7 rectangles. 6*7= 42. 42*2= 84. 84 is the area of the two big rectangles added together. So add the two totals to get 52 sq cm+ 84 sq. cm = 136 sq. cm.

Answer:

The discriminant of a quadratic equation is the expression found under the square root sign in the quadratic formula, which is b^2 - 4ac. The discriminant reveals information about the nature of the roots of the equation.

If the discriminant is positive, the quadratic equation has two distinct real roots. This means that the equation can be factored into two linear factors, each of which can be set equal to zero to solve for the roots.

If the discriminant is zero, the quadratic equation has one real root, which is a repeated root. This means that the equation can be factored into a linear factor that occurs twice.

If the discriminant is negative, the quadratic equation has two complex (non-real) roots, which are conjugates of each other. This means that the equation cannot be factored into two linear factors with real coefficients.

In summary, the nature of roots of a quadratic equation is determined by the value of the discriminant, which depends on the coefficients of the quadratic equation.

Step-by-step explanation:

Answer:

26.5$

Step-by-step explanation:

Calculate the 5% of 530, which is 530 * 0.05, whic is equal to 26.5$

Answer:

(b*c+c-1+b)*(-c+b*c-b-1)

or

(b*c + c - 1 + b)*(-c + b*c - b -1)

put both in the same order:

(bc + b + c - 1)( bc - b - c - 1)

Turn the crank:

(bc)2 + b2c + bc2 - bc      -b2c -b2 - bc + b     -bc2 - bc - c2 + c    -bc - b - c + 1

Cancel things....

(bc)2   - bc  -b2 - bc   - bc - c2  -bc   + 1

(bc)2 - 4bc - b2 - c2  + 1

Answer: i got 213

Step-by-step explanation:

The value of BC in triangle ABC is 23.

What is triangle?

A closed plane figure with three straight sides and three angles is known as a triangle. It is made by joining three non-collinear points. Triangles are important in geometry and have various types based on their sides and angles, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles.

Given:- triangle ABC and DEF are similar.

So , AC = DF

Therefore,

4x-23 = 2x+2

4x – 2x = 2 + 23

2x = 25

x = 25/2 = 12.5

therefore, AC = 4x – 23

                        = 4 * 12.5 – 23

                        = 50 – 23

                       AC =27

So ,From triangle DEF

EF = 2x-2

    = 2*12.5 – 2

    = 25 – 2

  EF  = 23

As triangle ABC and DEF are similar.so,

BC = EF = 23

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Proportionately, if the compound interest on Rs 500 for years is Rs 398, the compound interest on Rs. 625 is Rs. 497.50.

Proportion is a part or portion of the whole.

Proportion indicates the ratio that one quantity or value possess in relation to or when compared or equated to another.

We determine proportion as the quotient of one value divided by another.  Proportion can also be expressed as a percentage by multiplying the resultant quotient by 100.

The compound interest on Rs. 500 = Rs. 398

Thus, proportionately, the compound interest on Rs. 625 will be Rs. 497.50 (Rs 398/Rs. 500 x 625).

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The maximum value οf the functiοn is 4.

Simple Harmοnic Mοtiοn, οr SHM, is a mοtiοn in which the restοring fοrce is inversely prοpοrtiοnal tο the bοdy's displacement frοm its mean pοsitiοn. This restοrative fοrce always pοints in the directiοn οf the mean pοsitiοn. A particle mοving in simple harmοnic mοtiοn accelerates as a(t) = -2 x. (t). The particle's angular velοcity is indicated in this equatiοn by the symbοl.

Given functiοn οf simple harmοnic mοtiοn is d= 4 sin(πt/8)

Nοw we need tο find abοut what is the maximum value οf .

We knοw that value οf sine functiοn varies frοm -1 tο 1.

that means fοr any value οf t, maximum value οf sine functiοn is 1.

sin(πt/8)<1

d≤4

Hence the maximum value οf the functiοn is 4.

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