Consider the following problem:
The length s(t) of the side of the base of a square prism is decreasing at a rate of 7
kilometers per minute and the height h(t) of the prism is increasing at a rate of 10
kilometers per minute. At a certain instant to, the base's side is 4 kilometers and the
height is 9 kilometers. What is the rate of change of the surface area A(t) of the
prism at that instant?
Match each expression with its given value.

Answer:

45 and 63

Step-by-step explanation:

7x-5x=18

2x=18

2 2

x=9

7(9)=63

5(9)=45

Answer:

754.93 in total with an increase of 4.93

Step-by-step explanation:

Answer:

Volume of rectangular prism = 10/9 inch³

Step-by-step explanation:

Given:

Size of each cube = 1/3 inch

Find:

Volume of rectangular prism

Computation:

Length of rectangular prism = 2 x [1/3]

Length of rectangular prism = 2/3 inch

Width of rectangular prism = 3 x [1/3]

Width of rectangular prism = 3/3

Width of rectangular prism = 1 inch

Height of rectangular prism = 5 x [1/3]

Height of rectangular prism = 5/3 inch

Volume of rectangular prism = Length x Width X Height

Volume of rectangular prism = [2/3] x [1] x [5/3]

Volume of rectangular prism = 10/9 inch³

Answer:£21.00

Step-by-step explanation:

One pizza: (£35/5) =£7

Three pizza's: (£7x3)=£21

Answer:

5q + 9

Hope that helps! :)

-Aphrodite

Step-by-step explanation:

Answer:

P = 59/5

Step-by-step explanation:

Answer:

a) Combination of 5 out of 30:

b) Combination of 2 males:

Combination of 3 females:

The number of ways with 2 males and 3 females:

c) Required probability is:

Answer:

1 = 24 degrees

2 = 156 degrees

Step-by-step explanation:

Solve the equation for x:

x -  15 +4x = 180

5x = 195

x = 39

so 1 = (39-15) = 24 degrees

so 2 = (4x39) = 156 degrees

Answer:

18, 12

Step-by-step explanation:

Assuming this is follow-up from the previous question you asked? If not, I apologize for misunderstanding.

Dilation factor by 3 is bigger than 1 = Expansion

Originally 6, 4

6*3 = 18

4*3 = 12

Answer:

18,12

Step-by-step explanation:

W (1, -2), X (7,-2), Y (7,-6), and Z (1, -6).

To dilate the shape, multiply it's coordinates by the scale factor.

W'(3,-6), X'(21,-6), Y'(21,-18), Z(3, -18)

The distance formula: [tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]

plug W'(3,-6) and X'(21,-6) in to get the length

[tex]\sqrt{(3-21)^2+(-6-(-6))^2}=\sqrt{(-18)^2 +0^2}=\sqrt{324} =18[/tex]

plug X(21,-6) and Y(21,-18) to get the width

[tex]\sqrt{(7-7)^2+(-2-(-6))^2}=\sqrt{0^2 +4^2}=\sqrt{16} =4[/tex]

[tex]\sqrt{(21-21)^2+(-6-(-18))^2}=\sqrt{0^2 +12^2}=\sqrt{144} =12[/tex]

The Kilograms of type B that are in one bag of the Latoya's Coffee shop blend would be = 3kg

A mixture is defined as the combination of two or more components which can or cannot be separated by ordinary methods.

The coffee blend of LaToya shop = Type A and B

A bag of the coffee blend = 6kg of Type A.

4 bags of coffee blend = 36kg

Therefore 4 bags of coffee blend contains = 6 see×4 = 24 kg of Type A

Type B in each bag = 36 - 24 = 12/4 = 3kg.

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If Raj was getting a 5% commission, he would make 24000 * 5% = $<<240005.01=1200>>1200 on $24,000 of sales.

If he is now getting a 6.5% commission, he will make 24000 * 6.5% = $<<240006.5.01=1560>>1560 on $24,000 of sales.

Thus, Raj will make 1560 - 1200 = $<<1560-1200=360>>360 more on $24,000 of sales with his new commission rate of 6.5% than he did with his old commission rate of 5%.

Given:

Radius of the circle = 6 inches

Central angle = 75 degrees.

To find:

The length of subtended arc, i.e., x.

Solution:

The formula for arc length is:

[tex]s=2\pi r\times \dfrac{\theta}{360^\circ}[/tex]

Where, r is the radius and [tex]\theta [/tex] is the central angle.

Putting [tex]s=x, r=6, \pi=3.14, \theta =75^\circ[/tex] in the above formula, we get

[tex]x=2(3.14)(6)\times \dfrac{75^\circ}{360^\circ}[/tex]

[tex]x=2(3.14)(6)\times \dfrac{5}{24}[/tex]

[tex]x=7.85[/tex]

[tex]x\approx 7.9[/tex]

Therefore, the value of x is 7.9 inches.

Answer:Radius of the circle = 6 inchesCentral angle = 75 degrees.

Step-by-step explanation:

Answer:

It models exponential growth

Step-by-step explanation:

Use the formula f(x)=a(1+r)^x where r is the growth rate, a is the principal value, and x is the length of time.

Since r would be equal to 2.3-1=1.3, this means a growth rate of 130%, which means the model models exponential growth since r>1.

Answer:

A

Step-by-step explanation:

[tex]arc \ length = 2\pi r \frac{\theta}{360} = \\\\[/tex][tex]2 \pi *9 * \frac{135}{360} =21.205[/tex]

[tex]\frac{3\pi }{4} =\frac{3*180}{4}=135[/tex]

The error in the work lies in line 3 where the square root is calculated inaccurately.

The opposite of squaring an integer is finding its square root. The square root of a number can be found by looking for a number that, when squared, yields the original value.

The error is in line 3, line 4 and line 5.

The error in line 3 is inaccurate calculation of the value of square root of 4.

The error in line 4 is a mathematical calculation error.

The error in line 5 is a mathematical calculation error.

The correct answer in Line 3 is:

[tex]6 * 2 *\sqrt{5} -3\sqrt{5}[/tex]

The correct answer in Line 4 is:

[tex]12\sqrt{5} - 3\sqrt{5}[/tex]

The correct answer in Line 5 is:

[tex]9\sqrt{5}[/tex]

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The number of times 5×10³ greater than 15×10⁹ is 3×10⁶.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

Given that, 15×10⁹ and 5×10³.

Number of times 5×10³ greater than 15×10⁹ is

Now, 15×10⁹/5×10³

= 3×10⁶

Therefore, 3×10⁶ times 5×10³ greater than 15×10⁹.

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Answer:

71 in²

Step-by-step explanation:

surface area = (4×6)+(2×½×4×5)+(2×½×6×4.5)

= 24+20+27 = 71 in²

Answer:

18 degree

Step-by-step explanation:

The given drug experiment is an example of observation.

There are three major types of statistical studies :

Given is that a doctor gives 10 patients Drug A and 10 patients Drug B and records the differences.

Giving 10 patients Drug A and 10 patients Drug B and then recording the differences is an example of observation.

Therefore, the given drug experiment is an example of observation.

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60 is my resultados of area

Answer

[tex]54 \sqrt{3} [/tex]

Step-by-step explanation:

Each interior angle is 120°for an hexagon.... Bisecting each will give an angle of 60° and thus dividing the hexagon into 6 equilateral triangles as the Bisecting lines meet at the centre of the hexagon. So find area of each equilateral triangle and multiply by 6

Area=

[tex] \frac{1}{2} b \times h \times 6 \\ = 3bh \\ = 3 \times 6 \times 3 \sqrt{3} [/tex]

[tex] = 54 \sqrt{3 } cm ^{2} [/tex]

Answer:

y = 1/3x - 7

Step-by-step explanation:

start with the point-slope form:

(y-y1) = m(x-x1)

substitute the values of (x,y) into the formula:

(y-(-5)) = 1/3(x-6)

y+5 = 1/3x - 2

now write in slope-intercept form:

y = 1/3x - 2 - 5

y = 1/3x - 7

25 coins represent 25 percent of Jocelyn's collection.

A percentage is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The symbol "%" is frequently written after the number to indicate percentages.

given, Jocelyn has a collection of 100 coins.

100% of her collection represents = 100 coins

1 %  of her collection represents = 100/100 coins

1%  of her collection represents = 1 coin

thus,

25%  of her collection represents = 1*25 coins

25%  of her collection represents = 25 coins

therefore, 25 percent of the collection of Jocelyn represents 25 coins.

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Sean baked 372 cupcakes in total.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Sean bakes 18 dozen chocolate cupcakes,

and 13 dozen vanilla cupcakes.

There are 12 cupcakes in one dozen.

To find the number of cupcakes:

Using multiplication operation,

18 x 12 = 216.

13 x 12 = 156.

The number of cupcakes = number of chocolate cupcakes + number of vanilla cupcakes.

The number of cupcakes = 216 + 156

The number of cupcakes = 372

Therefore, the number of cupcakes are 372.

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7½

7×2+1/2

14+1/2

15/2

12½

12×2+1/2

24+1/2

25/2

Answer:

A

Step-by-step explanation:

multiple lines meeting at 90 degrees. hope this helped

Answer:

2695.49 m

Step-by-step explanation:

A = 2πrh + 2πr2

2 · π · 13 · 20 + 2 · π · 132

2695.4865

Explanation:

You have a right triangle with legs of 11 and 60. The hypotenuse is unknown.

Use the pythagorean theorem to find the hypotenuse.

[tex]a^2 + b^2 = c^2\\\\11^2 + 60^2 = c^2\\\\121 + 3600 = c^2\\\\3721 = c^2\\\\c^2 = 3721\\\\c = \sqrt{3721}\\\\c = 61\\\\[/tex]

The ramp is exactly 61 inches long.

Answer:

[tex](\frac{f}{g})(x) = \frac{\left(x+1\right)^2\left(x-3\right)}{x + 3}[/tex]

Step-by-step explanation:

The question is not properly formatted.

Given

[tex]f(x) = x^3 - x^2 - 5x - 3[/tex]

[tex]g(x) =x + 3[/tex]

Required

[tex](\frac{f}{g})(x)[/tex]

This is calculated as:

[tex](\frac{f}{g})(x) = \frac{f(x)}{g(x)}[/tex]

So, we have:

[tex](\frac{f}{g})(x) = \frac{x^3 - x^2 - 5x - 3}{x + 3}[/tex]

Factorize the numerator: using a calculator

[tex](\frac{f}{g})(x) = \frac{\left(x+1\right)^2\left(x-3\right)}{x + 3}[/tex]

Answer:

D. 8

Step-by-step explanation:

set up a proportion

3/20 = x/50

to get from 20 to 50 you have to multiply by 2.5

so multiply the top number (3) by 2.5 to find x

this comes out to 7.5 which you then round up to 8

Answer:

D

Step-by-step explanation: