How would you explain surface area and volume to a 6th grader who is just now learning about these concepts?

We have been given that the value of Vishal's car is depreciating exponentially.  The relationship between V, the value of his car, in dollars, and t, the elapsed time, in years, since he purchased the car is modeled by the equation [tex]V=22,500\cdot 10^{-\frac{t}{12}}[/tex]. We are asked to find the time, when Vishal's car will be worth $10,000.

To find the time, we will equate our given equation with 10,000 as:

[tex]10,000=22,500\cdot 10^{-\frac{t}{12}}[/tex]  

[tex]\frac{10,000}{22,500}=\frac{22,500\cdot 10^{-\frac{t}{12}}}{22,500}[/tex]

[tex]\frac{4}{9}=10^{-\frac{t}{12}}[/tex]

Now we will take log on both sides.

[tex]log_{10}\left(\frac{4}{9}\right)=log_{10}\left(10^{-\frac{t}{12}}\right)[/tex]

[tex]log_{10}\left((\frac{2}{3})^2\right)=-\frac{t}{12}[/tex]

[tex]-\frac{t}{12}=log_{10}\left((\frac{2}{3})^2\right)[/tex]

[tex]-\frac{t}{12}(-12)=(-12)log_{10}\left((\frac{2}{3})^2\right)[/tex]

[tex]t=(-12)log_{10}\left((\frac{2}{3})^2\right)[/tex]

Using property [tex]log(a^b)=b\cdot log(a)[/tex], we will get:

[tex]t=(-12)\cdot 2log_{10}\left(\frac{2}{3}\right)[/tex]

[tex]t=-24log_{10}\left(\frac{2}{3}\right)[/tex]

Therefore, the value of Vishal's car will be $10,000 after approximately  [tex]-24log_{10}\left(\frac{2}{3}\right)[/tex] years.

The surface area of the larger sphere is 366.2496 square centimeter.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, two spheres have volumes of 87 cm³ and 647 cm³.

We know that, the volume of a sphere = 4/3 πr³

Here, 647 cm³=4/3 πr³

647 = 88/21 r³

r³ = (647×21)/88

r³ = 154.39

r = 5.4 cm

We know that, surface area of a sphere is 4πr².

The surface area of the larger sphere = 4×3.14×5.4²

= 366.2496

Therefore, the surface area of the larger sphere is 366.2496 square centimeter.

To learn more about the volume visit:

https://brainly.com/question/13338592.

#SPJ7

"Your question is incomplete, probably the complete question/missing part is:"

Two spheres have volumes of 87 cm³ and 647 cm³. If the surface area of the smaller sphere is 167 cm², what is the surface area of the larger sphere?

64 cm²

96 cm²

128 cm²

256 cm²

Answer:

[tex]x=-\frac{14+2y}{5}[/tex]

Step-by-step explanation:

That is what i got and i also checked it on a website. so i hope it helps

Answer: the sum is 6, a small cone will be ordered . the sum is 7 or 8 , a medium cone will be ordered. If the sum is 9, a large cone will be ordered.

Step-by-step explanation:

Based on the question above,

P(6) = P(7 or 8) = P(9)

Hence,

The fair decision can be made if:

the sum is 6, a small cone will be ordered, when the sum is 7 or 8 a medium cone will be ordered and when the sum is 9, a large cone will be ordered.

Answer:

7x^2 -128x -19

Step-by-step explanation:

Answer:

-7x^2 -3x -2

Step-by-step explanation:

Answer:

t = - 3, t = - 1

Step-by-step explanation:

Given

h(t) = t² + 4t + 3

To find the zeros equate h(t) to zero, that is

t² + 4t + 3 = 0

Consider the factors of the constant term (+ 3) which sum to give the coefficient of the t- term

The factors are + 3 and + 1, since

3 × 1 = 3 and 3 + 1 = 4, thus

t² + 4t + 3 = (t + 3)(t + 1) = 0

Equate each factor to 0 and solve for t

t + 3 = 0 ⇒ t = - 3

t + 1 = 0 ⇒ t = - 1

smaller zero is t = - 3

larger zero is t = - 1

Answer:

triangular pyramid

Step-by-step explanation:

Let's make the central triangle the "base", or the bottom face, of our polyhedron. Try to visualise what will happen if we fold up the three triangles so that their top vertices meet at the center top (see diagram).

If we can do that, we'll see that it's a pyramid with a triangular base, so it's a triangular pyramid.

Answer:

C. V = two-thirds (27)

Step-by-step explanation:

Given

Solid Shapes: Cylinder and Sphere

Volume of Cylinder = 27π ft³

Required

Volume of the sphere.

From the question,

We have that

1.  The volume of the sphere is the same as the volume of the cylinder

2. The height of the sphere is the same as the height of the cylinder.

From (2) above;

This means that the height of the cylinder equals the diameter of the sphere.

Let h represent the height of the sphere and d represent the diameter of sphere.

Mathematical, d = h

Recall that radius, r = [tex]r = \frac{d}{2}[/tex]

Substitute h for d in the above expression

[tex]r = \frac{h}{2}[/tex]. ----- (take note of this)

Calculating the volume of a cylinder.

V = πr²h

Recall that  V = 27; This gives us

27 = πr²h

Divide both sides by h

[tex]\pi r^2 = \frac{27}{h}[/tex]

-------------------

Calculating the volume of a sphere

[tex]V = \frac{4}{3}\pi r^3[/tex]

Expand the above expression

[tex]V = \frac{4}{3}\pi r^2 * r[/tex]

Substitute [tex]\pi r^2 = \frac{27}{h}[/tex]

[tex]V = \frac{4}{3} * \frac{27}{h} * r[/tex]

Recall that [tex]r = \frac{h}{2}[/tex]

So,

[tex]V = \frac{4}{3} * \frac{27}{h} * \frac{h}{2}[/tex]

[tex]V = \frac{4}{3} * \frac{27}{2}[/tex]

[tex]V = \frac{2}{3} * 27[/tex]

[tex]V = \frac{2}{3} (27)[/tex]

V = two-third (27)

To find the value of t, apply the exponent rules and simplify to get t = [tex]j^{59[/tex], assuming j is not zero.

The value of t in the equation [tex](j^{-12})^{-5} = j \times t[/tex] can be found by understanding the properties of exponents. Since the equation involves a base raised to an exponent that is also raised to another exponent, one would apply the rule that states [tex](a^n)^m = a^{(n \times m).[/tex] Thus, simplifying gives us [tex]j^{(12 \times 5)} = j \times t \space or j^{60} = j \times t[/tex] Now, assuming that j is not 0, we divide both sides by j to isolate t, resulting in [tex]t = j^{59[/tex], and j will not be equal to zero, hence J [tex]\neq[/tex] 0.

Answer:

a triangle with three equal sides

Step-by-step explanation:

Base on the figure, the vertice length of A , B and C are equal. Therefore, a triangle with three equal sides is the correct answer.

Please find the attached file for the figure

Answer:

Its c, if you dont have time to match the answers.

Step-by-step explanation:

Answer:

x = 16

y = 16 sqrt(3)

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/hyp

sin 60 = y/ 32

Multiply each side by 32

32 sin 60 = y

32 ( sqrt(3) /2) = y

16 sqrt(2)

cos theta = adj/ hyp

cos 60 = x /32

32 cos 60 = x

32 (1/2) =x

16 =x

Answer:

16

Step-by-step explanation:

YOU NEED A CALCULATOR TO SOLVE THIS!

To solve this you need to use SOH-CAH-TOA

Do cos60° to find x

         [tex]cos60 = \frac{x}{32}[/tex]

Multiply both sides by 32 to get x alone

[tex]32(cos60) = x[/tex]

Now put 32(cos60) into your calculator

The answer you get is 16

Answer:

54

Step-by-step explanation:

64 + 62 = 126

180 - 126 = 54

Answer:

D

Step-by-step explanation:

because x and 53 are Alternate angles , they are in form of z which male them equal

there is only a certain amount of numbers  

i hope this helped you

Answer:

C

Step-by-step explanation

So you take the amount of digits total (which is 9) and the highest number you can make is 999,999,999 so basically everything between 000,000,0001 and 999,999,999 is a possible unique social security number. So its closest to 1 billion.

Pamela got B since the only logical explanation i can think of is that she rounded  incorrectly

Answer:

1, 2, 3, 5

Step-by-step explanation:

Answer:

1 and 2

or

A and B

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Start at 6 on the y axis. Draw an arrow so that it horizontally moves to the blue curve. Then draw an arrow straight down to vertically drop to x = 4

See the diagram below.

Follow this process in reverse to see that x = 4 leads straight up to the blue curve, and then to the left to land on y = 6. Keep in mind that the inverse reverses the input and output process, which is why I started with y instead of x.

An expression is defined as a set of numbers, variables, and mathematical operations. The value of the expression, f⁻¹(6) is 4.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The value of the expression can be found as shown below,

y = f(x)

When the value of y is 4, the value of x is 6, therefore, we can write f(6)=4.

Now, the given expression can be simplified as,

f⁻¹(6) = 1 / f(6)

       = 1 / 4

       = 0.25

Hence, the value of the expression, f⁻¹(6) is 4.

Learn more about Expression here:

https://brainly.com/question/13947055

#SPJ2

Answer:

The rating of a brand that costs $3.00 per bag is 7.

Step-by-step explanation:

A simple linear regression equation is used to estimate the value of the dependent variable based upon the independent variable.

The general form of a simple linear regression equation is:

[tex]y=a+bx[/tex]

Here,

y = dependent variable

x = independent variable

a = intercept

b = slope

The output of the least squares regression analysis for predicting rating from price is provided.

So, the dependent variable is the ratings and the independent variable is the price.

The regression equation for predicting rating from price is:

[tex]y=-0.39+2.52x[/tex]

Predict the rating of a brand that costs $3.00 per bag as follows:

[tex]y=-0.39+2.52x[/tex]

  [tex]=-0.39+(2.52\times \$3.00)\\=-0.39+7.56\\=7.17\\\approx 7[/tex]

Thus, the rating of a brand that costs $3.00 per bag is 7.

Answer:

[tex]x=\sqrt{13}[/tex] (C.)

Step-by-step explanation:

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex](2^{2} )+(3^{2})=x^{2}[/tex]

[tex]4+9=x^{2}[/tex]

[tex]13=x^{2}[/tex]

[tex]\sqrt{13} =\sqrt{x^{2} }[/tex]

[tex]x=\sqrt{13}[/tex]

Final answer:

To rewrite 1/6 with a denominator of 18, multiply both the numerator and the denominator by 3, resulting in the equivalent fraction 3/18. To confirm its equivalence, simplify 3/18 back to 1/6 by dividing both the numerator and the denominator by 3.

Explanation:

How to Rewrite a Fraction with a New Denominator

To rewrite the fraction 1/6 with a denominator of 18, we need to find a number that we can multiply both the numerator and the denominator of the fraction by so that the denominator becomes 18. Since 6 times 3 equals 18, we will use 3. The fraction then becomes:

(1 x 3) / (6 x 3) equals 3/18.

Verifying the Equivalent Fraction

To verify that 3/18 is indeed equivalent to 1/6, we can simplify 3/18 by dividing both the numerator and denominator by their greatest common factor, which is 3:

3 ÷ 3 / 18 ÷ 3 = 1/6.

This confirms that 3/18 is equal to 1/6 because it simplifies back to the original fraction.

Answer: X = 4.5

Step-by-step explanation:

The proportion is 8/9 for the lines. All we have to do is divide 4 by 8/9 to find the exact value of X.

4/(8/9) = 4.5

I hope this helps!

Answer:

D

Step-by-step explanation:

All you have to do is multiply -22.2 by -6.1

Answer: The answer is D

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

B=a/h

The missing base in the figure is 5 centimeter.

The area of a parallelogram is the product of the base and the height of the figure. Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly. Then summing all those pieces' area gives us the area of the main big region.

The area of a parallelogram = Base x Height

Given;

     Area of parallelogram= 40 square centimeters

      Height of parallelogram= 8cm

Solution;

       A= b x h

   substituting the given values in the formula;

                 40= b x 8

                  b= 40/8

                   b= 5

So, the answer is 5cm

Learn more about area of a parallelogram here:

https://brainly.com/question/4887838

#SPJ6

Answer:

[tex] \mu_{\bar X} = 90[/tex]

[tex] \sigma_{\bar X} =\frac{\sigma}{\sqrt{n}}= \frac{9.6}{\sqrt{144}}= 0.8[/tex]

Step-by-step explanation:

For this case we have a population with the following parameters:

[tex]\mu = 90, \sigma =9.6[/tex]

For this case we have a sample of n= 144 and this sample size is larger (>30) then we can apply the central limit theorem and the distirbution for the sample mean is given by:

[tex] \bar X \sim N( \mu, \frac{\sigma}{\sqrt{n}}) [/tex]

And replacing we got:

[tex] \mu_{\bar X} = 90[/tex]

And the standard deviation is given by:

[tex] \sigma_{\bar X} =\frac{\sigma}{\sqrt{n}}= \frac{9.6}{\sqrt{144}}= 0.8[/tex]

Start with the point-slope formula shown at the top in red.

Now, substitute your slope and coordinates in the formula.

Then distribute and combine lie terms.

Finally, add 2x to both sides to get your equation in standard form.

Answer:

48 video games were sold.

Step-by-step explanation:

We know that both 100% and 60 are divisable by 5. 100%÷5=20%. 60÷5=12. So now we know that 20% of 60 is 12. We need 80%, however. To get from 20% to 80%, we just multiply by four. 20 × 4 = 80. But what we do to one side, we must do to the other. 12×4=48. So 80% of 60 is 48.

Hope this helped, and good luck with future math problems!

Answer:

See explanation for answer.

Step-by-step explanation:

When the point on the number line is an open circle, that means that the inequality does not include that exact value. For instance, in this case the inequality only takes number higher than, but not equal to, -1. Hope this helps!

Answer:

When graphing a linear inequality on a number line, use an open circle for "less than" or "greater than", and a closed circle for "less than or equal to" or "greater than or equal to".

Step-by-step explanation:

Answer:

198+h

have a nice day

Answer:

4*2*3= 8*3= 24

Step-by-step explanation:

For every swimsuit there are 2 hats, that makes 8 combinations. For any of the 8 combinations there are 3 pairs of flippers, equaling 24.