A spherical shell has inner radius r and an outer radius r+h. Let h=0.1r. Find the volume of the shell in terms of r and then approximate the volume of the shell by 4πr^2h. Does this seem like a reasonable approximation if h is small compared to r?

Answer:

The amount to be pay for coat is $128.70.

Step-by-step explanation:

Given:

The sales tax rate is 7.25% in California.

The cost for a coat in Los angeles is $120.00.

Now, to find amount to be paid.

Sales tax = 7.25%.

Cost = $120.00.

So, amount to be paid = $120 + 7.25% of $120.00.

[tex]=120+\frac{7.25}{100} \times 120.[/tex]

[tex]=120+\frac{870}{100}.[/tex]

[tex]=120+8.70[/tex]

[tex]=\$128.70[/tex]

Therefore, the amount to be pay for coat is $128.70.

t = 5 + 3m is the required expression that represents weight of Tony fish

Let "t" represent the weight of Tony’s fish, and let "m" represent the weight of Mary’s fish

To find: expression that represents the weight of Tony's fish

According to given information,

Tony’s fish weighs five pounds more than three times the weight of Mary’s fish

Here the word "times" represents multiplication and "more than" represents addition

Weight of Tony fish = 5 + three times the weight of Mary’s fish

Weight of Tony fish = 5 + 3(m)

t = 5 + 3m

Thus the required expression is found out

Answer:

1 year

Step-by-step explanation:

Create two equations to represent each tree. Linear equations are written in the form y = mx + b. "m" is the slope or rate. "b" is the constant or starting value.

In this problem, "m" is the rate of growth in inches per year.

"b" is the starting height.

let "x" be the number of years

let "y" be the height in inches

Tree A: y = 8x + 3

Tree B: y = 9x + 2

Solve the system of equations. Since both are equal to "y", you can equate them to each other and solve for "x". Isolate by doing reverse operations.

8x + 3 = 9x + 2

8x + 3 - 3 = 9x + 2 - 3      Subtract 3 from both sides

8x = 9x - 1

8x - 9x = 9x - 9x - 1     Subract 9x form both sides

-x = -1       Divide both sides by -1 to isolate

x = 1         Number of years for the trees to be the same height

Therefore it will take 1 year for the trees to be the same height.

If you wanted to know how tall the trees will be at the same height, find y. You can substitute x=1 in one of the equations.

y = 8x + 3

y = 8(1) + 3

y = 11     Number of inches when trees are the same height

Answer: $10272.17

Step-by-step explanation: Please see attachment for explanation

Answer:

[tex]\$10272.17[/tex]

Step-by-step explanation:

Since it is compounded continuously, we will use:

[tex]A=A_0 \cdot e^{k t}[/tex]

[tex]A_0[/tex] is the amount invested.

[tex]k[/tex] is the rate.

[tex]t[/tex] is the number of years you let the money sit.

[tex]A[/tex] is the future amount after the [tex]t[/tex] years that has been accumulated.

(Note:

I'm going to write [tex]r=4%[/tex] as a decimal. [tex]r=\frac{4}{100}=0.04[/tex].)

[tex]A=5000 \cdot e^{0.04 \cdot 18}[/tex]

[tex]A=5000 \cdot e^{0.72}[/tex]

[tex]A=5000 \cdot 2.0544332[/tex] (approximated)

[tex]A=10272.16605[/tex] (approximated)

To the nearest cent this is [tex]\$10272.17[/tex].

Answer:

x² + y² - 3x - 13y + 18 = 0

Step-by-step explanation:

Recall that the general equation of a circle looks something like this:

x² + y² + Ax + By + C = 0

substituting each of the points into the equation we get:

for (-1,2)

(-1)² + (2)² + A(-1) + B(2) + C = 0

1 + 4 -A+2B + C = 0

-A + 2B + C + 5 = 0 ------------ eq 1

for (4,2)

(4)² + (2)² + A(4) + B(2) + C = 0

16 + 4 + 4A + 2B + C = 0

4A + 2B + C + 20 = 0 ------------- eq 2

for (-3,4)

(-3)² + (4)² + A(-3) + B(4) + C = 0

9 + 16 -3A + 4B + C = 0

-3A + 4B + C + 25= 0 ----- eq 3

Now we have a system of equations with 3 equations and 3 unknowns.

Solving for A, B and C, we eventually get:

A = -3, B = -13, C = 18

Substituting these into the general equation:

x² + y² + Ax + By + C = 0

x² + y² - 3x - 13y + 18 = 0

Function 1 has a greater y-intercept than function 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is because 6 yards equals 18 feet. If there is 15 feet needed to install a stereo, and we have 18 feet of cable, we have MORE THAN ENOUGH cable to install the stereo. So yes, there is enough cable to install the stereo.

I hope this helps!

- sincerelynini

Answer:

Yes.

Step-by-step explanation:

There is 3 feet in every yard. So LeBron has 18ft of cable.

12oz of the drink contains 159oz of calories.

A new energy drink advertises 106 calories for 8oz.

Based on the given conditions, formulate: 12*(106/8)

=12*(13.25)=159

Calories are in 12oz of the drink is 159oz

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Answer:

Step-by-step explanation:

If the axis of symmetry is located at x = 1, that is the h value of our vertex (h, k).  If we know h, all we have to do to find k is sub the value for h into the quadratic and evaluate.

[tex]f(1)=-2(1)^2+4(1)+1[/tex]

so f(1) = 3.  Your choice is (1, 3)

The solution is (1, 3) where the vertex of the function located.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have

given that,

The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1.

now, we have to find the vertex of the function.

If the axis of symmetry is located at x = 1, that is the h value of our vertex (h, k).

 If we know h, all we have to do to find k is sub the value for h into the quadratic and evaluate.

now, putting the value of x as 1 ,

so, we get,

f(1) = –2(1)^2 + 4*1+ 1

    =-2 + 4 +1

    =3

so f(1) = 3.  

The solution is (1, 3).

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Answer:

(5-1)/-11-(-6) = -4/5

Step-by-step explanation:

since the lines are parallel they have same slope/gradient

Answer:

-4/5

Step-by-step explanation:

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

m=(1-5)/(-6-(-11))

m=-4/(-6+11)

m=-4/5

Answer:

50/50 chance

Step-by-step explanation:

Answer: Classical Probability (also know as priori or theoretical probability)

Step-by-step explanation:

Answer: 188 months

Step-by-step explanation:

Principal = $129 000

Payment = $1000

Mortgage % = 5.15

Since,

Number of Months = log (1+[rate/(Payment/Principal)-rate] / log (1 + rate)

Also,

rate = 5.15/1,200 = 0.004292

Number of Months = log (1 + [0.004292/(1,000/129000) -0.004292] / log(1+0.004292)

Number of Months = log ( 1 + 0.004292/ ((0.007752 -0.004292) / log (1.004292)

Number of Months = log ( 1 + (0.004292/0.00346))/ log (1.004292)

Number of Months = log (1 + 1.240) / log (1.004292)

Number of Months = log (2.240) / log (1.004292)

Number of Months = 0.3502 / 0.001860

Number of Months = 188.28 months

Approximation to whole month,

Number of months = 188 Months.

Answer:

Step-by-step explanation:

7x + 95+2x + x+25 + 90 = 360

10x + 210 = 360

10x = 360 -210

10x = 150

x = 150/10

x = 15

Answer:

53

Step-by-step explanation:

The unit rate of speed is 52.5 miles per hour

Solution:

Given that On a trip to visit relatives you drive 1,115.625 miles over the course of 21  hours and 15 minutes

We know that, 1 hour = 60 minutes

21  hours and 15 minutes = 21 hours + (15/60) hours = 21 + 0.25 = 21.25 hours

So they drive 1115.625 miles in 21.25 hours

To find the unit rate of speed of your vehicle in miles per hour, divide the total miles by time taken

unit rate of speed means miles driven in 1 hour

[tex]\rightarrow \frac{1115.625}{21.25} = 52.5[/tex]

So the unit rate of speed is 52.5 miles per hour

The value of w is 10

Solution:

Given equation is:

[tex]8.25 + \frac{1}{4}w = 10.75[/tex]

We have to solve above given equation for "w"

[tex]8.25 + \frac{1}{4}w = 10.75[/tex]

We know that 1 divided by 4 gives 0.25

8.25 + 0.25w = 10.75

Moving 8.25 from L.H.S to R.H.S

0.25w = 10.75 - 8.25

0.25w = 2.5

[tex]w = \frac{2.5}{0.25}[/tex]

w = 10

Thus value of w is 10

Answer:

C. 6

Step-by-step explanation:

Since the number is greater than one million and less than ten million, the number is seven digit which ranges from two million to nine million

Therefore, Alex will use 6 as the exponent

Answer:

-3

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

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

m=(-13-(-1))/(1-(-3))

m=(-13+1)/(1+3)

m=-12/4

m=-3

Answer:

4

Step-by-step explanation:

3x = 5x - 8 is your equation. To solve for x, you want to get all the x's on the same side. You first subtract 5x from each side to get -2x = -8, and multiply both by 1- to get 2x = 8, and then divide both sides by 2 to find x = 4.

Answer:

Step-by-step explanation:

3x=5x -8​

3x - 5x = - 8

-2x = -8

x = -8/-2

x = 4

Answer:

Part A) The vertex is the point (22,100) see the explanation

Part B) The x-intercepts are the points (12,0) and (32,0 see the explanation

Part C) The y-intercept is the point (0,-384) see the explanation

Step-by-step explanation:

Let

x ----> the number of cups of coffee sold

f(x) ---> the amount of profit

we have

[tex]f(x)=-x^{2} +44x-384[/tex]

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

Part A) Determine the vertex. What does this calculation mean in the context of the problem?

Convert the quadratic equation in vertex form

Factor -1

[tex]f(x)=-(x^{2}-44x)-384[/tex]

Complete the square

[tex]f(x)=-(x^{2}-44x+22^2)-384+22^2[/tex]

[tex]f(x)=-(x^{2}-44x+484)+100[/tex]

Rewrite as perfect squares

[tex]f(x)=-(x-22)^{2}+100[/tex]

The vertex is the point (22,100)

That means ----> The maximum profit of $100 is when the number of cups of coffee sold is 22  

Part B)  Determine the x-intercepts. What do these values mean in the context of the problem?  

we know that

The x-intercepts are the values of x when the value of the function is equal to zero

so

we have

[tex]f(x)=-(x-22)^{2}+100[/tex]

For f(x)=0

[tex]0=-(x-22)^{2}+100[/tex]

solve for x

[tex](x-22)^{2}=100[/tex]

take square root both sides

[tex](x-22)=\pm10[/tex]

[tex]x=22\pm10[/tex]

so

[tex]x=22+10=32[/tex]

[tex]x=22-10=12[/tex]

The x-intercepts are the points (12,0) and (32,0)

That means -----> When the number of cups of coffee sold is 12 or 32 the profit is equal to zero

Part C) Determine the y-intercept. What does this value mean in the context of the problem?

we know that

The y-intercept is the value of the function  when the value of x is equal to zero

so

For x=0

[tex]f(x)=-x^{2} +44x-384[/tex]

substitute the value of x

[tex]f(x)=-(0)^{2} +44(0)-384[/tex]

[tex]f(x)=-384[/tex]

The y-intercept is the point (0,-384)

That means ----> When the number of cups of coffee sold is zero the profit is negative -$384 (the cost is greater than the revenue)

367.5, there are 367.5 8's in 2,940.

Hope this helps, if not, comment below please!!!!

Answer:

365.7

Step by step solving:

Answer:

Step-by-step explanation:

(-5,-8), (-7,3)

midpoint = (x₁+x₂/2, y₁+y₂/2)

        = ( -5+-7/2 , -8+3/2) = (-5-7/2,-8+3/2)

       = (-12/2, -5/2) = (-6,-5/2)

The company picnic cost $ 1300 for 80 employees

Solution:

Given that cost of a company picnic varies directly as the number of employees attending the picnic

Let "c" be the company picnic cost

Let "n" be the number of employees attending the picnic

Therefore,

[tex]cost \propto \text{ number of employees attending picnic }[/tex]

[tex]c \propto n\\\\c = kn[/tex]

Where "k" is the constant of proportionality

c = kn ---------- eqn 1

Given that company picnic costs $487.50 for 30 employees

Therefore substitute c = 487.50 and n = 30

[tex]487.50 = k(30)\\\\k = \frac{487.50}{30} = 16.25[/tex]

How much does a company picnic cost for 80 employees?

Substitute n = 80 and k = 16.25 in eqn 1

[tex]c = 16.25(80) = 1300[/tex]

Thus $ 1300 is the cost for 80 employees

Answer:

$1,300.00

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

If you add 6 to both sides, you get -3x-8+6=19+6 which is then -3x-2=25

Answer:

JKL and ABC

DEF and GHI

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding angles is proportional and its corresponding angles are congruent

so

In this problem

1) triangles JKL and ABC are similar

because

[tex]\frac{KL}{BC} =\frac{JL}{AC}[/tex]

substitute the given values

[tex]\frac{10}{20} =\frac{7}{14}[/tex]

Simplify

[tex]\frac{1}{2} =\frac{1}{2}[/tex]  ---> is true

therefore

The ratio of the corresponding sides is proportional

That means----> The triangles are similar

2) triangles DEF and GHI are similar

because

[tex]\frac{HI}{EF} =\frac{GI}{DF}[/tex]

substitute the given values

[tex]\frac{15}{10} =\frac{12}{8}[/tex]

Simplify

[tex]1.5=1.5[/tex]  ---> is true

therefore

The ratio of the corresponding sides is proportional

That means----> The triangles are similar

The pairs of triangles that are similar to each other are:

B. ΔDEF ~ ΔGHI

E. ΔJKL ~ ΔABC

Corresponding angles of two triangles that are similar are always congruent, however, their corresponding sides are proportional to each other. This means, their ratio is equal.

Thus, triangles KJL and ABC are similar triangles because:

BC/KL = AC/JL = 2

Also, triangles DEF and GHI are similar triangles because:

GI/DF = HI/EF = 1.5

Therefore, the pairs of triangles that are similar to each other are:

B. ΔDEF ~ ΔGHI

E. ΔJKL ~ ΔABC

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Answer:

The solution is the point (0.5,-3)

Step-by-step explanation:

we have

[tex]y=4x-5[/tex] ----> equation A

[tex]y=-3[/tex] ----> equation B

Solve the system by substitution

Substitute equation B in equation A

[tex]-3=4x-5[/tex]

Solve for x

Adds 5 both sides

[tex]-3+5=4x[/tex]

[tex]2=4x[/tex]

Divide by 4 both sides

[tex]x=0.5[/tex]

therefore

The solution is the point (0.5,-3)

Verify your  answer using the graph

using a graphing tool

Remember that the solution of the system of equations is the intersection point both graphs

The intersection point is (0.5,-3)

therefore

The solution is the point (0.5,-3)

see the attached figure

Answer:

Since y= -3, just put that in the equation.

-3 = 4x - 5

+5         +5

2 = 4x

/4    /4

x=1/2

Answer:

11.25 pi

Step-by-step explanation:

Pi is 180 degrees, a circle is 360 degrees, 9/10's of 180 is 162, and divide that by the full 360 which is .45. Then, multiply that by 25 and you have 11.25 pi is the area of that sector.

Answer:

With the first term is 2 and common difference is 13 then the series is 2,15,28,...

Step-by-step explanation:

Given first term is 2 and common difference is 13.

Arithmetic progression:

[tex]a_{1}=2[/tex] and d=2  [given]

Therefore we can find arithmetic series  [tex]a_{1},a_{2},a_{3},...[/tex] with [tex]a_{1}=2[/tex] and d=2

d can be written as  [tex]d=a_{2}-a_{1}[/tex]. Therefore we can write [tex]a_{2}[/tex] as below:

[tex]a_{2}=a_{1}+d[/tex]

Now substitute the values [tex]a_{1}=2[/tex] and d=2

[tex]a_{2}=2+13[/tex]

[tex]a_{2}=15[/tex]

Similarly we can find [tex]a_{3}[/tex]

d can be written as  [tex]d=a_{3}-a_{2}[/tex]. Therefore we can write [tex]a_{3}[/tex] as below:

[tex]a_{3}=a_{2}+d[/tex]

[tex]a_{3}=15+13[/tex]

[tex]a_{3}=28[/tex]

and so on.

Therefore the series is 2,15,28,...

Answer:

The larger angle is 70°

And The smaller angle is 20°  .

Step-by-step explanation:

Given as :

The ratio of two complementary angles = 7 : 2

Let The larger angle = 7 x

And The smaller angle = 2 x

Now, According to question

Complementary angle is define as when two angles were added to make right angle i.e 90° are complementary to each other .

So, here

7 x + 2 x =  90°

Or, 9 x =  90°

∴  x = [tex]\dfrac{90^{\circ}}{9}[/tex]

i.e x = 10°

Now, putting the value of x

So, The larger angle = 7 × 10° = 70°

And The smaller angle = 2 × 10° = 20°

Hence, The larger angle is 70°

And The smaller angle is 20°  . Answer

Final answer:

The larger angle in a pair of complementary angles with a ratio of 7:2 measures 70 degrees, found by figuring the common ratio as 10 and multiplying it by 7.

Explanation:

To find the measure of the larger angle when two angles are complementary and their ratio is 7:2, we first need to understand that complementary angles add up to 90 degrees. If the ratio of the angles is 7 to 2, we can express this as 7x and 2x for some number x. By adding these two expressions, 7x + 2x, we get the total amount of degrees in complementary angles, which is 90 degrees. Therefore, we have the equation 9x = 90, which we can solve for x by dividing both sides by 9 to get x = 10.

The larger angle, which is 7 parts of the ratio, will be 7x which is 7 times 10, so it is 70 degrees.

Answer:

4w+3

Step-by-step explanation:

2/3(7w+4)-1/3(2w-1)

14/3w+8/3-2/3w+1/3

14/3w-2/3w+8/3+1/3

12/3w+9/3

4w+3