An art student wishes to create a clay sphere as part of a sculpture. If the clay’s density is approximately 88 pounds per cubic foot and the sphere’s radius is 2 feet, what is the weight of the sphere to the nearest pound? Use 3.14 for pi, and enter the number only.

Answers

Answer 1

Answer:

The weight of the sphere = 2947 pounds

Step-by-step explanation:

* Lets revise the volume of the sphere

- The volume of the sphere is 4/3 π r³, where r is the radius of

  the sphere

- Density = mass ÷ volume

- Mass is the weight and volume is the size, so density is weight

 divided through size

- Density = weight ÷ volume

* Now lets solve the problem

∵ The clay's density ≅ 88 pounds/cubic foot

∵ The radius of the sphere is 2 feet

∵ The volume of the sphere = 4/3 π r³

∴ The volume of the sphere = 4/3 π (2)³ = 32/3 π feet³

∵ Density = weight/volume ⇒ by using cross multiply

∴ Weight = density × volume

∵ Density = 88 pounds/foot³

∵ Volume = 32/3 π feet³

∵ π = 3.14

∴ The weight of the sphere = 88 × 32/3 × 3.14 = 2947 pounds


Related Questions

Given the system of equations:

2x – y = –2
x = 14 + 2y

Answer the following:
A) What is the value of the system determinant?
B) What is the value of the y−determinant?
C) What is the value of the x−determinant?
D) What is the solution to the system of equations?

My mind is blank when I look at this, any help will be appreciated.

Answers

Answer:

The determinant of A (the main matrix) is -3; the determinant of y is 30; the determinant of x is 18; the solution to the system is (-6, -10)

Step-by-step explanation:

Set up the matrix to find the determinant of the main matrix.  Find the determinant by multiplying the numbers on the major axis and subtract from that the multiplication of the numbers on the minor axis:

[tex]\left[\begin{array}{ccc}2&-1&\\1&-2\\\end{array}\right][/tex]

Find the determinant by multiplication:

(2×-2)-(1×-1)= -3

To find the determinant of y, replace the second column with the solutions to have a matrix that looks like this:

[tex]\left[\begin{array}{ccc}2&-2\\1&14\\\end{array}\right][/tex]

To find the determinant of that matrix by multiplication:

(2×14)- (1× -2) = 30

Lastly, find the determinant of x by replacing the first column with the solutions.  That matrix will look like this:

[tex]\left[\begin{array}{ccc}-2&-1\\14&-2\\\end{array}\right][/tex]

Find the determinant of x by multiplication:

(-2 × -2) - (14 × -1) = 18

Now we want Cramer's Rule that tells us if we divide the determinant of [tex]A_{x}[/tex]

by the determinant of A, we will find the value of x:

[tex]\frac{A_{x} }{A}=\frac{18}{-3}  =-6[/tex]

and the same for y:

[tex]\frac{A_{y} }{A}=\frac{30}{-3}=-10[/tex]

So the solution to the system is (-6, -10)

2x - y = -2

x = 14 + 2y

2x - y = -2

x - 2y = 14

The system determinant = -3

2 (-2) - 1 (-1)

-4 + 1

-3

The y-determinant = 30

(14) - 1 (-2)

28 + 2

30

The x-determinant = 18

-2 (-2) - 14 (-1)

4 + 14

18

The solution is x = -6 and y = -10 or (-6,-10)

x = 18/-3

x = -6

y = 30/-3

y = -10

Plz help me out will mark as brainliest!!! Don’t copy anybody else’s answer 40 points

Answers

-Original Profit-

y = 22x ; where x is the number of necklaces sold and y is the mount of profit.

y = 29x ; where x is the number of necklaces sold and y is the amount of profit.

Xavier will earn an additional $7 if he proceeded in switching to a new type of pendant. The $7 is the difference of $29 and $22 profit.

if x is the amount sold and y is the profit, then the original equation would be y = 22x since originally he was selling them for $22 dollars each. That means that in the equation y = 29x, 29 is the amount of profit per each necklace. From here it's just simple subtraction. New profit - Old profit = How much more earned $29 - $22 = $7 extra earned per necklace. he would save $7.

Jana is decorating 6 picture frames by gluing straws around the borders and adding wooden stars at the corners. Each picture frame measures 20 centimeters by 120 millimeters. How many straws does she need if she uses all of each straw? Each straw is 80 millimeters long. A. 21 straws B. 24 straws C. 48 straws D. 50 straws

Answers

Answer:

C: 48 straws

Step-by-step explanation:

First, find the perimeter of one picture frame: (2 x length) + (2 x width).  Convert 20 centimeters to millimeters so that you are working in the same units; there are 10 millimeters in 1 centimeter, so 20 centimeters = 200 millimeters.  

(2 x 200) + (2 x 120) = 400 + 240 = 640

Each picture frame has a perimeter of 640 millimeters.

Next, figure out how many straws are needed for one picture frame:

640/80 = 8

Jana uses 8 straws for each picture frame.  Since she is decorating 6 picture frames, solve 6 x 8 = 48.  

Jana needs 48 straws to complete her project.

Can you please help me find the volume? The answer must also be rounded to the nearest tenth

Answers

Answer:

67.0 cm^3

Step-by-step explanation:

The volume of the cylinder is given by the formula ...

V = πr^2·h

The volume of the hemisphere is given by the formula ...

V = (2/3)πr^3

The volume of the two figures together will be ...

V = πr^2·h + (2/3)πr^3 = πr^2(h +2/3r)

V = π(2 cm)^2·(4 cm + 2/3·2 cm) = 64π/3 cm^3

V ≈ 67.0 cm^3

HELP PLEASE

factor each polynomial completely using the x-box method. must show work

Answers

 

2)  

x^2 - 14x - 32  = x^2 - 16x + 2x - 32  = x(x-16) + 2(x-16) = (x - 16)(x + 2)

⇒   x^2 - 14x - 32  = (x - 16)(x + 2)

---------

3)  

2n^2 - 7n - 15  =

= 2n^2 - 10n + 3n - 15 =

=  2n(n - 5) + 3(n - 5) =

= (n - 5)(2n + 3)

⇒ 2n^2 - 7n - 15  = (n - 5)(2n + 3)

---------

4)  

x^2 - 25 = (x - 5)(x + 5)

does anyone know the function of these graphs? please help and thank you. ​

Answers

Answer:

Step-by-step explanation:

f(x) is an easy one.  Because it's a parabola, it's standard form is

[tex]y=ax^2+bx+c[/tex]

But even simpler than that, look at a point on the graph, in particular, (2, 4).  If x = 2 and y = 4, we can square 2 to get 4, so the equation for that is the parent graph, [tex]y=x^2[/tex], plain and simple.

The next one requires a bit of doing.  Pick 3 points on the graph because we have 3 unknowns to find: a, b, and c.  The points that are easy to pick are (0, -2), (2, -4), (-2, -4).  Use the x and y coordinates from each one of those points to fill in the standard form of the parabola.  Because this parabola is "upside down" the leading coefficient is negative.  Start with the first coordinate first:

[tex](0, -2)-->-2=-a(0)^2+b(0)+c[/tex] which gives us that c = -2.  That's good...one down, 2 to go.

Next we will use the remaining 2 points to create a system of equations that we can solve simultaneously for a and b.  Using the second coordinate pair (2, -4):

[tex]-4=-a(2)^2+b(2)-2[/tex] gives us the simplified equation:

***-2 = -4a + 2b***

I put the stars in front and behind because we will need to come back to that one in a minute.

Using the last coordinate pair (-2, -4):

[tex]-4=-a(-2)^2-b(2)-2[/tex] simplifies down to:

***-2 = -4a - 2b***

Now put these together and solve the system by elimination, and you see that 2b and the -2b cancel each other out, leaving you with -4 = -8a, so a = 1/2.  Now we know a:  1/2 and c:  -2 and we can find b:

If -2 = -4a + 2b, then -2 = -4(1/2) + 2b, and b = 0.  That means that the equation for the upside down parabola is

[tex]y=-\frac{1}{2}x^2-2[/tex]

help please

must show work ​

Answers

Answer:

Step-by-step explanation:

23A:   Simplify

V^2  + 11V + 10

There are no like terms

Answer when simplify: V^2 + 11V + 10

23B.  Factor:

Steps: V^2  +  11V  + 10

Break the expression into groups:

(V^2  + V)  +  (10V   +  10)

Factor out: V From V^2  + V:   V(V  + 1)

Factor out:  10 From  10V  +  10:   10(V  +  1)

V(V  +  1)  +  10(V  +  1)

Factor out common term:  V  +  1

Factor: Therefore your Answer: (V  + 1) (V  +  10)

24:  Factor

Steps: k^2   +  11k  + 30

Break the expression into groups:

(K^2 + 5K)(6K + 30)

Factor out: k from K^2 + 5K ====>  K(K + 5)

Factor out 6  from 6K + 30 ===> 6(K + 5)

=  k(k + 5)  +  6(k  + 5)

Factor out common term: k  + 5

Factor:  Therefore your Answer is: (K + 5) (K + 6)

25:  Factor

Steps:     R^2   -   1

Rewrite:  1  as  1^2

R^2   -  1^2

Apply difference of two square formulas:

x^2   -   y^2   =   (x   +   y)(x   -  y)

r^2   -  1^2  =  (r  +  1)(r   -  1)

Therefore your answer:  (r  + 1)(r  -  1)

26:  Factor

Steps:  V^2  -  V  - 2

Break the expressions into groups:

(V^2  + V)  +   ( -2V   -  2)

Factor out V from V^2  + V:    V(V  +  1)

Factor out  -2  from  -2v   - 2:    -2(V  +  1)

V(V   +   1)   - 2(V  +  1)

Factor out common term:  V   +  1

Therefore your answer: (V  +  1)(V  -  2)

27:  Factor

Steps:  4N^2  -  15N   -  25

Break expression into groups:

(4N^2  +  5N)   +   ( -20N  -  25)

Factor out N from 4N^2  +  5N:   4(4N  +  5)

Factor out   -5   from  -20N  -  25:    -5(4N   +  5)

N(4N  +  5)  -  5(4N   +   5)

Factor out common term:  4N   +   5

Therefore your answer:   (4n  +  5)(N   -  5)

28: Factor:

Steps:   N^2   +  3N   -  54

Break the expression into group:

(N^2  -  6N)   +   (9N   -  54)

Factor out N from N^2  -  6N:    N(N   - 6)

Factor out   9  From 9N  -  54:    9(N  -  6)

N(N  -  6)    +   9(N   -   6)

Factor out common term:    N    -    6

Therefore your answer:   (N   -  6)(N   +   9)

Hope that helps, Have an awesome day!     :)


What transformation has changed the parent function f(x) = log2x to its new appearance shown in the graph below?

logarithmic graph passing through point 2, negative 2.

−2 • f(x)
2 • f(x)
f(x) − 2
f(x) + 2

Answers

Answer: First Option

−2 • f(x)

Step-by-step explanation:

The function [tex]y=log_2(x)[/tex] passes through point (2,1) since the exponential function [tex]2 ^ x = 2[/tex] when [tex]x = 1[/tex].

Then, if the transformed function passes through the point (2, -2) then this means that f(x) was multiplied by a factor of -2. So if an ordered pair [tex](x_0, y_0)[/tex] belonged to f(x), then [tex](x_0, -2y_0)[/tex] belongs to the transformed function. Therefore, if [tex]f(x) = log_2 (x)[/tex] passed through point (2, 1) then the transformed function passes through point (2, -2)

The transformation that multiplies to f(x) by a factor of -2 is:

[tex]y = -2 * f (x)[/tex]

and the transformed function is:

[tex]y = -2log_2 (x)[/tex]

Help me pleassseeeeeee

Answers

Answer:

a. y = 1/6x + 2

Step-by-step explanation:

You divide everything by 6, then move the -1/6x to the other side, which causes the sign to flip from - to +.

Todds flower garden is 4 feet wide and 8 feet long if the answer is 32 square feet what is the question

Answers

What is the area of Todd's flower garden with a height of 8⃣ feet and a base of 4 feet?

A tree casts a shadow 130 feet. If the angle of the elevation is 47, which is the closest to the distance from the top of the tree to the tip of the shadow

Answers

ANSWER

191 is closest to nearest whole number.

EXPLANATION

Let the distance from the top of the tree to the tip of the shadow be l feet as shown in the diagram.

This is the same as the hypotenuse of the right triangle.

The given side length, 130 ft is adjacent to the angle of elevation which is 47°

We use the cosine ratio to obtain,

[tex] \cos(47 \degree)= \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos(47 \degree)= \frac{130ft}{l} [/tex]

[tex]l= \frac{130ft}{\cos(47 \degree)} [/tex]

[tex]l =190.6162941[/tex]

Final answer:

The distance from the top of the tree to the tip of the shadow, given the length of the shadow is 130 feet and the angle of elevation is 47 degrees, is approximately 180 feet.

Explanation:

The question is asking us to find the distance from the top of the tree to the tip of the shadow using given information: the shadow cast by the tree is 130 feet long, and the angle of elevation is 47 degrees. For this, we can use the tangent function in trigonometry, which is defined as the opposite side over the adjacent side in a right triangle. Here, the length of the shadow (130 feet) serves as the adjacent side, and the height of the tree serves as the opposite side.

To find the hypotenuse (the distance from the top of the tree to the tip of the shadow), you can use the formula: Hypotenuse = Adjacent / cos(angle). So, the Hypotenuse = 130 feet / cos(47) = approximately 180 feet.

Learn more about Trigonometry here:

https://brainly.com/question/11016599

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A sinusoidal function whose period is 1/2 , maximum value is 10, and minimum value is −4 has a y-intercept of 3.

What is the equation of the function described?

Answers

f(x) = 7 sin (4πx) + 3. The function f(x) = 7 sin (4πx) + 3 describe a sinusoidal function whose period is 1/2, maximum value 10, minimum value -4, and it has a y-intercept of 3.

A sinudoidal function whose period is 1/2, maximum value is 10, minimum value is -4, and it has a y-intercept of 3. Let's write to the form f(x) = A sin (ωx +φ) + k, where A is the amplitude, ω is the angular velocity with ω=2πf, (ωx+φ) is the oscillation phase, φ the initial phase (horizontal shift), and k is y-intercept (vertical shift).

Calculating the amplitude:

A = |max - min/2|

A = |10 - (-4)/2| = 14/2

A = 7

calculating the ω:

The period of a sinusoidal is T = 1/f --------> f = 1 / T

ω = 2πf -------> ω = 2π ( 1/T) with T = 1/2

ω = 2π (1/(1/2) = 2π (2)

ω = 4π

The y-intercept k = 3

Writing the equation function with A = 7, ω = 4π, k = 3, φ = 0.

f(x) = A f(x) = A sin (ωx +φ) + k ----------> f(x) = 7 sin (4πx) + 3.

Consider the quadratic function f(x) = –2x2 + 4x – 2. Find the y-intercept and the equation of the axis of symmetry.

The y-intercept is 2.
The equation of the axis of symmetry is x = –1.

The y-intercept is 1.
The equation of the axis of symmetry is x = –2.


The y-intercept is –2.
The equation of the axis of symmetry is x = 1.

The y-intercept is –1.
The equation of the axis of symmetry is x = 2.

Answers

Answer:

The y-intercept is -2

The equation of the axis of symmetry is x = 1 ⇒ 3rd answer

Step-by-step explanation:

* Lets revise the general form of the quadratic function

- The general form of the quadratic function is f(x) = ax² + bx + c,

 where a, b , c are constant

# a is the coefficient of x²

# b is the coefficient of x

# c is the y-intercept

- The meaning of y-intercept is the graph of the function intersects

 the y-axis at point (0 , c)

- The axis of symmetry of the function is a vertical line

  (parallel to the y-axis) and passing through the vertex of the curve

- We can find the vertex (h , k) of the curve from a and b, where

 h is the x-coordinate of the vertex and k is the y-coordinate of it

# h = -b/a and k = f(h)

- The equation of any vertical line is x = constant

- The axis of symmetry of the quadratic function passing through

  the vertex then its equation is x = h

* Now lets solve the problem

∵ f(x) = -2x² + 4x - 2

∴ a = -2 , b = 4 , c = -2

∵ The y-intercept is c

∴ The y-intercept is -2

∵ h = -b/2a

∴ h = -4/2(-2) = -4/-4 = 1

∴ The equation of the axis of symmetry is x = 1

Select the correct answer from the drop down menu. with references to the figure, sin x =

Answers

Answer:

.894

Step-by-step explanation:

First thing to do is to solve for the height of the triangle, BD.  That's easy.  We have the length of the hypotenuse and the base, so Pythagorean's Theorem gives us that the height is 8.003255588 which rounds nicely to 8.  Now you have to call on the fond memories you have of the geometric mean in right triangles to solve the rest.  For the sin of x you need the hypotenuse of that smaller right triangle on the left, side AB.  First let's use geometric mean to find AD.  The formula for that, now that we know the height, is

[tex]BD^2=(AD)(DC)[/tex]

Filling that in with numbers we have

[tex]8^2=(AD)16[/tex] and

64 = 16(AD).  Solve for AD to get that AD has a length of 4.  Now we know two of the three sides in that smaller triangle on the left and can solve for the hypotenuse.

[tex]8^2+4^2=c^2[/tex] and

[tex]64+16=c^2[/tex] so

c=√80 which simplifies to 4√5.  That means that the sin ratio for x is

[tex]\frac{8}{4\sqrt{5} }[/tex]

which divides out to .894

The value of Sin{x} is equivalent to 0.89.

What are trigonometric functions?

There are six major trigonometric functions as -

Sine(x)Cosine(x)Tangent(x)Cotangent(x)Secant(x)Cosecant(x)

We can write the relation between them as -

Sine = 1/cosecantCosine = 1/secantTangent = 1/Cotangent

Given is a triangle ABC.

We can write -

cos {y} = DC/BC = 16/17.89

cos {y} = 16/17.89

cos {y} = 0.89

{y} = cos⁻¹(0.89)

{y} = 27.1°.

We can write -

∠x + ∠y + 90° = 180°

∠x + ∠y = 90°

∠x = 90 - 27.1

∠x = 62.9°

So, we can write -

Sin{x} = Sin{62.9°} = 0.89

Therefore, the value of Sin{x} is equivalent to 0.89.

To solve more questions on trigonometric functions, visit the link below-

https://brainly.com/question/30672622

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Urgently needed
see image

Answers

y2-y1 =M(x2-x1)

Ok Sir, you gave points : (2,1) and (3,4)

4-1/3-2 = 3

Ok we know our slope is 3, now pick any of the two points, and make an equation for this line, so lets go ahead and pick #1, (2,1)

Formula is same as before

y-1=3x-6

y=3x-5

I think its correct, pick as brainless sir, thanks.

Imagine an illness with two cures—drug X and drug Y. Drug X and drug Y are both made by the same firm.

Two events recently happened. First, a study was released showing that drug X is less effective than drug Y. Second, the ingredients used to produce drug X increased in price. What are the consequences of these events?


Choose one:

A. The demand for drug X shifts to the right, and the supply of drug X shifts to the left. The result is a rise in the equilibrium price for drug X and a fall in the equilibrium quantity of drug X.

B. The demand for drug X shifts to the right, and the supply curve for drug X shifts to the left. The result is an unknown change in the equilibrium price for drug X and a fall in the equilibrium quantity of drug X.

C. The demand for drug X shifts to the left, and the supply curve for drug X shifts to the left. The result is an unknown change in the equilibrium price for drug X and a fall in the equilibrium quantity of drug X.

D. The demand for drug X shifts to the left, and the supply curve for drug X shifts to the left. The result is a rise in the equilibrium price for drug X and a fall in the equilibrium quantity of drug X.

Answers

The correct answer is: C. The demand for drug X shifts to the left, and the supply curve for drug X shifts to the left. The result is an unknown change in the equilibrium price for drug X and a fall in the equilibrium quantity of drug X.

Explanation:

1. The study showing that drug X is less effective than drug Y implies a decrease in the perceived effectiveness of drug X. This could lead to a decrease in the demand for drug X as consumers may prefer the more effective drug Y.

2. The increase in the price of ingredients used to produce drug X would lead to an increase in the production cost of drug X. This could cause a leftward shift in the supply curve for drug X, as producers may be less willing or able to supply the same quantity at the previous prices.

Both a decrease in demand and a leftward shift in the supply curve would result in a fall in the equilibrium quantity of drug X. The impact on the equilibrium price is uncertain and would depend on the magnitude of the shifts in demand and supply. Therefore, option C reflects these potential changes in demand and supply without making specific predictions about the equilibrium price.

The correct answer is C: The demand for drug X shifts to the left, and the supply curve for drug X shifts to the left, resulting in an unknown change in equilibrium price for drug X and a decrease in the equilibrium quantity.

The student asked about the consequences on equilibrium price and equilibrium quantity for drug X following two events: a study showing drug X is less effective than drug Y, and an increase in the price of ingredients used to produce drug X.

Analyze each event's impact on demand and supply separately: The less effective study would cause the demand for drug X to shift to the left, implying a decrease in the quantity demanded at each price because consumers now prefer drug Y. Additionally, the increase in production costs would create a supply curve shift for drug X to the left, representing a decrease in supply at each price point. When both supply and demand shift to the left, the equilibrium quantity will clearly decrease; however, the impact on the equilibrium price is uncertain without knowing the relative magnitude of the shifts.

Choosing from the provided options, answer C is correct: The demand for drug X shifts to the left, and the supply curve for drug X shifts to the left. The result is an unknown change in the equilibrium price for drug X and a fall in the equilibrium quantity of drug X.

The graph of a quadratic function is shown above.



According to the fundamental theorem of algebra, the function above has [___] real zeros and [___] complex zeros.

Answers

Answer:

0 real zeros2 complex zeros

Step-by-step explanation:

The "fundamental theorem of algebra" says a polynomial of degree n will have n zeros. If the polynomial has real coefficients, the complex zeros will appear in conjugate pairs.

The graph of this quadratic (degree = 2) does not cross the x-axis, so there are no real values of x that make y=0. That means the two zeros are both complex.


The angles of elevation of a hot air balloon from the two points on level ground are 20° and 42° respectively. If the points are 4.8 miles apart and the balloon is between the points, approximate, to the nearest tenth of a mile, the height of the balloon above the ground.

Answers

Answer:

To the nearest tenth, the height of the balloon is 2.9 miles

Step-by-step explanation:

The nearer point takes the greater angle of elevation.

The diagram is shown in the attachment.

The height of the balloon above the ground is c unit.

From triangle ABD,

[tex]\tan 42\degree=\frac{c}{x}[/tex]

[tex]\implies x=\frac{c}{\tan 42\degree}[/tex]...eqn1

From triangle ABC,

[tex]\tan 20\degree=\frac{c}{x+4.8}[/tex]

[tex]\implies x+4.8=\frac{c}{\tan 20\degree}[/tex]

[tex]\implies x=\frac{c}{\tan 20\degree}-4.8[/tex]..eqn2

We equate both equations and solve for c.

[tex]\frac{c}{\tan 42\degree}=\frac{c}{\tan 20\degree}-4.8[/tex]

[tex]\frac{c}{\tan 42\degree}-\frac{c}{\tan 20\degree}=-4.8[/tex]

[tex]\implies (\frac{1}{\tan 42\degree}-\frac{1}{\tan 20\degree})c=-4.8[/tex]

[tex]\implies -1.636864905c=-4.8[/tex]

[tex]\implies c=\frac{-4.8}{-1.636864905}[/tex]

[tex]c=2.932435039[/tex]

To the nearest tenth, the height of the balloon is 2.9 miles

Answer:

on usatestprep its 1.2

Step-by-step explanation:

which expression represents the phrase "the cost of p pounds of rice at $1.97 per pound"?


WORTH 50 POINTS IF YOU HELP ME
PLZ HELP QUICKLY

Answers

That would be p times 1.97 or 1.97p (letter D) this is because each pound is worth 1.97 dollars more so if you bought 1 pound of rice you'd pay only $1.97 but if you bought 5 pounds of rice you'd pay $9.85 since 1.97 times 5 is 9.85

Hope this helped!

Let me know if this helped!

Please assist! Limited time

Answers

The answer would be c.

[tex] \sqrt{28} [/tex]

Which could be the area of one face of the rectangular prism?Check all that apply

Answers

the area of the rectangle=length x width area=11x6=66

Answer:

24 cm², 44 cm², and 66 cm²

Step-by-step explanation:

The rectangular prism has six faces.  The opposite faces have the same area, so we can say there are three faces with unique areas.

The face on the bottom of the rectangular prism has an area of:

A = 11 cm * 4 cm = 44 cm²

The face on the side of the rectangular prism has an area of:

A = 4 cm * 6 cm = 24 cm²

And the face on the front of the rectangular prism has an area of:

A = 11 cm * 6 cm = 66 cm²

So 24 cm², 44 cm², and 66 cm² are all answers that apply.

Nicole opened a savings account with an initial deposit of $5,000. Since then, she has never made any other deposits or withdrawals. Her savings account earns 4% interest compounded monthly.

Which equation gives the approximate amount, A(x), she has in her savings account as a function of x, the number of years since her initial deposit?

Answers

Answer:

[tex]A(x)=\$5,000(1.04)^{x}[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nx}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

x is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]P=\$5,000\\ r=0.04\\n=12[/tex]  

substitute in the formula above  

[tex]A(x)=\$5,000(1+\frac{0.04}{12})^{12x}[/tex]  

[tex]A(x)=\$5,000(\frac{12.04}{12})^{12x}[/tex]  

[tex]A(x)=\$5,000(1.04)^{x}[/tex]  

Kim uses the Fermi process to estimate the number of buckets of rocks she could store in a warehouse. The buckets are shaped like cylinders. The warehouse is shaped like a rectangular prism. She estimates the buckets have a height of 25 inches and a diameter of 10 inches. She estimates the warehouse is 100 feet long, 50 feet wide, and 20 feet high. Which expression should Kim use in the process?

Answers

Answer:

2x10^8 / 2x10^3

The answer is n=2*10^8/2*10^3.

It is given that the buckets have a height of 25 inches and a diameter of 10 inches. The volume of a cylinder is

V=[tex]\pi[/tex]r²h

V1= [tex]\pi[/tex](10/2)²(25)

=[tex]\pi[/tex](5)²(25)

=625[tex]\pi[/tex]

=1963.495

The scientific notation is

V1= 1.963* 10³

≅2*10³

The warehouse is 100 feet long, 50 feet wide, and 20 feet long.

1 feet = 12 inches

The volume of a cube is

V=Length*breadth*height

Using the above conversion the volume of cube in cubic inches is  

V2=(100*12)*(50*12)*(20*12)

V2= 172800000

The scientific notation is

V2= 1.728*10^8

V2≅2*10^8

The number of buckets of rocks she could store in a warehouse is

n=2*10^8/2*10^3.

Learn more about volume of cylinder: https://brainly.com/question/971817

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need help asap please

Answers

Answer:

136

Step-by-step explanation:

since AB and BC are congruent, then angles BAC and BCA are congruent, so if angle BAC is 22 degrees, BCA is also 22 degrees. 22 + 22 = 44 and since the angles inside of a triangle always add up to 180, you can subtract 44 from 180 to get the measure of the angle ABC = 136. Hope this help 0.0

which can be the first step in finding the equation of the line that passes through the points( 5, -4) and( -1, 8) in slope intercept form?​

Answers

Answer:

Option A is the correct answer.

Step-by-step explanation:

The slope intercept form is: y=mx+b

We need to find m slope and b is the y intercept.

So, first we find the slope m of the given points.

[tex]m = \frac{y_{2} -y_{1}}{x_{2} -x_{1}} \\m= \frac{8-(-4)}{-1-(5)}\\ m= \frac{12}{-6}\\ m=-2[/tex]

After finding the slope, we can find the y intercept.

So, Option A is the correct answer.

Answer:

A

Step-by-step explanation:

A kite has a height of 36 inches and a width of 30 inches. Explain how to use the area formula for a triangle to find the area of the kite. 34

Answers

Answer:

You can view a kite as 4 triangles

Step-by-step explanation:

A geometric kite can easily be viewed as 4 triangles.  The formula to calculate the area of a kite (width x height)/2 is very similar to the one of a triangle (base x height)/2.

According to the formula to calculate the area of a kite, we would get:

(36 x 30)/2 = 540.

If we take the approach of using 4 triangles, we could imagine a shape formed by 4 triangles measuring 18 inches wide with a height of 15.

The area of each triangle would then be: (18 x 15)/2 = 135

If we multiply this 135 by 4... we get 540.

Answer:

Draw a vertical line to break the kite into two equal triangles with a base of 36 and a height of 15. Use the formula A = 1/2bh to find the area of each. The sum of the areas is the area of the kite.

Step-by-step explanation:

1. In a game, if you roll a 6 on a 6-sided number cube, you lose a turn. (a) What is the probability that you roll a 6? Explain your reasoning. (b) What is the probability that you don’t roll a 6? Explain your reasoning. (c) What is the probability that you either roll a 6 or do not roll a 6? Explain your reasoning. (d) Suppose you rolled the 6-sided number cube 120 times, how many times would you expect to roll a 6? Explain and show all of your work.

Answers

Try this options:

a. total - 6 digits, '6' - 1 digit, then probability of rolling a '6' is 1/6;

b. total - 6 digits, '6' - 1 digit, then probability of rolling 1,2,3,4,5 is 5/6;

c. if probability of rolling a '6' is p and not rolling a '6' is q, then p+q=1;

d. if expected probability of one rolling a '6' is 1/6, then numbers of times of rolling a '6' during 120 times is 120/6=20 times.

Write a verbal expression to represent the given equation.

4p+3=-5
a Four times a number plus 3 is equal to 5.

b A number plus 3 is equal to –5.

c Four times a number is equal to –5.

d Four times a number plus 3 is equal to –5.

Answers

For this case we have the following expression:

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

We must indicate an equivalent verbal expression.

If "p" is a variable that represents any number, we can write:

Four times a number plus 3 equals -5.

Answer:

Four times a number plus 3 equals -5.

Option D

The soldering iron’s highest temperature setting is 400 °F. What is the soldering iron’s temperature in Centigrade?

Answer: ( 400-32) *5/9=204.444C

Answers

Hello!

The answer is: [tex]T(\°C)=204.44\°C[/tex]

Why?

To convert from Fahrenheit degrees to Celsius degrees, we must use the following formula:

[tex]T(\°C)=(T(\°C)-32)*\frac{5}{9}[/tex]

We are given the temperature: 400°F

So, converting we have:

[tex]T(\°C)=(400\°F-32)*\frac{5}{9}=368*\frac{5}{9}=204.44\°C[/tex]

Hence, the 400°F is equal to 204.44°C.

Have a nice day!

The twice–differentiable function f is defined for all real numbers and satisfies the following conditions: f(0)=3 f′(0)=5 f″(0)=7 The function g is given by g(x)=eax+f(x) for all real numbers, where a is a constant. Find g ′(0) and g ″(0) in terms of a. Show the work that leads to your answers. The function h is given by h(x)=cos(kx)[f(x)]+sin(x) for all real numbers, where k is a constant. Find h ′(x) and write an equation for the line tangent to the graph of h at x=0. For the curve given by 4x2+y2=48+2xy show that dy dx = y−4x y−x . For the curve given by 4x2+y2=48+2xy, find the positive y-coordinate given that the x-coordinate is 2. For the curve given by 4x2+y2=48+2xy, show that there is a point P with x-coordinate 2 at which the line tangent to the curve at P is horizontal.

Answers

[tex]g(x)=e^{ax}+f(x)\implies g'(x)=ae^{ax}+f'(x)\implies g''(x)=a^2e^{ax}+f''(x)[/tex]

Given that [tex]f'(0)=5[/tex] and [tex]f''(0)=7[/tex], it follows that

[tex]g'(0)=a+5[/tex]

[tex]g''(0)=a^2+7[/tex]

###

[tex]h(x)=\cos(kx)f(x)+\sin x\implies h'(x)=-k\sin(kx)f(x)+\cos(kx)f'(x)+\cos x[/tex]

When [tex]x=0[/tex], we have

[tex]h(0)=\cos0f(0)+\sin0=f(0)=3[/tex]

The slope of the line tangent to [tex]h(x)[/tex] at (0, 3) has slope [tex]h'(0)[/tex],

[tex]h'(0)=-k\sin0f(0)+\cos0f'(0)+\cos0=5+1=6[/tex]

Then the tangent line at this point has equation

[tex]y-3=6(x-0)\implies y=6x+3[/tex]

###

Differentiating both sides of

[tex]4x^2+y^2=48+2xy[/tex]

with respect to [tex]x[/tex] yields

[tex]8x+2y\dfrac{\mathrm dy}{\mathrm dx}=2y+2x\dfrac{\mathrm dy}{\mathrm dx}[/tex]

[tex]\implies(2y-2x)\dfrac{\mathrm dy}{\mathrm dx}=2y-8x[/tex]

[tex]\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{y-4x}{y-x}[/tex]

On this curve, when [tex]x=2[/tex] we have

[tex]4(2)^2+y^2=48+2(2)y\implies y^2-4y-32=(y-8)(y+4)=0\implies y=8[/tex]

(ignoring the negative solution because we don't care about it)

The tangent to this curve at the point [tex](x,y)[/tex] has slope [tex]\dfrac{\mathrm dy}{\mathrm dx}[/tex]. This tangent line is horizontal when its slope is 0. This happens for

[tex]\dfrac{y-4x}{y-x}=0\implies y-4x=0\implies y=4x[/tex]

and when [tex]x=2[/tex], there is a horizontal tangent line to the curve at the point (2, 8).

The equation for the line tangent to the graph of h at x = 0 is:

y - 3 = 6(x - 0)

y = 6x + 3

How can Find g'(0) and g''(0)?

The function g is given by:

g(x) = a[tex]e^x[/tex]+ f(x)

where a is a constant. We are given that f(0) = 3, f'(0) = 5, and f''(0) = 7.

To find g'(0), we need to differentiate g(x):

g'(x) = a[tex]e^x[/tex]+ f'(x)

Substituting x = 0, we get:

g'(0) = a[tex]e^0[/tex] + f'(0) = a + 5

To find g''(0), we need to differentiate g'(x):

g''(x) = a[tex]e^x[/tex] + f''(x)

Substituting x = 0, we get:

g''(0) = a[tex]e^0[/tex]+ f''(0) = a + 7

Therefore, g'(0) = a + 5 and g''(0) = a + 7.

To Find h'(x) and write an equation for the line tangent to the graph of h at x = 0

The function h is given by:

h(x) = cos(kx)[f(x)] + sin(x)

where k is a constant. We need to find h'(x):

h'(x) = -ksin(kx)[f(x)] + cos(kx)f'(x) + cos(x)

Substituting x = 0, we get:

h'(0) = -ksin(0)[f(0)] + cos(0)f'(0) + cos(0)

h'(0) = f'(0) + 1

We are given that f'(0) = 5, so h'(0) = 6.

To find the equation for the line tangent to the graph of h at x = 0, we need to use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where:

y is the y-coordinate of any point on the line

y1 is the y-coordinate of the point where the line intersects the graph

m is the slope of the line

x is the x-coordinate of any point on the line

x1 is the x-coordinate of the point where the line intersects the graph

We know that x1 = 0 and h'(0) = m = 6. We also know that h(0) = cos(0)[f(0)] + sin(0) = 3 + 0 = 3.

Therefore, the equation for the line tangent to the graph of h at x = 0 is:

y - 3 = 6(x - 0)

y = 6x + 3

Learn more about line tangent at:

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