What is the volume of the cone? What is the volume of the cylinder? What is the volume of the sphere? At the craft store discussed above, the clay cone is $12, the clay cylinder is $30, and the clay sphere is $28. Which is the best buy? Explain. Hint: Which shapes gives you more clay for less money?

Answer:

The correct options are (A), (C) and (D).

Step-by-step explanation:

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

It is provided that the 99% confidence interval for the mean widget width is:

CI = 14.3 < μ < 30.4

The 99% confidence interval for population mean widget width (14.3, 30.4), implies that there is a 0.99 probability that the true value of the mean widget width is included in the above interval.

Or, the 99% confidence interval for the mean widget width implies that there is 99% confidence or certainty that the true mean widget width value is contained in the interval (14.3, 30.4).

Thus, the correct options are (A), (C) and (D).

Using confidence interval concepts, it is found that the correct options are:

A. With 99% confidence, the mean width of all widgets is between 14.3 and 30.4.

C. There is a 99% chance that the mean of the population is between 14.3 and 30.4.

The interpretation of a x% confidence interval is that we are x% sure that the population mean is in the interval.

In this problem, 99% confidence interval for widget width is between 14.3 and 30.4, hence we are 99% sure that the population mean, that is, the mean width of all widgets is between 14.3 and 30.4, hence options A and C are correct.

A similar problem is given at https://brainly.com/question/15043877

Answer:

False

Step-by-step explanation:

[tex]y = x^2-3x+8[/tex]

Y-intercept is when x = 0

So, Putting x = 0 in the above equation

[tex]y = (0)^2-3(0)+8\\y = 0-0+8\\y = 8[/tex]

So, y-intercept = 8

y-intercept = -3 is a false statement.

Answer:

[tex]\boxed{false}[/tex]

Step-by-step explanation:

The y-intercept is when the value of x is 0.

Let x = 0

y = 0² - 3(0) + 8

y = 0 - 0 + 8

y = 8

The y-intercept is 8.

Answer:

They are both equal to 7.07

Step-by-step explanation:

Using SohCahToa to find x you use the opposite and the hypotenuse if you use the 45 degree angle.

Now you use sin(45)=x/10

x=7.07

Now using SohCahToa to find y you use hypotenuse and adjacent, if using the 45 degree angle.

Now you use cos(45)=y/10

y=7.07

Answer: side y=7.1

side x= 7.1

Step-by-step explanation:

[tex]sin(45)=\frac{x}{10}[/tex]

[tex]x=7.07...[/tex]

[tex]cos(45)=\frac{y}{10}[/tex]

[tex]y=7.07...[/tex]

Answer:

a. 15/23

b. 13/27

c. 400g

Step-by-step explanation:

a. When the denominators are the same, you can just sum the numerators.

Which becomes, 13+2=15--> 15/23

b. Same, when the denominator is the same, you can just minus the numerators. Which becomes, 25-12=13--> 13/27

c. 1kg=1000g. 1000/5=200✖️2=400

Answer:

2 triangles are possible.

Step-by-step explanation:

Given

a=6

b=10

[tex]\angle[/tex]A=33°

To find:

Number of triangles possible ?

Solution:

First of all, let us use the sine rule:

As per Sine Rule:

[tex]\dfrac{a}{sinA}=\dfrac{b}{sinB}[/tex]

And let us find the angle B.

[tex]\dfrac{6}{sin33}=\dfrac{10}{sinB}\\sinB = \dfrac{10}{6}\times sin33\\B =sin^{-1}(1.67 \times 0.545)\\B =sin^{-1}(0.9095) =65.44^\circ[/tex]

This value is in the 1st quadrant i.e. acute angle.

One more value for B is possible in the 2nd quadrant i.e. obtuse angle which is: 180 - 65.44 = [tex]114.56^\circ[/tex]

For the value of [tex]\angle B = 65.44^\circ[/tex], let us find [tex]\angle C[/tex]:

[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow 33+65.44+\angle C = 180\\\Rightarrow \angle C = 180-98.44 = 81.56^\circ[/tex]

Let us find side c using sine rule again:

[tex]\dfrac{6}{sin33}=\dfrac{c}{sin81.56^\circ}\\\Rightarrow c = 11.02 \times sin81.56^\circ = 10.89[/tex]

So, one possible triangle is:

a = 6, b = 10, c = 10.89

[tex]\angle[/tex]A=33°, [tex]\angle[/tex]A=65.44°, [tex]\angle[/tex]C=81.56°

For the value of [tex]\angle B =[/tex][tex]114.56^\circ[/tex], let us find [tex]\angle C[/tex]:

[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow 33+114.56+\angle C = 180\\\Rightarrow \angle C = 180-147.56 = 32.44^\circ[/tex]

Let us find side c using sine rule again:

[tex]\dfrac{6}{sin33}=\dfrac{c}{sin32.44^\circ}\\\Rightarrow c = 11.02 \times sin32.44^\circ = 5.91[/tex]

So, second possible triangle is:

a = 6, b = 10, c = 5.91

[tex]\angle[/tex]A=33°, [tex]\angle[/tex]A=114.56°, [tex]\angle[/tex]C=32.44°

So, answer is : 2 triangles are possible.

Answer:

1/3(x+5)

Step-by-step explanation:

f(x) = 3x-5

y = 3x-5

Exchange x and y

x = 3y-5

Solve for y

Add 5 to each side

x+5 = 3y

Divide each side by 3

1/3 ( x+5) = 3y/3

1/3 ( x+5) = y

The inverse is 1/3(x+5)

Answer:

[tex]f^{-1}(x)=\frac{x+5}{3}[/tex]

Step-by-step explanation:

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

[tex]\mathrm{We \: need \: to \: find \: the \: inverse \: of \: the \: function.} \\ \mathrm{The \: inverse \: of \: a \: function \: reverses \: the \: original \: function.}[/tex]

[tex]\mathrm{Plug \: f(x) \: as \: y.}[/tex]

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

[tex]\mathrm{Solve \: for \: x.}[/tex]

[tex]\mathrm{Add \: 5 \: to \: both \: sides \: of \: the \: equation.}[/tex]

[tex]y+5=3x[/tex]

[tex]\mathrm{Divide \: both \: sides \: of \: the \: equation \: by \: 3.}[/tex]

[tex]\frac{y+5}{3} =x[/tex]

[tex]\mathrm{Switch \: variables.}[/tex]

[tex]\frac{x+5}{3} =y[/tex]

[tex]\mathrm{Plug \: y \: as \: f^{-1}(x).}[/tex]

[tex]f^{-1}(x)=\frac{x+5}{3}[/tex]

Answer:

336m^2

Step-by-step explanation:

The triangle area is half of base times height so: 1/2*8*12=48m^2

There are 4 triangles so 48*4=192

Then the square base area is side times side so: 12*12=144m^2

Then surface area of model is 192m^2+144m^2=336m^2

Answer:

336 m²

Step-by-step explanation:

We can find the surface area of this pyramid by finding the surface area of one of the sides, multiplying it by 4 (as there are 4 sides to the pyramid) then adding it to the surface area of the base.

Each side of this (excluding the base) is a triangle, and to find the area of a triangle we use the equation [tex]\frac{b \cdot h}{2}[/tex].

[tex]\frac{12 \cdot 8}{2}[/tex]

[tex]\frac{96}{2}[/tex]

48.

So, one side of this is 48. Multiplying it by 4 gets us 192.

Now we have to add the area of the base. The area of the bass is a square with side lengths of 12, so we can square 12 to get the area of the bass. 12² = 144.

Now let's add these numbers:

192+144 = 336

So, 336 m² is what this comes out to.

Hope this helped!

Answer:

-25 and -23

Step-by-step explanation:

The arithmetic sequences are the same so we will have the same formula for each of them. The first term (a₁) is 3 and the common difference (d) is -2.

Explicit formula: aₙ = a₁ + (n - 1) * d

Our formula is aₙ = 3 + (n - 1) * (-2) = -2n + 5

a₁₅ = -2 * 15 + 5 = -25

a₁₄ = -2 * 14 + 5 = -23

Answer: -25 and -23

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

We are given the two points (2,7) and (4,-1).  In order to determine the linear equation, we need to find the slope and the y-intercept. First, find the slope m. Let (2,7) be x1 and y1, and let (4,-1) be x2 and y2:

[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{-1-7}{4-2}=-8/2=-4[/tex]

Thus, the slope is -4.

Now, to find the y-intercept, we can use the point-slope form. Recall that the point slope form is:

[tex]y-y_1=m(x-x_1)[/tex]

Where (x1, y1) is a coordinate pair and m is the slope.

Use either of the two coordinate pair. I'm going to use (2,7). Substitute them for x1 and y1, respectively:

[tex]y-(7)=-4(x-(2))\\y-7=-4x+8\\y=-4x+15[/tex]

This is also slope-intercept form. The answer is A.

Answer:

A. y=-4x+15

Step-by-step explanation:

First, you want to find the slope by using the formula

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

The first step is to put in the right numbers,

[tex]\frac{-1-7}{4-2}[/tex]

Then, subtract the numbers accordingly

[tex]\frac{-8}{2}[/tex]

Then simplify

[tex]\frac{-4}{1}[/tex] or -4

The next step is finding the y-intercept, you can do this by drawing it out or using the formula (i will be using the point (2,7) where y is 7 and x is 2)

y=-4x+b   Plug in the values

7=-4(2)+b   Multiply

7=-8+b   add 8 to both sides to isolate the variable

15=b

so y=-4x+15

Hope this helps, if you have any questions, feel free to ask.

Have a good day! :)

To generate a point, you plug in a number for x to get the corresponding y value.

If x = 0 for instance, then the y value is...

y = x^2 - 4

y = 0^2 - 4 ... x is replaced with 0

y = 0 - 4

y = -4

So x = 0 and y = -4 pair up to get the point (0,-4). This is the y intercept as the parabola crosses the y axis here. It turns out that this is also the vertex point as it is the lowest point on the parabola.

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

If x = 1, then,

y = x^2 - 4

y = 1^2 - 4

y = 1 - 4

y = -3

meaning (x,y) = (1,-3) is another point on this line.

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

Repeat for x = 2

y = x^2 - 4

y = 2^2 - 4

y = 4-4

y = 0

Since we got a y output of 0, we have found an x intercept located at (2,0). The other x intercept is (-2,0).

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

The idea is to generate as many points as possible. Plot all of the points on the same xy coordinate grid. Then draw a curve through those points the best you can. You should get what you see in the diagram below. I used GeoGebra to make the graph. Desmos is another handy tool I recommend.

Note: the more points you generate, the more accurate the graph will be

Answer:

There will be 128 holes

Step-by-step explanation:

Simply think of each fold as doubling the number of holes.  So since we have 6 folds, that will be 2^6 and then we have 2 holes in those folds, which makes 2*2^6 == 2^7 == 128 holes.  Cheers.

Folding of the paper is an illustration of a geometric sequence

The number of holes in the rectangular paper is 128

The given parameters are:

[tex]\mathbf{h = 2}[/tex] --- holes

[tex]\mathbf{t = 6}[/tex] --- number of times

The sheet was folded in halves i.e. in 2's.

So, the amount of each time is:

[tex]\mathbf{f(t) = 2 \times h^t}[/tex]

Substitute values for h and t

[tex]\mathbf{f(6) = 2 \times 2^6}[/tex]

Evaluate the exponent

[tex]\mathbf{f(6) = 2 \times 64}[/tex]

Multiply

[tex]\mathbf{f(6) = 128}[/tex]

Hence, the number of holes in the rectangular paper is 128

Read more geometric sequence at:

https://brainly.com/question/10564422

So option (D) is Correct.

Answer:

The answer is

Step-by-step explanation:

Let the unknown angle be x

To find x we use cosine

cos∅ = adjacent / hypotenuse

From the question

The hypotenuse is 56

The adjacent is 48

So we have

cos x = 48/56

cos x = 6/7

x = cos-¹ 6/7

x = 31.003

x = 31° to the nearest degree

Hope this helps you

Answer:

[tex]24 units^2[/tex]

Step-by-step explanation:

Well we can divide the given polygon into smaller triangles.

The triangle on the upper right corner has a base of 4 units and a height of 3 units.

So we use the following formula,

[tex]\frac{b*h}{2}[/tex]

4*3 = 12

12 / 2 = 6 units^2

Now we can do the bottom triangle.

It has a base of 4 units and a height of 1 unit.

So 4*1 = 4

4 / 2 = 2 units^2

Now for the top left triangle.

It has a base of 4 units and a height of 2 units.

So 4*2 = 8

8 / 2 = 4 units^2

Now all we have is the middle part.

Its a triangle with a base of 4 units and a height of 2 units.

So 4*2 = 8

8 / 2 = 4 units^2

6 + 2 + 4 + 4 = 16 units^2

Thus,

after adding everything up the total area of the polygon is 16 units^2.

Hope this helps :)

Answer:

[tex]\boxed{\sf Average \ Speed = 54\ km/hr}[/tex]

Step-by-step explanation:

Given:

Distance = S = 18 km

Time = t = 20 min = 20/60 = 0.33 hours

Required:

Average Speed = <v> = ?

Formula:

Average Speed = Total Distance Covered / Total Time Taken

Solution:

A . S = 18 / 0.33

A.S = 54 km/hr

Answer:

0.9km/minute

or

54km/hour

Step-by-step explanation:

18km in 20 minutes = 18km/20min

18km/20min = 0.9km/min

1 hour = 60 minutes

20 minutes = 20/60 = 0.3333 hours

18km/20mins = 18km/0.3333hours = 54km/hour

Answer:

Option B. an = 3• 6ⁿ¯¹

Step-by-step explanation:

The following data were obtained from the question:

First generation = 3

2nd generation = 1st generation x 6

2nd generation = 3 x 6 = 18

3rd generation = 2nd generation x 6

3rd generation = 18 x 6 = 108

Therefore, we can thus form a sequence as:

3, 18, 108

Since the 2nd term is obtained by multiplying the previous term (i.e the 1st term) by 6 and also, the 3rd is obtained by multiplying the 2nd by 6, the sequence is a geometric progression.

Thus,

The common ratio (r) = 6

The first term (a) = 3

The nth term (an) =?

The nth term of geometric progression is given as

an = arⁿ¯¹

Inputing the value of the first term (a) and common ratio (r) into the above equation, we obtained:

an = arⁿ¯¹

an = 3• 6ⁿ¯¹

Therefore, the explicit formula which can be used to find the number of rabbits in the nth generation is

an = 3• 6ⁿ¯¹

Answer:

7.1%

The percentage increase is 7.1%

Step-by-step explanation:

Percentage increase %∆P is the percentage change in the price.

Percentage increase %∆P = ∆P/Pr × 100%

Where;

∆P = change in sales price = $241,500-$225,400

Pr = regular price = $225,400

Substituting the given values;

%∆P = (241,500-225,400)/225,400 × 100%

%∆P = 7.142857142857% = 7.1%

The percentage increase is 7.1%

Answer:

Step-by-step explanation:

Let the first number be x

Let the second number be y

For the first equation

One number is 7 less than 3 times the second number is written as

x = 3y - 7

For the second equation

The sum of the two numbers is 29

So we have

x + y = 29

Substitute the first equation into the second one

That's

3y - 7 + y = 29

4y = 29 + 7

4y = 36

Divide both sides by 4

Substitute y = 9 into x = 3y - 7

That's

x = 3(9) - 7

x = 27 - 7

The numbers are 20 and 9

Hope this helps you

Answer:

(x + 1)² + (y - 10)² = 4

Step-by-step explanation:

Standard form of the equation of a circle is given by,

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and 'r' is the radius.

In the given question coordinates of the center A are (-1, 10) and radius of the circle is 2 units.

By substituting these values in the formula,

(x + 1)² + (y - 10)² = 2²

(x + 1)² + (y - 10)² = 4

Therefore, standard form of the equation of the given circle is (x + 1)² + (y - 10)² = 4

Answer:

[tex]\frac{x3 + 5x2 + 4x + 4}{x}[/tex]

Step-by-step explanation:

x2+5x+ 4/x+4

Answer:

y<=-x+3 and y<=2x+1

Step-by-step explanation:

y=-x+3 is the orange line. The shaded region is below so its y<-x+3

y=2x+1 is the blue line. The shaded region is below so y<2x+1

Answer:

6x - 5y = 15 and x + 2y = 0

Step-by-step explanation:

Here we are given the following equations:

i) x-2y= 4

ii) 4x+5y= 8

iii) 6x-5y=15

iv) x+2y=0

Required:

Which system of equations has a solution of approximately (1.8, –0.9).

To find the approximate equations, substitute x and y for  1.8 and  -0.9 into all the equations respectively and check the resulting values

i) Substitute (1.8, -0.9) in x-2y= 4:

1.8 - 2(-0.9) = 4.

1.8 + 1.8 = 4.

3.6 ≠ 4.

ii) Substitute (1.8, -0.9) in 4x+5y= 8

4(1.8) + 5(-0.9) = 8

7.2 - 4.5 = 8.

2.7 ≠ 8.

iii) Substitute (1.8, -0.9) in 6x-5y=15

6(1.8) - 5(-0.9) = 15.

10.8 + 4.5 = 15

15.3 ≠ 15.

This equation has a solution that is close, therefore it is correct.

iv) Substitute (1.8, -0.9) in x+2y=0

1.8 + 2(-0.9) = 0.

1.8 - 1.8 = 0.

0 = 0.

x + 2 y = 0 has the exact value, therefore it is also correct.

The system of equations that has a solution of approximately (1.8, –0.9) are:

x+2y=0 and 6x-5y=15

Answer:

the correct answer is A

Step-by-step explanation:

I think it is C. Pls comment right or wrong!

The equation 2(x + 5) = 40 is true for the value x = 15 which is the correct answer would be option (C)

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

To determine the required equation which is true for the value x = 15

We have to simplify the given equations and solve for x.

A. 2(x + 3) = 40

⇒ 2x + 6 = 40

⇒ 2x = 40 - 6

⇒ 2x = 34

⇒ x = 34/2

⇒ x = 17

B. 2(x − 5) = 30

⇒ 2x - 10 = 30

⇒ 2x = 30 + 10

⇒ 2x = 40

⇒ x = 20

C. 2(x + 5) = 40

⇒ 2x + 10 = 40

⇒ 2x = 40 - 10

⇒ 2x = 30

⇒ x  = 15

Hence, the equation 2(x + 5) = 40 is true for the value x = 15 which is the correct answer would be option (C)

Learn more about the equations here:

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Answer:

No

Step-by-step explanation:

The sum of two random sides of a triangle must be bigger than the third side and their differences must be smaller than the third side

For example

3 - 4 - 5 can be made into a triangle because 3 + 4 > 5 and 4 - 3 < 5

Answer:

[tex]\boxed{V = 434.9 \ cm^3 }[/tex]

Step-by-step explanation:

Volume of Sphere = [tex]\frac{4}{3} \pi r^3[/tex]

Where r = 4.7 cm

V = [tex]\frac{4}{3} (3.14)(4.7)^3[/tex]

V = [tex]\frac{4}{3} (3.14)(103.8)[/tex]

V = [tex]\frac{1304.7}{3}[/tex]

V = 434.9 cm³  (Up to 1 dp)

Answer:

Step-by-step explanation:

4/3×22/7×4.7^3=435.1cm

As an approximate decimal, this is 0.5556 which converts to 55.56%

======================================================

Explanation:

Let's say there are 100 households (just for the sake of simplicity). We are told that 90% of them have answering machines. So that means 90 households have answering machines. In addition, 50 households have answering machines and call waiting. Those 50 households are part of the 90 mentioned previously.

We then select a house at random. Someone tells us (or we have some kind of prior knowledge) that whichever house is selected, they have an answering machine. We can ignore the 10 households that don't have an answering machine. Out of those 90 households, 50 have both features. So 50/90 = 5/9 is the probability of getting a household with both features.

The answer would be 1/2 or 50% if we didn't have the prior knowledge of the household having an answering machine. But with this prior knowledge, the conditions change and so does the probability.

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

You could also compute 0.50/0.90 to get the same answer.

Answer:

None

Step-by-step explanation:

You wrote:

"Determine what type of quadrilateral ABCD is, given the following points. A(0,0) B(5,0) C(0,4) D(5,4) Parallelogram, Rectangle, Rhombus, or Square"

According to what you wrote, you don't have any of the listed quadrilaterals.

ABCD (in that precise order) is not a simple polygon according to the coordinates of the points since there is an internal intersection of sides.

ABDC, though, is a rectangle.

The quadrilateral with points A(0,0), B(5,0), C(0,4) and D(5,4) is a rectangle, option B is correct.

To find the type of quadrilateral find the length of four sides:

For A(0,0) and B(5,0)

AB=√(5-0)²+(0-0)²

AB=5 units

For  B(5,0) and D(5,4)

BD=√(5-5)²+(4-0)²

BD=√16

BD=4 units

For C(0,4) and D(5,4):

BD=√(5-0)²+(4-4)²

=5 units

For A(0,0) and C(0,4):

AC=√(0-0)²+(4-0)²

= 4 units.

In the quadrilateral the opposite sides are equal, so it is a rectangle.

Hence, the quadrilateral is a rectangle. Option B is correct.

To learn more on Quadrilateral click here:

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Complete question:

Determine what type of quadrilateral ABCD is, given the following points. A(0,0) B(5,0) C(0,4) D(5,4)

(A) Parallelogram

(B) Rectangle

(C) Rhombus
(D)Square

Answer:

Step-by-step explanation:

Given,

Cost price ( CP ) = 12

Selling price ( SP ) = 15

Since, CP < SP , she made a profit

Actual profit = SP - CP

plug the values

[tex] = 15 - 12[/tex]

Subtract the numbers

[tex] = 3[/tex]

Profit = 3

Now,

Profit percent = [tex] \frac{actual \: profit}{cost \: price} \times 100[/tex] %

Plug the values

[tex] = \frac{3}{12} \times 100[/tex] %

Calculate

[tex] = 25[/tex] %

Hope this helps...

Best regards!!

Answer:

25%

Step-by-step explanation:

Cost Price: ₦12

Selling Price: ₦15

Profit: ₦15 - ₦12 = ₦3

Profit Percentage = [tex]\frac{profit}{cost price}[/tex]  ×  [tex]\frac{100}{1}[/tex]

Profit Percentage = [tex]\frac{3}{12}[/tex] × [tex]\frac{100}{1}[/tex]

Profit Percentage = [tex]\frac{1}{4}[/tex] × [tex]\frac{100}{1}[/tex] = 25%

Final Answer = 25%