What is the probability of rolling a 6 on a die?

1/5

1/6

5/6

1/4

What is the probability of not rolling a 6 on a die?

Answer:

Note: the last sentence in the problem statement text should read, "Therefore, the volume of the sphere is 4/3πr³ by Cavalieri's principle.

Step-by-step explanation:

I believe it can help a lot if you have seen and understand this derivation of the volume of a sphere. Here is the basic idea.

Shown in the attachment is a cross section of half the volume under consideration. Basically, it is showing one cone and the (red) top hemisphere in a (green) cylinder of radius R and height R. (The problem text refers to a sphere and two cones in a cylinder of height 2R. This is the top half of that geometry.) Actually, only the left edge of the cone is represented here, in order to avoid cluttering the diagram.

We can use this figure to think about a horizontal cross section (cut plane) of this geometry at height h from the center of the sphere. We want to consider the annulus of inner radius C between the cylinder of radius R and the cone, and we want to consider the circle of radius S where the cut plane intersects the hemisphere.

Because the cone has a height of R and a radius of R, the radius C of the cross section will be the same as the height h. That is, in our figure, h = C. We know from the Pythagorean theorem that ...

  h² + S² = R²

  S² = R² - C² . . . . . . subtract h² and substitute C for h

The area of the circular cross section of the hemisphere is πS², and the area of the annulus between the cylinder and cone is π(R² - C²). The above equation tells us these areas are the same.

By Cavalieri's principle, since the cross sections have the same area at every height, the volume of the space between the cylinder and cone is the same as the volume of the hemisphere. Using the formulas for the volumes of cylinder and cone, we find the difference to be ...

  difference volume = hemisphere volume = πr²·r - 1/3πr²·r = 2/3πr³

__

Once this approach to the sphere volume formula derivation is understood, filling in the blanks in your problem statement may become much simpler.

Answer:

  360 minutes

Step-by-step explanation:

(1.5 h/wk)·(4 wk)·(60 min/h) = 1.5·4·60 min = 360 min

Multiply reading time per week by the number of weeks to get reading time. Multiply the number of hours by the number of minutes in an hour to get minutes.

Answer:

[tex]\large\boxed{x=\dfrac{5-\sqrt{73}}{4}\ or\ x=\dfrac{5+\sqrt{73}}{4}}[/tex]

Step-by-step explanation:

[tex]\text{The quadratic formula for}\ ax^2+bx+c=0\\\\\text{If}\ b^2-4ac>0,\ \text{then the equation has two different solutiions:}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\text{If}\ b^2-4ac=0,\ \text{then the equation has one solution:}\ x=\dfrac{-b}{2a}\\\\\text{If}\ b^2-4ac<0,\ \text{then the equation has no solution.}[/tex]

[tex]\text{We have}\ 2x^2=5x+6.\ \text{Convert to the form of}\ ax^2+bx+c=0:\\\\2x^2=5x+6\qquad\text{subtract}\ 5x\ \text{and}\ 6\ \text{from both sides}\\\\2x^2-5x-6=0\\\\a=2,\ b=-5,\ c=-6\\\\b^2-4ac=(-5)^2-4(2)(-6)=25+48=73>0\\\\x=\dfrac{-(-5)\pm\sqrt{73}}{2(2)}=\dfrac{5\pm\sqrt{73}}{4}[/tex]

Do 15 divided by 3 equals 5

Final answer:

To determine Alyssa's age, we set up the equation 15 = 3A, based on the assumption that Eric being '3 times older' than Alyssa means he is 3 times her age. We divide both sides by 3 to get Alyssa's age, which is 5 years old.

Explanation:

To find Alyssa's age, we need to write an equation based on the information provided: Eric is 3 times older than his sister Alyssa, and we know that Eric is 15 years old. The phrase '3 times older' would technically mean 3 times Alyssa's age plus her age again (Alyssa's age times 4). However, this phrase can sometimes be used colloquially to mean '3 times Alyssa's age,' which is more common. So, we need clarification on the intended meaning. If we assume the latter, more common interpretation, the equation based on the information provided would be:

Let A be Alyssa's age. Since Eric is 15 years old and 3 times Alyssa's age, we have: E = 3A, where E is Eric's age.

Substituting Eric's age into the equation, we get: 15 = 3A

To find Alyssa's age, we then divide both sides by 3: 15 / 3 = A

Alyssa's age A would then be 5 years old. So, the equation to find Alyssa's age is: 15 = 3A

Answer:

  an = 5·2^(n-1)

Step-by-step explanation:

The explicit formula for a geometric sequence with first term a1 and common ratio r is ...

  an = a1·r^(n-1)

Your sequence has a1=5 and r=2, so the explicit formula is ...

  an = 5·2^(n-1)

Final answer:

The explicit formula for the geometric sequence 5, 10, 20, 40, 80, 160,... is ,[tex]a_{n}=5(2^{n-1} )[/tex], where 'aₙ' represents the nth term in the sequence.

Explanation:

The student is asking for the explicit formula for a given geometric sequence. In mathematics, a geometric sequence is one where any term after the first is found by multiplying the previous term by a fixed, non-zero number known as the common ratio. Looking at the sequence provided (5, 10, 20, 40, 80, 160,...), we can observe that each term is twice the previous term, thus the common ratio is 2.

To find the explicit formula of a geometric sequence, we use the formula ,[tex]a_{n}=a_{1} (r^{n-1} )[/tex], where an is the nth term, a₁ is the first term in the sequence, r is the common ratio, and n is the term number. For this sequence, a₁ is 5, and r is 2.

The explicit formula for the given geometric sequence is therefore [tex]a_{n}=5(2^{n-1} )[/tex].

The 10 cm string is 7 times smaller than the 70 cm string

The best prediction for the fish population is 16,079.

Hello i hope you are having a good day :)

Question 1 : A cooking show currently has about 223,000 regular viewers. The number of regular viewers has been decreasing at a rate of 4.7% per year. Which is the best prediction for the number of regular viewers the show will have in 6 years? = y = 223000(1-0.047)⁶ = 223000(0.953)⁶ = 167,056.

Question 2 : A population of 30,000 fish is expected to shrink at a rate of 7.5% per year.  Which is the best prediction for the fish population in 8 years?       = 30,000(1−7.5/100)8≈ 16078.9

Question 3 : Bromine-82 has a half-life of about 35 hours.  After 140 hours, how many millilitres of an 80 ml sample will remain?  = Divide 80(1/2)^4 to get 5.

Question 4 : Polonium-218 has a half-life of about 3 minutes.  After 15 minutes, how many milligrams of a 120 mg sample will remain? = 3.75 mg

Question 8 : Pippa is holding the end of her kite string 1.4 m above the ground. The kite string rises at a 63° angle of elevation. Pippa has let out all 75 m of string.  To the nearest tenth of a meter, how high above the ground is the kite? = 68.2 m

Question 9 : Using his telescope, Tommy watches a bald eagle as it sits on the top of a cliff. The telescope is positioned so that the line of sight to the eagle forms a 38° angle of elevation. The telescope sits 1.3 m above the ground and the base of the telescope is 116 m from the base of the cliff.  To the nearest tenth of a meter, how high above the ground is the eagle? = 91.9 m

Question 10 : A photographer's camera sits on a tripod that is 1.8 m above the ground. The base of the tripod is 44 m from the base of a tree. The photographer spots a woodpecker in the tree at a 39° angle of elevation. To the nearest tenth of a meter, how high above the ground is the woodpecker? =  37.4 m

[tex]175 - 14[/tex]

I think that will help you I'm not sure you just have to try to resolve if you get ranked if you get it wrong just send me a message cuz I am a fifth grade teacher

Answer:

the correct solution is letter A.

Step-by-step explanation:

We have the following expression:

6sqrt(7) - 5x*sqrt(7) - x*sqrt(7)

Grouping the expression, we have:

=sqrt(7)*[6 - 5x - x]

=sqrt(7)*[6 - 6x]

=  6*sqrt(7)- 6x*sqrt(7)

So the correct solution is letter A.

Answer:

12 in²

Step-by-step explanation:

Since the figures are similar

linear ratio = a : b , then

area ratio = a² : b²

linear ratio of sides = 8 : 12 = 2 : 3

ratio of areas = 2² : 3² = 4 : 9

let the area of smaller figure be x then

[tex]\frac{4}{x}[/tex] = [tex]\frac{9}{27}[/tex] ( cross- multiply )

9x = 108 ( divide both sides by 9 )

x = 12

Area of smaller figure is 12 in²

Answer:

B. [tex]r_{x-axis}(x,y) \circ R_0,90\degree)[/tex]

Step-by-step explanation:

The vertices of triangle ABC have coordinates A(5,2) B(2,4) and C(2,1).

The mapping for reflection in the x-axis is

[tex](x,y)\to (x,-y)[/tex]

When we reflect triangle ABC in the x-axis, we obtain

A1(5,-2) B1(2,-4) and C1(2,-1).

The mapping for 90 degrees clockwise rotation about the origin is

[tex](x,y)\to (y,-x)[/tex]

When we rotate the resulting triangle through 90 degrees clockwise above the origin, we obtain;

A2(-2,-5) B2(-4,-2) and C2(-1,-2).

The vertices of triangle A''B''C'' also have coordinates A''(-2,-5) B''(-4,-2) and C''(-1,-2).

Hence the rule that describes the composition of transformation that maps ABC to A''B''C'' is

[tex]R_0,90\degree \circ r_{x-axis}(x,y)[/tex]

The correct choice is B.

The equation of the tangent plane to the surface x=h(y,z) at the point (3,0,3) given that ∂h/∂y=−5 and ∂h/∂z=−3 is x = -5y -3z + 12.

In Mathematics, the equation for the tangent plane to a surface x = h(y,z) at a point can be determined by the following formula: x - x0 = ∂h/∂y(y - y0) + ∂h/∂z(z - z0). In your expression ∂h/∂y (derivatives of h with respect to y) is given as -5 and ∂h/∂z (derivatives of h with respect to z) is given as -3. By plugging the value of these derivatives and the point (3,0,3) into the formula, the equation of the tangent plane would be: x - 3 = -5(y - 0) - 3(z - 3).

After simplifying this, we'll get x = -5y -3z + 12. It's worth noting that derivation of the equation for a tangent plane to a parametrized surface relies heavily on partial derivatives and the study of multi-variable calculus.

https://brainly.com/question/33705650

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60.0 is the area of the triangle

Answer: First option

[tex]g(x) = \frac{1}{8}x^2[/tex]

Step-by-step explanation:

Step-by-step explanation:

If the graph of the function [tex]y=cf(x)[/tex]  represents the transformations made to the graph of [tex]y= f(x)[/tex]  then, by definition:

If  [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.

If  [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c

If [tex]c <0[/tex]  then the graph is reflected on the x axis.

In this problem we have the function [tex]f(x)=x^2[/tex] If this function is vertically compressed by a factor of 8 then  [tex]0 <c <1[/tex]  and [tex]c=\frac{1}{8}[/tex]

Therefore the graph of g(x) is  [tex]g(x)=\frac{1}{8}f(x)[/tex]

[tex]g(x) = \frac{1}{8}x^2[/tex]

The answer is the first option

Answer:

The price of one gallon of milk is $3.5

Step-by-step explanation:

Let

x----> the price of one loaves of bread

y----> the price of one gallon of milk

we know that

4x+y=12.50 ----> equation A

2x+2y=11.50 ----> equation B

Solve the system of equations by graphing

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

The solution is the point (2.25,3.5)

see the attached figure

therefore

The price of one loaves of bread is $2.25

The price of one gallon of milk is $3.5

Answer:

A

Step-by-step explanation:

The volume (V) of a pyramid is calculated using the formula

V = [tex]\frac{1}{3}[/tex] × area of base × height

note the height = 48 × 10 = 480 ( 48 storeys at 10 feet )

V = [tex]\frac{1}{3 }[/tex] × 571,536 × 480

  = 91,445,760 ft³

[ 1 yd³ = 27 ft³ ], hence

V = [tex]\frac{91445760}{27}[/tex] = 3, 386, 880 yd³ → A

Answer:  C & D

Step-by-step explanation:

A binomial experiment must satisfy ALL four of the following:

A) When the spinner is spun three times, X is the sum of the numbers the spinner lands on.

  → #3 is not satisfied  (#4 is also not satisfied)

B) When the spinner is spun multiple times ...

    → #1 is not satisfied

C)  When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.

    → Satisfies ALL FOUR

D) When the spinner is spun five times, X is the number of times the spinner lands on 1.

   → Satisfies ALL FOUR

Answer:

8x^2 - 14xy + 3y^2

Step-by-step explanation:

You need to find the product of (2x - 3y )(4x - y ). To solve this, we're going to be using the distributive distribution as follows:

(2x - 3y )(4x - y ) = 8x^2 - 2xy - 12xy + 3y^2

Combining like-terms:

(2x - 3y )(4x - y ) = 8x^2 - 14xy + 3y^2

Therefore, the result is: 8x^2 - 14xy + 3y^2

Answer:

8x^2 - 14xy - 3y^2

the other explains it, it just forgets to factor in a negitive

Answer: Option D

D. [tex]880 = 45d + 70[/tex]; [tex]18\ days[/tex]

Step-by-step explanation:

We know that the cost of preschool is $ 45 per day plus a monthly fee of $ 70.

We also know that a total of $ 880 was paid last month

To write an equation that represents this situation, let us call "d" the number of days that Barry attends school

So the cost was:

[tex]45d + 70 = 880[/tex]

Now we solve the equation for the variable d

[tex]45d= 880-70[/tex]

[tex]d= \frac{810}{45}[/tex]

[tex]d= 18\ days[/tex]

Therefore answer is the option D

Answer:

D

Step-by-step explanation:

I usually use a z-score table, but you can do this with a calculator.

If we go to a z-score table, we first look up the first two digits (in this case, 2.8) in the far left column.  Then we find the hundredths digit in the top row (0.07).  Where they intersect is P(z < 2.87).

P(z < 2.87) = 0.9979

Answer D.

Using the normal distribution, it is found that the correct option regarding P(z < 2.87) is given by:

D. 0.9979

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Hence, P(z < 2.87) is the p-value of Z = 2.87, which is of 0.9979, hence option D is correct.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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Step-by-step explanation:

A, B, and C have the same area.  So P(A) = 1/3 and P(B) = 1/3, which means P(A or B) = 2/3.

P(success) = 2/3 and P(failure) = 1/3.

The probability of 2 failures is:

P = (1/3)² = 1/9

The probability of 2 successes is:

P = (2/3)²= 4/9

The probability of 1 success and 1 failure can be found either with binomial probability, or simply by subtracting the probabilities we found earlier from 1.

P = 1 - 1/9 - 4/9

P = 4/9

So the answer is the one in the bottom left corner.

Answer: C

X              P

0             1/9

1              4/9

2             4/9

Step-by-step explanation:

Screenshot provided

Answer:

Option C is correct

Step-by-step explanation:

First we will convert the mixed fractions into fraction form.

5/4, 5/8, 3/4, 1/2, 3/2, 7/4

Now, to find the range the formula used is:

Range= Maximum Value - Minimum Value

To find the maximum value and minimum value in fractions, we need to make the denominator of each fraction same. Since the highest value of denominator is 8, so other fractions denominator should be 8.

10/8, 5/8, 6/8,4/8,12/8,14/8

Maximum Value = 14/8 (having highest numerator)

Minimum value = 4/8 (having lowest numerator)

Range of data set = Maximum Value - Minimum value

                             = 14/8 - 4/8

                             = 10/8 = 5/4

                             = 1 1/4

so, option C is correct.

Answer:

The answer is C. 1 1/4

Step-by-step explanation:

To get the range of a set of data, all you need to do is get the difference between the highest value and the lowest value. Since you have different fractions, you first need to determine which is the highest and the lowest.

Since your given are not similar fractions (they do not have the same denominator), you need to make them similar first.

What I did first is make all mixed fractions into improper to make it easier for me to make them similar.

[tex]1\dfrac{1}{4},\dfrac{5}{8},\dfrac{3}{4},\dfrac{1}{2},1\dfrac{1}{2},1\dfrac{3}{4}\\\\\\\dfrac{5}{4},\dfrac{5}{8},\dfrac{3}{4},\dfrac{1}{2},\dfrac{3}{2},\dfrac{7}{4}[/tex]

The LCD of all fractions is 8 so I will need to get the proper proportion that will make all of them have 8 as the denominator.

[tex]\dfrac{5}{4}\times\dfrac{2}{2}[/tex] , [tex]\dfrac{5}{8}\times\dfrac{1}{1}[/tex] , [tex]\dfrac{3}{4}\times\dfrac{2}{2}[/tex] , [tex]\dfrac{1}{2}\times\dfrac{4}{4}[/tex] , [tex]\dfrac{3}{2}\times\dfrac{4}{4}[/tex] , [tex]\dfrac{7}{4}\times\dfrac{2}{2}[/tex]

So now we have the new set of fractions to compare:

[tex]\dfrac{10}{8}, \dfrac{5}{8},\dfrac{6}{8}, \dfrac{4}{8}, \dfrac{12}{8},\dfrac{14}{8}[/tex]

Looking at the set, all you have to do is get the fraction with the highest numerator (which will be our highest value) and get the fraction with the lowest numerator (which is the lowest value), then get the difference.

[tex]\dfrac{14}{8}-\dfrac{4}{8} = \dfrac{10}{8}[/tex] or [tex]1\dfrac{2}{8}[/tex]

Simplify it and you will get:

[tex]1\dfrac{1}{4}[/tex]

Answer:

tan(B)

Step-by-step explanation:

we know that

The tangent of an angle is equal to divide the opposite side to the angle by the adjacent side to the angle

In this problem

tan(B)=AC/AB

substitute

tan(B)=8/15

Answer:

Step-by-step explanation:

since the order of choosing out students to hand out papers doesnt matter because the paper handed is just the same and that the purpose or task of each student is just the same, combination should be used. Otherwise, when the order is based on ranking of students for example, permutation is used. answer is true

For this case we have the following equation:

[tex]3-2z = \frac {1} {10}[/tex]

We must find the value of z that represents the solution of the equation:

We follow the steps below:

We multiply by 10 on both sides of the equation:

[tex]10 (3-2z) = 1[/tex]

We apply distributive property to the terms of parentheses;

[tex]30-20z = 1[/tex]

We subtract 30 from both sides of the equation:

[tex]-20z = 1-30\\-20z = -29[/tex]

We divide between -20 on both sides of the equation:

[tex]z = \frac {-29} {- 20}\\z = \frac {29} {20}\\z = 1.45[/tex]

If we substitute the value of z in the original equation, equality is satisfied.

Answer:

[tex]z = 1.45[/tex]

Answer:

option D

Step-by-step explanation:

So we know that [tex]\sqrt{a} \sqrt{b} = \sqrt{ab}[/tex]

Applying this to our function, we have that:

[tex]\sqrt{(x-5)} \sqrt{(x+2)} = \sqrt{(x+2)(x-5)}[/tex]

We know that the argument of a square root should always BE POSITIVE.

So we need to evaluate in which points the expression (x+2)(x-5) is positive.

So we know that (x+2) is possitive when x>-2 and negative when x<-2.

Also we know that (x-5) is possitive when x>5, if x<5 then x is negative.

Then we have:

if x<-2, then:

(x-5) is negative

(x+2) is negative

Then (x+2)(x-5) is positive.

If x>5 then:

(x-5) is positive

(x+2) is positive.

Then (x+2)(x-5) is positive.

If -2<x<5 then:

(x-5) is negative

(x+2) is positive

Then (x+2)(x-5) is negative, so it's undefined.

So the function is defined for x>5 and x<-2

So the correct option is option D.

Answer:

y = 3 cos (x + π/2) + 2

Step-by-step explanation:

The transformed equation of y = Cos x  is  y=a cos⁡(x−c)+d

Where

Keeping these points in mind, the correct equation should have a = 3, c = + π/2, and d = +2

So we can write:

y = 3 cos (x + π/2) + 2

first answer choice is right.

Answer:

c

Step-by-step explanation:

Answer:

limaçon (no inner loop)

Step-by-step explanation:

The equation of a limaçon is written generically as ...

r = b + a·cos(θ)

For b=2 and a=1, this would put the flat side on the left. Rotating it 180° can be accomplished by adding or subtracting π from θ. Then the equation can be ...

r = 2 + cos(θ-π) . . . . or ...

r = 2 - cos(θ)

Answer:

b.120in3

Step-by-step explanation:

you just take the high width and length and times together

4*5*6=120