Flipping through a magazine, Hiccup sees an advertisement for Toothless Toothpaste. The ad says that it is recommended by 4 out of 7 dragons dentists. toothless If 1,500 dragon dentists were surveyed, about how many would recommend Toothless Toothpaste? Explain your reasoning!

Answer:1/3

Step-by-step explanation:

3 (amount of reds)

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

3+2+4 (sum of all marbles red+Blue+Yellow)          

simplfy

3 /3    

----   =1/3

9 /3            

To find out the theoretical probability of drawing a red marble, divide the total number of red marbles (3) by the total number of marbles (9). Therefore, the theoretical probability is 1/3.

The subject of your question falls under the branch of Mathematics and it's about a concept known as theoretical probability. In this case, the total number of marbles in the bag is 3 red + 2 blue + 4 yellow = 9 marbles. The probability of drawing a red marble from the bag is calculated by dividing the number of red marbles by the total number of marbles. Therefore, the theoretical probability of pulling a red marble is 3/9 which simplifies to 1/3, meaning there is a one in three chance of drawing a red marble.

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Answer:

A trinomial of degree 5

Step-by-step explanation:

A monomial has only 1 term

A binomial has 2 terms

A trinomial has 3 terms

4[tex]x^{5}[/tex] + 3x³ - 7x ← has 3 terms and is therefore a trinomial

The degree of a polynomial is determined by the largest exponent of the variable in the expression

4[tex]x^{5}[/tex] is the term with the largest exponent in the expression

Hence a polynomial of degree 5

Answer:

(x - 3)² + (y - 2)² = 17

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r the radius

here (h, k) = A(3,2), thus

(x - 3)² + (y - 2)² = r²

The radius is the distance from the centre to a point on the circle

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (- 1, 1) ← point on circle

r = [tex]\sqrt{(-1-3)^2+(1-2)^2}[/tex] = [tex]\sqrt{(-4)^2+(-1)^2}[/tex] = [tex]\sqrt{17}[/tex]

Hence r² = ([tex]\sqrt{17}[/tex] )² = 17

(x - 3)² + (y - 2)² = 17 ← equation of circle

Answer:

2 (4/5) = 2.80

2 (11/20) = 2.55

2 (1/2) = 2.50

2 (9/20) = 2.45

2 (3/20) = 2.15

Step-by-step explanation:

Answer:

The Angles of △SPT are

[tex]m\angle STP=35\°[/tex]  

[tex]m\angle SPT=126\°[/tex]

[tex]m\angle PST=19\°[/tex]

Step-by-step explanation:

step 1

Find the measure of angle PET

we know that

The inscribed angle is half that of the arc it comprises.

[tex]m\angle PET=\frac{1}{2}(arc\ PT)[/tex]

substitute the given values

[tex]m\angle PET=\frac{1}{2}(70\°)[/tex]

[tex]m\angle PET=35\°[/tex]

step 2

Find the measure of angle PTE

we know that

The sum of internal angles of a triangle must be equal to 180 degrees

In the triangle PET

[tex]m\angle PET+m\angle EPT+m\angle PTE=180\°[/tex]

substitute the given values

[tex]35\°+54\°+m\angle PTE=180\°[/tex]

[tex]m\angle PTE=180\°-89\°=91\°[/tex]

step 3

Find the measure of angle STP  

we know that

The inscribed angle is half that of the arc it comprises.

[tex]m\angle STP=\frac{1}{2}(arc\ TP)[/tex]

substitute the given values

[tex]m\angle STP=\frac{1}{2}(70\°)=35\°[/tex]

step 4

Find the measure of angle SPT

we know that

[tex]m\angle SPT+m\angle EPT=180\°[/tex] ----> by supplementary angles

[tex]m\angle SPT+54\°=180\°[/tex]

[tex]m\angle SPT=180\°-54\°=126\°[/tex]

step 5

Find the measure of angle PST

we know that

The sum of internal angles of a triangle must be equal to 180 degrees

In the triangle SPT

[tex]m\angle STP+m\angle SPT+m\angle PST=180\°[/tex]

substitute the given values

[tex]35\°+126\°+m\angle PST=180\°[/tex]

[tex]m\angle PST=180\°-161\°=19\°[/tex]

Answer:

D. Events E and B are independent.

Step-by-step explanation:

It can be determined that Events E and B are independent. The correct answer is: D.

To determine independence between events, we can use the formula:

[tex]\[ P(A \cap B) = P(A) \times P(B) \][/tex]

Let's check for events D and A:

[tex]\[ P(D \cap A) = 0.2 \][/tex]

[tex]\[ P(D) \times P(A) = 0.5 \times 0.2 = 0.1 \][/tex]

Since [tex]\(0.2 \neq 0.1\),[/tex] events D and A are not independent.

Checking for events D and B:

[tex]\[ P(D \cap B) = 0.3 \][/tex]

[tex]\[ P(D) \times P(B) = 0.5 \times 0.3 = 0.15 \][/tex]

Since [tex]\(0.3 = 0.15\)[/tex], events D and B are independent.

Similarly, events A and B:

[tex]\[ P(A \cap B) = 0.15 \][/tex]

[tex]\[ P(A) \times P(B) = 0.2 \times 0.5 = 0.1 \][/tex]

Since [tex]\(0.15 \neq 0.1\)[/tex],events A and B are not independent.

For events E and B:

[tex]\[ P(E \cap B) = 0.15 \][/tex]

[tex]\[ P(E) \times P(B) = 0.3 \times 0.5 = 0.15 \][/tex]

Since [tex]\(0.15 = 0.15\)[/tex], events E and B are independent.

Therefore, the correct answer is: D. Events E and B are independent.

Answer:

Choice B

Step-by-step explanation:

We can perform a least squares regression model in Ms. Excel to determine the equation of the line of best fit for the data given;

The first step is to enter the data into any two adjacent columns of an excel workbook. Next, click on the Data ribbon followed by the Data Analysis tool pack. We then proceed to select regression from the pop-up window. The final step is to select the y range and the x range of values from our data.

Once we click ok, Excel returns our least squares regression model as shown in the attachment below.

The coefficient of X variable 1 is our slope.

Answer:

b

Step-by-step explanation:

Answer:

  they are complementary

Step-by-step explanation:

The sum of angles in a triangle is 180°. When one of those angles is a right angle (90°), the sum of the other two must be 90°. When the sum of two angles is 90°, they are said to be complementary angles.

I believe the time would be about 4 seconds

Answer:

9.29 seconds

Step-by-step explanation:

Attached is my work because it's difficult to type

Attached is an image of where I got my equations from

the answer may be wrong

Answer:

1/2

Step-by-step explanation:

Final answer:

The exact value of sin 30 degrees is 0.5, and this is derived from the special 30-60-90 triangle.

Explanation:

The value of sin 30 degrees is 0.5.

This can be determined using the unit circle or by using the trigonometric function of 30 degrees.

When we evaluate sin 30 degrees, we can look at the special right triangle with angles 30-60-90 where the ratio of the opposite to the hypotenuse in a 30-degree angle is 1/2. In this triangle, the side opposite to the 30-degree angle is half the length of the hypotenuse. Therefore, sin 30 degrees is equal to 1/2 or 0.5.

Answer:

1.69 ft (approx.)

Step-by-step explanation:

Formula for Volume of cylinder: pi x radius squared x height

Plug in 108 for volume, 3.14 for pi and 12 for height:

108 = 3.14 x r squared x 12

Multiply 3.14 and 12

108 = 37.68 x r squared

Divide both sides by 37.68

2.87 = r squared

"Unsquare" both sides (square root)

1.69 ft. = radius (approximate answer, rounded to nearest hundredth)

Answer:

1.69 ft

Step-by-step explanation:

V = πr²h formula  of a cylinder.

Volume = 108 ft

Height = 12 ft

Radius = r

V = πr²h

108 ft = 22/7 × r² × 12 ft

π = 22/7 or 3.14

108 ft = 264/7r²

108 ft  = 37.71r²

divide both sides by 37.71

108 ft/37.71 =r²

2.86 ft = r²

square root both side

√2.86 ft = √r²

the square cancels the square root

1.69 ft.

                                 To check

V = πr²h

108 = 22/7 × (1.69)² 12

108 = 22/7 × 2.8561 × 12

108 = 107.61≈108

108 ft = 108 ft.

The answers are:

C) [tex](3+xz)(-3+xz)[/tex]

D) [tex](y^2-xy)(y^2+xy)[/tex]

F) [tex](64y^2+x^2)(-x^2+64y^2)[/tex]

To know which of the products results in a difference of square, we need to remember the difference of squares from:

The difference of squares form is:

[tex](a+b)(a-b)=a^{2}-b^{2}[/tex]

So, discarding each of the given options in order to find which products result in a difference of squares, we have:

[tex](x-y)(y-x)=xy-x^{2}-y^{2} +yx=-x^{2} -y^{2}[/tex]

So, the obtained expression is not a difference of squares.

[tex](6-y)(6-y)=36-6y-6y+y^{2}=y^{2}-12y+36[/tex]

So, the obtained expression is not a difference of squares.

[tex](3+xz)(-3+xz) =(xz+3)(xz-3)=(xz)^{2}-3xz+3xz-(3)^{2}\\\\(xz)^{2}-3xz+3xz-(3)^{2}=(xz)^{2}-(3)^{2}[/tex]

So, the obtained expression is a difference of squares since it matches with the form of the difference of squares.

[tex](y^2-xy)(y^2+xy)=(y^{2})^{2}+y^{2}*xy-y^{2}*xy-(xy)^{2} \\\\(y^{2})^{2}+y^{2}*xy-y^{2}*xy-(xy)^{2}=(y^{2})^{2}-(xy)^{2}[/tex]

So, the obtained expression is a difference of squares since it matches with the form of the difference of squares.

[tex](25x-7y)(-7y+25x)=-175xy+(25x)^{2}+49y^{2}-175xy\\\\-175xy+(25x)^{2}+49y^{2}-175xy=(25x)^{2}+49y^{2}-350xy[/tex]

So, the obtained expression is not a difference of squares

[tex](64y^2+x^2)(-x^2+64y^2)=(64y^2+x^2)(64y^2-x^2)\\\\(64y^2+x^2)(64y^2-x^2)=(64y^{2})^{2} -(x^{2}*64y^{2})+(x^{2}*64y^{2})-(x^{2})^{2}\\ \\(64y^{2})^{2} -(x^{2}*64y^{2})+(x^{2}*64y^{2})-(x^{2})^{2}=(64y^{2})^{2}-(x^{2})^{2}[/tex]

So, the obtained expression is a difference of squares since it matches with the form of the difference of squares.

Hence, the products that result in a difference of squares are:

C) [tex](3+xz)(-3+xz)[/tex]

D) [tex](y^2-xy)(y^2+xy)[/tex]

F) [tex](64y^2+x^2)(-x^2+64y^2)[/tex]

Have a nice day!

Answer: C.

Step-by-step explanation: popcorn are made out of corn

Answer is D (: !!!!!!!!!!

Find the Greatest Common Factor (GCF)

GCF = 6y^6

Factor out the GCF. (Write the GCF first. Then, in parenthesis divide each term by the GCF.)

6y^6(24y^8/6y^6 + 6y^6/6y^6)

Simplify each term in parenthesis

6y^6(4y^2 + 1)

Answer:

Total number of plants = 3t - 15 = 3(t-5) tomato plants

Explanation:

We are given that:

Erin planted t tomato plants

Leo planted 5 fewer tomato plants than Erin, this means that:

Leo planted = t - 5 tomato plants

Fillip planted 10 fewer tomato plants than Erin, this means that:

Fillip planted = t - 10 tomato plants

Now, we want to find the total number of tomato plants

This means that we will add the number of plants planted by Erin, Leo and Fillip

Therefore:

Total number of plants = t + t - 5 + t - 10

Total number of plants = 3t - 15 = 3(t-5) tomato plants

Hope this helps :)

Final answer:

The expression that represents the total number of tomato plants Erin, Leo, and Filipe planted is 3t - 15, where t is the number of plants Erin planted.

Explanation:

If Erin planted t tomato plants, then we can express the number of tomato plants Leo and Filipe planted using algebraic expressions that are based on this initial quantity. Leo planted 5 fewer tomato plants than Erin, so we can describe the number of plants Leo planted as t - 5. Similarly, Filipe planted 10 fewer tomato plants than Erin, and his number can be represented by t - 10.

To find the total number of tomato plants all three of them planted together, you would add these expressions:

Total number of plants = Erin's plants + Leo's plants + Filipe's plants

Total = t + (t - 5) + (t - 10)

Simplify the expression by combining like terms:

Total = t + t - 5 + t - 10

Total = 3t - 15

So the expression that represents the total number of tomato plants Erin, Leo, and Filipe planted in all is 3t - 15.

Answer:

Step-by-step explanation:

Height is 5 feet

Answer:

31

Step-by-step explanation:

For rectangle ABCD, AC and BD are the lengths of the diagonals. The diagonals of a rectangle are congruent.

AC = BD

3x + 7 = 131 - x

Add x to both sides.

4x + 7 = 131

Subtract 7 from both sides.

4x = 124

Divide both sides by 4.

x = 31

Answer: Equation to describe this situation.

[tex]3s=6300[/tex]

Number of steps in one mile for Gustave =2100

Step-by-step explanation:

Given : Gustave measured his pace and determined that for him, s steps make up one mile.

1 mile = s steps  (1)

One day Gustave walked 6300 steps, which was 3 miles.

i.e. 3 miles = 6300 steps (2)

Using (2), the number f steps in 3 steps will be :_

3 miles = 3s steps                (3)

From (2) and (3), we have

[tex]3s=6300[/tex]

Dividing both sides by 3 , we get

[tex]s=\dfrac{6300}{3}=2100[/tex]

Hence, the number of steps in one mile for Gustave =2100

Gustave takes 189 steps to walk one mile. We derived this by dividing the total steps, 63,000, by the distance in miles, 333. The equation used was 63000 = s * 333.

To determine how many steps are in one mile for Gustave, we start with the information provided:

Step 1: Write the Equation

We can write the equation as:

63000 = s * 333

Step 2: Solve for s

To find out how many steps make up one mile, we solve for s by dividing both sides of the equation by 333:

s = 63000 / 333

Step 3: Calculate the Value

When we divide 63,000 by 333, we get:

s = 189

This means that Gustave takes 189 steps to walk one mile.

Example Calculation

Since 63,000 steps equal 333 miles, and dividing both 63,000 steps by 333 miles gives us the number of steps per mile:

189 steps per mile.

In conclusion, Gustave takes 189 steps to walk one mile. This equation and process help us determine the number of steps per mile based on the given total steps and distance covered.

Answer:

option D

Step-by-step explanation:

Given in the question, a right angle triangle FGH.

Base of triangle = 12

Height of triangle = 5

Hypotenuse of triangle = 13

To solve the question we will use trigonometry identity.

cos(F) = height / hypo

cos(F) = 5 / 13

So the cosine ration for angle F is 5 / 13

5 feet 6 inches is equal to ((5*12)+6) inches, which is equal to 66 inches since 5*12=60 and 60+6=66

2 feet 9 inches is equal to ((2*12)+9) inches, which is equal to 33 inches since 2*12=24 and 24+9=33

Since 66 and 33 are the length and width (there isn't any specific order as to which measurement is the length or width) and the question is asking for square inches,(which is the area) so what needs to be done next is 66*33, which equals 2178, the square inches of plastic needed is 2718 square inches.

I couldn't keep the answer in the format of _ft _in because they are asking for the area in inches, and I don't think it would be smart to convert inches to decimal values of feet for reasons I won't talk about.

So yeah, your answer is 2178 square inches of plastic.

Step-by-step explanation:

for the each year, the interest is increased by 2%,

so after 1 year, earned interest is 2% of $400

=2/100 × 400=$8

so the earned balance is $(400+8)=$408

so after 2 year, earned interest is 2% of $408

=2/100 × 408=$8.16

so the earned balance is $(408+8.16)=$416.16

after 3 year, earned interest is 2% of $416.16

=2/100 × 416.16=$8.32

so the earned balance is $(416.16+8.32)=$424.48

after 4 year, earned interest is 2% of $424.48

=2/100 × 424.48=$8.48

so the earned balance is $(424.48+8.48)=$480.48

after 5 year, earned interest is 2% of $480.48

=2/100 × 480.48=$9.6

so the earned balance is $(480.48+9.6)=$490.08

after 6 year, earned interest is 2% of $490.08

=2/100 × 490.08=$9.8

so the earned balance is $(490.08+9.8)=$499.88

therefore the interest earned after 6 years is

$(8+8.16+8.32+8.48+9.6+9.8)=$52.36

and the balance after 6 years is $499.88

Answer:

The area of the base B is equal to [tex]770\ cm^{2}[/tex]

The volume  is equal to [tex]10,087\ cm^{3}[/tex]

Step-by-step explanation:

I will proceed to resolve the problem indicated in the attached figure.

The figure shown a inverted rectangular pyramid

The base is a rectangle

The area of the base B is equal to

[tex]B=(35)(22)=770\ cm^{2}[/tex]

To find how many cubic centimeters of titanium are needed to manufacture one tip, calculate the volume of the figure

Find the volume of the inverted rectangular pyramid

The volume of the pyramid is equal to

[tex]V=\frac{1}{3}BH[/tex]

we have

[tex]B=770\ cm^{2}[/tex]

[tex]H=39.3\ cm[/tex]

substitute

[tex]V=\frac{1}{3}(770)(39.3)=10,087\ cm^{3}[/tex]

For this case we have the variable [tex]x = -3[/tex]:

[tex]A) 6x = 6 (-3) = - 18\\B) 4x = 4 (-3) = - 12\\C) -3x = -3 (-3) = + 9\\D) -7x = -7 (-3) = + 21[/tex]

Now, matching each expression with its value we have:

A goes with 4

B goes with 3

C goes with 2

D goes with 1

ANswer:

A goes with 4

B goes with 3

C goes with 2

D goes with 1

Hello there!

Answer:

The slope is 9, and the y-intercept is –2

Step-by-step explanation:

The equation is y = 9x - 2

This follows the equation y = mx + b

Where as:

m = slope

b = y-intercept

When you know this, you would figure out that 9 is in the same place as m, and -2 is in the same place as b.

The y-intercept would not be a positive 2 because when there's a minus sign next to the number in the y-intercept spot, then you would have to bring that over to the number. We can also say the minus sign belongs to the 2, making it a -2.

With the information we know now, we can say that the slope of the equation is 9, and the y-intercept would be -2.

Therefore, giving your answer as "The slope is 9, and the y-intercept is –2"

Final answer:

The slope of the linear function represented by y=9x-2 is 9, and the y-intercept is -2. This is determined by comparing the equation to the slope-intercept form y = mx + b.

Explanation:

The slope and y-intercept of the linear function represented by the equation y=9x-2 can be identified by comparing it to the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. In the given equation, 9 is the coefficient of x, which means it is the slope of the line. The constant term, -2, is the y-intercept because it indicates the point at which the line crosses the y-axis.

Answer:

  10.24 square feet

Step-by-step explanation:

The area of one triangular face is ...

  A = (1/2)bh = (1/2)(0.8 ft)(6 ft) = 2.4 ft²

Then the four triangular faces will have a total area of ...

  lateral area = 4·(2.4 ft²) = 9.6 ft² . . . . . sufficient to help you choose the correct answer

__

The area of the square base is the square of the side length:

  base area = (0.8 ft)² = 0.64 ft²

Then the total surface area is ...

  surface area = lateral area + base area

  surface area = 9.6 ft² + 0.64 ft² = 10.24 ft²

You would multiply the Area of a square which is B x H the Area for the square is 0.8 x 0.8 = 0.64

Then you multiply the Area of a triangle and the Area of a triangle is B x H divided by 2  and so you multiply the number of triangles there are which is 0.8 x 6 = 4.8 then divide that by 2 which is 2.4 then multiply that with the number of triangles we have all together. there are 4 triangles.

Multiply 2.4 x 4 = 9.6 then add the Area of the square which is 0.64 + 9.6 and the answer is 10.24  

Hope this helps

ANSWER

[tex](n - 2) \times 180 \degree[/tex]

EXPLANATION

The sum of the interior angles of a triangle is 180°

We can rewrite this as:

[tex]1 \times 180 \degree = (3 - 2) \times 180 \degree = 180 \degree[/tex]

The sum of interior angles of a quadrilateral is 360°

We can also rewrite this as:

[tex]2 \times 180 \degree = (4- 2) \times 180 \degree = 360 \degree[/tex]In general an n-sided polygon has

the sum of the interior angles given by the formula:

[tex](n - 2) \times 180[/tex]

Answer:

Step-by-step explanation:

88

The distance between the lions and the monkeys is 88 feet

To determine the distance between the lions and the monkeys, we make use of the following equivalent ratio

x : 132 = 80 : 120

Express as fraction

[tex]\frac{x}{132} = \frac{80}{120}[/tex]

Solve for x

[tex]x = \frac{80}{120} * 132[/tex]

Multiply

[tex]x = 88[/tex]

Hence, the distance between the lions and the monkeys is 88 feet

Read more about equivalent ratios at:

https://brainly.com/question/2328454

To calculate the conditional probability, we need to find the probability of transferring two red balls and two blue balls from Bowl I to Bowl II and the probability of selecting a blue ball from Bowl II which is 0.0923

To calculate the conditional probability, we need to find the probability of transferring two red balls and two blue balls from Bowl I to Bowl II and the probability of selecting a blue ball from Bowl II.

First, we calculate the probability of transferring two red balls and two blue balls from Bowl I to Bowl II. There are 14 balls in Bowl I, so the probability of transferring a red ball on the first draw is 8/14. After transferring one red ball, there are now 13 balls in Bowl I, so the probability of transferring another red ball is 7/13. Similarly, the probability of transferring a blue ball on the first draw is 6/14, and the probability of transferring another blue ball is 5/13. To find the overall probability, we multiply these probabilities: (8/14) * (7/13) * (6/14) * (5/13).

Next, we calculate the probability of selecting a blue ball from Bowl II. After transferring four balls from Bowl I, there are now 10 balls in Bowl II, with 6 blue balls. The probability of selecting a blue ball is therefore 6/10.

Finally, we calculate the conditional probability by dividing the probability of transferring two red balls and two blue balls from Bowl I to Bowl II by the probability of selecting a blue ball from Bowl II:

= (8/14) * (7/13) * (6/14) * (5/13) / (6/10)

= 0.0923 (rounded to four decimal places).

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Answer:

Your answer would be 288

Step-by-step explanation:

You start off with the equation ( V= Bh )

Where "B" represents the area of the base ( which case you multiply 8 and 12 and thus getting 96 as your answer for finding "B")

and Lastly you multiply your "B" with the "h" ( which represents the height) and therefore you multiply 96 and 3

which equals to 288

( hope this helps )

Answer: 144

Step-by-step explanation:

Area = base * height

Area = 15 * 8 = 120 square centimeters