A tetrahedron has 4 sides. If the numbers 1, 2, 3, and 4 are on the faces of the tetrahedron, what
is the probability of randomly rolling a 3?

The solution is 10x² + 7x - 1

Step-by-step explanation:

(8x² + 10x - 10) - (-2x² + 3x - 9) = 8x² + 10x - 10 + 2x² - 3x + 9

                                                 = 10x² + 7x - 1

Step-by-step explanation:

[tex]\huge\bold\purple{ 10x^2+7x-1 }[/tex]

Volume of the cone is 100 in³

Step-by-step explanation:

Volume = 1/3 × 3.14 × 3² × 9

             = 84.78 in³ ≈ 100 in³ (rounding off to nearest hundredth)

Final answer:

The volume of a cone with a radius of 3 inches and a height of 9 inches is approximately 84.78 cubic inches.

Explanation:

To find the volume of a cone with a radius of 3 inches and a height of 9 inches, you can use the formula for the volume of a cone, which is:

[tex]V = (1/3)\pi r^2h[/tex]

Plugging the given values into the formula gives us:

[tex]V = (1/3) * 3.14 * (3 inches)^2 * 9 inches[/tex]

Now, calculate the square of the radius:

[tex]V = (1/3) * 3.14 * 9 * 9[/tex]

Next, multiply all the numbers together:

[tex]V = 3.14 * 27[/tex]

V = 84.78 cubic inches

Therefore, the volume of the cone is approximately 84.78 cubic inches, rounded to the nearest hundredth.

Answer: Warming up and drinking enough water

Step-by-step explanation:

You should really ask yourself this, but you can talk about your perserverance, and not being afraid to try something new.

Answer:

160 beads

Step-by-step explanation:

let x be the number of beads to make a bracelet, then

It requires 5x beads to make a necklace and the sum is

x + 5x = 192, that is

6x = 192 ( divide both sides by 6 )

x = 32

Number of beads to make a necklace = 5x = 5 × 32 = 160

Answer:

160 beads

Step-by-step explanation:

Beads for bracelet: b

Beads for necklace: 5b

b + 5b = 192

6b = 192

b = 32

Beads for necklace: 5b = 5(32)

= 160

Answer:

X=0.8 or x=4/5

Step-by-step explanation:

Answer:

x = 0.8

Step-by-step explanation:

Step 1:  Divide both sides by 5

4 / 5 = 5x / 5

0.8 = x

Answer:  x = 0.8

Answer:

Length:15 cm

Width: 12 cm

Step-by-step explanation:

The complete question is

Amanda uses a rectangular canvas for a painting. The length is 6x - 3 centimeters. The width is 2x + 6 centimeters, and is 4/5 of the length. What are the dimensions of the canvas?

Let

L ----> the length of the rectangular canvas

W ---> the width of the rectangular canvas

we know that

The width is 4/5 of the length

so

[tex]W=\frac{4}{5}L[/tex] ----> equation A

substitute the given values in equation A

[tex](2x+6)=\frac{4}{5}(6x-3)[/tex]

solve for x

[tex]10x+30=24x-12\\24x-10x=30+12\\14x=42\\x=3[/tex]

Find the dimensions of the canvas

substitute the value of x

[tex]L=6(3)-3=15\ cm[/tex]

[tex]W=2(3)+6=12\ cm[/tex]

Step-by-step explanation:

even number cards is 7 cards (2,4,6,8,10,12,14)

so probability is 7/15

The probability of pulling out an even number from a set of 15 numbers (1-15) is 8/15, but none of the provided multiple choice options match this answer.

The correct answer to this question could be found using the basic concepts of probability. Here, you have 15 cards in total. Among these 15, there are 8 even numbers: 2, 4, 6, 8, 10, 12, 14. The probability of choosing an even number (Event E) is thus Number of favourable outcomes (Event E) divided by Total number of outcomes.

This boils down to Probability (Event E) = Number of even numbers / Total numbers = 8 / 15. As such, none of the provided multiple choice answers are correct.

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Answer:

The scale factor is 1.25 and this represents an enlargement.

Step-by-step explanation:

As shown at the figure

The side length of the first hexagon = 5

The side length of the second hexagon  = 6.25

So, the scale factor = 6.25/5 = 1.25

and the second hexagon is larger than the first hexagon.

So,

The scale factor is 1.25 and this represents an enlargement.

Answer:

Step-by-step explanation:

Step-by-step explanation:

Sequence 1:

term1=26

term2=26-3=23

term3=23-3=20

term4=20-3=17

term5=17-3=14

sequence2:

term1=-3

term2=-3+10=7

term3=7+10=17

term4=17+10=27

term5=27+10=37

The first sequence starts at 26 and subtracts 3 to find the next terms: 26, 23, 20, 17. The second sequence starts at -3 and adds 10 to find the next terms: -3, 7, 17, 27.

The first term of the sequence is 26. To find the next term, subtract 3 from 26, which gives you 23. Continuing this pattern, the second term is 23. To find the third term, subtract 3 from 23, which gives you 20. The fourth term is 20. To find the fifth term, subtract 3 from 20, which gives you 17. The fifth term is 17.

The first term of the second sequence is -3. To find the next term, add 10 to -3, which gives you 7. Continuing this pattern, the second term is 7. To find the third term, add 10 to 7, which gives you 17. The fourth term is 17. To find the fifth term, add 10 to 17, which gives you 27. The fifth term is 27.

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Answer:

No, 40(2x - 16y) is not equivalent to 42 - 56y

Step-by-step explanation:

40(2x -16y)

If we expand the above expression, we will have

80x - 16y which is not equivalent to 42 - 56y

Step-by-step explanation:

The Mathematical transformation of the given statement would be:

[tex]2x - 3 = y[/tex]

Question

What fraction choose dogs?

Answer:

[tex]\frac {3}{8}[/tex]

Step-by-step explanation:

When 2 choose rabbits then to get the number that choose other anomals apart from dogs is given by getting the difference between total people and those who choose dogs. This then is expressed as 8-2=6 choose either cat or dogs. These six, half of them choose choose cats and the remaining choose dogs. Therefore 6/2=3

For 3 out of 8, this fraction is equal to

[tex]\frac {3}{8}[/tex]

Therefore, the fraction that choose dogs or cats is equal to

[tex]\frac {3}{8}[/tex]

Answer: 94.3%

Step-by-step explanation:

Average daily attendance = total sum of attendance ÷ frequency

=754.4/8

= 94.3%

Answer:

36 total muffins

Step-by-step explanation:

5*4=20

8*2=16

20+16=36

Hey there!

To write an expression to represent this:

We know that the four red plates each have 5 muffins, and 4 x 5 = 20.

So we can say 20 + 2y is the expression, because we add 20 to the muffins on the two yellow plates.

The number of muffins on each yellow plate is represented by the variable y.

If each yellow plate has 8 muffins, so y = 8, the expression will look like this:

20 + 2(8)

Multiply 2 x 8.

20 + 16

Add 20 + 16.

36

Belle baked 36 muffins total.

Hope this helps!

Answer:

For this question, x = 16

Step-by-step explanation:

x/20 = 4/5

if we cross multiply, we will have

x × 5 = 4 × 20

5x = 80

x = 80/5

x = 16

Answer: 16

Step-by-step explanation:

X/20 = 4/5

Cross multiply

(5×X) = (20×4)

5x = 80

x = 80/5

x = 16

Equation:

37.29 = 34.85 + 34.85(x)

Solving:

37.29 = 34.85 + 34.85x

2.44 = 34.85x

x = 0.07

The approximate sales tax rate is 7%.

Hope this helps!! :)

Answer:

im pretty sure its 0.07

Step-by-step explanation:

[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$70000\\ P=\textit{original amount deposited}\\ r=rate\to 5.46\%\to \frac{5.46}{100}\dotfill &0.0546\\ t=years\dotfill &20 \end{cases} \\\\\\ 70000=Pe^{0.0546\cdot 20}\implies 70000=Pe^{1.092}\implies \cfrac{7000}{e^{1.092}}=P \\\\\\ 23488.13 \approx P~\hfill \stackrel{~\hfill \textit{the earned interest will be}}{70000-23488.13\implies 46511.87}[/tex]

Answer:

Step-by-step explanation:

Answer:

Use compatible numbers that are close to the actual numbers

Choose 36 for 35 3/4 and 6 for 5 7/8 because the divide evenly.

Step-by-step explanation:

Compatible numbers are numbers that are close to the actual values of a particular number. They make estimating easier when yo udo the different operations.

We choose 36 for 35 3/4 because 36 is closer to its value that 34. Conveniently, 5 7/8 is closer to 6 than 5, and they divide evenly. So a best estimate for the number of rows Holly can make would be:

36/6 = 6 rows.

Answer:

The height is 67 cm

Step-by-step explanation:

Remember that

[tex]1\ in=2.54\ cm[/tex]

we know that

The size of a TV is measured by its diagonal

Convert 60 inches to centimeters

[tex]60\ in=60(2.54)=152.4\ cm[/tex]

Applying the Pythagorean Theorem

[tex]D^2=H^2+W^2[/tex]

where

D is the diagonal

H is the height

W is the width

we have

[tex]D=152.4\ cm\\W=137\ cm[/tex]

substitute

[tex]152.4^2=H^2+137^2[/tex]

solve for H

[tex]H^2=152.4^2-137^2\\H^2=4,456.76\\H=67\ cm[/tex]

Answer:

(x+11)(x-11)

Step-by-step explanation:

A ^2 - B ^2 =(A+B) (A-B).. (*)

x^2 - 121=

x^2 - 11^2=(*)

(x+11)(x-11)

Answer:

75 miles

Step-by-step explanation:

We can use cross products to solve

3 in                   5 in

--------------- = -------------------

45 mi               x miles

3 * x = 5 * 45

3x = 225

Divide each side by 3

3x/3 = 225/3

x =75 miles

To find the actual distance between two towns on a map, use the scale provided. Set up a proportion using the scale and the map distance to find the actual distance. In this case, the actual distance is 75 miles.

To find the actual distance between two towns on a map, you can use the scale provided. In this case, the scale is 3 in: 45 mi. This means that 3 inches on the map represents 45 miles in the real world. If the map distance between the two towns is 5 inches, you can set up a proportion to find the actual distance.

Using the scale, you can set up the equation:

3 inches / 45 miles = 5 inches / x miles

Cross-multiplying, you get:

3 * x = 5 * 45

Simplifying, you get:

x = (5 * 45) / 3

x = 75 miles

Therefore, the actual distance between the two towns is 75 miles.

Answer:

[tex]m\angle A=98^o[/tex]

Step-by-step explanation:

we know that

In a parallelogram opposite angles are congruent and consecutive angls are supplementary

In this problem

we have the parallelogram  ABCD

so

[tex]m\angle A=m\angle C[/tex] ----> by opposite angles

[tex]m\angle B=m\angle D[/tex] --> by opposite angles

and

[tex]m\angle A+m\angle B=180^o[/tex] ----> by consecutive angles

[tex]m\angle B+m\angle C=180^o[/tex] ----> by consecutive angles

we have

[tex]m\angle C=98^o[/tex]

therefore

[tex]m\angle A=98^o[/tex]

Answer:

Step-by-step explanation:

help me

Answer:

85/99

Step-by-step explanation:

[tex]\frac{171717}{200000}[/tex]

Answer:

x= 33.8

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

In this equation, when x = -8 , Y = 2

Answer check using either equation =

(1) 2x + y = -7y   ===> 2(-8) + 2 = -7(2)  ===>  -14 = -14

(2) Y= x + 10  ===>  2 = -8 + 10  ===> 2 = 2

Step-by-step explanation:

Assuming that you are looking for "x" and "y", Let

2x + y = -7y  ................. (1)

Y= x + 10     ................. (2)

From equation (2), Y = x + 10, therefore substitute for "Y" in equation (1) to get the value of "x"

2x + x + 10 = -7(x + 10)

3x + 10 = -7x - 70

gather like terms on each side.

3x + 7x = -70 - 10

10x = -80

divide through by 10

x = -8

Now substitute for "x" in equation (2)

Y = x + 10

Y = -8 + 10

Y = 2

Step-by-step explanation:

Set up a systems of equations (x = kids, y = adults)

3x+9y=75 --> 15x+45y=375

8x+5y=67 --> 72x+45y=603

Subtract the two equations

57x = 228

x = 4

A KID'S TICKET IS $4

Plug that in for x

4(3)+9y=75

12+9y=75

9y=63

y=7

AN ADULT'S TICKET IS $7

Step-by-step explanation:

[tex]10 \times 9 \sqrt{72} \\ = 90 \sqrt{36 \times 2} \\ = 90 \times 6 \sqrt{2} \\ = 540\sqrt{2} [/tex]

Final answer:

To find the product of 10 and 9√72, simplify √72 to 6√2, then multiply the outside coefficients (10 and 9) to get 90, and attach the simplified radical. The final answer is 90√2.

Explanation:

The question asks to find the product of 10 and 9√72 in simplest radical form. First, recognize that the square root of 72 can be simplified by factoring out perfect squares. The square root of 72 is equal to the square root of 36 times 2, which simplifies to 6√2. Now, multiply the outside coefficients (10 and 9) and then multiply the result by the simplified radical. The final simplification is 90√2, which is the product of 10 and 9√72 in simplest radical form.

Answer:

B) 9/2

Step-by-step explanation:

4½ = 4 + ½

= 8/2 + 1/2 = 9/2

Answer: 9/2

Step-by-step explanation: To write a mixed number as an improper fraction, first multiply the denominator times the whole number, then add the numerator.

So here, we multiply the denominator, 2, times the whole number, 4, then we add the numerator, 1. So we have (2 × 4) + 1 of 8 + 1 which is 9.

Finally, we put our new number over our old denominator and we have our answer, 9/2. There is also an image provided showing my work.

So 4 and 1/2 can be rewritten as the improper fraction 9/2.