There are 12 donuts in one dozen donuts. Which equation could be used to find the total (T) number of donuts (d) in 6 dozen?

The circumference of a circle with diameter 8 units is equal to 25.14 units.

Circumference is the perimeter of a circle, circles are featured solely by diameter. The formula for circumference is described below:

s = π · D

Where D is the diameter, in units.

If we know that D = 8 units, then the circumference of the circle is:

s = π · 8

s = 8π

s = 25.14

The circle (diameter: 8 units) has a circumference of 25.14 units.

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An obtuse triangle and right angle triangle can always be used as counter examples to the given statement.

What is acute angle?

An angle which is measuring less than 90 degrees is called an acute angle. This angle is smaller than the right angle

What is obtuse angle?

An obtuse angle is a type of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.

What is right angle?

A right angle is an angle of exactly 90 degrees or \pi /2 radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles..

Hence, an obtuse triangle and right angle triangle can always be used as counterexamples to the given statement " All angles in a triangle are acute".

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The area of a triangle is calculated using the formula A = 1/2bh, where b is the base and h is the height. If Charlie draws a second triangle with dimensions that are halved, then the base and height of the second triangle are half of the base and height of the first triangle.

This means that the area of the second triangle is 1/2(1/2bh) = 1/4bh, which is one-fourth of the area of the first triangle. In other words, the area of the second triangle is 25% of the area of the first triangle. Therefore, the relationship between the areas of the two triangles is that the area of the second triangle is one-fourth of the area of the first triangle.

When Charlie draws a triangle with given dimensions and then creates a second triangle with dimensions halved, the relationship between the areas of the two triangles is a ratio of 1:4. This is because the area of a triangle is calculated using the formula A = 0.5 * base * height. When both the base and height are halved, the new area becomes A = 0.5 * (base/2) * (height/2), which simplifies to A = 0.25 * base * height. Comparing the original area to the new area (1 * base * height versus 0.25 * base * height), we see that the area of the second triangle is one-fourth or 25% the area of the original triangle.

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An equation highlighting the discount: y = (65 - 7)x

A simpler equation: y = 58x

The probability that he would have done at least this well if he had no ESP is 0.99979

To determine the probability, we need to first find the probability of doing well with ESP.

The probability of having 20 correct answers out of 23 coin flips is:

\(\mathbf{=(\dfrac{1}{2})^{20}}\)

Since we have 20 correct answers, we also need to find the probability of getting 3 answers wrong, which is:

\(\mathbf{=(\dfrac{1}{2})^{3}}\)

There are \((^{23}_{20})\) = 1771 ways to get 20 correct answers out of 23.

Therefore, the probability of doing well with ESP is:

\(\mathbf{= 1771 \times (\dfrac{1}{2})^{20}} \times (\dfrac{1}{2})^{3}}\)

= 0.00021

The probability that he would have at least done well if he had no ESP is:

= 1 - 0.00021

= 0.99979

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The base of the triangle is 9 inches and the height is 2 inches.

Let's denote the height of the triangle as h, and the base as b.

We know that the area of a triangle is given by the formula:

Area = (1/2) * base * height

Substituting the values we have:

9 = (1/2) * b * h

Multiplying both sides by 2 gives:

18 = b * h

We also know that the base is 5 inches more than 2 times the height:

b = 2h + 5

Substituting this expression for b in terms of h in the area equation, we get:

18 = (2h + 5) * h

Expanding the right-hand side, we get:

18 = 2h^2 + 5h

Rearranging this equation, we get:

2h² + 5h - 18 = 0

We can solve for h by using the quadratic formula:

h = [-b ± \(\sqrt{b² - 4ac}\)] / 2a

where a = 2, b = 5, and c = -18.

Plugging these values into the formula, we get:

h = [-5 ± \(\sqrt{5^{2} - 4(2)(-18) }\)] / (2 * 2)

Simplifying:

h = [-5 ± \(\sqrt{169}\)] / 4

Taking the positive solution:

h = [-5 + 13] / 4

h = 2

Now that we know the height is 2 inches, we can use the equation b = 2h + 5 to find the base:

b = 2(2) + 5 = 9

Therefore, the base of the triangle is 9 inches and the height is 2 inches.

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Answer:

Step-by-step explanation:

6x-y=1

-y=-6x+1

y=6x-1

4x-3y=-11

True. The equation Ax = 0 gives an explicit description of its solution set.

When A is a matrix and x is a vector, the equation Ax = 0 represents a homogeneous system of linear equations. The solution set of this system consists of all vectors x that satisfy the equation and make the left-hand side equal to zero.

The explicit description of the solution set can be obtained by using techniques such as Gaussian elimination or matrix factorizations. These methods allow you to perform row operations on the augmented matrix [A | 0] to obtain the reduced row echelon form. The reduced row echelon form reveals the structure of the solution set by identifying pivot and free variables.

If there are no free variables (all columns of A are pivot columns), then the solution set consists of only the zero vector, x = 0. In this case, the solution set is a singleton set {0}.

If there are one or more free variables, you can express the solutions in terms of those variables. The free variables introduce parameters that allow for infinitely many solutions. The explicit description of the solution set will involve expressing the dependent variables (those corresponding to pivot columns) in terms of the free variables.

In summary, the equation Ax = 0 gives an explicit description of its solution set, either as the singleton set {0} or as a set of vectors expressed in terms of free variables.

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Answer:

You need to rent

14

videos, and you'll pay the same amount for both. Renting

15

will make the membership a better method of payment.

Explanation:

We can create an equation. Say the number of videos you rent is given by

n

. We can write that, if we rent

n

videos without membership, we'll have to pay

4

n

. If we rent the same amount of videos with membership, we'll have to pay

21

+

2.5

n

.

To find the value of

n

such that the amount you pay without membership is equal to the amount you pay with, we write:

4

n

=

21

+

2.5

n

1.5

n

=

21

n

=

21

1.5

n

=

14

You need to rent

14

videos, and you'll pay the same amount for both. Renting

15

will make the membership a better method of payment.

Answer:

Both graphs intersect the x-axis to the right of 0

The domain  -∞ ≤ x ≤ +∞ and range is -3≤ x ≤ 1.

All input values shown on the x-axis make up a graph's domain. The y-axis on a graph represents the possible output values, or range.

The domain would be determined by the set of all x-coordinates at all curve points, and the range would be determined by the set of all y-coordinates at all curve points. Both a set and an interval can be used to express each domain and range.

According to the domain is

from -∞ on left side and reaches to +∞ on the right side

So, domain is -∞ ≤ x ≤ +∞

Now, the range of the graph is -3 to 1

So, -3≤ x ≤ 1

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Answer:

4cm

Step-by-step explanation:

l³= 64cm³

l = ³√64 = 4cm

Answer: The answer would be

B. 1/2

C. 1/3

Step-by-step explanation:

The solution of the equation 6x² - x - 1 = 0 are x = 1/2 and x = -1/3 after using the quadratic formula.

The simplest form of complex expression is (a+bi) = 50+(-68)i.

What is complex expression?

A complex number is a number that is written as a + ib, in which “a” is a real number, and “b” is an imaginary number. The complex number contains a symbol “i” which satisfies the condition i^2 = −1.

Given,

8(5-9i)+2(5+2i)

= 40 - 72i +10 +4i

=50 - 68i

or we can write it as

= 50 + (-68i)

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Answer:

C. 0

Step-by-step explanation:

0 / 7 = 0 ÷ 7

recall that zero divided by any number is zero

hence 0 ÷ 7 = 0

Answer:

Let

x

be the number of quarters, and

y

be the number of dimes.

x

+

y

=

100

0.25

x

+

0.10

y

=

14.05

Solve by substitution:

y

=

100

−

x

∴

0.25x + 0.10(100 - x) = 14.05#

0.25

x

+

10

−

0.10

x

=

14.05

0.15

x

+

10

=

14.05

0.15

x

=

4.05

x

=

27

Solve for

y

now:

y

+

27

=

100

y

=

100

−

27

y

=

73

Hence, Marcy has

27

quarters and

73

dimes.

Hopefully this helps!

Step-by-step explanation:

The two values of y such that the barn is 50 yards from the well are given as follows:

y = -47 and y = 53.

Suppose that we have two points with coordinates \((x_1,y_1)\) and \((x_2,y_2)\). The shortest distance between them is given by the following equation:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

For this problem, we have that D = 50, hence the equation is given as follows:

sqrt[(-2 - (-2))² + (y - 3)²] = 50

y - 3 = ±50.

Hence the values of y are given as follows:

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Opposite angles of a cyclic quadrilateral are supplementary, so

\(x+17+6x-5=180 \\ \\ 7x+12=180 \\ \\ 7x=168 \\ \\ x=24 \\ \\ \\ \implies \angle QRO=2(24)+19=\boxed{67^{\circ}}\)

Answer:

x = 8

Step-by-step explanation:

-4x + 10 = -2x - 6

-4x + 2x = -6 - 10 (Calculate)

-2x = -16 (Divide both sides by -2)

x = 8

Have a nice day! :D

Answer:

x=8

Step-by-step explanation:

-4x+10=-2x-6   original equation

-4x+16=-2x      add 6 both sides

16=2x              add 4 both sides

x=8                 divide 2 both sides

Answer: $1,312.5 difference

Step-by-step explanation:

1050 x 1.5 = 1575

1575 x 1.5 = 2,362.5

2,362.5 - 1050 = 1,312.5

Answer:56.25

Step-by-step explanation: 450 divided by 8

Answer:

It will take 50 weeks for Shannon to have $450 on her account.

Step-by-step explanation:

Since we know that she already has $50 in her bank account we know that in order for her to have $450 she needs to put extra $400 (450 - 50 = 400). Now in order to find out how much weeks will it take we just need to divide the number of dollars that she still has to save by 8 (since she puts $8 each week), and so we get.....

400 / 8 = 50 weeks

The whole Dipper is visible at this time on this date.b. To see it, you should face N (North).

c. To see it, you would look directly at the circled Polaris. You would need to look up, about 41.3 degrees above the horizon.

7. How the Big Dipper’s position changes as you change the time from 9 PM to 12 midnight:

a. Yes, it was still visible during all of this time.

b. It appears to move around Polaris in a counterclockwise direction.

8. Other constellations that are visible on the current date at 10 PM are Ursa Minor, Cassiopeia, Draco, Hercules, and Boötes.9. a. Orion and Taurus constellations are missing now.

b. The Sagittarius and Scorpius constellations have appeared that were not visible on the current date. c. The visible constellations have changed because the Earth's orbit has moved around the Sun by 6 months.

10. Ursa Major, Cassiopeia, Cepheus, Draco, and Cynus appear to be visible all year. They are always up at night because they are located near the North Pole and are circumpolar constellations.11. Report about Orion constellation:a. A graphic with the constellation outlined.  

b. The names of one or two of the most prominent stars in the constellation: Betelgeuse, Rigel.

c. A brief overview of the story or mythology of the constellation’s name: In Greek mythology, Orion was a hunter who was killed by a scorpion. Zeus placed him in the sky as a constellation to honor his bravery.

d. To locate the Orion constellation in your night sky, you would need to face SSW (South-Southwest).e. My experience trying to locate the Orion constellation in the sky using the star wheel is quite challenging at first, but once I figured out which direction to face and how high above the horizon to look, it became easier.

The problems I experienced are light pollution and cloudiness, but I was surprised by how bright and distinct the stars in Orion are.

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(7) If x = (3 - √13) / 2, the value of the expression x² + 1/x² is 10.98.

(8)  If x = 1 / (8 - √60), the value of the expression x³ - 5x² + 8x - 4, is 11.02.

(7) If x = (3 - √13) / 2, the value of the expression x² + 1/x² is calculated as follows;

we can simplify the value of x as follows;

x = (3 - √13) / 2 = -0.303

The value of the expression x² + 1/x² is calculated as;

x² + 1/x² = (-0.303²) + 1/(-0.303)²

⇒ (-0.303²) + 1/(-0.303)²  = 10.98

(8)  If x = 1 / (8 - √60), the value of the expression x³ - 5x² + 8x - 4, is calculated as follows;

x = 1 / (8 - √60)

x = 3.937

x³ - 5x² + 8x - 4 = (3.937)³ - 5(3.937)² + 8(3.937) - 4

= 11.02

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The number of favorable outcomes for events A and B would be: (1,2,3,4)

The sample space that is used to determine the probability of A given B is  (2, 4.6)

The probability for event A and B occurring would be: 1/6

The probability of event A given event B will be 2/3

The sample space refers to the collection of all the outcomes that can be expected from a set of randome experiments. Probability refers to the number of favorable outcomes divided by the number of tottal outcocmes.

From the data given, the probability of getting an even number and a number less than 5 will be 5/6 amd this is in the same ratio as 2/3. The probability of event A and B occurring will be 1/6.

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Answer:

3.96 months or close to 4 months

Step-by-step explanation:

\(\frac{33}{100} *\frac{x}{12}\)

Cross multiply

396 = 100x

Divide both sides by 100 to get x alone

396/100 = 100x/100

3.96 = x

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Answer:

3.96 or 4 rounded

Step-by-step explanation:

4 because is you multiply 12*.33 = 3.96

If you round it is 4 months.

Hope this helps!!

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

Answer:

cosx

Step-by-step explanation:

using the identity

• sin² = 1 - cos²x

cos²x + cosx - 1 + sin²x

= cos²x + cosx - 1 + 1 - cos²x ← collect like terms

= cos x