How many equilateral triangles make a regular hexagon 6?

The critical value of t for a two-tailed test with 6 degrees of freedom using α = .05 is b. 2.447.

The critical value of t for a two-tailed test with 6 degrees of freedom using a significance level (α) of .05 can be found using a t-distribution table. In this case, the critical value of t would be approximately 2.447.

This means that if the calculated t-value from your experiment is greater than 2.447 in either direction (positive or negative), it would indicate that the null hypothesis can be rejected and that there is a statistically significant difference between the means of the groups being compared.

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The number of months should be 25.

The calculation is as follows:

Plan A: 70x  

Plan B: 50x+500

Now we have to make the equivalent equation

70x=50x+500

70x - 50x = 500

20x = 500

x = 25

Therefore we can conclude that The number of months should be 25.

The answer is 25 months.

step by step explanation:

Plan A: 70x  

Plan B: 50x+500

the equivalent equation is :

70x=50x+500

70x - 50x = 500

20x = 500

x = 25

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The area of the sector with theta as π/12 radian and radius as 4 is 2 / 3π.

A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them.

The sector has the central angle as π/2 radian and a radius of 4 units. Therefore, let's find the area of the sector using the formula as follows:

area of a sector = ∅ / 2 r²

where

Therefore,

∅ = π / 12

r = 4 units

Hence,

area of a sector = π / 12 × 1 / 2 × 4²

area of a sector = π / 4 × 16

area of a sector = 16 / 24 π

area of a sector = 2 / 3π

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To choose 8 flats at random using the cluster sampling approach, there are thus 36 possible options.

(a) Given that there are nine stories in the building, N = nine clusters are assumed. 4 units are found on each floor. 8 flats will be chosen using the cluster sampling technique. By using the cluster sampling approach, a sample of any size n = 2 floors (clusters) will be chosen from the population of N = 9 clusters. To choose 8 flats at random using the cluster sampling approach, there are thus 36 possible options.

(b) In contrast, there is no guarantee that a sample using the cluster sampling method will include both of the characteristics—flats with children and apartments without children—in a representative manner. In the course of this operation, we occasionally obtain floors 3, 4, 6, or 3, 4, which do not contain any of the sample's apartments with children. As a result, the sample will not accurately reflect the population.

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It is not possible to make paper quilts with 24 paper squares in 5 rows because the quilt shape would be incomplete.

To make a quilt with paper squares we must establish the averages we want for our quilt. In this case we want a quilt with 5 rows of paper squares. Additionally, we have 24 square pieces of paper.

In that case we would have to divide the number of pieces of paper available in the number of rows to find out how many pieces we should put in each row.

According to the above, it is not possible to make a quilt with 24 square pieces of paper because the shape would be incomplete. Therefore, we must use more square pieces of paper. In this case, it could be 25 pieces of square paper.

To make a 5 row quilt, where each row has 5 square pieces of paper, we would have 25 square pieces of paper and the quilt shape would be complete.

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Answer:

See below

Step-by-step explanation:

Are you asking for the equation?

y = 2.5x + 20  

y = the total cost

x = number of movies.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question \#1.}[/tex]

[tex]\mathsf{\dfrac{5}{8}\times 2}[/tex]

[tex]\mathsf{= \dfrac{5}{8}\times\dfrac{2}{1}}[/tex]

[tex]\mathsf{= \dfrac{5\times2}{8\times1}}[/tex]

[tex]\mathsf{= \dfrac{10}{8}}[/tex]

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

[tex]\huge\textbf{Question \#2.}[/tex]

[tex]\mathsf{6\times\dfrac{4}{5}}[/tex]

[tex]\mathsf{= \dfrac{6}{1}\times\dfrac{4}{5}}[/tex]

[tex]\mathsf{= \dfrac{6\times4}{1\times5}}[/tex]

[tex]\mathsf{= \dfrac{24}{5}}[/tex]

[tex]\mathsf{= 4\dfrac{4}{5}}[/tex]

[tex]\huge\text{Question \#1. answer is:}\\\\\huge\boxed{\mathsf{\dfrac{10}{8}\ or\ 1\dfrac{1}{4}}}\huge\checkmark\\\\\\\\\huge\text{Question \#2. answer is:}\\\\\huge\boxed{\mathsf{\dfrac{24}{5}\ or \ 4\dfrac{4}{5}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Moment of inertia is [tex]I_{1} = \frac{5Ir^{2} }{4}[/tex] for rotation about a diameter.

What is momentum ?

Whenever you toss a ball at someone as well as it smacks him square in the face. It indicates how difficult it would have been to stop the thing. A baseball is swooping through the air. A large truck is moving. A bullet discharged from such a firearm. Momentum is important in Physics because it describes the relationship between speed, mass and direction. It also describes the force needed to stop objects and to keep them in motion. A seemingly small object can exert a large amount of force if it has enough momentum.

Have given ,

radius of a sphere = r and moment of inertia = [tex]I_{1}[/tex]

[tex]I = \frac{1}{2} Mr^{2}[/tex]

∵ [tex]M = \frac{5}{2} Mr^{2}[/tex]

∴ [tex]I_{1} = \frac{5Ir^{2} }{4}[/tex]

Hence , Moment of inertia is [tex]I_{1} = \frac{5Ir^{2} }{4}[/tex] for rotation about a diameter.

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Answer:

  364 miles

Step-by-step explanation:

You want to know the distance from (9, 17) to (7, 10) if each unit on the map represents 50 miles.

The map distance can be found using the distance formula:

  d = √((x1 -x1)² +(y2 -y1)²)

  d = √((7 -9)² +(10 -17)²) = √((-2)² +(-7)²) = √53 ≈ 7.28011

The distance on the ground is 50 miles for each map unit, so is ...

  (50 mi)(7.28011) = 364.0055 ≈ 364.0

You travel about 364.0 miles.

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The angle B has a measure of 55 degrees

From the question, we have the following parameters that can be used in our computation:

Angle A = 53 degrees

Side AC = 13 units

Side AB = 15 units

The measure of the length BC is needed in order to calculate the angle B,

This is represented using the following cosine law

BC = √(AC² + AB² - 2 * AC * AB * cos(A))

When the known values are substituted in the above equation, we have the following representation

BC = √(13² + 15² - 2 * 13 * 15 * cos(53 degrees))

Evaluate the equation

This gives

BC = 12.6

Solving further, we need to make use of the following sine law

AC/sin(B) = BC/sin(A)

This gives

sin(B) = AC * sin(A)/BC

Substitute the known values in the above equation, so, we have the following representation

sin(B) = 13 * sin(53)/12.6

Evaluate

sin(B) = 0.8239890183

Take the arc sin

B = 55 degrees

Hence, the angle is 55 degrees

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Answer:

Mixed Number: 4 9/20
Decimal Form: 4.45

If this help please set brainliest.

Explanation:
To add these fractions, we first need to find a common denominator. 4 and 5 have a common multiple of 20, so we can express each fraction using a denominator of 20:

-4/5 = (-8)/20

5 1/4 = 21/4 = (215)/(45) = 105/20

Now we can add the fractions:

(-8)/20 + 105/20 = (105 - 8)/20 = 97/20

To express the result as a mixed number, we can divide 97 by 20 to get the integer part, which is 4 with a remainder of 17. The fraction part is 17/20, which can be simplified to 9/20 by dividing both the numerator and denominator by 8. The final result is:

4 9/20

This fraction can be simplified to 4.45 by dividing both the numerator and denominator by 5:

4 9/20 = (4*4 + 9)/(20/5) = (16 + 9)/4 = 25/4 = 6.25/1 = 6.25

So the final result is 4.45.

When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression

Answer:

domain = {6,16,41,49}

range = {4,-10,7}

The trigonometric identity 1 - sin²θ/(1 + cosθ) = cosθ is true since L.H.S = R.H.S

Trigonometric identities are equations that shows the relationship between trigonometric ratios.

Given the trigonometric identity

1 - sin²θ/(1 + cosθ) = cosθ

We need to show that the left hand side (L.H.S) equals the right hand side (R.H.S) of the equation

So, we proceed as follows

Given that

1 - sin²θ/(1 + cosθ) = cosθ

Starting with the left hand side

L.H. S = 1 - sin²θ/(1 + cosθ)

Taking the L.C.M, we have that

[(1 + cosθ)  - sin²θ]/(1 + cosθ) = [1 + cosθ  - sin²θ]/(1 + cosθ)

Using the trigonometric identity sin²θ + cos²θ = 1

Substituting this into the equation, we have that

[1 + cosθ  - sin²θ]/(1 + cosθ) =  [sin²θ + cos²θ + cosθ  - sin²θ]/(1 + cosθ)

= [cos²θ + cosθ + sin²θ - sin²θ]/(1 + cosθ)

= [cos²θ + cosθ + 0]/(1 + cosθ)

= [cos²θ + cosθ]/(1 + cosθ)

Factorizing out cosθ from the numerator, we have that

= [cos²θ + cosθ]/(1 + cosθ) = cosθ(cosθ + 1)/(1 + cosθ)

= cosθ(1 + cosθ)/(1 + cosθ)

= cosθ

= R.H.S

So, 1 - sin²θ/(1 + cosθ) = cosθ

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Answer:

= cos θ

Step-by-step explanation:

A trigonometric identity that we already know is

[tex]\sin {}^{2} \theta + \cos {}^{2} \theta = 1[/tex]

From the question given we want to prove that the left side equals the right side:

[tex]1 + \frac{\sin {}^{2} \theta }{1 + \cos \theta }[/tex]

Let's rewrite sin²θ using the identity sin²θ+cos²θ=1 by subtracting cos²θ:

sin²θ=1-cos²θ, so we can write 1-cos²θ in place of sin²θ to give:

[tex]1 - \frac{1 - \cos {}^{2}\theta }{1 + \cos \theta }[/tex]

Now that everything is in terms of cos, we can solve this fraction.

1-cos²θ can be written as a difference of two squares which is (1+cosθ)(1-cosθ):

[tex]1- \frac{(1+cos \theta)(1-cos \theta)}{1+cos \theta}[/tex]

We can cancel out 1+cosθ from the fraction to give:

[tex]1 - (1 - cos \theta)[/tex]

Expand the brackets out:

[tex]= 1 - 1 + cos \theta[/tex]

= cos θ

A p-chart is used to monitor the fraction defective.

A p-chart is a type of control chart used to monitor the proportion of nonconforming units in a sample. It is used when the sample size is constant and the process is in statistical control.

It plots the proportion of nonconforming units in each sample on the y-axis and the sample number on the x-axis.

The chart can be used to detect changes in the process and to determine if the process is in control. It can also be used to estimate the process capability and to identify the causes of nonconformities.

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Answer:

Step-by-step explanation:

You need to look carefully at the inequality signs in the first question. Thew amount of pillowcases she buys needs to be AT LEAST 10, but the maximum amount of money she can spend is 100. So I think C would be the best answer.

Answer:

C and then D

Step-by-step explanation:

s = number of small pillow cases

l = number of large pillow cases

s + l >= 10 (but at least 10 cases)

8s + 12l <= 100 (cannot spend more than $100)

remember, every small pillow case costs $8, every large $12.

so, answer C.

8×12 + 3×8 = $120

so, that's not possible.

4×12 + 7×8 = 48 + 56 = $104

so, that's not possible.

6×12 + 3×8 = 72 + 24 = $96

that would work but

6 + 3 = 9 which is not >= 10

so, that's not possible.

2×12 + 9×8 = 24 + 72 = $96

2 + 9 = 11

so, that (D) is a valid solution.

The linear function that describes the amount of money left is f(a) = $84 - $48 . You would not have enough money to buy the sweatshirt.

A linear function is a function that has a single variable raised to the power of 1. An example of a linear function is x + 2. The variable x is raised to the power of 1. 2 is the constant terms

The form of the linear function is : a = amount taken on vacation - (amount spent each day x number of days)

f(a) = $84 - (3 x 16)

f(a) = $84 - $48

f(a) = $36

You would not have enough money to buy the sweatshirt because the sweatshirt costs more than the amount have left.

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Option 4 is correct graph for linear equation.

According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this statement can be replaced with any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠). The different types of mathematical inequality include absolute value inequality, rational inequality, and polynomial inequality.

Given inequality,

-6x > 42

divide both side by 6

-6x/6 > 42/6

-x > 7

so x < -7

the  equation says that the value of x should be less the then -7 in which -7 is not included,

so the graph of option 4 is best fit for inequality.

Hence the  correct graph for  inequality is option 4.

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Answer:

This equation shows that the pet groomer uses 3.75 ounces of shampoo per dog.

The relationship between the amount of shampoo used and the number of dogs groomed is proportional. We can represent this relationship with an equation using the form y = kx, where y is the amount of shampoo used, x is the number of dogs groomed, and k is the constant of proportionality.

Given that the pet groomer uses 26.25 ounces of shampoo per day when 7 dogs need to be groomed, we can use this information to find the value of k.

26.25 = k * 7

Solving for k, we get:

k = 26.25/7

k = 3.75

So the equation representing the relationship between the amount of shampoo used and the number of dogs groomed is y = 3.75x

This equation shows that the pet groomer uses 3.75 ounces of shampoo per dog.

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"s"ampoo varies directly with "d"ogs}}{s = k(d)}\hspace{5em}\textit{we also know that} \begin{cases} d=7\\ s=26.25 \end{cases} \\\\\\ 26.25=k(7)\implies \cfrac{26.25}{7}=k\implies 3.75=k~\hfill \boxed{s=3.75d}[/tex]

A Perpendicular bisector is a line that divides a given line segment exactly into two halves forming 90 degrees angle at the intersection point.

A line known as a perpendicular bisector divides a specified line segment precisely in half, creating a 90° angle at the intersection. The intersection of a line segment's midpoint with a perpendicular bisector. It can be built with a compass and a ruler. On both sides of the line segment being divided, it forms a 90° angle.

Step 1: Sketch a line segment of any appropriate length, XY.

Step 2: Using a compass, draw arcs above and below the line segment, with X serving as the center and XY's width is greater than 50%.

Step 3: Carry out Step 2 but use Y as the center.

Step 4: Write "P" and "Q" next to the junction points.

Step 5: Join the points 'P' and 'Q'. The point at which the perpendicular bisector PQ intersects the line segment XY is its midpoint. Label it as 'O'.

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Using the algebraic approach, the solution to the inequality, 5x - 1 < 2x + 11 is: D. x < 4.

An inequality is a mathematical statement that says that two values are not equal. It is written using one of the following symbols:

For example, the inequality "x > 5" means that the value of x is greater than 5. "y ≤ 3" means that the value of y is less than or equal to 3.

Given the inequality, 5x - 1 < 2x + 11, solve for the value of x algebraically as shown below:

5x - 1 < 2x + 11 [given]

Combine like terms:

5x - 2x < 1 + 11

3x < 12

3x/3 < 12/3 [division property of equality]

x < 4

The solution is: D. x < 4.

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The probability range that the data fit the expected 1:1:1:1 ratio of phenotypes is between 0.50 and 0.70.

1. Calculate the observed ratio of phenotypes in the data.

2. Calculate the expected ratio of phenotypes for the data.

3. Calculate the probability of the observed ratio being equal to the expected ratio using the Chi-square test.

4. Calculate the probability range that the data fit the expected 1:1:1:1 ratio of phenotypes.

To calculate the probability range that the data fit the expected 1:1:1:1 ratio of phenotypes, first calculate the observed ratio of phenotypes in the data. Then calculate the expected ratio of phenotypes for the data. Next, calculate the probability of the observed ratio being equal to the expected ratio using the Chi-square test. Finally, calculate the probability range that the data fit the expected 1:1:1:1 ratio of phenotypes, which is between 0.50 and 0.70. This is a measure of how likely it is that the data fit the expected ratio.

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Tina's average rate per hour was $12.

Answer:

Step-by-step explanation:

B people

a) The function is increasing on these following intervals: (0,1), (3,5).

b) The function is decreasing on these following intervals: (1,3) and (5,6).

c) The extremas are given as follows:

The function is increasing when the derivative is positive, hence the intervals are given as follows:

(0,1) and (3,5).

The function is decreasing when the derivative is negative, hence the intervals are given as follows:

(1,3) and (5,6).

The relative extremas are the values for which the derivative is of zero, hence:

The graph of the derivative is given by the image presented at the end of the answer.

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Answer:

Step-by-step explanation:

100/50=2

so 10 x 2 = 20

they walk 20 feet

Answer:

Using the distributive property to re-write the expression, 18 - 9 + 18 - 91 = 18 - (9 + 91) = 18 - 100 = -82 Therefore, the solution to the expression is -82.

The amount Ray paid for the car is at a value of $50000

Percentage decrease is the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.

Let's represent the price ray bought the car by x

It loses its value by 25% firstly. This means that 25/100 × x = 25x/100

the new value of the car = x - 25x/100 = 75x/100

It later losses 50% of its value. This means that 50/100× 75x/100 = 75x/200

The new value of the car = 75x/100 - 75x/200

= $18750

multiply all terms by 200

150x - 75x = 3750000

75x = 3750000

divide both sides by 75

x = 3750000/75

x = $50000.

Therefore Ray bought the car at $50000

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2x + 6y when x is -4/5 and y is 1/3

Evaluate:

2(-4/5) + 6(1/3)

= 2/5 or 0.4(decimal form)

2/5 or 0.4 would be your answer.

Hope this helps!