a circle is divided into 5 equal parts what is the measure of the angle that turns through 2 parts

So, the measure of angle B is 90 degrees.

An angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. The two rays or line segments are called the sides or arms of the angle. Angles are typically measured in degrees or radians, and they are used to measure the amount of rotation between two lines or planes. A full rotation is 360 degrees or 2π radians, while a half rotation is 180 degrees or π radians. Angles play an important role in geometry, trigonometry, physics, engineering, and many other fields of science and mathematics.

by the question.

To find the measure of angle B, you need to use the fact that angle DB bisects angle ADC. This means that angle ADB and angle CDB are congruent, or have the same measure. So you can set the measure of angle ADB equal to the measure of angle CDB and solve for x.

Once you have found the value of x, you can substitute it into either equation for angle ADB or angle DBC to find the measure of that angle. Finally, since angle B is an exterior angle of triangle ADB, its measure is equal to the sum of the measures of angles ADB and DBC.

So, the steps to find the measure of angle B are:

Set the measure of angle ADB equal to the measure of angle CDB:

(3x - 12) = (2x + 6)

Solve for x:

x = 18

Substitute x = 18 into either equation for angle ADB or angle DBC to find the measure of that angle:

angle ADB = (3x - 12) = (318 - 12) = 48 degrees

angle DBC = (2x + 6) = (218 + 6) = 42 degrees

Find the measure of angle B as the sum of the measures of angles ADB and DBC:

angle B = angle ADB + angle DBC = 48 + 42 = 90 degrees.

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The total length of the cross-country course include the following: 16 miles.

In Mathematics and Geometry, the perimeter of a rectangular shape such as a parallelogram can be calculated by using this mathematical expression;

P = 2(L + B)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangular shape, we have the following;

P = 2(L + B)

P = 2(6 + 2)

P = 2(8)

P = 16 miles.

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Complete Question:

A cross-country course is in the shape of a parallelogram with a base of length 6 mi and a side of length 2 mi.

What is the total length of the cross-country course?

Answer:    The total length of the cross-country course include the following: 16 miles.

How to calculate the perimeter of a rectangle?

In Mathematics and Geometry, the perimeter of a rectangular shape such as a parallelogram can be calculated by using this mathematical expression;

P = 2(L + B)

Where:

P represent the perimeter of a rectangle.

B represent the breadth of a rectangle.

L represent the length of a rectangle.

By substituting the given side lengths into the formula for the perimeter of a rectangular shape, we have the following;

P = 2(L + B)

P = 2(6 + 2)

P = 2(8)

P = 16 miles.

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Complete Question:

A cross-country course is in the shape of a parallelogram with a base of length 6 mi and a side of length 2 mi.

What is the total length of the cross-country course?

Step-by-step explanation:

The required expected number of employees who will pass the test from given 11 potential employees is equal to 10.

Probability of passing a drug test is 90%,

Then the probability of failing is 10%.

For each potential employee,

Probability of passing is 0.9, and the probability of failing is 0.1.

The number of potential employees who would be expected to pass the test,

Calculated using the binomial distribution with n = 11 and p = 0.9.

P(A = x) = (ⁿCₓ) × pˣ ×  (1-p)ⁿ⁻ˣ

where,

A is the number of potential employees who pass the test

x is the number of potential employees who pass the test

n is the number of potential employees

p is the probability of passing the test

Using this formula, the expected number of potential employees who would pass the test is,

E(A) = n ×p

      = 11 × 0.9

      = 9.9

Rounding to the nearest whole number, we can expect 10 potential employees to pass the test.

Therefore, the expected number of employees from the given  probability who would pass the the test is 10.

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An equation that is the best model for a line of best fit for the data include the following: C. y = 3/4x + 5.

In order to determine an equation for the line of best fit that models the data points contained in the graph (scatter plot), we would have to use a graphing calculator (Microsoft Excel).

Based on the scatter plot (see attachment) which models the relationship between the x-values and y-values, an equation for the line of best fit is given by

y = 3x/4 + 5

In conclusion, we can reasonably infer and logically deduce that the scatter plot most likely indicates a linear relationship between the x-values and y-values.

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Complete Question:

Which of the following equations is the best model for a line of fit for the data?

y= 1/4x + 5.

y= -1/4x + 5.

y= 3/4x + 5.

y= -3/4x + 5.

The person who has the fastest speed is given as follows:

Aubri and Tyler(tied).

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

The constant for each person, representing the velocity, is given as follows:

The problem asks for the person who has the fastest speed.

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Answer: The median decreases to 6.5.

Step-by-step explanation:

The median before 4 was added was 6.75.

When 4 is added the median is 6.5.

Let's order them from most likely to least likely to occur:

To calculate the probability of selecting each type of ball, we need to find the total number of balls in the bin first.

Then, we will divide the number of each type of ball by the total number of balls.

Total number of balls = 15 baseballs + 12 basketballs + 8 soccer balls + 5 footballs + 10 volleyballs

Total number of balls = 50 balls

Now, let's calculate the probability of selecting each type of ball:

Baseballs: P(Baseballs) = (Number of baseballs) / (Total number of balls) = 15/50 = 0.3

Basketballs: P(Basketballs) = (Number of basketballs) / (Total number of balls) = 12/50 = 0.24

Soccer balls: P(Soccer balls) = (Number of soccer balls) / (Total number of balls) = 8/50 = 0.16

Footballs: P(Footballs) = (Number of footballs) / (Total number of balls) = 5/50 = 0.1

Volleyballs: P(Volleyballs) = (Number of volleyballs) / (Total number of balls) = 10/50 = 0.2

Now, let's order them from most likely to least likely to occur:

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Answer: 7

Step-by-step explanation:

Step 1: 6^9 * 6^x = 6^2

Step 2: 9 + x = 2

Step 3: x = 2 - 9

Step 4: x = -7

Step 5: Since the power of a number cannot be negative, x must be 7.

If the perimeter of the base of the pyramid is 314 centimeters, then radius of the cone is approximately 17.44 centimeters.

Perimeter is a measurement of the distance around the outside of a two-dimensional shape. It is the sum of the lengths of the shape's sides.

Since the pyramid and cone have the same base and slant height, they are similar geometric figures. Therefore, their corresponding dimensions are proportional. Let's denote the radius of the cone as r.

Since the perimeter of the base of the pyramid is 314 centimeters, and the base of the pyramid is a square, we can find the length of one side of the square base by dividing the perimeter by 4:

Length of one side = Perimeter / 4 = 314 cm / 4 = 78.5 cm

Since the pyramid and the cone have the same area of the base, and the base of the pyramid is a square, we can find the area of the base by squaring the length of one side:

Area of the base = (Length of one side)² = (78.5 cm)²= 6,152.25 cm²

Since the pyramid and the cone have the same surface area, we can use the formula for the surface area of a cone to find the radius of the cone:

Surface area of the cone = πr(r + l), where l is the slant height.

The surface area of the cone is equal to the surface area of the pyramid, so we have:

πr(r + l) = 2 × Area of the base + Perimeter × l

Substituting the known values, we get:

πr(r + 13) = 2 × 6,152.25 cm² + 314 cm × 13 cm

Simplifying and solving for r, we get:

πr² + 13πr - 4,059.5 = 0

Using the quadratic formula, we find:

r ≈ 17.44 cm (rounded to two decimal places).

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The burger costs $0.625, the souvenir costs $3.75, and the pass costs $5.00.

Let's name the burger price "b," the souvenir price "s," and the pass price "p." Then, using the information provided, we can construct an equation system:

b + s + p = 35.75  (1) (The three things cost a total of $35.75.)

b = (1/6)s               (2) (the burger was one-sixth the price of the memento).

s = (3/4)p     (3) (the memento cost one-quarter the price of the pass)

b + s + p + 2 = 35.75       (4) (After purchasing these products, Dion had                        $2.00 left over.)

To remove s from the equations, we can apply equations (2) and (3):

b + (3/4)p + p = 35.75    (equations (1) and (3))

b = (1/6)(3/4)p                (Applying Equation (2))

b = (1/8)p

This expression can now be substituted by Input b into equation (1):

(1/8)p + (3/4)p + p = 35.75

(7/8)p = 35.75

p = 35.75 / (7/8)

p = $5.00

We may calculate the cost of the keepsake using equation (3):

s = (3/4)p = (3/4)($5.00) = $3.75

Finally, we can calculate the cost of the burger using equation (2):

b = (1/6)s = (1/6)($3.75) = $0.625

As a result, the burger costs $0.625, the souvenir costs $3.75, and the pass costs $5.00.

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Answer:

A. True

Step-by-step explanation:

If two angles of a triangle are congruent to the corresponding angles or the second triangle than the third angles must be congruent to each other.

The sum of the interior angles of a triangle is 180.  Let's say 2 angles to one triangle is 100 and the second angle is 35.  That forces the third angle to be 45 (100 + 35 + 45 = 180)

Helping in the name of Jesus.

Answer:

A. True

Step-by-step explanation:

In congruent triangles...All angles and sides have to be equal.

Emily new boots cost a total of $71.4 with the tax included as 5% and the original cost of the boots being $68.

The sales tax rate in Emily's city = 5% and the cost of Emily's new boots is $68

we need to find the amount of sales tax Emily will pay for her boots,

The formula we will use =

Sale tax = Percent sales tax x Cost of the product

when we put the values in the formula, we get:

Sales tax = 5% x $68

= $3.4

now we need to also calculate the total cost for Emily's boots,

Therefore, the total cost = Cost of boots + Sales Tax

when we put the values in the formula, we get:

Total cost = $68 + $3.4

= $71.4

Therefore, the total cost Emily will pay for her boots is $71.4

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A raccoon consumes 500 calories of food. Of those calories, 50 are transformed into biomass. In other words, 50 calories of energy are stored In Its body. So, option D is correct.

When a raccoon eats 500 calories of food, some of those calories go towards its daily needs for warmth, movement, and reproduction. The raccoon's body does not store this energy; instead, it is transformed into other forms, including heat and movement. In addition, a portion of the energy in meals is expelled as waste rather of being absorbed. Nonetheless, 50 calories of the food's energy are transformed into biomass, which is then stored as fat or tissue in the raccoon's body. Thus, the right response is D) Its body stores 50 calories of energy.

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The actual question is:

A raccoon consumes 500 calories of food. Of those calories, 50 are transformed into biomass. In other words:

A) 50 calories turn into plant matter.

B) 50 calories leave the raccoon's body as waste.

C) In order to stay warm, reproduce, and move around, it needs 50 calories of energy.

D) 50 calories of energy are stored In Its body

The volume of a standard size golf ball can be calculated using the formula for the volume of a sphere:

V = (4/3)πr^3

where r is the radius of the golf ball. The diameter of the golf ball is 1.680 inches, so the radius is 0.840 inches.

V = (4/3)π(0.840)^3

= 2.468 in^3

The weight of the golf ball can be calculated by multiplying its volume by the density of the material:

W = V × D

where D is the density of the material. The density of the material is 0.6523 ounces per cubic inch.

W = 2.468 in^3 × 0.6523 oz/in^3

= 1.6095 oz

Therefore, the weight of one golf ball is approximately 1.61 ounces (rounded to the nearest hundredth of an ounce).

In the given problem,  the distance from point A to point B is approximately 658 feet (rounded to the nearest foot).

Let's define some variables:

Using trigonometry, we can write the following equations:

For triangle ACT, we have:

tan(15°) = h/d

For triangle BCT, we have:

tan(50°) = h/(d+x)

We want to find the value of x, so let's rearrange the second equation:

tan(50°) = h/(d+x)

tan(50°)*(d+x) = h

d+x = h/tan(50°)

x = h/tan(50°) - d

Substituting the given values:

x = 115/tan(50°) - d

Now we need to find the value of d. For that, we can use the first equation:

tan(15°) = h/d

d = h/tan(15°)

Substituting the given value:

d = 115/tan(15°)

Now we can substitute both values into the equation for x:

x = 115/tan(50°) - 115/tan(15°)

Using a calculator, we get:

x ≈ 658.4 ft

Therefore, the distance from point A to point B is approximately 658 feet (rounded to the nearest foot).

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The sοlutiοn tο the  radical equatiοn is x = 5.

In mathematics, a radical is the οppοsite οf an expοnent, which is symbοlised by the symbοl "," alsο referred tο as rοοt. A square rοοt οr a cube rοοt can be used, and the number befοre the symbοl οr radical is regarded as an index number οr degree. The expοnent οf this number cancels the radical and is a whοle number.

The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Starting with:

-5√(2x - 1) = -15

Divide bοth sides by -5:

√(2x - 1) = 3

Square bοth sides:

2x - 1 = 9

Add 1 tο bοth sides:

2x = 10

Divide bοth sides by 2:

x = 5

Hence, the solution to the equation is x = 5.

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Answer:

x=7

Step-by-step explanation:

First, try to bring all your X's together

3x+9x=6x+42

   12x=6x+42

   -6x  -6x

    6x=42

    /6   /6

     x = 7

Step-by-step explanation:

To find the remainder when 3x^3 - x^2 + 2x - 4 is divided by (x - 2), we can use synthetic division.

First, we write the coefficients of the polynomial in descending order of powers of x, with any missing terms represented by a coefficient of 0:

3 1 -1 2 -4

To perform synthetic division, we bring down the first coefficient (1) and multiply it by the divisor (x - 2) to get the first entry in the second row, which we then add to the second coefficient:

3 1 -1 2 -4

1

1

We repeat the process with the new coefficient in the third row, multiplying it by the divisor and adding it to the next coefficient:

3 1 -1 2 -4

1 3

1 2

Finally, we repeat the process with the new coefficient in the third row to get the last entry in the second row:

3 1 -1 2 -4

1 3 8

1 2 4

The last entry in the third row is the remainder, which is 4. Therefore, the remainder when 3x^3 - x^2 + 2x - 4 is divided by (x - 2) is 4.

The area of the shaded segment of the circle is calculated by substracting the area of triangle from area of sector of circle So, area of shaded segment of the above circle is equals to the (12π - 9√3) cm².

Assume a sector having a radius r and a central angle of α degrees. The sector's area will be A= (α/360∘)πr². Similarly, different shapes have different area formulas. We have been provided a circle of radius 6cm. Assume that its center is O and the segment is AB. Radius of circle , r = 6 cm

Central angle,α = 120°

Area of shaded segment is calculated by the area of sector AOB of circle minus area of triangle AOB formed there. So, Area of sector AOB , A = (α/360∘)πr²

= ( 120°/360°) π6²

= (1/3) 36π = 12π cm²

As we know, OA = OB= 6cm

=> m∠OAB = m∠OBA

and m∠AOB + m∠OAB + m∠OBA = 180∘

=> 120∘ + m∠OAB + m∠OAB= 180∘

=> 2(m∠OAB) = 180∘− 120∘ = 60°

=> m∠OAB = 30° = m∠OBA

So, it is an isosceles triangle. Draw a perpendicular OC on AB then there is formed two right angled triangles. In right angled triangle OAC, 90°, 60°, 30° and OA = 6 cm then OC/6 = Sin 30°

=> OC= 3 cm and

AC = √36 - 9 = √27 = 3√3 cm

Similarly, BC = 3√3 cm so, AB = 6√3 cm. Now, area of triangle AOB = (1/2) × AB × OC = (1/2)× 6√3 ×3 = 9√3 cm²

So, required area = 12π cm² - 9√3 cm². Hence, required value is (12π - 9√3) cm².

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Complete question:

The above figure completes the question. Find the area of the shaded segment of the circle.

If there is sufficient evidence to reject a null hypothesis at the 10% level, then there is sufficient evidence to reject it at the 5% level.

What is hypothesis testing?

A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters through hypothesis testing.

Here,

We have to find the correct statement about hypothesis testing.

We concluded that  If there is sufficient evidence to reject a null hypothesis at the 10% level, then there is sufficient evidence to reject it at the 5% level.

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Answer:

In this case, B is true.

Whether to use a one-sided or a two-sided test is typically decided BEFORE the data are gathered, not after.

Be careful while reading the options on the quiz, because depending on the question you get, the options may be worded slightly differently. Because of the wording, the answer may be different as well (on the FLVS quiz, I got different answer choices for this question). Be careful and read cautiously!

Have a great day.

"type of orange" because it is a bar graph therefore it is supposed to be categories, not numbers :)

In conclusion Rounding to four decimal places, we get:

f(t) = 9100e²(0.1398t)

How to solve?

To write the function F(t) = 9100(1.15)²t in the form f(t) = ae²(kt), we need to first take the natural logarithm of both sides:

ln(F(t)) = ln(9100(1.15)²t)

ln(F(t)) = ln(9100) + ln(1.15²t)

ln(F(t)) = ln(9100) + t × ln(1.15)

Now, we have the form ln(F(t)) = ln(a) + kt, where k = ln(1.15) and a = 9100. We can exponentiate both sides of this equation to get:

F(t) = e²(ln(a) + kt)

F(t) = e²ln(a) × e²(kt)

F(t) = a × e²(kt)

Substituting the values of a and k, we get:

F(t) = 9100 × e²(0.1398t)

Rounding to four decimal places, we get:

f(t) = 9100e²(0.1398t)

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[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &20000\\ r=rate\to 25\%\to \frac{25}{100}\dotfill &0.25\\ t=\textit{elapsed time}\dotfill &2\\ \end{cases} \\\\\\ A = 20000(1 - 0.25)^{2} \implies A=20000(0.75)^2\implies A = 11250[/tex]

Answer:

6(2y-3)

Step-by-step explanation:

Both 12 and 18 divide by 6.

12/6= 2 and 18/6 = 3

So we can take 6 out and put it outside the bracket and have 2y and 3 on the inside.

If a company understates its ending balance of inventory in year 1 and states its inventory correctly in year 2, then the correct statement is option (c) Net income is understated in year 2

Understating the ending balance of inventory in year 1 would result in the cost of goods sold (COGS) being overstated and net income being understated in that year. This is because the COGS is calculated as the beginning inventory plus purchases minus ending inventory. By understating the ending inventory balance, the COGS for year 1 would be overstated, which would result in a lower net income for year 1.

In year 2, if the inventory is stated correctly, it would not have an impact on the COGS for that year. However, if the net income for year 1 was understated due to the understated ending inventory balance, the cumulative effect would be an understated net income for both years. This means that the correct answer is c. Net income is understated in year 2.

Therefore, the correct option is (c) Net income is understated in year 2

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Step-by-step explanation:

[tex]{ \tt{x(y + 2)}}[/tex]

We need to multiply inner terms i.e. y+2 with x

[tex]{ \red{ \tt{xy + 2x}}}[/tex]

Answer:

xy +2x

Step-by-step explanation:

x(y+2)

Distribute the x to each term inside the parentheses.

x*y + x*2

xy +2x