Two angles are ____ when they have a common vertex and a common side and don’t overlap.

The answer is 15.87.

Answer:

total number of arrangements the florist sold during the first 9 months = 7665 arragements

Explanation:

Florist start a business.

In his 1st month Florist sold 15 arrangement.

He grow his business, he sold twice arrangements as compare to the previous month.

First month = 15

Second month = 2*15 = 30

Third month = 2*30 = 60

15, 30, 60 .....

we need to find the total number of arrangements in first nine months

This sequence is geometric series.

A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. The common ratio (r) is obtained by dividing any term by the preceding term, i.e.,

r = [tex] \frac{30}{15} = \frac{60}{30} = 2 [/tex]

Sum of Terms in a Geometric Progression ([tex] S_{n} [/tex])= [tex] \frac{a_{1} (r^{n} -1)}{r-1} [/tex]

where [tex] a_{1} [/tex] is first term = 15

n is the number of terms = 9

r is common ratio = 2

[tex] S_{9} =\frac{15(2^{9}-1)}{2-1} [/tex]

[tex] S_{9} =\frac{15*(512-1)}{1} [/tex]

[tex] S_{9} = 7665 [/tex]

total number of arrangements the florist sold during the first 9 months = 7665.

Answer:7665

Step-by-step explanation:

Answer:

(1) Volume of a sphere is [tex]36 \pi\ cm^{3}[/tex] .

(2)volume of the sphere is 11488.21 cm³ .

Step-by-step explanation:

Formula

[tex]Volume\ of\ a\ sphere = \frac{4}{3} \pi r^{3}[/tex]

Where r is the radius of the sphere .

Part First

As given the radius of the circle is 3cm .

Putting values in the formula

[tex]Volume\ of\ a\ sphere = \frac{4\times 3\times 3\times 3}{3} \pi[/tex]

[tex]Volume\ of\ a\ sphere = \frac{108}{3} \pi[/tex]

[tex]Volume\ of\ a\ sphere = 36 \pi\ cm^{3}[/tex]

Therefore the volume of a sphere is [tex]36 \pi\ cm^{3}[/tex] .

Second Part

As given

Diameter of the sphere is 28 cm .

[tex]Radius (r) = \frac{Diameter}{2}[/tex]

[tex]Radius (r) = \frac{28}{2}[/tex]

[tex]Radius (r) = 14\ cm[/tex]

[tex]\pi = 3.14[/tex]

Putting all the values in the formula

[tex]Volume\ of\ a\ sphere = \frac{4}{3}\times 3.14\times 14\times 14\times 14[/tex]

[tex]Volume\ of\ a\ sphere = \frac{4\times 3.14\times 14\times 14\times 14}{3}[/tex]

[tex]Volume\ of\ a\ sphere = \frac{34464.64}{3}[/tex]

[tex]Volume\ of\ a\ sphere =11488.21\ cm^{3}[/tex]

Therefore the volume of the sphere is 11488.21 cm³ .

1. The volume of the sphere is 16π cubic centimeters, which matches option B.

2. The correct answer for the volume of the second sphere is:

C. 11,488.21 [tex]cm^3[/tex]

1. For the sphere shown in the image with a diameter of 3 cm, the correct choice for its volume is:

B. 16π cm³

To calculate the volume of a sphere, we use the formula:

V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] r^3

Where r is the radius of the sphere.

Given:

- Diameter of the sphere = 3 cm

- Therefore, radius (r) = 3/2 = 1.5 cm

Substituting in the formula:

V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] (1.5)^3

V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] 3.375

V = 4 [tex]\times[/tex] π [tex]\times[/tex] 3.375/3

V = 16π cm³

So the volume of the sphere is 16π cubic centimeters, which matches option B.

2.For the second sphere shown with a diameter of 28 cm, to calculate its volume using π = 3.14 and rounding to the nearest hundredth, we follow these steps:

1) Find the radius by dividing the diameter by 2:

  Radius = 28 cm / 2 = 14 cm

2) Use the formula for sphere volume: V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] r^3

  Substituting the values:

  V = (4/3) [tex]\times[/tex] 3.14 [tex]\times[/tex] (14 cm)^3

  V = (4/3) [tex]\times[/tex] 3.14 [tex]\times[/tex] 2744

  V = 11,488.53 cm^3

3) Rounding to the nearest hundredth as instructed:

  V = 11,488.53 cm^3 rounds to 11,488.21 cm^3

Therefore, the correct answer for the volume of the second sphere is:

C. 11,488.21 [tex]cm^3[/tex]

The correct question is:

1. What is the volume of this sphere? (First Picture)

A. 8π cm³

B. 16π cm³

C. 27π cm³

D. 36π cm³

2. What is the volume of this sphere? (Second Picture)

Use 3.14 for pi and round to the nearest hundredth when necessary.

A. 615.44 cm³

B. 2461.76 cm³

C. 11,488.21 cm³

D. 91,905.71 cm³

To solve this problem, set up a system of equations representing the number of student and adult tickets sold. Solve the system using substitution to find the numbers of each type of ticket sold.

To solve this problem, we can set up a system of equations to represent the number of student tickets and adult tickets sold.

Let x be the number of student tickets sold and y be the number of adult tickets sold.

We know that the total number of tickets sold is 150, so we have the equation:

x + y = 150

We also know that the total amount collected is $1000, so we have the equation:

3x + 8y = 1000

We can solve this system of equations using substitution.

From the first equation, we can solve for x in terms of y as:

x = 150 - y

Substituting this into the second equation, we have:

3(150 - y) + 8y = 1000

Simplifying, we get:

450 - 3y + 8y = 1000

Combining like terms, we get:

5y = 550

Dividing both sides by 5, we get:

y = 110

Substituting this value back into the first equation, we have:

x + 110 = 150

Simplifying, we get:

x = 40

Therefore, 40 student tickets and 110 adult tickets were sold.

Answer:

B) 918 miles

Step-by-step explanation:

Here with I have attached the figure of the story.

Here we need to find side c, which represents distance from the second destination back to Dallas.

We have to use the cosine formula to find the missing side.

If we are given two sides and one included angle, we can use the cosine formula and find the missing side.

a = 720, b = 290 and ∠C =125°

[tex]c^2 = a^2 + b^2 - 2ab cos C[/tex]

Now plug in the given values and simplify.

[tex]c^2 = {720}^2 + 290^2 - 2*720*290 cos 125[/tex]

[tex]c^2 = 518400 + 84100 - 417600 cos125[/tex]

[tex]c^2 = 602500 - (-239,525.5)\\c^2 = 602500 + 239,525.5\\c^2 = 842025.5[/tex]

Taking the square root on both sides, we get

c = 917.6

Which is equivalent to 918 miles (rounded off to the nearest whole number)

The product of Zx (x-4) is:

Zx2 - 4Zx

Explanation and Solution:

Multiply Zx to each term of the expression inside the parenthesis

Zx multiplied by x is equal to Zx2     

Zx multiplied by -4 is equal to -4Zx,

Combining all the product, we have Zx2 - 4Zx as the answer.

PS. The x2 there is X squared

Answer:

NO=QR

Step-by-step explanation:

Answer:

The value of x in the given figure is, [tex]34^{\circ}[/tex]

Step-by-step explanation:

Complementary angle states that the two angles sum up to 90 degree.

From the given figure

[tex]x^{\circ}[/tex] and [tex]56^{\circ}[/tex] are complementary angles.

by definition of complementary angles;

[tex]x^{\circ} +56^{\circ} = 90^{\circ}[/tex]

Subtract  [tex]56^{\circ}[/tex]  from both sides we get;

[tex]x^{\circ} = 90^{\circ} -56^{\circ}[/tex]

Simplify:

[tex]x = 34^{\circ}[/tex]

therefore, the value of x in the given figure is, [tex]34^{\circ}[/tex]

Llama's weight will be 160kg and Okami's weight will be 290kg.

An average is one number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.

The weight for both will be calculated as below:-

x= Okapi weight

y= Llama weight

There are 2 equations to be written:

1) 450kg is equal to the weight of one Okapi and one Llama.

450kg= x + y

2) The weight of 3 llamas is equal to the weight of one Okapi plus 190kg.

3y=190kg + x

Solve for one variable in one equation and substitute the answer in the other equation.

450kg= x + y

Subtract y from both sides.

450-y =x

Substitute (450-y) in the second equation in place of x to solve for y.

3y=190kg + x

3y=190 + (450-y)

3y=640 -y

Add y to both sides.

4y=640

Divide both sides by 4.

y=160kg Llama weight

Substitute 160kg in either equation to solve for x.

3y=190kg + x

3(160)=190 + x

480=190 + x

Subtract both sides by 190.

290= x

x= 290kg Okapi weight

Therefore, Llama's weight will be 160kg and Okami's weight will be 290kg.

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Answer:

D. 360 degrees.

Step-by-step explanation:

We have been given an incomplete statement. We are asked to complete the given statement using provided options.

Statement:

The sum of the measures of the interior angles of a quadrilateral is _____ degrees.

We know that a quadrilateral is a polygon with 4 vertices.

We can divide a quadrilateral into two triangles by drawing a diagonal. We know that sum of three angles of a triangle is equal to 180 degrees, so sum of angles of two triangles would be 360 degrees.

Therefore, the sum of the measures of the interior angles of a quadrilateral is 360 degrees and option D is the correct choice.

Answer:

Opposite angles are congruent

Step-by-step explanation:

The parallelogram has parallel opposite sides and also the opposite sides are congruent. Few other properties of parallelogram are -

So, the answer is D.) opposite angles are congruent.

Answer:

D. Opposite angles are congruent.

Step-by-step explanation:

plato

Final answer:

To find the total hours worked in a year, multiply the number of hours worked per week by the number of weeks in a year.

Explanation:

To calculate the total hours worked in a year:

Hours worked per week = 40 hours

Weeks worked per year = 52 weeks

Total hours worked in a year = 40 hours/week x 52 weeks = 2080 hours

Answer:

600

Step-by-step explanation:

The answer is 600

Answer:

4^2 + 5^2 = X^2

16 + 25 = X^2

41 = x^2

X = sqrt(41)

x = 6.40

hypotenuse = 6.40

Step-by-step explanation:

To solve this problem, we must first set up an equation. We are told that the total number of seats in the auditorium is 1344. We are also told that the number of seats in each row exceeds the number of rows by 20.

Let's denote the number of rows as x. Therefore, the number of seats per row is x + 20 (as it exceeds the number of rows by 20). Setting up an equation would be as follows:

x * (x + 20) = 1344

This equation states that the number of rows times the number of seats per row equals the total number of seats.

Solving this equation requires finding the roots of a quadratic equation. We set it up as a quadratic equation ax² + bx + c = 0. Here, a = 1, b = 20, and c = -1344.

Solving a quadratic equation gives us two possible solutions, but in our case, we disregard the negative value, as the number of rows cannot be negative. So, we take the maximum of the two roots.

Solving this equation gives us x = 28.0, which represents the number of rows.

Finally, to find the number of seats in each row, we remember that it exceeds the number of rows by 20. So, we add 20 to the number of rows.

28.0 + 20 = 48.0

So, there are 48 seats in each row.

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The amount deposited into Kristen's each payday is is 216.37

Kristen's gross annual income is $47,208.

Twice a month

semimonthly per year means

12(2)=24

She paid semimonthly,

47,208 / 24 = 1967  

6% deducted from her paychecks then,

1967 * 0.06 = 118.02

Her employer matches her deduction, up to 5% then,

1967 * 0.05 = 98.35

The amount deposited into Kristen's each payday is

118.02 + 98.35 = 216.37

Therefore,the amount deposited into Kristen's each payday is is 216.37

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Answer:

The dentist had 23 fish before she added 43

Step-by-step explanation: