Solve each triangle using the Law of Cosines.

Answer: [tex]\sqrt[5]{3}-1[/tex]

Step-by-step explanation:

Let the annual rate of increase be [tex]r[/tex].

[tex]3000=1000(1+r)^5\\\\3=(1+r)^5\\\\\sqrt[5]{3}=1+r\\\\r=\sqrt[5]{3}-1[/tex]

On solving the provided question, we can say that  D, diameter pizza will produce the largest slice is 16

Any straight line segment with an endpoint on the circle and that travels through its center is considered a circle's diameter in geometry. The longest chord of a circle is another way to describe it.

Let r be the radius and  be the angle of a circle.

According with the graph, the area of the sector is given by

A = 1/2r^2∅

The arc length of a circle with radius r  and angle∅   is r∅

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches.

Thus the perimeter has length

2r + r∅ = 32 in

r∅ = 32 - 2r

∅ = 32- 2r / r

Now,

A = 1/2r^2[32- 2r / r]

A = 16r - r^2

A' = 16 - 2r 16 -2r = 0

r = 8

A" = -2

so, D, diameter pizza will produce the largest slice is 16

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Answer:

1) Nikhil 16 years & Mae 4 years

Step-by-step explanation:

x = 4y {equation 1}

Hence, x - 4y = 0 { equation 2}

x = 8 + 2y {equation 3}

Then, x - 2y = 8 { equation 4}

{equation 4-2}

x -x -2y - ( - 4y) = 8 -0

-2y +4y = 8

2y = 8

2 2

y = 4

By substituting { equation 1}

x = 4y

x = 4 × 4

= 16//

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Answer:

60°

Step-by-step explanation:

To find the angle of the terminal side through a point P on the unit circle, we can use the coordinates of the point. The angle is given by the inverse tangent (atan) of the y-coordinate divided by the x-coordinate.

The point P is given as (√15/5, √10/5)

Using the arctan function we have:

theta = arctan(√10/5/√15/5) = arctan(√2/√3)=atan(√2/√3) = pi/3

The angle theta is in radians, to convert it to degree we multiply it by 180/pi

Theta = (pi/3) * (180/pi) = 60. Therefore, the angle of the terminal side through the point P is 60°.

a) The unit rate of change of d with respect to t is equal to 1.6

b) the graph of the line in the attached figure.

Given: A proportionate relationship between d and t with the characteristic that a rise in t of 5 units causes a rise in d of 8 units.

To locate: A rise of 5 units in t causes a rise of 8 units in d, according to the line's unit rate of change with respect to t.

=> Slope  =   Δd/Δt   = 8/5 = 1.6

the proportional relationship between d  and t

=> d ∝ t

=> d = 1.6t

t           d=1.6t

0          0

1           1.6

2           3.2

3           4.8

Plot the points and draw a line passing through points.

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Answer:

NOLO

Step-by-step explanation:

Answer: [tex]y=3[/tex]

Step-by-step explanation:

The intersection point of the graphs is the solution. So, you need to find the [tex]y[/tex]-coordinate of the intersection point.

Answer:

-7

Step-by-step explanation:

(fog)(-3) = f(g(-3)) = f (2(- 3) - 4) = f(-10) = -10 + 3 = -7

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The shaded region corresponding to all values of x and y that satisfy these requirements is shown the graph

Suppose the considered function whose graph is to be made is

f(x)

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values

f(x)

are plotted on the vertical axis.

They are together plotted on the point

(x,y) = (x, f(x))

This is why we usually write the functions as:

y = f(x)

Therefore, the graph is given with shaded region

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The remainder when N is divided by 1000 is 106.

The Principle of Inclusion-Exclusion, often known as PIE, offers a method/formula for organizing information about the size of each set, the number of elements in the union of a given set of sets, and the size of all potential set intersections.

From the question,

First, we think about all the possible divisions of the 7×1 board. Since we require at least one tile of each color, we exclude the cases of just one or two pieces.

Three pieces = 5+1+1 , 4+2+1 , 4+1+2 etc (6C2) = 15 ways

Four pieces = 6C3 = 20

Five pieces = 6C4 = 15

Six pieces = 6C5 = 6

Seven pieces =6C6 = 1

Now, we apply the Principle of Inclusion-Exclusion to consider how many ways to color them:

Three pieces : 3³ - 3 × 2³ + 3 = 6

Four pieces: 3⁴ - 3 × 2⁴ + 3 = 36

Five  pieces : 3⁵ - 3 × 2⁵ + 3 = 150

Six pieces : 3⁶ - 3 × 2⁶ + 3 = 540

Seven pieces : 3⁷ - 3 × 2⁷ + 3 = 1806

Adding them together, we get

15×6 + 20×36 + 15×150 + 6×540 + 1×1806 = 8106

Hence, the remainder when it is divided by 1000 is 106.

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Answer:

106

Step-by-step explanation:

Answer:

5/8 is greater than 5/7. 5/8 is 0.625, while 5/7 is 0.714.

Step-by-step explanation:

5/8 is greater than 5/7. 5/8 is 0.625, while 5/7 is 0.714.

Answer:

5/7

A fraction is a fragment of a whole number, used to define parts of a whole.  The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

If we think about 5/7, we can relate this to a circle split into 7 parts, with 5 shaded in.

You can do the same for 5/8. Think of a circle with 8 parts, and 5 shaded in.

A way to figure out which is bigger is to find a common denominator between the two.

A common denominator is two fractions with the same denominator (Hence the name). Solving for a common denominator can be done with cross multiplication.

5/7 = 40/56

5/8 = 35/56

We can visibly see, that 40/56 (5/7) is bigger, therefore making 5/7 the greater fraction.

Answer: A. p + 3 = 49

B. p = 46

Step-by-step explanation:

A. represents the equation that represents the word problem. In this case, the original number of paintbrushes Kaitlyn had is represented by (p) and Claire gives her 3 more paintbrushes, the total number of paintbrushes she has is 49.

B. represents the original number of paintbrushes Kaitlyn had. To find this, we can simply solve the equation from part A for (p) by isolating it on one side of the equation.

Therefore, Kaitlyn originally had 46 paintbrushes.

On solving the provided question, we can say that  the unique point equidistant from points in tetrahedron are PQ/AQ = 3/8

A polyhedron with four triangular faces, six straight edges, and four vertex corners is known as a tetrahedron in geometry, also known as a triangle pyramid. The only regular convex polyhedron with fewer than five faces is the tetrahedron, which is also the simplest of them all. Tetrahedra make up the pyramid at the bottom of the triangle. It is a tetrahedron if it has four faces that are triangular in shape. Regular tetrahedrons are those that have isosceles triangles for their faces and equilateral triangles for their bases. with four sides, a polyhedron

here,

the unique point equidistant from points

PQ/AQ = 3/8

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Answer:

G.1/4

Step-by-step explanation:

The probability of getting two heads when two fair coins are tossed is 1/4 or 0.25. This is because for each coin there are two possible outcomes, heads or tails, and the probability of getting heads is 1/2. Therefore, the probability of getting two heads when both coins are tossed is (1/2) * (1/2) = 1/4. So the correct answer is G. 1/4

So, on solving the provided question we can say that by probability we have [tex]256.014[/tex]= sample mean for 80th percentile

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

[tex]P(x < 240)[/tex]

Transform to z score =  (sample mean - population mean)/(standard deviation(std)[tex]/sample size^0.5)[/tex]

[tex]P(z < (240-250)/(50/49^0.5)[/tex]

[tex]P(z < -1.4) = 0.0808[/tex]

z-score corresponding to 80th percentile is 0.842

0.842 = (sample mean -[tex]250)/(50/49^0.5)[/tex]

[tex]6.014[/tex] = sample mean - [tex]250[/tex]

[tex]256.014[/tex]= sample mean for 80th percentile

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Answer:

36 hours

Step-by-step explanation:

3 x 12 = 36

Answer:

36 hours

Step-by-step explanation:

if it took 3 people to paint a room in 12 hours, we have,

3 people = 12 hours

divide by 3.      multiply by 3

1 person = 36 hours.

Answer:

28 cups

Step-by-step explanation:

[tex]\frac{2}{1}[/tex] = [tex]\frac{x}{14}[/tex]

1 x 14 = 14, so 2 x 14 = 28

According to the algebraic fundamental theorem, a polynomial equation of degree n has exactly n roots, be they real or imaginary.

Any polynomial of degree n has n roots, which is the fundamental theorem of algebra. Any polynomial has at least one solution, according to this statement. The theorem only reveals how many roots there are, not what the roots of a polynomial are. The theorem merely specifies how many roots there are in a polynomial; understanding what the roots are required knowledge of elementary mathematics. Additionally, it helps with the solution of polynomial equations [tex]x^2-9=0[/tex]. Use the definition of the algebraic fundamental theorem to determine the number of roots in the equation [tex]x^2-9=0[/tex].

Now, Solving above equation

[tex]x^2-9=0[/tex]

[tex](x-3)*(x+3)=0\\x=3,-3[/tex]

As here degree of equation is 2 and root of equation are also 2.

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Answer: The one below the top.

Step-by-step explanation: In order to tell if it is a function or not, you need to do the vertical line test. By examining the graph you can see that majority of the graphs has two points in the same x-axis. The only one that pasts the test is the graph below the top one.

Answer: The second one is because there can't be two y's in a straight line of a function and all of the other graphs have two y's in a line.

Step-by-step explanation:

Step-by-step explanation:

The area of a circle is radius²· π​

12x12=144

So the answer is 144π​.

Answer:

37.71428571425567788

June has 27 coins, made up of quarters and dimes. in total, the coins are worth $4.20. Therefore, there are 10 quarters and 17 dimes she have.

Dime Coin:

A cent is a dime in US parlance, one tenth of the US dollar, and is officially called a "one cent". The name was first authorized by the Money Act of 1792.

The 10-cent coin is the smallest in diameter and the thinnest US coin in circulation, measuring 17.91 mm (0.705 inches) and 1.35 mm (0.053 inches) in diameter thickness. The obverse of the current cent features a profile of President Franklin D. Roosevelt, while the reverse depicts, from left to right, an olive branch, a torch, and an oak branch.

Quarter Coin:

The quarter (short for quarter dollar) is a United States coin denominated in 25 cents (quarter dollar). The obverse of the coin depicts George Washington in profile, and since 1998 the design of the reverse has changed frequently. In continuous production from 1796 to 1831. 955 inches (24.26 mm), 0.069 inches (1.75 mm) thick. The current version consists of two layers of cupronickel (75% copper, 25% nickel) plated on a pure copper core. The overall composition of the coin is 8.33% nickel and 91.67% copper, as the cupronickel layer accounts for 1/3 of the total weight. Its weight is 0.1823 troy ounces or 0.2000 regular Dupo ounces (5,670 grams).

We can consider that:

Let d = the number of dimes

Let q = the number of quarters

Now,

   d + q = 27                        -------------------------- (1)

⇒ d = 27 - q                      

⇒ 0.10d + 0.25q = 4.20                -------------------------- (2)    

Multiply both sides of this equation by 100 to get rid of the decimal points.

10d + 25q = 420

⇒ 10(27- q) + 25q = 420

⇒ 270 - 10q + 25q = 420

⇒ 15q = 150

⇒ q = 10

Now, Putting the value of q = 10 in equation (1) :

   d + 10 = 27

⇒ d = 27 - 10

⇒ d = 17

Therefore, there are 10 quarters and 17 dimes she have.

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Answer:

1.2

Step-by-step explanation:

[tex]\frac{v}{5}[/tex] = [tex]\frac{3}{13}[/tex]  Cross multiply and solve for v

13v = 15  Divide both sides by 13

[tex]\frac{13v}{13}[/tex] = [tex]\frac{15}{13}[/tex]

v = 1.2 rounded to the nearest tenth

Why  this works

[tex]\frac{v}{5}[/tex] = [tex]\frac{3}{13}[/tex]  we can clear the fraction by multiplying both sides of the equal sign by (5·13)

[tex]\frac{(5x13)}{1}[/tex] · [tex]\frac{v}{5}[/tex] = [tex]\frac{(5x13)}{1}[/tex] ·[tex]\frac{3}{13}[/tex]  On the left of the equal sign the 5's cancel out and the on the right of the equal sign the 13's cancel out.

13v = 5(3)

13v = 15

The four types of roots are: square roots, cube roots, fourth roots and nth roots, where n is any positive integer greater than 1.

The four types of roots are square roots, cube roots, fourth roots and nth roots. Square roots are the inverse of a number multiplied by itself. For example, the square root of 25 is 5, because 5 multiplied by 5 equals 25. Cube roots are the inverse of a number multiplied by itself twice. For example, the cube root of 27 is 3, because 3 multiplied by 3 multiplied by 3 equals 27. Fourth roots are the inverse of a number multiplied by itself three times. For example, the fourth root of 256 is 4, because 4 multiplied by 4 multiplied by 4 multiplied by 4 equals 256. Nth roots are the inverse of a number multiplied by itself n times. N is any positive integer greater than 1. For example, the fifth root of 243 is 3, because 3 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 3 equals 243.

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Characteristic of binomial distribution Mean should be n *p n is the number of trials p is the successful outcome of the process

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Relative frequency for the class with lower class limit 27 is 20.0%.

To find the relative frequency for the class with lower class limit 27, we must first find the total frequency of the data set. The total frequency is 28 (2+7+5+5+6+3=28). Since the class with lower class limit 27 has a frequency of 5, we can calculate the relative frequency of this class by dividing the frequency of the class by the total frequency.

Formula:

Relative Frequency = (Number of Students in the Class)/(Total Number of Students in the Group) x 100

Relative Frequency = (5)/(28) x 100

Relative Frequency = 0.1786 x 100

Relative Frequency = 17.86%

Rounded to one decimal place, Relative Frequency = 20.0%.

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Hope it helps.

If you have any query, feel free to ask.

Answer:

------------------------------------

If you add a parallel line through the point Q, then angle TQR will be divided by two angles.

One of them is congruent to ∠STQ and another one is congruent to ∠PRQ as alternate interior angles.

Therefore:

40m  is the sound concentrated after reflection from the back wall of the niche.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                           Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

with radius 2.60m , the cylindrical wall is a highly efficient mirror  for sound , with focal length

     f = R/2 = 2.60/2 = 1.30

in  a vertical plane the sound disperses as usual butthat radiated in a horizontal plane is concentrated in a soundimage at a distance q from the back of niche ,

so 1/p+1/q = 1/f

 so 1/1.70 +1/q = 1/1.3

  1/q = 1/1.3 - 1/1.70

 q = 40m

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The probability that the flight would be delayed when it is not raining is 12.46%.

Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. Probability measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.

To determine what is the probability that the flight would be delayed when it is not raining, the following calculation must be performed:

Probability that it will not rain = 1 - probability that it will rain

X = 1 - 0.11

X = 0.89

Probability that the flight would be delayed when it is not raining = probability that it is not raining x probability that the flight will be delayed

X = 0.89 x 0.14

X = 0.1246

0.1246 x 100 = 12.46

Therefore, the probability that the flight would be delayed when it is not raining is 12.46%.

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