The radius of a circle is 6 inches. What is the area of a sector bounded by a central angle measuring 120°

The population of Blueville in 2012 from the exponential function is;

⇒ 9000

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Here, We are given the equation of the function as;

⇒ f (x) = 9000(0.985)ⁿ

where;

x is the number of years since 2012

Thus, In the year 2012, it means that n will be 0,

Hence, As number of years is 0 by then we get;

f(0) = 9000(0.985)⁰

f(0) = 9000 * 1

f(0) = 9000

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85 degrees Celsius is equal to 185 degrees Fahrenheit.

To convert Celsius (C) to Fahrenheit (F), you can use the formula:

F = (C × 9/5) + 32

where C is the temperature in Celsius and

F is the temperature in Fahrenheit.

Using this formula,

we can convert 85 degrees Celsius to Fahrenheit as follows:

F = (85 × 9/5) + 32

F = 153 + 32

F = 185

The average body temperature is widely regarded to be between 36.5 °C (97.7 °F) and 37.5 °C (99.5 °F).

Fever is defined as an increase in body temperature of one degree Celsius or more over the average of 37.0 degrees Celsius (98.6 degrees Fahrenheit).

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The ratio of cars to trucks is 1 to 3, which means that for every three trucks, there is one car. Since there are 51 trucks, this means that there is 17 cars (51/3 = 17). Therefore, the dealer has 17 cars for sale.

The automotive dealer sells both cars and trucks and the ratio of cars to trucks on the lot is 1 to 3. This means that for every three trucks, there is one car. Therefore, if there are 51 trucks currently for sale, then the number of cars can be determined by dividing this number by 3. This equals 17 cars. Thus, the dealer has 17 cars for sale.

The ratio of cars to trucks is 1 to 3, which means that for every three trucks, there is one car. Since there are 51 trucks, this means that there is 17 cars (51/3 = 17). Therefore, the dealer has 17 cars for sale.

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Based on the data, it can be inferred that the magnitude and direction of PQ is 9.5 north of east for 6.1 miles (option D).

To identify the magnitude and direction of the plane, we must carefully look at the information in the graph and identify the option that corresponds to the information.

So, we can say that this is moving from the south to the north and from the west to the east, so options A and C would be ruled out. Now we must identify the magnitude and degrees. Taking a completely horizontal line as a reference, we could say that the plane has 9.5 degrees in its trajectory. So the correct option would be D.

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The value of probability P (even | less than 3) is, 1/3.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

A 6-sided die is tossed.

Here, Two numbers 1 and 2 are less than 3.

Hence, The value of P (even | less than 3) is,

⇒ 2 / 6

⇒ 1 / 3

Thus, The value of P (even | less than 3) is, 1/3.

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The most precise term for quadrilateral ABCD with vertices A(4, 4), B(5, 8), C(8, 8) is a kite.

Option C is the correct answer.

A kite is a quadrilateral where the adjacent sides are equal which means there are two pairs of equal sides.

We have,

Quadrilateral ABCD:

A = (4, 4)

B = (5, 8)

C = (8, 8)

D = (8, 5)

Now,

A__________B

|                      |

|                      |
|                      |

D_________ C

We see the distance between the two points.

AB = √(8 - 4)² + (5 - 4)² = √(4² + 1) = √17

AD = √(5 - 4)² + (8 - 4)² = √(1² + 4²) = √17

AB = AD

BC = √(8 - 8)² + (8 - 5)² = √9 = 3

CD = √(5 - 8)² + (8 - 8)² = √9 = 3

BC = CD

AB and AC are adjacent sides.

CD and DB are adjacent sides.

So,

The quadrilateral ABCD is a kite.

Thus,

The quadrilateral ABCD is a kite.

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Answer:

15 over 1

Step-by-step explanation:

no explanation

Answer:

-4a² + 7a + 4

Step-by-step explanation:

Subtract -4 + 3a² from 7a - a².

(7a - a²) - (-4 + 3a²) =

= 7a - a² + 4 - 3a²

= -4a² + 7a + 4

Answer:

x+y-200=0

Step-by-step explanation:

ax = x

by = y

c = 200 but we convert it to negative 200 after moving it from the RHS to LHS

So x+y=200 will be x+y-200=0 in the form ax + by + c =0

The converted to product four times as much in the CSTR than it was in the PFR that is 400%.

Conversion is a term used to describe the process of transferring a reactant into a product.

In this case, the reactant is being transferred from a 72 l plug flow reactor (PFR) to a 24 l continuous stirred tank reactor (CSTR). The conversion achieved by this process can be determined by calculating the ratio of product to reactant in the CSTR.

Specifically, if the PFR has a conversion of x%, then the conversion achieved in the CSTR will be x/(1-x), where x is the conversion in the PFR.

Therefore, if the PFR has a conversion of 80%, then the CSTR will have a conversion of 80/(1-80) = 400%.

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185 centimeter is approximately equal to 6.0696 feet

To convert 185cm to feet, we can use the following formula:

1 cm = 0.0328 feet

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The distance in feet = conversion factor × The distance in centimeter

Substitute the values in the equation

185 cm = 185 x 0.0328

Multiply the numbers

= 6.0696 feet ( rounded to four decimal places )

Therefore, 185cm is 6.0696 feet.

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Answer: The scale factor is 2/5 and the length of BC is 10

Given: We have to find the factor of dilatation by looking at the pre-image ABCD and the image A'B'C'D' and then we have to find the length of the segment BC.

Explanation: To calculate the dilatation factor we have to look at two given segments, the side D'C' and the side DC since the segment DC belong to the pre-image and the segment D'C' belongs to the image we know that the factor of dilation will be the same for the change relation between those two sides and any other side of the figure so:

Scale factor = 2/5

Now in order to find the measure of the side BC we have to multiply 4 by the inverse scale factor because we are going from the image to the pre-image so:

Length of BC = 4 * 5/2 = 10

The price after the discount is,

⇒ $58.5

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

A jersey originally cots $50.

And, It was marked up 30% after a championship win and then discounted 10% a few months later.

Now, The markup price is,

⇒ $50 + 30% of $50

⇒ $50 + 30/100 × $50

⇒ $50 + $15

⇒ $65

And, After 10% discount the price is,

⇒ $65 - 10% of $65

⇒ 65 - 10/100 × 65

⇒ $65 - $6.5

⇒ $58.5

Thus, The price after the discount is,

⇒ $58.5

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the dimensions of the largest mosaic he can make on that wall are 840 by 700cm.

What is a rectangle?

Rectangles are quadrilaterals in the Euclidean plane of geometry that have four right angles. A closed, four-sided rectangle is a two-dimensional shape, according to a number of definitions, as is an equiangular quadrilateral. All of a rectangle's angles are exactly 90 degrees, and its opposite sides are equal and parallel to one another.

Rectangle area is equal to A = a*b.

From the given data, the dimension of the scale model shown as a plan for a large wall mosaic are: 10m =1000cm

Now the wall of width 700cm

The scale factor 700/10 =7

hence increase in width by same scale factor 70*12 = 840

Therefore, the dimensions of the largest mosaic he can make on that wall are 840 by 700cm.

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Answer:

Inequality form: -2 ≤ x ≤ 1

Interval Notation: [-2, 1]

Step-by-step explanation:

Move all terms not containing x from the center section of the inequality.

Answer:

yes

Step-by-step explanation:

yes

Step-by-step explanation:

The prime factor of the 144 is 24 x 32. The exponents in the prime factorisation are 4 and 2. Add the number 1 with the exponents and multiply it. (4+1)(2+1) = 5 x 3 = 15.

Answer:hello again

Step-by-step explanation:

Answer:

5.90551 inches

Step-by-step explanation:

To solve for the number of inches, we can use this equation:

15 × 0.393701 = 5.90551

Therefore, for every 15 cm, it is equivalent to 5.90551 inches.

Using pattern, The sum of the digits obtained when you divide (1024 - 1) by 11 is 12.

In the real world, in artificial design, or in abstract concepts, a pattern is a regularity. As a result, a pattern's components repeat in a predictable way. An example of a geometric pattern is one that repeats geometric shapes, much like a wallpaper pattern would. Patterns can be immediately observed with any sense.

Given that 99=11×9;  1001=11×91 and 9999=11×909

(1024-1) = 11 * x

x = 1023 ÷ 11

x = (990 + 33) ÷ 11

x = (90* 11 + 3*11) ÷ 11

x = 90 + 3

x = 93

So the sum of digits is 9 + 3 = 12

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The linear equation for salary will be S=$35000+$2000n where n=no. of years.

What is a linear equation, exactly?

When the greatest power of a variable is 1, the equation is said to be linear. Another term for it is a one-degree equation. The standard form of a linear equation with one variable is Ax + B = 0. There are three variables in this equation: x, A, and B. A denotes a coefficient. A linear equation with only two variables is commonly written as Ax + By = C. There are three more constants in addition to the constant C: the variables x and y, the coefficients A and B, and the variables.

Now,

Given that Initial salary=$35000

Increment of $2000 every year

Then after n years salary will be

S=35000+2000n

where n=no. of years

hence,

          The linear equation for salary will be S=$35000+$2000n.

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Answer: 29

Step-by-step explanation:

40 - 5 = 35

35 - 6 = 29

So, 29 + 6 = 5 less than 40

Answer: The number is 29 and the Sum is 35

Step-by-step explanation:

How you set up the equation 6+x = 40-5

Subtract 5 from 40 and you get 6+x = 35

Now subtract 6 from 35 to find your missing variable x = 35-6

x = 29

Assuming that the iron plate is lifted to a height against the gravitational force, we can use the formula for potential energy:

Potential Energy = mass x gravity x height

where mass is in kg, gravity is 9.81 m/s^2, and height is in meters.

Rearranging the formula to solve for height, we have:

height = Potential Energy / (mass x gravity)

Plugging in the given values, we have:

height = 2000 J / (10 kg x 9.81 m/s^2)

height = 20.34 meters (rounded to two decimal places)

Therefore, the height of the iron plate is approximately 20.34 meters.

The equation can be used to solve for b is b = 5 / tan30°

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a triangle, ∠ BCA = 90°, ∠ CAB = 30°, we need to find the equation for AC,

The equation for AC(b) =

tan30° = 5/b

b = 5 / tan30°

Hence, the equation can be used to solve for b is b = 5 / tan30°

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By doing some changes of units, we will see that Oliver has the tallest plant.

Here we need to do some changes of units, let's write all the units in centimeters.

First, we know that 1m = 100cm

Then:

0.38m = 0.38*100cm = 38cm

We also know that:

1 mm = 0.1cm

Then:

420mm = 420*(0.1)cm = 42cm

Then the 3 measures are:

Oliver: 45cm

Neil: 38cm

Elizabeth: 42cm

We can see that Oliver has the tallest tomato plant.

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Using the recursive formula we will see that:

f(2) = 5

Here we have a sequence such that we know that:

f(0) = 2

And the recursive formula is:

f(n + 1) = -2*f(n) + 3

So, first let's find f(1), to get that we use n = 0.

f(1) = -2*f(0) + 3

    = -2*2 + 3 = -4 + 3 = -1

And the next term is:

f(2) = -2*f(1) + 3

     = -2*-1 + 3

    = 2 + 3 = 5

Then the correct option is the third one.

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Answer: If pqr ~ stu, then we know that the corresponding sides are proportional.

We have pq=25 and st=10, so we can find the ratio of corresponding sides as:

25 / 10 = 2.5

This means that each side of stu is 2.5 times smaller than the corresponding side of pqr.

The perimeter of pqr is 75, so we can find the length of the other sides by subtracting the length of pq from the perimeter and dividing by 2:

(pq + qr + rp)/2 = (25 + qr + rp)/2 = 75/2

25 + qr + rp = 75

qr + rp = 50

Since pqr ~ stu, we know that the ratio of perimeters is also 2.5. Therefore, the perimeter of stu is:

Perimeter of stu = 2.5 (st + tu + us)

We know st=10, so we can find the other sides as:

tu = qr / 2.5 = 50 / 2.5 = 20

us = rp / 2.5 = 50 / 2.5 = 20

Therefore, the perimeter of stu is:

Perimeter of stu = 2.5 (10 + 20 + 20) = 2.5 (50) = 125

So the perimeter of stu is 125.

Step-by-step explanation:

A 15-ounce bottle of the same medicine contains 90 doses.

The unitary method is a method used to solve problems related to proportionality. It involves finding the value of a single unit or the value of a given quantity when the value of one or more units is known.

In the given problem, we will find the number of doses in 1 unit from that will find the number of doses in a 15-ounce bottle.

Here we have

A 6-ounce bottle of medicine contains 36 doses.

Number of doses in a 1-ounce bottle

= 36/6 = 6 doses  

Then the number of doses in a 15-ounce bottle of medicine  

= 15 × Number of doses in 1 ounce

= 15 × 6

= 90

Therefore,

A 15-ounce bottle of the same medicine contains 90 doses.

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hese two equations can be used to solve for the values of c and m.

Let's define:

c = the number of commercials on which Nakeisha's songs were played

m = the number of movies on which Nakeisha's songs were played

Based on the problem statement, we can set up the following system of equations:

Nakeisha's songs were played on 2 more commercials than movies:

c = m + 2

Nakeisha's total earnings on the royalties from all commercials and movies was $760:

30c + 110m = 760

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Answer:

means

Step-by-step explanation:

The first term and the fourth term of a proportion are called extreme terms, and the second term and the third term are called means.

A) Sum of (Score) ΣX equal to 63 and (Mean)M equal to 7.

B) Sum of Score ΣX equal to 96.

C) On the other side of the seesaw, the sixth score must be one point below the mean.

D)The sample has 7 scores.

E) To get the mean for the combined sample, the scores for each sample added together are 6.

A) Here we have to calculate the sum of scores (ΣX),

Add all of the scores together:

8 + 2 + 5 + 7 + 12 + 9 + 11 + 3 + 6

= 63

We sum up all of the scores and divide by the total number of scores (in this example, 9), which gives us the mean (M):

M = ΣX / n

M = 63 / 9

M = 7

B)The following formula may be used to get the value of X when the sample size (n) is 12 and the mean (M) is 8.

ΣX = M x n

ΣX = 8 x 12 = 96

Therefore, ΣX = 96.

C) The sixth score would need to be one point below the mean to balance the total if we know that the first five scores are all one point above the mean. This is thus because, like a seesaw, the mean represents the point of equilibrium in a group of scores. The seesaw is skewed up on one side if five scores are above the mean; the only way to balance it out is to position the sixth score on the other side, one point below the mean.

D) The following formula may be used to get the total number of scores in a sample with a mean (M) of 8 and a sum (X) of 56 scores:

ΣX = M x n

56 = 8 x n

n = 7

Hence, The sample has 7 scores.

E) The sum of the scores for each sample must first be determined in order to get the mean for the combined sample:

First sample, n = 10, M = 8, and the following:

ΣX1 = M x n

ΣX1 = 8 x 10

ΣX1 = 80

Second sample with n = 5 and M = 2:

ΣX2 = M x n

ΣX2 = 2 x 5

ΣX2 = 10

We just put the two amounts together to obtain the combined sample's overall sum of scores (ΣX):

ΣX = ΣX1 + ΣX2

ΣX = 80 + 10

ΣX = 90

We divide the entire sum of scores by the total number of scores to determine the mean for the combined sample:

M = ΣX / n

M = 90 / (10 + 5)

M  = 6

Hence, six is the sample's overall mean.

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