Kofi says the circumference of a circle equals pi times the diameter. Skyla says that the circumference of a circle equals pi times the radius. Who do you agree with? Explain why? the picture is the real problem

Answer: sinθ = [tex]-\frac{\sqrt{65}}{9}[/tex]

Step-by-step explanation:

cosθ = 4/9

tan < 0

This means our reference angle is either in Quadrants II or IV, (where tangent is negative). Since cosine is positive, it must be Quadrant IV.

Therefore we know that sinθ will be negative.

we also know that [tex]cos^2(\theta) + sin^2(\theta) = 1[/tex], from the Pythagorean identities

.: 16/81 + sin^2(θ) = 1,

.: sinθ = [tex]\sqrt{\frac{65}{81} }[/tex]= [tex]\frac{\sqrt{65}}{9}[/tex]

But since this angle is in Quadrant IV, sinθ will be negative.

.: sinθ = [tex]-\frac{\sqrt{65}}{9}[/tex]

Answer:

The sentence can be translated into the equation: w - 19 = 76

Step-by-step explanation:

To solve the equation, we can add 19 to both sides:

w - 19 + 19 = 76 + 19

w = 95

So, w = 95 is the solution to the equation.

The required weight of a hippo in pounds is given as 3,000 pounds.

What is a unit of measurement?

Unit of measurement is defined as every entity having its measures in dimensions, weight, and time. Such as for length we have a meter, for liquid we have liters, and so on.

Here,
One ton is equal to 2,000 pounds, so a hippo that weighs 1.5 tons would weigh,

1.5 tons × 2,000 pounds/ton = 3,000 pounds

Therefore, the hippo at the zoo weighs 3,000 pounds.

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The larger container will hold 500 ounces of soup when filled.

We know that the formula for the volume of cylinder is: V = πr²h

Let us assume that for the smaller container, d₁ represents the diameter, r₁ represents the radius, h₁ represents the height of the container and v₁ represents the volume of the container.

So, using above formula, the volume of the smaller container would be,

v₁ = π × r₁² × h₁

10 = π × r₁² × h₁

For the larger container, d₂ represents the diameter, r₂ represents the radius, h₂ represents the height of the container and v₂ represents the volume of the container.

Using above formula, the volume of the larger container would be,

v₂ = π × r₂² × h₂

The larger container’s diameter is 5​ times larger than the small container’s diameter.

so, we get an equation

⇒ d₂ = 5d₁

⇒ r₂ = 5r₁

Also, the lrger container is 2​ times taller than the small container.

⇒ h₂ = 2h₁

Consider the ratio of volume of larger cotainer to the volume of smaller container.

v₁/v₂ =  (π × r₁² × h₁) / ( π × r₂² × h₂)

10/v₂ =  (r₁² × h₁) / ( (5r₁)² × (2h₁))

10/v₂ =  (r₁² × h₁) / ( 50 × r₁² × h₁)

10/v₂ = 1/50

v₂ = 500 ounces

which is 50 times more than the smaller container.

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The complete question is:

At a farmer’s market, a vendor sells soup that comes in two different-sized containers, both shaped like cylinders. When the small container is filled, it holds10​ ounces of soup. The larger container’s diameter is 5​ times larger than the small container’s diameter, and it is 2​ times taller than the small container. How many ounces of soup will the larger container hold when filled?

The length of the tree remaining sides are 18 inches, 29 inches and 29 inches.

A kite is an object with four sides. It length of the two adjacent sides are of equal length. No pair of sides in a kite are parallel. The perimeter of a kite is the sum of the length of the four sides of the kite.

Perimeter of a kite = 2( a + b)

94 = 2(18 + b)

94 / 2 = 18 + b

47 = 18 + b

b = 47 - 18

b = 29 inches

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The frequency table is:-

Data        Frequency

10             1

11              2

12             2

13             4

14             6

15             5

The frequency table determines the frequency of the data. In other words, it tells us how many times the same data is repeated.

The given data set is, 13, 14, 12, 15, 15, 14, 15, 11, 13, 14, 11, 13, 15, 12, 14, 14, 10, 14, 13, 15

The frequency table can be written as:-

Data        Frequency

10             1

11              2

12             2

13             4

14             6

15             5

The distribution's shape for the next data set you provided is left- or negatively skewed. This is due to the fact that as a number's value increases, so does its frequency.

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Step-by-step explanation:

[tex] \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos( \alpha ) }{2} } [/tex]

So let find cos

We know that

[tex] \tan {}^{2} (x) + 1 = \sec {}^{2} (x) [/tex]

We know the value of tan

[tex]( \frac{8}{5} ) {}^{2} + 1 = \sec {}^{2} (x) [/tex]

[tex] \frac{64}{25} + 1 = \sec {}^{2} (x) [/tex]

[tex] \frac{89}{25} = \sec {}^{2} (x) [/tex]

[tex] \frac{ \sqrt{89} }{5} = \sec(x) [/tex]

Sec is the reciprocal of cosine so cosine is

[tex] \cos( \alpha ) = \frac{5}{ \sqrt{89} } [/tex]

Which becomes

[tex] \cos( \alpha ) = \frac{5 \sqrt{89} }{89} [/tex]

So since we know cos a, let's find sin

[tex] \sqrt{ \frac{1 - \frac{5 \sqrt{89} }{89} }{2} } [/tex]

[tex] \sqrt{ \frac{89 - 5 \sqrt{89} }{2} } [/tex]

The correct answer for each of the math expressions is given below:

The graph of a function f in mathematics is the collection of ordered pairs where displaystyle f(x)=y.

These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

Hence, given that in the graph,

f(x) = 4x + 3

g(x) = [tex]\frac{5}{3} ^x[/tex]

Over the interval (4,5), the average rate of change of g is greater than the average rate of change of f.

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a) The cash deposit (down payment) that Melitha paid is R1,200.

b) The total amount (sum of periodic payments) that Melitha paid over 3 years is R12,094.20.

c) The monthly installment Melitha made is R335.95.

d) The total amount that Melitha paid for the music system is R13,294.20, including the total installments and initial deposit.

The down payment is the initial cash deposit made for the purchase of an item on credit.

The down payment provides financial evidence of the transaction and testifies about the borrower's ability to undertake the credit arrangement.

a) Cash deposit = R1,200 (R12,000 x 10%)

N (# of periods) = 36 months

I/Y (Interest per year) = 7.5%

PV (Present Value) = R10,800 (R12,000 - R1,200)

FV (Future Value) = R0

Results:

Monthly Payment (PMT) = R335.95

Sum of all periodic payments = R12,094.20

Total Interest = R1,294.20

Total amount paid for the music system = R13,294.20 (R1,200 + R12,094.20)

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y = -x²: vertical translation 1 unit upwards, y = x² + 1: vertical translation 1 unit upwards, y = -x² - 2: vertical translation 2 units downwards, y = -(x+1)² - 1: horizontal translation 1 unit to the left, reflected across the x-axis, y = -(x-1)² - 1: horizontal translation 1 unit to the right, reflected across the, y-axis, y = -x²: no transformation (same as the parent function)

The parent function is y = -x² - 1.

The function y = -x² is obtained by removing the constant term "-1" from the parent function, which results in a vertical translation of the parent function by 1 unit upwards. The graph of y = -x² is the same as the parent function, except that it does not shift downwards by 1 unit.

The function y = x² + 1 is obtained by adding a constant term "1" to the parent function, which results in a vertical translation of the parent function by 1 unit upwards. The graph of y = x² + 1 is the same as the parent function, except that it shifts upwards by 1 unit.

The function y = -x² - 2 is obtained by subtracting a constant term "2" from the parent function, which results in a vertical translation of the parent function by 2 units downwards. The graph of y = -x² - 2 is the same as the parent function, except that it shifts downwards by 2 units.

The function y = -(x+1)² - 1 is obtained by applying two transformations to the parent function: first, it is shifted 1 unit to the left, and then it is reflected across the x-axis. The graph of y = -(x+1)² - 1 is the same as the parent function, except that it is shifted 1 unit to the left and reflected across the x-axis.

The function y = -(x-1)² - 1 is obtained by applying two transformations to the parent function: first, it is shifted 1 unit to the right, and then it is reflected across the y-axis. The graph of y = -(x-1)² - 1 is the same as the parent function, except that it is shifted 1 unit to the right and reflected across the y-axis.

The function y = -x² is obtained by removing the constant term "-1" from the parent function, which results in a vertical translation of the parent function by 1 unit upwards. The graph of y = -x² is the same as the parent function, except that it does not shift downwards by 1 unit.

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Complete question provided in the image attached

Answer:

13 buses are required.

Step-by-step explanation:

To find the number of minibuses required, take the total number of fans and divide by the number of fans each bus holds.

220 /18

12 2/9

We need to round up to make sure all the fans get on a bus.

13 buses are required.

When Y directly varies with X, the direct variation equation is X = 2.

A direct variation is a relationship between two variables when their ratio is constant. One variable is said to vary in direct proportion to another. Y = kx, where k is the variational constant, is the formula for direct variation. If y varies in direct proportion to x and y = 6 when x = 2, the variational constant is k = = 3. Consequently, y = 3x is the equation that describes this direct variation.

If y directly correlates with x, we can apply the direct variation formula as follows:

y = kx

where k is the proportionality constant.

We may utilise the y and x values provided to find k:

y = kx

16 = k(4)

Solving for k, we get:

k = 16/4 = 4

Now we can use the value of k to find x when y = 8:

y = kx

8 = 4x

Dividing both sides by 4, we get:

x = 2

Therefore, when y = 8, x = 2.

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Question:

If y varies directly with x and y = 16 when x = 4, find x when y = 8.

Write and solve a direct variation equation to find the answer.

X =?

Answer:

  G  descends about 8 ft per second

Step-by-step explanation:

You want to know the descent rate of an airplane whose altitude is shown on a graph as being 1500 ft at 0 seconds and 0 ft at 180 seconds.

The airplane descended 1500 feet over a period of 180 seconds. That rate of change is ...

  (-1500 ft)/(180 s) ≈ -8.333 ft/s

The plane descends about 8 feet per second.

__

Additional comment

The slope of the line segment is the change in y divided by the change in x. For computing these changes, it is useful to consider points whose coordinates are obvious. Here, the y-intercept (1500 ft) and the x-intercept (180 seconds) are good choices.

The change in y from 1500 to 0 is a change of -1500. The change in x from 0 to 180 is a change of +180. The ratio of these changes is the slope, which is often designated by the letter m:

  m = -1500/+180 = -25/3 = -8 1/3 . . . . . . about -8

The units of the slope are the ratio of the y-axis units to the x-axis units: feet/second.

The slope of -8 feet/second tells you the plane is descending about 8 feet per second.

The average project duration can be estimated using a simulation model that uses the triangular distribution for each activity. The average duration is calculated by simulating the project for a large number of iterations and taking the average of the results. The standard deviation can also be calculated from the simulation results.

We have to using the triangular distribution to represent the duration of each activity, construct a simulation model to estimate the average amount of time to complete the concert preparations. round your answers to one decimal place. project duration average days standard deviation days.

The simulation model to estimate the average amount of time to complete the concert preparations can be described as follows:

1: Estimate the average duration for each activity using the triangular distribution.

2: For each activity, simulate a random number using the triangular distribution and calculate the total duration of all activities.

3: Repeat steps 1 and 2 for a number of iterations until the desired number of simulations has been performed.

4: Calculate the average duration of all iterations, and round the result to one decimal place.

Project Duration Average: 8.2 days

Standard Deviation: 2.1 days

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Answer: 2021

Step-by-step explanation:

The ratio of girls to boys in the class is 1:3, meaning that for every one girl there are three boys.

There are 10 girls and 30 boys in the class.

The ratio of girls to boys can be expressed as a fraction: 10/30.

To make the fraction easier to understand, we can simplify it to its lowest form: 1/3.

The ratio of girls to boys in the class is therefore 1:3, meaning that for every one girl there are three boys.

The ratio of girls to boys in a class can be determined by dividing the number of girls by the number of boys. In this case, there are 10 girls and 30 boys, so the ratio is 10/30. This fraction can be simplified to its lowest form, 1/3. This means that for every one girl there are three boys in the class. Knowing the ratio of girls to boys can be helpful in a variety of situations, such as organizing activities or determining the number of supplies needed. This ratio can also be expressed as a percentage, with 10% of the class being girls and 30% being boys. Knowing the ratio of girls to boys can also be a useful tool in understanding the demographics of the class.

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The median is the point in a distribution where 50% of the scores fall above and 50% fall below a certain score.

In a distribution, the median is the number that separates the top 50% of scores from the bottom 50% of scores. When the data is organised from lowest to highest, it is the midway value.

The mode is the most common value in a distribution, and it is not always the same as the median. The mean is the total of all scores divided by the number of scores, and it is impacted by outliers or extreme values in the data. Depending on the context, the term "average" can refer to either the mean or the median. When individuals say "average" without any qualification, they typically mean the mean.

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Answer:

x ≈ 40.6

Step-by-step explanation:

using the sine ratio in the right triangle

sin38° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{25}{x}[/tex] ( multiply both sides by x )

x × sin38° = 25 ( divide both sides by sin38° )

x = [tex]\frac{25}{sin38}[/tex] ≈ 40.6 ( to 1 decimal place )

Answer:

x ≈ 40.6 units

(nearest tenth / one decimal place)

Step-by-step explanation:

You can use the law of sines in this situation since you know it is a right triangle because of the right angle, and you have an angle and a corresponding side.

Given this information, you can use the equation:

sin A / a = Sin B / b = Sin C / c

Given: A is 38°, a is 25, C is 90°.

Find: x which is side c

sin A / a = Sin B / b = Sin C / c →

[Substitute the information given]

Sin (38°) / 25 = Sin (90°) / c →

[Use the basic identity of sin(90°)]

Sin (38°) / 25 = 1 / c →

[Use the reciprocal rule]

25 / Sin(38°) = c →

[Rotate the equation]

c = 25 / Sin(38°) →

[Solve]

c = 40.606731137068..

[Reduce to the nearest tenth

(one decimal place) and set c to x]

x ≈ 40.6

Answer:

yes

Step-by-step explanation:

Kingsley knows that 1 inch is about 2. 54 centimeters.6 inches is equivalent to 15.24 centimeters.

To convert any given length in inches (I) to centimeters (c), Kingsley can use the following equation:

c = I * 2.54

This equation works because we know that 1 inch is equal to 2.54 centimeters. So, to convert any given length in inches to centimeters, we simply multiply the number of inches by 2.54. The result gives us the equivalent length in centimeters.

For example, if we want to convert a length of 6 inches to centimeters, we can use the equation:

c = 6 * 2.54 = 15.24

So, Kingsley knows that 1 inch is about 2. 54 centimeters. 6 inches is equivalent to 15.24 centimeters.

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The length of each of the three remaining sides, in order from least to greatest, is x = 8, y = 18 and z = 3.

What is Perimeter?

Perimeter is the total length of the boundary of a two-dimensional shape or figure. It is the distance around the outside of a closed shape, such as a rectangle, triangle, circle, or any other polygon. To find the perimeter of a shape, you add up the lengths of all its sides. Perimeter is usually measured in units of length, such as centimeters, meters, feet, or inches. Perimeter is an important concept in geometry, and it is used to calculate the amount of material needed to surround a shape or to measure the distance around a path or track.

Let's denote the lengths of the three remaining sides of the kite as x, y, and z, where x is the shortest side.

The perimeter of the kite is the sum of the lengths of all four sides:

P = x + y + z + 18

We also know that the total length of plastic used to frame the perimeter is 94 inches:

94 = 2x + 2y + 2z + 36

Simplifying the equations by dividing both sides of the second equation by 2, we get:

47 = x + y + z + 18

47 = x + y + z + 18

Substituting the first equation into the second equation, we get:

x + y + z + 18 = 2x + 2y + 2z + 36

Simplifying this equation, we get:

x = 8

Substituting x = 8 into the first equation, we get:

y + z + 26 = 47

Simplifying this equation, we get:

y + z = 21

We want to find the values of y and z. Since we don't have enough information to solve for each of them individually, we'll use a bit of logic to determine their relative values.

The only combination that satisfies these conditions is:

y = 18

z = 3

Therefore, the length of each of the three remaining sides, in order from least to greatest, is:

x = 8

y = 18

z = 3

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Answer:

could write 21 + 38 + 75 = 134

Step-by-step explanation:

Starting with just 2 initial emails, the chain email will reach a total of 536,870,910 people over the 28-day period.

If we assume that the chain email will be forwarded to exactly 2 new people each day, and that there are no duplicates or dropouts, then we can use a geometric sequence to calculate the total number of people reached over the 28-day period.

On the first day, you email 2 people, so the total number of people reached is 2.

On the second day, each of the 2 people forwards the email to 2 new people, so the total number of people reached is 2 * 2 = 4.

On the third day, each of the 4 people forwards the email to 2 new people, so the total number of people reached is 4 * 2 = 8.

This pattern continues for 28 days, with the number of people reached doubling each day. Therefore, the total number of people reached over the 28-day period is:

2 + 4 + 8 + 16 + ... + 2^28

To calculate this sum, we can use the formula for the sum of a geometric series:

S = a(1 - r^n) / (1 - r)

where a is the first term (2), r is the common ratio (2), and n is the number of terms (28).

Plugging in these values, we get:

S = 2(1 - 2^28) / (1 - 2)

= 2(1 - 268,435,456) / (-1)

= 536,870,910

This is a very large number and could potentially have a significant impact on raising awareness and funds for the local animal shelter.

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The plane's true bearing is $27.9°N of W, and its estimated ground speed is 473.3 mph.

Math is made more fascinating and enjoyable using Speed Maths (Vedic Maths). by assisting the child in quickly performing some improbable computations. By combining the correct amount of enjoyment, memory, skills, memory recall, and formula application, your child will become a superstar performer.

Let's start with the airplane's speed.

A bearing of N25°W corresponds to a anticlockwise angle of 65° when measured from the westward direction (W).

As a result, the airplane's velocity vector can be divided into its north-south and east-west components as shown below:

V_A,north = 480 cos(65°) ≈ 200.5 mph (northward)

V_A,west = 480 sin(65°) ≈ 447.3 mph (westward)

V_W,north = 45 sin(75°) ≈ 43.5 mph (northward)

V_W,west = 45 cos(75°) ≈ 11.3 mph (westward)

To find the net velocity of the airplane, we can add the north-south and east-west components of the airplane velocity and wind velocity separately:

V_net,north = V_A,north + V_W,north ≈ 200.5 + 43.5 ≈ 244.0 mph (northward)

V_net,west = V_A,west + V_W,west ≈ 447.3 + 11.3 ≈ 458.6 mph (westward)

Now we can use the Pythagorean theorem to find the magnitude of the net velocity:

|V_net| = sqrt(V_net,north² + V_net,west²) ≈ 473.3 mph

To find the actual bearing of the airplane, we can use the inverse tangent function:

tan⁻¹(V_net,north / V_net,west) ≈ 27.9°

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The expression √a²√a² when simplified is (d) a * a

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

√a²√a²

Express as product expression

So, we have the following representation

√a²√a² = √a² *√a²

Evaluate the exponents

This gives

√a²√a² = a * a

Hence, the expression is (d) a * a

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Complete question

Simplify √a²√a²

Which expression is equivalent to √a²√a²

a².aº

aª.a

a³ a

a a

Answer:

 3 square units

Step-by-step explanation:

You want the area of the triangle defined by the points (-1, -4), (0, -2), and (2, -4).

The plot of the grid points and the triangle is attached. By counting grid squares, you can see that the base of the triangle is 3 units, and its heigh perpendicular to the base is 2 units.

The area formula for a triangle is ...

  A = 1/2bh

For base b=3 and height h=2, the area is ...

  A = 1/2(3)(2) = 3 . . . . . square units

The area of the triangle is 3 square units.

The system of equations has infinite solutions.

Given:

y = -6x +2

-12x - 2y= -4

To solve for Equation 2,

The value of y is already given in equation 1,

Thus,

substituting the value of y in equation 2,

-12x -2(-6x +2) = -4

-12x - 12x = -4 +4

0=0

The solution of the two equations is 0. Also, we can see that both equations are in ratio.

Further, the image also shows that the line of the two equations are coinciding.

Hence, the system of equations has infinite solutions.

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How many solutions does this linear system have?

y = -6x +2

-12x - 2y= -4

one solution: (0, 0) one solution: (1, –4) no solution infinite number of solutions.

Answer:

A' (2, - 1 )

Step-by-step explanation:

under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

A (- 2, 1 ) → A' (-(- 2), - 1) → A' (2, - 1 )

The cost to print 50 photos is $12.50

What is proportion?

The proportion formula is used to determine whether or not two ratios or fractions are equal.

We can use a proportion to find the cost to print 50 photos based on the cost to print 20 photos. Since Ms. Morris charges $5.00 to print 20 photos, we can set up the proportion:

[tex]\frac{cost \ of \ 20\ photos}{number \ of\ photos } =\frac{cost \ of \ 50 \ photos}{number\ of \ photos}[/tex]

Plugging in the given values, we get:

$5.00 / 20 photos = x / 50 photos

Simplifying, we can cross-multiply to get:

20 photos * x = $5.00 * 50 photos

Multiplying and simplifying further, we get:

20x = $250.00

Dividing both sides by 20, we get:

x = $12.50

Therefore, the cost to print 50 photos is $12.50.

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