The formula for the area of a circle is shown, where d
is the diameter. A=πd2(exponent is the2) over 4


What is the equation for the diameter d
of a circle in terms of the area A? a: d=4πA. b: d=A4π−−√ c: d=2Aπ−−√. d: d=4π−−√A2

The distance between two trains is 224 miles.

The speed of one train is 75 miles per hour and the speed of the second train is 85 miles per hour.

The train is moving towards each other. So the relative speed of the train is,

So the distance between trains 224 miles is covered at the speed of 160 miles per hour.

Determine the time after which trains meet each other.

So two trains meet after 1.4 hours.

Answer: 1.2 grams

Step by step explanation : divide the mass value by 1000

A study compared two alloys for lead-free soldering, measuring the melting points of 21 pieces from each. Alloy 1 had a mean and standard deviation denoted as x₁ and s₁, respectively.

In this study, the researchers evaluated the melting points of solder made from two different alloys intended for lead-free soldering.

They collected a random sample of 21 pieces from each alloy and measured the temperature at which each piece melted.

The summary indicates that the mean and standard deviation of the sample for alloy 1 are represented as x₁ and s₁, respectively.

These values provide important information about the central tendency and variability of the melting points for the samples obtained from alloy 1, which can be used for further analysis and comparison with the other alloy.

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Answer:

(-8) is the missing value here, so

the coordinates will be (-8,8)

Answer:

-8

Step-by-step explanation:

→ Substitute y = 8 into -4x - y = 24

-4x - 8 = 24

→ Add 8 to both sides to isolate -4x

-4x = 32

→ Divide both sides by -4 to isolate x

x = -8

Answer:

y-4 =-5(x+1)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line

y-4 = -5(x- -1)

y-4 =-5(x+1)

Answer:

y-4 = -5 (x- (-1))

Step-by-step explanation:

blank 1 = -4

blank 2 = -5

blank 3 = -1

The four steps to solve a radical equation are: Isolate the radical, square both sides, solve the resulting equation, and check for extraneous solutions.

To solve a radical equation, follow these four steps:

1. Isolate the radical: Move any terms that don't contain the radical to the other side of the equation. This step ensures that the radical term is alone on one side of the equation.

2. Square both sides: Raise both sides of the equation to the power that eliminates the radical. If you have a square root, square both sides. If you have a cube root, cube both sides, and so on. This step helps eliminate the radical.

3. Solve the resulting equation: Once you've eliminated the radical, solve the resulting equation for the variable. At this stage, you should have an equation without any radicals.

4. Check for extraneous solutions: After finding a potential solution, substitute it back into the original equation and verify if it satisfies the equation. Sometimes, in the process of eliminating the radical, you may introduce extraneous solutions that don't actually satisfy the original equation. If the substituted solution doesn't satisfy the equation, discard it as an extraneous solution.

By following these four steps, you can solve radical equations systematically and ensure that you find all valid solutions.

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The number of packages of hot dogs is 4 hot dogs.

The number of packages of hamburgers is 5 hamburgers.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of hamburgers respectively, and then translate the word problem into algebraic equation as follows:

Since Mrs Vahey bought a total of 9 hot dogs or hamburgers, the linear equation to represent this is as follows:

x + y = 9

Additionally, hot dogs are $1.50 and hamburgers are $4, and she spent a total of $26;

1.50x + 4y = 26

Next, we would use an online graphing calculator to plot the above system of linear equations in order to determine the solution (point of intersection) as shown in the graph attached below.

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Answer:

-13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Step-by-step explanation:

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

Answer:

30 km/h car

Step-by-step explanation:

From analysis the   car traveling at 30 km/h has greater kinetic energy

we can deduce it from the expression of kinetic energy which is

\(KE=\frac{1}{2} mv^2\)

Assuming the mass m= 1 kg

For the 30 km/h

\(KE=\frac{1}{2}*1*30^2 \\\\KE=\frac{1}{2}*1*900\\\\\KE=450 J\)

For the 15 km/h

\(KE=\frac{1}{2}*2*15^2 \\\\ KE=\frac{1}{2}*2*225 \\\\\ KE=\frac{1}{2}*450 J\\\\\ KE=225 J\)

Though the kinetic energy is a function of mass and velocity, but from our analysis the faster moving object has more KE

Answer:

Length is 14 yd width is 11 yd

Step-by-step explanation:

The equation to find the perimeter is  ( 2 x Length ) + ( 2 x Width ), so first you divide the perimeter by 2 so we only have to add length + width, you get 25 yds. Since the length is 3 yds longer than width, you can mentally assume Length is going to be 14 yds and width is 11 yd, since Length is 3 yd longer, and finally if you add them together, 14 + 11 = 25. (Apologies if you don't understand I'm not good at explaining)

The equation x = 5t^2 + 4t best matches the motion diagram shown in the figure.

To determine which equation best matches the motion diagram shown in the figure, we need to analyze the characteristics of the diagram and compare them to the given equations.

From the figure, we observe that the motion starts from a positive position, then reaches a peak, and finally returns to a negative position. This indicates that the motion involves a parabolic path.

Among the given equations, the equation that represents a parabolic path is:

c) x = 5t^2 + 4t

This equation represents a quadratic function with a positive coefficient for the squared term, indicating an upward-opening parabola. Additionally, it includes a linear term (4t) that contributes to the overall shape of the parabolic path.

Therefore, the equation x = 5t^2 + 4t best matches the motion diagram shown in the figure.

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Answer:

(a) 1416

(b) 2 × 2 × 2 × 3 × 59

Step-by-step explanation:

The prime numbers between 0 and 10 are 2, 3, 5,7 (1 is not considered prime)
Therefore m = 2357

The square numbers between 0 and 10 are  1, 4, 9 and in descending order 9,4.1so n = 941

m - n = 2357 - 941 = 1416

Unique prime factors of 1416 are 2,3,59

1416 as a product of prime factors = 2 × 2 × 2 × 3 × 59

$50 can purchase 40 sports drinks.

A purchase is the acquisition of goods or services in exchange for money or other forms of payment. It is a common transaction that takes place in everyday life and can range from small purchases such as buying groceries, to larger purchases such as buying a car or a house.

When making a purchase, a buyer typically identifies a need or desire for a particular product or service, and then selects a seller or retailer who offers the desired item. The buyer then pays the seller the agreed-upon price, either in cash, by credit card, or through other forms of payment.

Purchases can take place in a variety of settings, including physical stores, online marketplaces, and through person-to-person transactions. The process of making a purchase may involve comparing prices, negotiating with the seller, and evaluating the quality and features of the product or service being purchased.

In addition to individual purchases, businesses and organizations also make purchases to acquire the resources and materials needed to operate and grow. This can include purchasing raw materials, equipment, and services from suppliers, as well as acquiring other businesses through mergers and acquisitions.

Overall, purchases are an important aspect of economic activity and play a crucial role in the functioning of markets and the economy as a whole.

Let's start by finding the cost of one sports drink:

$29.99 / 24 = $1.25 per sports drink

To find how many sports drinks can be purchased for $50, we divide $50 by the cost of one sports drink:

$50 / $1.25 per sports drink = 40 sports drinks

Therefore, $50 can purchase 40 sports drinks.

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The formula for the volume of a cone is:

V = (1/3)πr²h

where r is the radius of the base, h is the height of the cone, and π is pi.

In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:

h² = s² - r²

h² = 17² - 8²

h² = 225

h = 15

Now that we have the height, we can plug in the values for r and h into the formula for the volume:

V = (1/3)π(8²)(15)

V = (1/3)π(64)(15)

V = (1/3)(960π)

V = 320π

Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.

Answer:

22) 3 in<x<11 in

23) 8 cm<x<26 cm

24) 0 ft<x<10 ft

25) 9 m<x<31 m

26) 2 km<x<14 km

27) 13 in<x<61 in

Step-by-step explanation:

It has to be greater than the difference and smaller than the sum.

22) 7-4=3, 4+7=11, so the answer is 3<x<11

23) 8<x<26

24) 0<x<10

25) 9<x<31

26) 2<x<14

27) 13<x<61

At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

The speed of an object is the ratio of distance and time it takes for the object to travel that distance.

Mathematically,

S = D/T

where

S is velocity

D is the distance traveled or distance traveled

T is the time it takes to travel that distance

Velocity is considered a scalar quantity. A scalar size only has a size. It does not provide information about the direction of object movement.

If an object moves at a constant speed, it means that the object moves the same distance in the same time interval.

Acceleration of an object is the ratio of velocity and time. vector size. Vector quantities have both magnitude and direction.

Mathematics,

a = v/t

When an object is in motion, its acceleration is never zero.

When an object moves, it moves a constant distance over time. Therefore, body positions cannot be the same from the same coordinate system.

Given in the question:

First the plane was travelling at a constant rate of 250  miles per hour.

Initial height was 20000 feet

Now,

As the speed increases and travels at a constant rate of 400 miles per hour.

Now,

   (400 /250 ) × 20000

=  1.6 × 20000

= 32000 feet

Thus, At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

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Answer:

$20.45

Step-by-step explanation:

When the angle of depression is 40° then the distance of the car from the foot of the building is 20.9775 m.

Here given that,

Height of the building =  150 m

Angle of depression = 40°

We have to find distance of car from the foot of the building.

x m be the distance between the car and the building.

So here let imagine it as ΔABC,

Tan 40° = AC/AB

Tan 40° = 0.8391

Therefore the distance,

x = 25 x 0.8391

x = 20.9775 m

Therefore the distance of car from the foot of the building is 20.9775m

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A 40 gram sample of a substance that’s used for drug research has a k-value of 0.1472. The substance's half-life, in days, is approximately 4.7 days.

The half-life of a substance is the time it takes for half of the substance to decay or undergo a transformation. The half-life can be determined using the formula:

t = (0.693 / k)

where t is the half-life and k is the decay constant.

In this case, we are given that the sample has a k-value of 0.1472. We can use this value to calculate the half-life.

t = (0.693 / 0.1472) ≈ 4.7 days

Therefore, the substance's half-life, rounded to the nearest tenth, is approximately 4.7 days.

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For the binomial distribution, √npq formula finds the standard deviation.

See the image below for the complete solution to the question:

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The time she would finish the last piece of equipment is 8 : 05 pm

The first step to determine the total time spent using all the equipment. In order to determine the total time, add the time spent on each equipment together.

Total time = 18 minutes + 15 minutes + 27 minutes + 1 hour 05 minutes

Total time = 2 hours 05 minutes

The next step is to determine the total time spent on breaks between the pieces of equipment.

Total break time = 3 x 5 = 15 minutes

Add the total break time to the total time spent on the pieces of equipment:

Total time = 15 minutes +  2 hours 05 minutes =  2 hours 20 minutes

Time she would finish the last piece of equipment = 5:45pm + 2 hours 20 minutes = 8 : 05 pm

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The slope of the line passing through the points (-5, -4) and (-13, 2) is -3/4.

Slope is simply expressed as a change in y over the change in x.

It is expressed as

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Given the points:
(-5, -4) and (-13,2)​

Point (-5, -4):

x₁ = -5

y₁ = -4

Point (-13,2)​:

x₂ = -13

y₂ = 2

Plug the given x and y values into the slope formula and simplify.

\(m = \frac{y_2 - y_1}{x_2 - x_1}\\\\m = \frac{2 - (-4)}{-13 - (-5)}\\\\m = \frac{2 + 4}{-13 + 5}\\\\m = \frac{6}{-8}\\\\m = -\frac{3}{4}\)

Therefore, the slope of the line is -3/4.

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Answer:811.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

(7.5ftx9ftx12ft)+[5(9ftx12ft)+2(1/2x5x√(4.5^2+1.5^2)ft)]

=810ft+[540ft+2(1/2x5x6.75)ft]

=810ft+(540ft+33.75ft)

=1383.75ft

(sorry I'm not too sure if it is correct )

The value of the obligation on January 1, 2017, is approximately $340,654.78.

To find the value of the obligation on January 1, 2017, discount the debt of $421,567 back to that date. assume the compounding is done quarterly at an interest rate of 6%.

The time difference between January 1, 2022, and January 1, 2017, is 5 years.

Since compounding is done quarterly,

5 * 4 = 20 compounding periods.

To calculate the present value (value on January 1, 2017),  use the formula:

\(Present Value = Future Value / (1 + r)^n\)

where:

Future Value is the debt of $421,567,

r is the interest rate per period (6% / 4 = 1.5% = 0.015), and

n is the number of compounding periods (20).

Substituting the values into the formula:

\(Present Value = $421,567 / (1 + 0.015)^{20}\)

Calculating this using a calculator or spreadsheet software,

Present Value ≈ $340,654.78

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As per given by the question,

There are given that the triangle in quadrant III.

Now,

From the quadrant III, there are given a triangle.

Then,

If we wiil rotate the triangle on counterclockwise or anticlockwise direction , then it will be matched with given triangle on fourth quadrant at angle of 90 degree.

Hence, the option A is correct.

The answer is "A" 90 Degrees

Answer:

5/9

Step-by-step explanation:

Experimental was what actually happened.

Theoretical was what should happen in a perfect, equal world.

E: 6/6 = 1

T: 4/9

E-T= 1-4/9=5/9