One circular table has a diameter of 9 ft, and another circular table has a diameter of 20 ft. How much greater is the area of the larger table? Round to the nearest whole number.

Answer:

6 races

Step-by-step explanation:

If he won 40% of the races he competed in, and he raced 15 times, this means that he won roughly 4/10 races.

4/10= ?/15

cross multiply 4 and 15 = 60

60/10 = 6

He won 6 races

Give brainliest please!

hope this helps :)

The circumference of the circle is 8π cm.

Given the diameter of the circle as 8cm,

The radius (r) can be gotten by dividing the diameter by 2

r = 8cm / 2 = 4cm

The area (A) of a circle is: A = πr^2

So, substituting the value of r, we get:

A = π(4cm)^2 = 16π cm^2

Therefore, the area of the circle is 16π cm^2.

The circumference (C) of a circle is C = 2πr

So, substituting the value of r, we get:

C = 2π(4cm) = 8π cm

Therefore, the circumference of the circle is 8π cm.

Learn more about circumference at https://brainly.com/question/20489969

#SPJ1

Answer:

\(\huge\boxed{slope=-\dfrac{7}{11}}\)

Step-by-step explanation:

The slope-intercept form of an equation of a line:

\(y=mx+b\)

\(m\) - slope

\(b\) - y-intercept

We have the equation in the general form \((Ax+By+C=0)\).

Convert to the slope-intercept form:

\(7x+11y-2=0\)    subtract 7x from both sides

\(11y-2=-7x\)     add 2 to both sides

\(11y=-7x+2\)     divide both sides by 11

\(y=-\dfrac{7}{11}x+\dfrac{2}{11}\)

The general form of an equation of a line:

\(Ax+By+C=0\)

The slope:

\(m=\dfrac{-A}{B}\)

We have

\(7x+11y-2=0\\\\A=7;\ B=11;\ C=-2\)

Substitute:

\(m=\dfrac{-7}{11}=-\dfrac{7}{11}\)

Answer:

3 glasses

Step-by-step explanation:

1 glass= 1 cup

3 cups= 3 glasses

Answer:

Step-by-step explanation:3 glasses

There were 144 students when the contest began

Equation is formed when an algebraic expression is equated by a constant or another algebraic expression.

On the basis of given data :

Let the total number of students are x

50% of the students are eliminated after the first round

the remaining students are 0.5x

After the second round = (1/3) * 0.5 x were remaining

and

(1/3) * 0.5 x = 24

then solving this equation will give the total number of students

0.5x = 24 * 3

x = 24*3 /0.5 = 144

Therefore there were 144 students when the contest began

To know more about Equation

https://brainly.com/question/10413253

#SPJ1

The probability that a srs of 20 students will spend an average of between 600 and 700 dollars is 0.92081.

We need to find the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars.

To solve this problem, we will use the central limit theorem, which states that the sampling distribution of the sample means will be approximately normally distributed with a mean of μ and a standard deviation of σ/√(n), where n is the sample size.

Thus, the mean of the sampling distribution is μ = 650 and the standard deviation is σ/sqrt(n) = 120/√(20) = 26.83.

We need to find the probability that the sample mean falls between 600 and 700 dollars. Let x be the sample mean. Then:

Z1 = (600 - μ) / (σ / √(n)) = (600 - 650) / (120 / √t(20)) = -1.77

Z2 = (700 - μ) / (σ / √(n)) = (700 - 650) / (120 / √(20)) = 1.77

Using a standard normal distribution table or calculator, we can find the area under the standard normal distribution curve between these two Z-scores as:

P(-1.77 < Z < 1.77) = 0.9208

Therefore, the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars is 0.9208, or approximately 0.92081 when rounded to five decimal places.

Learn more about probability here:

brainly.com/question/14228383

#SPJ11

Answer:

\(2.9 cm^2\)

Step-by-step explanation:

Given,

Angle of sector = 30°

Radius of circle, r = 8 cm

Area of the shaded region, A =?

The diagram is attached below.

Now,

Area of shaded region = Area of sector - Area of triangle

Area of triangle = \(\frac{1}{2}\times base \times height\)

We know that,

\(\sin \theta = \dfrac{P}{H}\)

\(\sin 30^\circ= \dfrac{P}{8}\)

\(P = \dfrac{8}{2}\)

\(P = 4\ cm\)

And

\(\cos \theta =\dfrac{B}{H}\)

\(\cos 30^\circ = \dfrac{B}{8}\)

\(B = \dfrac{8\times \sqrt{3}}{2}\)

\(B = 4\sqrt 3\)

Area of sector = \(\dfrac{\theta}{360^\circ}\times \pi r^2\)

Area of sector =  \(\dfrac{30^\circ}{360^\circ}\times \pi \times 8^2\)

                        = 16.75 cm^2

Area of triangle = \(\dfrac{1}{2} \times 4\sqrt 3 \times 4\)

                          = 13.85 cm^2

Area of shaded region = 16.75 - 13.85

                                      = \(2.9 cm^2\)

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

Read more about Equivalent fractions at: https://brainly.com/question/17220365

#SPJ1

The probability that the committee consists of 3 men and 2 women is 10/63.

As per the given question.

The committee consists of 9 people (6 women ad 3 men).

5 are choosen at random.

Then, the probability that the committee will have the of 3 men and 2 women is;

P(3 men + 2 women) = (select 3 men of of 3 men)(select 2 women out of 5 women) / (choose 5 out of 9 total)

P(3 men + 2 women) = (³C₃ . ⁵C₂)/ ⁹C₅

Solve the combination.

P(3 men + 2 women) = 1 x 20 / 126

P(3 men + 2 women) = 10/63

Thus, the probability that the committee consists of 3 men and 2 women is 10/63.

To know more about the combinations, here

https://brainly.com/question/28065038

#SPJ4

The complete question is-

A committee of 5 is to be selected from a group of 6 women and 3 men. If the selection is made randomly, what is the probability that the committee consists of 3 men and 2 women?.

Answer:

they are integers

Step-by-step explanation:

The major problem in the passage is that it assumes the existence of a smallest element in the set A, which is not true for all non-empty subsets of the real numbers .a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion.

The real numbers are fundamental in calculus (and more generally in all mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. Real intervals play an important role in the theory of integration, because they are the simplest sets whose "length" (or "measure" or "size") is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure.

To know more about  real number .Click on the link.

https://brainly.com/question/10547079

#SPJ11

Answer:

A

Step-by-step explanation:

y = 79.31(1.48)^6

y=833.84

Answer:

y = 1/3x + 10/3

Step-by-step explanation:

Slope: 1/3

Point (-4,2)

b = 2 - (1/3)(-4) = 10/3

The value of the derivative for dy/dx is dy/dx = (2 - 3y) / (3x + 2y - 1).

We have,

To find dy/dx using implicit differentiation for the equation

3xy + y² = 2x + y, we differentiate both sides of the equation with respect to x:

d/dx(3xy + y²) = d/dx(2x + y)

Using the product rule for the left side and the chain rule for the right side, we get:

(3y + 3xy') + 2yy' = 2 + y'

Now, let's isolate the terms containing y' on one side:

3y + 3xy' + 2yy' - y' = 2

Grouping the terms:

(3x + 2y - 1)y' = 2 - 3y

Finally, solving for y', we divide both sides by (3x + 2y - 1):

y' = (2 - 3y) / (3x + 2y - 1)

Therefore,

The expression for dy/dx is dy/dx = (2 - 3y) / (3x + 2y - 1).

Learn more about derivatives here:

https://brainly.com/question/29020856

#SPJ4

Answer:

The answer is D

Step-by-step explanation:

To find out how far a car will travel (in feet) before a driver reacts to an obstacle, given that the car is moving at 34 miles per hour in a residential neighborhood, we need to convert the speed of the car from miles per hour to feet per second. This can be done using the conversion factor that 1 mile per hour is equal to 1.46667 feet per second. Therefore, 34 miles per hour is equal to 34 x 1.46667 = 49.86678 feet per second.

We know that the average reaction time of the driver is 1.2 seconds, and we can use the following formula to calculate the distance traveled by the car before the driver reacts to the obstacle:

d = v x t

where d is the distance, v is the velocity, and t is the time taken. Using the formula above, we can calculate the distance traveled by the car before the driver reacts to the obstacle as:

d = 49.86678 x 1.2 = 59.84014 feet

Therefore, the car will travel 59.84014 feet before a driver reacts to an obstacle.

Know more about Speed and distance here:

https://brainly.com/question/31756299

#SPJ11

Answer:

Let's first calculate the amount of interest that would be earned if the interest were compounded annually. The formula for the future value of a single sum is:

F = P * (1 + r/n)^(nt)

Where:

F is the future value

P is the principal (the initial deposit)

r is the annual interest rate

n is the number of compounding periods per year

t is the number of years

For our calculation, we have:

P = $10,000

r = 1.8% = 0.018

n = 1 (annual compounding)

t = 30

So, the future value of the account with annual compounding is:

F = $10,000 * (1 + 0.018/1)^(1 * 30) = $10,000 * (1.018)^30 = $21,784.08

Now, let's calculate the amount of interest that would be earned if the interest were compounded monthly. The formula for the future value of a single sum is the same, but we need to use the monthly compounding rate (r/12) instead of the annual rate and the number of months (12t) instead of the number of years:

F = P * (1 + r/n)^(nt)

Where:

F is the future value

P is the principal (the initial deposit)

r is the annual interest rate

n is the number of compounding periods per year

t is the number of years

For our calculation, we have:

P = $10,000

r = 1.8% = 0.018

n = 12 (monthly compounding)

t = 30

So, the future value of the account with monthly compounding is:

F = $10,000 * (1 + 0.018/12)^(12 * 30) = $10,000 * (1.0015)^360 = $22,254.51

The difference in the two future values is $22,254.51 - $21,784.08 = $470.43.

So, the account would be worth $470.43 more if interest were compounded monthly rather than annually over a period of 30 years. Round to the nearest dollar, the answer is $470.

Step-by-step explanation:

To determine if it is possible to find a vector field a such that ∇ × a = (-9xyz, y^2z, yz^2/2), we can use a  theorem from vector calculus known as Helmholtz's theorem.

This theorem states that any sufficiently smooth and well-behaved vector field in three dimensions can be decomposed into a sum of two vector fields: a curl-free (or irrotational) field and a divergence-free (or solenoidal) field.

In other words, if we can find a vector field b such that ∇ × b = 0 (i.e., b is curl-free) and a scalar field φ such that ∇ · (φa) = -9xyz, y^2z, yz^2/2 (i.e., φa is divergence-free), then we can write the original vector field a as a sum of the two vector fields:

a = b + (1/φ)∇ × (φa)

Since the curl of any gradient field is always zero, we can choose b to be the gradient of a scalar field ψ:

b = ∇ψ

Now, we need to find a scalar field φ such that φa is divergence-free. This means that we need to solve the following partial differential equation:

∇ · (φa) = -9xyz, y^2z, yz^2/2

If we can find a solution to this equation, then we can write a as a sum of b and the curl of (φa) divided by φ. However, it is not always possible to find a solution to this equation, especially if the right-hand side has non-zero divergence (which is the case here).

Therefore, it is not possible to find a vector field a that satisfies ∇ × a = (-9xyz, y^2z, yz^2/2) in general.

Learn more about Helmholtz's theorem here brainly.com/question/19085658

#SPJ11

Where the above conditions are given in the equation,  x is 45.

Given equations are  -

m∠PQR = x + 7 ,

m∠SQR = x + 3 ,

and m PQR + m SQR = m PQS = 100

using those equations we need to find value of x.

Plug value of (m PQR = x + 7) and (m SQR = x + 3 ) into (m PQR + m SQR = m PQS = 100 )

(x+7) + ( x+3) = m PQS = 100

(x+7) + (x +3) = 100

Remove parenthesis

x+7 + x+3 = 100

Rearrange terms

x + x +3+7 = 100

Combine like terms

2x+10 = 100

2x= 100 - 10

2x=90

x=90/2

x=45

Learn more about equation at:

https://brainly.com/question/29174899

#SPJ1

Full Question:

Although part of your question is missing, you might be referring to this full question:

What is the value of x? Identify the missing justifications. M PQR = x + 7 , m SQR = x + 3 , and m PQR + m SQR = m PQS = 100

An expression that represents the height of a tree is 6.7 + 2.9.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Here, we have

Given

The initial height of the tree is 6.7 feet

The increase in height per year = 2.9 feet

Thus,

The expression will be = 6.7 + 2.9t,

Here t represents the number of years.

Hence, an expression that represents the height of a tree is 6.7 + 2.9.

To learn more about the expression visit:

brainly.com/question/25968875

#SPJ1

Answer:

-1/2

Step-by-step explanation:

We can see the points (0, 3) and (2, 2) on the graph given.

We can use the formula [ y2-y1/x2-x1 ]

2-3/2-0

-1/2

Best of Luck!

Solve It... Brainlist Too Pls For I Can Get To Next Level

I Have Stumbled Across This, Lol

Answer:

a lot of different answers

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

amswer that was on hegarty mathss

To construct the augmented matrix for the given system of equations, we need to arrange the coefficients of the variables and the constants in a matrix form. The augmented matrix is obtained by combining the coefficient matrix and the constant matrix.

Let's denote the variables as x, y, and z. The system of equations can be written as follows:

Equation 1: 4x + 4y - z^3 = 22

Equation 2: 2(3z - 7x) = y - 3

Equation 3: x - 7z = 6y

Now, let's arrange the coefficients and constants in matrix form. The augmented matrix is a matrix that combines the coefficient matrix and the constant matrix by appending them together.

The coefficient matrix consists of the coefficients of the variables:

```

[4   4   -1^3]

[-14   0   6]

[1   0   -7]

```

The constant matrix consists of the constants on the right-hand side of each equation:

```

[22]

[-3]

[0]

```

To construct the augmented matrix, we append the constant matrix to the right of the coefficient matrix, using a vertical line to separate them:

```

[4   4   -1^3 | 22]

[-14   0   6 | -3]

[1   0   -7 | 0]

```

This augmented matrix represents the given system of equations. Each row corresponds to an equation, and the columns represent the coefficients and constants associated with each variable. The augmented matrix allows us to perform row operations and apply matrix methods to solve the system of equations, such as Gaussian elimination or matrix inverses.

By manipulating and reducing the augmented matrix using row operations, we can find the solution to the system of equations, if one exists.

Learn more about Augmented Matrix :

https://brainly.com/question/12994814

#SPJ11

If we were to measure a dependent variable's frequency, the appropriate method would be to count the number of times it occurred.

Frequency refers to the rate at which a behavior or event happens within a given timeframe. By counting the occurrences of the dependent variable, we can determine how often it happens or the number of times it is observed. The other options mentioned—timing the interval between responses, measuring the shape of the behavior, and timing how long it took to achieve—are not directly related to measuring frequency.

Timing the interval between responses would be more relevant for measuring the interresponse time or the duration between two consecutive instances of the behavior. Measuring the shape of the behavior would involve analyzing the pattern or characteristics of the behavior, such as its intensity or duration. Timing how long it took to achieve something would focus on the duration or latency of the behavior rather than its frequency.

Therefore, the correct approach for measuring frequency would be to count the number of occurrences of the dependent variable, providing an objective and quantitative assessment of how frequently the behavior or event takes place.

Learn more about variable here: brainly.com/question/15078630

#SPJ11

Answer:

1/4, 32%,.4

Step-by-step explanation:

Put each of them in decimal form and 1/4=.25, 32%=.32 and .4=.4, then put them in order in decimal form and there you go