A wheel makes 13 revolutions to cover a distance of 65 m. Find the radius of the wheel.

Answer:

282.74in

Step-by-step explanation:

You can use either a numerical (integer or floating-point) variable or a Boolean variable to store the value of a logical expression.

Numerical Variable: You can use a numerical variable, such as an integer or floating-point variable, to store the result of a logical expression. In this case, the logical expression would be evaluated and assigned a numerical value, typically 0 or 1, representing false or true, respectively. For example, if you have a logical expression "x > 5", you can assign the result to a numerical variable like "result = (x > 5)", where the value of "result" would be 0 if the expression is false and 1 if it is true.

Boolean Variable: Alternatively, you can use a Boolean variable to directly store the truth value of a logical expression. A Boolean variable can only have two possible values: true or false. In this case, the logical expression would be evaluated and directly assigned to the Boolean variable. For example, if you have a logical expression "x > 5", you can assign the result to a Boolean variable like "isGreaterThanFive = (x > 5)", where "isGreaterThanFive" would be true if the expression is true and false if it is false.

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The mean is affected by the skewness, whereas the median is not.

==================================

Let's go through the answer choices to see which are true and which are false.

The first common integer that comes to mind is 40, so multiple the numerator and denominator of the left fraction by 4, and the right by 5. This gives us:

36/40 and 35/40, respectively.

Thus, the left fraction is greater than the right fraction

Answer:

Sure, I can help you with that.

Part A:

The wavelengths 0.0001 and 10^-3 are equal. This is because 0.0001 = 10^-3.

Part B:

The shortest wavelength is 0.0001 nanometers. This is because it is the smallest number in the list.

Part C:

The speed of the wave is 10^y, where y > 3. This means that y must be greater than 3. Therefore, the inequality in terms of x to represent all possible values of x is x > -3.

Part D:

The wavelength of the seventh wave is greater than 2x10^-2 nanometers and less than 5/100 nanometers. This means that the wavelength is between 0.004 and 0.05. A possible wavelength for the seventh wave is 4/100, which is equal to 0.04 nanometers.

Here is a table summarizing the answers:

Step-by-step explanation:

The length of the arc with a central angle of 145º is 8,056 miles.

We need to find the circumference of the circle.

We know that the string produced in a year is 20,000 miles, which represents the entire circumference of the circle.

Circumference of the circle = 20,000 miles

Next, we need to find the proportion of the circle's circumference represented by an angle of 145º. To do this, we use the formula:

Proportion of circumference = (angle/360º) × Circumference

Proportion of circumference = (145º/360º) × 20,000 miles

Proportion of circumference = (0.4028) × 20,000 miles

Proportion of circumference = 8,056 miles

Therefore, the length of the arc with a central angle of 145º is 8,056 miles.

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The correct value of mn - 2√5 is -4.

To solve this problem, we'll break it down into smaller steps.

Step 1: Find the integer part and decimal part of √5.

The square root of 5 (√5) is approximately 2.23607.

The integer part (m) of √5 is 2.

The decimal part (n) of √5 is 0.23607.

Step 2: Calculate mn.

mn = 2 * 0.23607 = 0.47214.

Step 3: Calculate 2√5.

2√5 = 2 * √5 = 2 * 2.23607 = 4.47214.

Step 4: Calculate mn - 2√5.

mn - 2√5 = 0.47214 - 4.47214 = -4.

Therefore, mn - 2√5 is equal to -4.

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Answer:

47.5

Step-by-step explanation:

19÷2=9.5x5=47.5

Answer:

He invested approximately $2,215

Step-by-step explanation:

Mr Y invested $2000 in two accounts.

One pays 7%, and the other pays 5%.

At the end of one year, Mr Y earned $155 in interest. We want to know how much Mr Y invested in the account paying 7%.

Let the amount he invested be X, then

7% of X = 155

(7/100)X = 155

0.07X = 155

X = 155/0.07

= 2,215

He invested approximately $2,215

Answer:

you need to upload a pic

Step-by-step explanation:

.

Answer:

x-coordinate of point A

Step-by-step explanation: Khan Academy

Nevertheless, we cannot draw any additional judgements about the expressions students' general performance or how representative this sample of pupils is of the larger community.

In mathematics, an expression is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that expresses a quantity or value. Expressions might be simple, like "3 + 4", or complex, like "(3x2 - 2) / (x + 1)". They may also include functions such as "sin(x)" or "log(y)". Expressions can be evaluated by substituting values for the variables and carrying out the mathematical operations in the given order. For instance, if x = 2, the formula "3x + 5" is 3(2) + 5 = 11. In mathematics, expressions are widely used to explain real-world situations, build equations, and simplify complex mathematical issues.

We can make the following observations about Mrs. Perkins' students based on the line plot:

A student's highest possible score is ten.

The most frequently occurring score is 6, which happens three times.

The scale goes from 2 to 10.

The plot displays a total of ten scores.

As a result, we may deduce that Mrs. Perkins' kids scored between 2 and 10, with 6 being the most common. Nevertheless, we cannot draw any additional judgements about the students' general performance or how representative this sample of pupils is of the larger community.

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Using a system of equations, Phyllis invested the following at each rate:

A system of equations is two or more equations solved concurrently, simultaneously, or at the same time.

The total investment = $8,000

Investment A's simple interest rate per year = 4% = 0.04 (4/100)

Investment B's simple interest rate per year = 1% = 0.01 (1/100)

The total earnings after one year from Investments A and B = $95.00

Let the amount invested in Investment A = x

Let the amount invested in Investment B = y

x + y = 8,000 Equation 1

0.04x + 0.01y = 95 Equation 2

Multiply Equation 1 by 0.04:

0.04x + 0.04y = 320 Equation 3

Subtract Equation 2 from Equation 3:

0.04x + 0.04y = 320

-

0.04x + 0.01y = 95

0.03y = 225

y = 7,500

x = 500 (x = 8,000 - 7,500)

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To find the smallest possible value of $n$, we need to find the smallest value that satisfies all three conditions.

From the first condition, we know that $n = 9a + 5$ for some positive integer $a$.
From the second condition, we know that $n = 7b + 3$ for some positive integer $b$.
From the third condition, we know that $n = 5c + 1$ for some positive integer $c$.
We can set these equations equal to each other and solve for $n$:
$9a + 5 = 7b + 3 = 5c + 1$
Starting with the first two expressions:
$9a + 5 = 7b + 3 \Rightarrow 9a + 2 = 7b$
The smallest values of $a$ and $b$ that satisfy this equation are $a=2$ and $b=3$, which gives us $n = 9(2) + 5 = 7(3) + 3 = 23$.
Now we need to check if this value of $n$ satisfies the third condition:
$n = 23 \not= 5c + 1$ for any positive integer $c$.
So we need to try the next possible value of $a$ and $b$:
$9a + 5 = 5c + 1 \Righteous 9a = 5c - 4$
$7b + 3 = 5c + 1 \Righteous 7b = 5c - 2$
If we add 9 times the second equation to 7 times the first equation, we get:
$63b + 27 + 49a + 35 = 63b + 45c - 36 + 35b - 14$
Simplifying:
$49a + 98b = 45c - 23$
$7a + 14b = 5c - 3$
$7(a + 2b) = 5(c - 1)$
So the smallest possible value of $c$ is 2, which gives us $a + 2b = 2$. The smallest values of $a$ and $b$ that satisfy this equation are $a=1$ and $b=1$, which gives us $n = 9(1) + 5 = 7(1) + 3 = 5(2) + 1 = 46$.
Therefore, the smallest possible value of $n$ is $\boxed{46}$.

To find the smallest possible value of $n$ which is a four-digit positive integer such that dividing $n$ by $9$, the remainder is $5$, dividing $n$ by $7$, the remainder is $3$, and dividing $n$ by $5$, the remainder is $1$, follow these steps:
Step 1: Write down the congruences based on the given information.
$n \equiv 5 \pmod{9}$
$n \equiv 3 \pmod{7}$
$n \equiv 1 \pmod{5}$
Step 2: Use the Chinese Remainder Theorem (CRT) to solve the system of congruences. The CRT states that for pairwise coprime moduli, there exists a unique solution modulo their product.
Step 3: Compute the product of the moduli.
$M = 9 \times 7 \times 5 = 315$
Step 4: Compute the partial products.
$M_1 = M/9 = 35$
$M_2 = M/7 = 45$
$M_3 = M/5 = 63$
Step 5: Find the modular inverses.
$M_1^{-1} \equiv 35^{-1} \pmod{9} \equiv 2 \pmod{9}$
$M_2^{-1} \equiv 45^{-1} \pmod{7} \equiv 4 \pmod{7}$
$M_3^{-1} \equiv 63^{-1} \pmod{5} \equiv 3 \pmod{5}$
Step 6: Compute the solution.
$n = (5 \times 35 \times 2) + (3 \times 45 \times 4) + (1 \times 63 \times 3) = 350 + 540 + 189 = 1079$
Step 7: Check that the solution is a four-digit positive integer. Since 1079 is a three-digit number, add the product of the moduli (315) to the solution to obtain the smallest four-digit positive integer that satisfies the conditions.
$n = 1079 + 315 = 1394$
The smallest possible value of $n$ is 1394.

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The correct option is (a).

To find the value of k such that the point P(k, -4) lies on the line 3x - 2y = 13, we substitute the coordinates of P into the equation and solve for k.

Substituting x = k and y = -4 into the equation 3x - 2y = 13, we have:

3(k) - 2(-4) = 13.

Simplifying the equation, we get:

3k + 8 = 13.

Subtracting 8 from both sides, we have:

3k = 5.

Dividing both sides by 3, we find:

k = 5/3.

Therefore, the value of k that satisfies the equation is k = 5/3, which corresponds to option (a).

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======================================================

Explanation:

If you have exactly one right angle, then it is possible to have no parallel lines.   See the diagram below. Refer to the upper figure.

If you had exactly 2 right angles, then that would form a trapezoid. A trapezoid has exactly one pair of parallel lines.

If you had 4 right angles, then it would form a rectangle. Any rectangle is a parallelogram, so we have 2 pairs of parallel lines by this point.

It's not possible to have a quadrilateral with exactly 3 right angles (and the fourth angle is some non-right angle). This is because all four angles of any quadrilateral must add to 360 degrees.

Answer: 220 miles

Step-by-step explanation:

Distance travelled is calculated as:

= Speed × Time

Based on the scenario on the question, the total distance, in miles, of Darius' trip will be:

= (60 × 2) + (50 × 2)

= 120 + 100

= 220 miles

The population of the given samples are defined below.

a) The populations for apple prices at two stores near your house could be:

i) All the prices for apples at all the stores in your city.

ii) The prices for apples at all the stores in your neighborhood.

b) The following populations might correspond to the days of the week that your maths students placed food orders:

i) The days of the week when every student at your school placed a meal order.

ii) The days of the week that all maths students from various schools purchased lunch.

c) The following populations might be based on the average daily high temperatures for the 59 state capitals over the preceding year:

i) The 59 U.S. states' cities' average daily high temperatures.

ii) The average daily high temperature for all capital cities worldwide throughout the previous year.

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To show that if two n × n matrices A and B have a common eigenvector x, then x will also be an eigenvector of any matrix of the form C = αA + βB, we can use the definition of eigenvectors and some basic algebra.

First, let v be the common eigenvector of A and B, such that Av = λv and Bv = μv for some eigenvalues λ and μ. Then, consider the matrix C = αA + βB. We can rewrite this as C = αAv + βBv, and substitute in the expressions for Av and Bv in terms of v:

C = αλv + βμv = (αλ + βμ)v

Thus, we see that Cv = (αλ + βμ)v, which shows that x is an eigenvector of C with eigenvalue αλ + βμ. Therefore, any common eigenvector of A and B is also an eigenvector of any linear combination of A and B.

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Pan tool do the data analyst use to select the area on the map representing Finland.    

A data analyst is working with the world happiness data in table. To use Pan tool to select the area on the map representing Finland.

A data professional examines data to uncover critical insights about a company's consumers and how the data may be utilized to address problems. They also share this information with corporate executives and other stakeholders.

Pan allows us to shift the map to focus on it or present the areas in the way we wish. Simply pick the Pan Option and move the map around to suit your needs. Alternatively, you may move the map by holding down the Shift key.

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We want to complete the steps to convert the given quadratic equation into vertex form.

Eventually we will get:

y = (x + 1)^2 - 2

For a quadratic equation with the vertex (h, k), the vertex form is:

y = a*(x - h)^2 + k

Here we start with:

y = x^2 + 2x - 1

1) First, we complete the perfect-square trinomial, we need to add and subtract 1 to get that:

y = x^2 + 2x - 1 + 1 - 1

2) Now we rewrite the equation to be able of completing squares:

y = (x^2 + 2x + 1) - 1 - 1

y = (x^2 + 2x + 1) - 2

3) Now we complete squares

y = (x + 1)^2 - 2

And this is the equation in vertex form, where you can see that the vertex is the point (-1, - 2)

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Here's the explanation :

we know,

\( \boxed{\sin( \theta) = \frac{opposite \: \: side}{hypotenuse} }\)

so,

\( \sin(k) = \dfrac{11}{61} \)

hence, option b. is correct

Answer:

68.9 in^2

Step-by-step explanation:

first lets find the height of the blue triangle

hypotenuse = 15 in

one side is 12 in whereas other has to be find.

take 50 degree as reference angle

using sin rule

sin 50 = opposite/hypotenuse

0.76 = opposite/15

0.766*15 = opposite

11.49 = opposite

area of triangle = base*height/2

=12*11.49/2

=136.88/2

=68.94

=68.9 in^2

Answer:

A = 68.9 in²

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) ab sinC ( a, b are 2 sides and C the angle between them )

Here a = 12, b = 15 and C = 50° , then

A = \(\frac{1}{2}\) × 12 × 15 × sin50°

   = 6 × 15 × sin50°

   = 90 × sin50° ≈ 68.9 in² ( to the nearest tenth )

Answer:

60 ft

Step-by-step explanation:

3 times 20 is 60 ft so there is your answer

Answer:

C

Step-by-step explanation:

Diameter is 3 feet, and the radius is half the diameter.

Circumference

Distance travelled in 20 rotations

There are 364 different committees of 3 people. There are 436 different committees of 4 people.

There are different scenarios for which we can calculate the number of possible committees. Here are a few examples:

To calculate the number of different committees of 3 people, we can use the combination formula, which is:

\(${n \choose k} = \frac{n!}{k!(n-k)!}$\)

where n is the total number of people and k is the number of people needed for the committee. Using this formula, we get:

\(${14 \choose 3} = \frac{14!}{3!(14-3)!} = \frac{14!}{3!11!} = 364$\)

Therefore, there are 364 different committees of 3 people that can be formed from this group.

To solve this problem, we can use the principle of inclusion-exclusion. First, we calculate the total number of committees of 4 people, which is:

\(${14 \choose 4} = \frac{14!}{4!(14-4)!} = \frac{14!}{4!10!} = 1001$\)

Next, we calculate the number of committees that do not include a freshman, which is:

\(${12 \choose 4} = \frac{12!}{4!(12-4)!} = \frac{12!}{4!8!} = 495$\)

Similarly, we calculate the number of committees that do not include a sophomore, a junior, and a senior, which are:

\(${11 \choose 4} = \frac{11!}{4!(11-4)!} = \frac{11!}{4!7!} = 330$\)

\(${10 \choose 4} = \frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} = 210$\)

\(${9 \choose 4} = \frac{9!}{4!(9-4)!} = \frac{9!}{4!5!} = 126$\)

Now we can apply the principle of inclusion-exclusion, which is:

Total number of committees - (number of committees without a freshman + number of committees without a sophomore + number of committees without a junior + number of committees without a senior) + (number of committees without a freshman and without a sophomore + number of committees without a freshman and without a junior + number of committees without a freshman and without a senior + number of committees without a sophomore and without a junior + number of committees without a sophomore and without a senior + number of committees without a junior and without a senior) - number of committees without any freshmen, sophomores, juniors, or seniors.

Plugging in the values, we get:

$1001 - (495 + 330 + 210 + 126) + (66 + 120 + 165 + 84 + 55 + 35) - 1 = 436$

Therefore, there are 436 different committees of 4 people that can be formed, with at least one person from each grade level.

Note that for the last step, we subtracted 1 because there is only one committee that has no freshmen, sophomores, juniors, or seniors.

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The number of ways in which you can win first prize and your mom went the second prize will be 8. Then the correct option is D.

A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.

You and your mom enter the drawing with three different prices the prizes are awarded at random is a total of 8 people entered the drawing.

Then the number of the ways in which you can win first prize and your mom went the second prize will be

Let x be the number of different ways.

Then we have

\(\rm x = \ ^8C_1\\\\x = 8\)

Thus, the number of ways in which you can win first prize and your mom went the second prize will be 8.

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Answer:

75%, 0.75, 3/4. 3 quarters.

Step-by-step explanation:

Answer:

Step-by-step explanación

0.02

When the mean number of points scored per game next season is 60, the model predicts that the mean home attendance will be 11902

The function that predicts the attendance is given as:

\(y = -7628+325.5x\)

When the mean number of points scored per game next season is 60, it means that the value of x is 60

i.e. x = 60

Substitute 60 for x in the function

So, we have:

\(y = -7628+325.5 \times 60\)

Evaluate the product

\(y = -7628+19530\)

Add -7628 and 19530

\(y = 11902\)

Hence, the model predicts that the mean home attendance will be 11902

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Answer:

95.625 or if you have to round it 96

Step-by-step explanation:

you can do cross multiplacation so 255 × 8 ÷ 3

Answer:

they would receive 680 applications

Step-by-step explanation:

you use the formula 3x=(8)(255), you multiply 8 and 255 to get 2040, then you divide both sides by 3, and simplify to get your answer

Answer:

In the year 2026 population of both the states will be the same.

Step-by-step explanation:

It has been given in the question that the population y of State A in year x will be represented by the equation

-3x + y = 11,400

⇒ y = 11,400 + 3x --------(1)

Similarly, an equation that represents the population for State B is

-138x + y = 8,000

⇒ y = 138x + 8,000 -------(2)

If population y for both the states are equal then

3x + 11,400 = 138x + 8,000

11400 - 8000 = 138x - 3x

135x = 3400

x = 25.19 [After 25 years ]

Since  x = 0 represents the population of the states in the year 2000

therefore, population y will be the same in both the states in the year (2000 + 26)

= 2026

Answer:

1.03

Step-by-step explanation:

multiplying by 1.3 would increase the amount by 30%