There were ten tables with the same amount of chairs around it in the cafeteria. There were 5 more chairs lined up against the wall. There were 65 chairs in all. How many chairs were at each table?

1,470

Step-by-step explanation:

because if he 4 miles and than 3 miles you would add them and get 7. you would take that 7 and double the 7 and multiply it by 105 cause that's how many calories he burnt each miles he ran then you would get the total of 1470 calories

Answer:

9.

he washes 9 cars on Tuesday.

Step-by-step explanation:

28 * 7 = 196.

448 - 196 = 252

252 / 28 = 9

On solving the linear equation  28x + 196 = 448, we get that Craig washed 9 cars on Tuesday.

Linear equation is an equation containing one unknown variable with power one and constants.

The standard form of an linear equation in one variable x is :

ax + b = 0 , where a, b are constants

x= -b/ a is solution if this equation or we can solve this equation by adding or subtracting , multiplying or dividing same number to both sides.

Given that Craig washes cars and earns $ 28 for each car . He washed 7 cars on Monday.

Let on Tuesday he washed x cars

Total money earned on Tuesday and Monday by Craig = $448

Money earned on Monday = $ 7× 28 = $ 196

Money earned on Tuesday  = $ x×28 = $ 28x

⇒ 28x + 196 = 448

Subtracting 196 from both sides we get

⇒ 28x + 196 -196 = 448 - 196

⇒ 28 x = 252

Dividing both sides by 28

⇒ x = 252/28 = 9

Therefore, Craig washed 9 cars on Tuesday.

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Considering the given triangle :

GIVEN :

• Opposite side to angle = 34

• Adjacent side to angle = 48

• We will use Tan = opposite /adjacent trigonometric fuction tocalculate angle

CALCULATIONS:

Answer:

a.  f+g = -3x+5 + x^2

b.  f-g =  -3x+5 - x^2

Step-by-step explanation:

g(x) = x^2

I'll assume the other two equations were meant to be:

f(x) = -3x+5, and h(x) = -4x-2

a.  f+g = -3x+5 + x^2

b.  f-g =  -3x+5 - x^2

Distance (D): 150 miles

Time (t): 3 hours

Answer: 50 miles / hour

The solution of the expression will be 3, -2, and -22 respectively.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expressions are:-

2x²−3x−2 if x is less than or equal to -1

E = 2x²−3x−2

E = 2 (-1) ² - 3 x -1 -2

E = 2 + 3 - 2

E = 3

E = −x²+2x+1 if -1

E = -(-1)² + 2 x -1 + 1

E = -1 - 2 + 1

E = -2

E = −2x²−x−1

E = -2 ( 3 )² - 3 - 1

E = -18 - 3 - 1

E = -22

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The Fourier series representation of the output \(y(t)\) for different inputs can be found by convolving the input signal with the impulse response \(h(t)\).

For the given input \(x(t) = 1\), the output can be found by convolving \(x(t)\) with \(h(t)\). The Fourier series representation of the output can be obtained by taking the Fourier transform of the convolved signal.

Since \(h(t)\) is an even function, the Fourier transform of \(h(t)\) is a real and even function. Thus, the Fourier series representation of the output will only contain cosine terms.

To calculate the Fourier series coefficients, we need to find the integral of the product of the impulse response and the cosine functions.

Using the property that \(\cos(at)\) is even and \(\int_{-\infty}^{\infty} \cos(at) \, dt = \pi \delta(a)\), where \(\delta\) is the Dirac delta function, we can simplify the calculation.

By evaluating the integrals, we can determine the values of the Fourier series coefficients, and thus, obtain the Fourier series representation of the output \(y(t)\).

In summary, to find the Fourier series representation of the output \(y(t)\) for the given inputs, we need to convolve the inputs with the impulse response \(h(t)\), calculate the Fourier series coefficients using the properties of even functions and the Dirac delta function, and then express the output in terms of the cosine terms.

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a) The mean can be calculated by adding all values and then divide by the total number of values:

b) The median is the middle value in the list of numbers, then you have to order the numbers as follows: 0, 0, 1, 3, 6.

c) The mode is the value that occurs most often, as you have a 0 value twice, then

d) To calculate the sample variance you can use this formula

The sample standard deviation is the square root of sample variance, then

50 hopefully this will help you

Answer:

50

Step-by-step explanation:

Let "x" represent the number that makes them equal. No wet up a fraction;

\(\frac{5}{10}=\frac{x}{100}\)

Step 1: Switch sides

\(\frac{x}{100}=\frac{5}{10}\)

Step 2: Multiply both sides by 100

\(\frac{x}{100}\cdot \:100=\frac{5}{10}\cdot \:100\)

Simplify

\(x=50\)

Therefore, 50 is the number that will make the fractions equal.

The data points to use is based on two companies knowledge to accomplice.

Here in this question we have been given an example of our time in a school team in which you have to realize on data to convince a group about the recommendation.

Here we also know that when we were making any recommendation to convince a group we have to keep its positive wherever we response to a question about the time you had to convince someone to do something your way.

Here we have also know that you may be tempted so may be tempted to put a negative spin on situation.

So, in order to accomplish the we have to accomplice and will have knowledge two companies knowledge to accomplice

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The statement (b) the sum is a binomial with a degree of 3 is correct.

Expressions are defined as the combination of constants and variables with mathematical operators.

We have expressions:

6s²t – 2st²

4s²t – 3st²

Adding the above two expressions, we get;

= (6s²t – 2st²) + (4s²t – 3st²)

Combining like terms:

= 10s²t - 5st²

The above expression has degree 3(2+1)

Thus, statement (b) the sum is a binomial with a degree of 3 is correct.

Complete question:

What is true about the sum of the two polynomials?

6s2t – 2st2

4s2t – 3st2

a.) The sum is a binomial with a degree of 2.

b.) The sum is a binomial with a degree of 3.

c.) The sum is a trinomial with a degree of 2.

d.) The sum is a trinomial with a degree of 3.

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Answer:

I believe it to be the first answer. Since, similar triangles always have the same slope.

Step-by-step explanation:

Using models to to illustrate the proportions is similar to reducing or increasing a ratio by a common factor. The solutions to the exercise are given below :

1.)

8 : 6

Reducing each side of the ratio by an half(1/2) :

8 × ½ : 6 × ½

4 : 3

2.)

15 : 3

Reducing each side of the ratio by ⅓:

15 × ⅓ : 3 × ⅓

5 : 1

3.)

12 : 6

Reducing each side of the ratio by (one-third) ⅓:

12 × ⅓ : 6 × ⅓

4 : 2

4.)

11 : 7

Increasing the proportion by 4 :

11 × 4 : 7 × 4

44 : 28

5.)

25 eggs : 3 hens

Increasing the number of hens by 3, then egg production will also triple

25 eggs × 3 : 3 hens × 3

75 eggs to 9 hens

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There are 27,720 different arrangements of red and yellow roses.

The total number of roses is 8 + 4 = 12. To find the number of different arrangements, we can use the formula for permutations, which is:

n! / (n - r)!

where n is the total number of objects and r is the number of objects we want to arrange.

In this case, we want to arrange all 12 roses, so n = 12. The number of red roses is 8, so r = 8. Therefore, the number of different arrangements of the roses is:

12! / (12 - 8)! = 12! / 4! = 27,720

So there are 27,720 different arrangements of the 8 red roses and 4 yellow roses.

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Answer:

15

the answer is 15 all data equal 135 divide by nine equal 15

To determine a formula for the n-th term of an arithmetic sequence, we need to find the common difference (d) first.

The common difference is the constant value that is added or subtracted to each term to get to the next term.

In this case, we can find the common difference by subtracting the fourth term from the seventh term:

d = a₇ - a₄

d = 31 - 19

d = 12

Now that we have the common difference, we can use it to find the formula for the n-th term of the arithmetic sequence. The formula is given by:

aₙ = a₁ + (n - 1)d

In this formula, aₙ represents the n-th term, a₁ represents the first term, n represents the position of the term, and d represents the common difference.

Since we don't have the first term (a₁) given in the problem, we can find it by substituting the known values for a₄ and d:

a₄ = a₁ + (4 - 1)d

19 = a₁ + 3(12)

19 = a₁ + 36

a₁ = 19 - 36

a₁ = -17

Now we can substitute the values of a₁ and d into the formula to get the final formula for the n-th term:

aₙ = -17 + (n - 1)(12)

Therefore, the formula for the n-th term (aₙ) of the given arithmetic sequence is aₙ = -17 + 12(n - 1).

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the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

n the given problem, we have an implicit equation ln(x+y+z) = x+2y+3z that defines z as a function of x and y. We are given the values dy = (-1, 5, -3).

To find the derivative dy/dx, we can use the total derivative formula and apply it to the implicit equation. The total derivative is given by dy/dx = - (∂F/∂x)/(∂F/∂y), where F = ln(x+y+z) - x - 2y - 3z.

Differentiating F partially with respect to x and y, we have (∂F/∂x) = 1/(x+y+z) - 1 and (∂F/∂y) = 1/(x+y+z) - 2.

Plugging in the given values of dy = (-1, 5, -3), we can calculate dy/dx = - (∂F/∂x)/(∂F/∂y) = -(-1)/(5-2) = 1/3.

Therefore, the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

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Answer:

1 in^2

Step-by-step explanation:

area of a rectangle=l*w

l=7/6

w=6/7

7/6 * 6/7 = 1

Given:

Radius of circle is 13 cm

Height of triangle is 5 cm

To find:

Value of 'a' and 'b'

Steps:

To find value of 'a', we will use Pythagoras theorem as the triangle is a right angle triangle,

A² + B² = C²

\(a^{2} + 5^{2} = 13^{2}\)

\(a^{2} + 25 = 169\)

\(a^{2} = 169 - 25\)

\(a^{2} = 144\)

\(\sqrt{a^{2}}=\sqrt{144}\)

\(a = 12\)

Now to find the value of 'b', i will use law of cosine,

\(c=\sqrt{a^{2}+b^{2}-2ab(cos\beta ) }\)

\(12 = \sqrt{13^{2}+5^{2}-2(5)(13)(cos\beta )}\\12=\sqrt{169 + 25-130(cos\beta )}\\12=\sqrt{194-130(cos\beta )}\\144 = 194 - 130(cos\beta )\\50 = 130(cos\beta )\\cos\beta = 0.3846\\\beta = cos^{-1}(0.3846)\\\beta = 67.38\)

Therefore, the values of 'a' and 'b' is 12 and 67.38 respectively

Happy to help :)

If u need any help feel free to ask

Answer:

Proved

Step-by-step explanation:

Solving (a):

Let the numbers be: \(x, x + 1, x + 2.\)

Their sum is:

\(Sum = x + x + 1 + x + 2\)

Collect Like Terms

\(Sum = x + x + x + 1 + 2\)

\(Sum = 3x + 3\)

Divide sum by 3.

\(Result = \frac{Sum}{3}\)

\(Result = \frac{3x+3}{3}\)

\(Result = \frac{3(x+1)}{3}\)

\(Result = x + 1\)

Hence, this is true because there is no fractional part after the division

Solving (b):

Let the numbers be: \(x, x + 1, x + 2,x+3,x+4\)

Their sum is:

\(Sum = x + x + 1 + x + 2+x + 3 + x + 4\)

Collect Like Terms

\(Sum = x + x + x + x + x+1 + 2 + 3 + 4\)

\(Sum = 5x+10\)

Divide sum by 5.

\(Result = \frac{5x + 10}{5}\)

\(Result = \frac{5(x + 2)}{5}\)

\(Result = x + 2\)

Hence, this is true because there is no fractional part after the division

Solving (c):

Let the numbers be: \(x, x + 1, x + 2,x+3\)

Their sum is:

\(Sum = x + x + 1 + x + 2+x + 3\)

Collect Like Terms

\(Sum = x + x + x + x + 1 + 2 + 3\)

\(Sum = 4x+6\)

Divide sum by 4.

\(Result = \frac{4x + 6}{4}\)

Split

\(Result = \frac{4x}{4} + \frac{6}{4}\)

\(Result = x + 1.5\)

The 1.5 means that the sum can not be divisible by 4

Answer:

6n-5

Step-by-step explanation:

Some different types of sequences

To find sequence patterns, often the sequences are arithmetic (adding by a constant amount) or geometric (multiplying by a constant amount).  

To test if something is a geometric sequence, find the quotient of (divide) adjacent terms.

To test if something is an arithmetic sequence, find the difference of (subtract) adjacent terms.

Finding the type of our sequence

Note the following:

19-13=6

13-7=6

7-1=6

So, to get each next term, add 6.  However, what is the nth term?

Finding an expression for our sequence

You'll be adding up "n" sixes to get there (expressed with multiplication, because multiplication is shorthand for repeated addition), but we need a starting point so that when n=1, the expression equals 1, and when n=2, the expression equals 7... and so on.  This starting point shifts the "6n" piece of our expression so that it lines up on the sequence.  I'm going to call this starting point "b" for the base that is supporting this sequence.

So the expression will look something like \(6n+b\)

Knowing that the expression needs to equal 1 when n=1, we can set up an equation and solve for "b".

\(6n+b=n^{\text{th}} \text{ term}\\6(1)+b=(1)\\6+b=1\\(6+b)-6=(1)-6\\b=-5\)

So, the expression for the nth term of the sequence is \(6n-5\)

Verifying

To verify that the expression we found is right, we can test our expression for each of the terms we do know:

The first term (n=1) is 1

\(6n+b=n^{\text{th}} \text{ term}\\\)

\(6(1)-5 \overset{?}{=} (1)\)

\(6-5 \overset{?}{=} 1\)

\(1 \overset{\checkmark}{=} 1\)

The second term (n=2) is 7

\(6n+b=n^{\text{th}} \text{ term}\\\)

\(6(2)-5 \overset{?}{=} (7)\)

\(12-5 \overset{?}{=} 7\)

\(7 \overset{\checkmark}{=} 7\)

The third term (n=3) is 13

\(6n+b=n^{\text{th}} \text{ term}\\\)

\(6(3)-5 \overset{?}{=} (13)\)

\(18-5 \overset{?}{=} 13\)

\(13 \overset{\checkmark}{=} 13\)

The fourth term (n=4) is 19

\(6n+b=n^{\text{th}} \text{ term}\\\)

\(6(4)-5 \overset{?}{=} (19)\)

\(24-5 \overset{?}{=} 19\)

\(19 \overset{\checkmark}{=} 19\)

Answer:

∠DCB = 32

Step-by-step explanation:

∠A + ∠B = 90

∠B = 90 - ∠A = 90 - 32 = 58

∠DCB + ∠B = 90

∠DCB = 90 - ∠B = 90 - 58 - 32

Answer:

solving the linear equation in terms of y and x will give you

y = -8

x = -2

Answer:

x=-2

y=-8

that's basically it.

Answer:

  (a)  15 -18i

Step-by-step explanation:

You want the simplified form of the expression -2i(5- i) + (17- 8i).

For many purposes, the value i in a complex number can be treated in the same way a variable would be treated. When simplifying an expression involving i, any instances of i² can be replaced with the real value -1.

  -2i(5- i) + (17- 8i) = -10i +2i² +17 -8i

  = -2 +17 +(-10 -8)i

  = 15 -18i

__

Additional comment

Your scientific or graphing calculator can probably help you evaluate such expressions.

Possible options:

uppercase letter: 26

lowercase letter: 26

number: 10

upper or lowercase letter: 50

Note: I'm interpreting the "no upper or lower case letters can be repeated in the sequence" to mean you could have Aa0b, where A is used as the uppercase and a is used as the lower case letter, but then you can't use A or a for the last character.

26 · 26 · 10 · 50 = 338,000 combinations

Now is using "A" and "a" isn't allowed, then you have:

Possible options:

uppercase letter: 26

lowercase letter: 25

number: 10

upper or lowercase letter: 48

26 · 25 · 10 · 48 = 312,000 combinations

Answer:

y = x^2 - 4.

Step-by-step explanation:

This graph is the reslt of translating y = x^2 down by 4 nits

Answer:

(2/3, 8/3)

Step-by-step explanation:

Using the line segment equation we get: (x,y)=(-6+2/3(4-(-6)), -4+2/3(6-(-4))=(2/3,8/3)

Answer:

Full Answer

Step-by-step explanation:

(-2,0)

As per given by the question,

There are given that a length of three sides of the triangle.

The length of sides are, 14cm, 22cm, and 30cm.

Now,

For finding the measure of the smallest angle,

The smallest angle in a triangle is always opposite the shortest side. and also the bigest angle is always opposite the longest side.

So,

Suppose length A is 14cm, B is 22 cm and C is 30cm.

Then,

From the law of cosines,

Let A be the smallest angle.

So,

Now,

Find the value of angle A,

Now,

Then,

Hence, the measure of the smallest angle is 25.84 degree.