A restaurant has a capacity of 120 patrons. If the restaurant is full, how many patrons are at the restaurant?

The equation that can be used to find the cost of each ticket is 4x = 52.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 6 is an equation.

We have,

Number of people who bought the tickets = 4

The total cost of tickets = $52

Now,

The cost of each ticket.

= 52 ÷ 4

= 13

Now,

Cost of one ticket = x

4x = 52

x = 52/4 = 13

Thus.

The cost of each ticket is $13.

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Answer:

the opposite of the fraction is 3/8

Answer: 4, -40, -3

Step-by-step explanation: got it right

Answer:

4, -40, -3    

I hope this helps :)

The value of c in the triangle is (b) 5 units

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

The right triangle

The length c is the hypotenuse of one of the triangles and can be calculated using the following Pythagoras theorem

c² = sum of squares of the legs

Using the above as a guide, we have the following:

c² = 3² + 4²

Evaluate

c² = 25

Take the square roots

c = 5

Hence, the hypotenuse of the right triangle is 5

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Answer:

gehsjskkskskkskdhdhjs

\(f(x) +g(x) = 3x^2 +x -9\)

Given:

\(f(x) = x -9\)

\(g(x) = 3x^2\)

Writing \(f(x) +g(x)\):

\(f(x) +g(x) \\ (x -9) +(3x^2) \\ x -9 +3x^2 \\ 3x^2 +x -9\)

Answer:

Proof below

Step-by-step explanation:

Irrational and Rational Numbers

We need to use the basic property of logarithms:

\(log_b\ a=x\ \ \Rightarrow b^x=a\)

We are given:

\(log_3\ 7\)

And we will prove it's an irrational number, i.e., it's not a rational number.

Recall a rational number can always be expressed as a fraction a/b, where a and b are integer numbers. Thus, if the expression was a rational number, then:

\(\displaystyle log_3\ 7=\frac{a}{b}\)

Applying the property:

\(\displaystyle 3^{\frac{a}{b}}=7\)

Raising to the power of b:

\(3^a=7^b\)

It's not possible to find two integers a and b that satisfy the condition above. That contradiction comes from the assumption that \(log_3\ 7\) is rational, thus, it's proven \(log_3\ 7\) is irrational.

Answer:

3.25

Step-by-step explanation:

thats how absolute value works

The reflection of the graph in the x-axis gives the function

g(x) = -x² - 3x - 2

The given function is of the form f(x) = x² + 3x + 2 which represents a parabola.

The vertex of the function is at (-3/2 , -1/4)

The focus is at ( 3/2 , 0 )

The axis of symmetry is 2x+3 = 0 and the directrix is at 2x + 1 = 0

Now when the parabola is reflected along the x-axis we get

the focus at ( -3/2 , 0 )

the vertex is at  (-3/2 , 1/4)

Axis of symmetry remains the same

The directrix becomes 2y-1 =0

The red graph denotes the function f(x) while the blue graph denotes the function g(x) reflected on the x-axis.

Hence the reflection on the x-axis gives the function g(x) = -x² - 3x - 2

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It takes 10 minutes for the number of bacteria in the population to double.

To determine the time it takes for the number of bacteria in a population to double, we need to find the value of t when the function f(t) equals twice the initial number of bacteria.

The given function is f(t) = 60,000 * 2^(t/10).

To find the time it takes for the number of bacteria to double, we set f(t) equal to twice the initial number of bacteria, which is 2 * 60,000 = 120,000:

120,000 = 60,000 * 2^(t/10).

Next, we can simplify the equation by dividing both sides by 60,000:

2 = 2^(t/10).

Since both sides of the equation have the same base (2), we can equate the exponents:

t/10 = 1.

To solve for t, we multiply both sides by 10:

t = 10.

Therefore, it takes 10 minutes for the number of bacteria in the population to double.

This result is obtained by setting the growth rate of the bacteria population in the given function. The exponent t/10 determines the rate of growth, and when t is equal to 10, the exponent becomes 1, resulting in a doubling of the initial number of bacteria.

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The blank spaces in the statements area. S, R, and Q  are distinct points that are collinear: b. TX and QS are distinct lines that intersect. c. Point Y and line QS are coplanar. d. Another name for plane P is: plane QSY.

Points that lie on the same straight line are collinear points.

If two lines are lie on the same plane, they are referred to as coplanar lines.

(a.) S, R, and Q are on a straight line. Therefore S, R, and Q  are distinct points that are collinear.

b. TX and QS are distinct lines that intersect.

c. Point Y and line QS are on the same plane. Therefore:

Point Y and line QS are coplanar.

d. Another name for plane P is: plane QSY.

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Answer: If you divide a trinomial by a monomial the result is a bionomial

A. True

B. False

Step-by-step explanation: tell me the correct answer and I'll tell you

Answer:

The distance formula is an algebraic expression used to determine the distance between two points with the coordinates (x1, y1) and (x2, y2).

Example

Find the distance between (-1, 1) and (3, 4).

This problem is solved simply by plugging our x- and y-values into the distance formula:

Sometimes you need to find the point that is exactly between two other points. This middle point is called the "midpoint". By definition, a midpoint of a line segment is the point on that line segment that divides the segment in two congruent segments.

If the end points of a line segment is (x1, y1) and (x2, y2) then the midpoint of the line segment has the coordinates: HOPES THIS HELPS

Step-by-step explanation:

Answer:

0.75 U.S. dollars

Step-by-step explanation:

Answer: seventy-five cents

Answer: 4.8

Step-by-step explanation:

Answer:

Did you even look at it? g(x)=2x

Step-by-step explanation:

2x-6=2(x-3), or 2(x).

The required formula of g(x) is 2x.

We have to determine, formula for g(x) if it is known that g(x-3) = 2x-6.

To obtain the formula of g(x) follow all the steps given below.

According to the question,

The formula of g(x),

g(x - 3) = 2x - 6

          Then,

           \(g(x - 3) = 2x - 6 = 2x - 2\times 3\)

            \(=2x -2\times 3\\\\ = 2(x - 3)\\\\\ let \ x-3 = y\\\\ = 2y\)

           Then,

            \(g( x - 3) = g(y) = 2y\)

       Then,

       g(x) = 2x

Hence, The required formula of g(x) is 2x.

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Answer:

b. 5 meters

Step-by-step explanation:

1 meter = 1000 millimeters

5 meter = 5000 millimeters

Which is longer 5 meters or 400 millimeters?

5000 > 400

So, the answer is b. 5 meters.

Answer:

Step-by-step explanation:

3.6*

It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2

For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.

We get

36 = s^2

Now, we need to get the square root of both sides, which gives us

s = √36 s = 6 cm

Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.

Therefore, the perimeter of the square is 24 cm.

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Answer:

9.358

9.36 (rounded to the nearest hundredths)

9.4 (rounded to the nearest tenth)

Step-by-step explanation:

d = C/π = 29.4/π ≈ 9.358

Given:

The instruction to draw equilateral triangle inscribed in a circle.

Required:

Mark instruction as step 1, step 2 in correct order.

Explanation:

So, the order for constructing equilateral triangle is as points are given. We will give each one by one name step 1, step 2, step ,step 4, step 5, step 6, step 7, step 8.

Answer:

1, 2, 3, 4, 5, 6, 7, 8 are the answers of respective boxes.

To contrast the measurements we convert them with inches. For this, we really want to realize that there are 12 inches in a foot and 3 feet in a yard. So there are 3×12=36 inches in a yard.

Sarah's height is now in inches. Jake's height is 414 feet. This is the same as 4+14 feet. Since there are 12 inches in a foot, there are 4×12=48 inches in 4 feet, and 3 inches in a 14 foot. So Jake's height in inches is 48+3=51 inches.

For Andy, we have seen that there are 36 inches in a yard, so there are 18 inches in half a yard, so in inches, Andy's height is 36+18=54.

At long last, Emily is 4 feet and 4 inches tall. There are 4×12=48 inches in 4 feet, so Emily is 48+4=52 inches tall.

The table shows every one of the heights in inches, in decreasing order.

Student Height in Inches

Andy 54

Emily 52

Jake 51

Sarah 50

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the complete question is:

Mr. Liu asked the students in his fourth-grade class to measure their heights. Here are some of the heights they recorded:

Student Height

Sarah 50 inches

Jake 414 feet

Andy 112 yards

Emily 4 feet and 4 inches

List the four students from tallest to shortest.

\(\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o\)

Make sure your calculator is in Degree mode.

The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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Answer:

Step-by-step explanation:

To factor the expression, we need to identify any common factors that can be pulled out of the terms.

The terms g²r and 9²₂² have a common factor of g². The terms 6g²rs²t and -6g²rs²t have a common factor of -6g²rs²t. The term 5422 does not have any factors in common with the other terms.

Therefore, the expression can be factored as:

(-6g²rs²t)(g²r + 9²₂²) + 5422

This is the fully factored form of the expression.


????

Answer:

2

Step-by-step explanation:

mean = sum of data / no of data

=2+2+2+2+2/5

=10/5

=2

Answer:

42

Step-by-step explanation:

2+10+3*10 =42 because there are 2 boxes inside each there are 5 then inside each boxes are 3

To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.

First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:

C = π × 26

C ≈ 81.64 inches

This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.

Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:

1200 / 81.64 ≈ 14.68 revolutions

Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.

Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.

Therefore, the tack is located 13 inches above the ground.

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Answer:

\(\displaystyle 64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\approx3.66\)

Step-by-step explanation:

\(\displaystyle \iint_R(3x-y)\,dA\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r\cos\theta-r\sin\theta)\,r\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r^2\cos\theta-r^2\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0r^2(3\cos\theta-\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\frac{64}{3}(3\cos\theta-\sin\theta)\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\biggr(64\cos\theta-\frac{64}{3}\sin\theta\biggr)\,d\theta\)

\(\displaystyle =\biggr(64\sin\theta+\frac{64}{3}\cos\theta\biggr)\biggr|^\frac{\pi}{2}_\frac{\pi}{4}\\\\=\biggr(64\sin\frac{\pi}{2}+\frac{64}{3}\cos\frac{\pi}{2}\biggr)-\biggr(64\sin\frac{\pi}{4}+\frac{64}{3}\cos\frac{\pi}{4}\biggr)\\\\=64-\biggr(64\cdot{\frac{\sqrt{2}}{2}}+\frac{64}{3}\cdot{\frac{\sqrt{2}}{2}}\biggr)\\\\=64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\biggr\\\\\approx3.66\)

Answer:

\(\mathbf{\iiint_W (x^2+y^2) \ dx \ dy \ dz = \dfrac{2}{15}}\)

Step-by-step explanation:

Given that:

\(\iiint_W (x^2+y^2) \ dx \ dy \ dz\)

where;

the top vertex = (0,0,1) and the  base vertices at (0, 0, 0), (1, 0, 0), (0, 1, 0), and (1, 1, 0)

As such , the region of the bounds of the pyramid is: (0 ≤ x ≤ 1-z, 0 ≤ y ≤ 1-z, 0 ≤ z ≤ 1)

\(\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \int ^{1-z}_0 \int ^{1-z}_0 (x^2+y^2) \ dx \ dy \ dz\)

\(\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \int ^{1-z}_0 ( \dfrac{(1-z)^3}{3}+ (1-z)y^2) dy \ dz\)

\(\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \ dz \ ( \dfrac{(1-z)^3}{3} \ y + \dfrac {(1-z)y^3)}{3}] ^{1-x}_{0}\)

\(\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \ dz \ ( \dfrac{(1-z)^4}{3}+ \dfrac{(1-z)^4}{3}) \ dz\)

\(\iiint_W (x^2+y^2) \ dx \ dy \ dz =\dfrac{2}{3} \int^1_0 (1-z)^4 \ dz\)

\(\iiint_W (x^2+y^2) \ dx \ dy \ dz =- \dfrac{2}{15}(1-z)^5|^1_0\)

\(\mathbf{\iiint_W (x^2+y^2) \ dx \ dy \ dz = \dfrac{2}{15}}\)