62% of the people in a cinema are children.
If there are 93 children in the cinema, calculate the total number of people in the
cinema.
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\(\\ \sf\longmapsto \frac{7}{x} = \frac{15}{10} \\ \\ \sf\longmapsto 7 \times 10 = 15x \\ \\ \sf\longmapsto 15x = 70 \\ \\ \sf\longmapsto x = \frac{70}{15} \\ \\ \sf\longmapsto \boxed{ \sf x = 4.6cm}\)

Answer:

i can help you i know this answer

The below calculation allows us to determine the amount of fruit juice and punch needed to create a fruit punch that is entirely fruit juice.

To create a fruit punch that is entirely fruit juice, we must calculate the ratio of fruit juice to total punch. To do this, we will use the following formula:

Fruit Juice Ratio = (Fruit Juice / (Fruit Juice + Punch)) x 100

For example, if we have 10 ounces of fruit juice and 10 ounces of fruit punch, the ratio of fruit juice to total punch is 50%. Therefore, we need to mix 50% fruit juice with 50% punch to create a fruit punch that is entirely fruit juice.

To calculate this for any given amount of fruit juice and punch, we simply plug the numbers into the formula. For instance, if we have 20 ounces of fruit juice and 60 ounces of punch, the ratio of fruit juice to total punch is 25%. Therefore, we need to mix 25% fruit juice with 75% punch to create a fruit punch that is entirely fruit juice.

By using this formula, we can easily determine the amount of fruit juice and punch needed to create a fruit punch that is entirely fruit juice.

We can use the formula Fruit Juice Ratio = (Fruit Juice / (Fruit Juice + Punch)) x 100 to calculate the ratio of fruit juice to total punch. This allows us to determine the amount of fruit juice and punch needed to create a fruit punch that is entirely fruit juice.

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Answer: The area is 6.5

Answer:

Kayla and Rachel raised $8.39, Francesca raised $18.89.

Step-by-step explanation:

Knowing that $35.67 is the total amount raised, that Rachel and Kayla raised the same amount (x) each, and that Francesca raised $10.50 more than them (x + 10.50), then the equation would look like:

35.67 = x + x + (x + 10.50)

or

35.67 = 3x + 10.50

From here, you can solve algebraically.

Isolate the variable by subtracting 10.50 from both sides

25.17 = 3x

Then, find X by dividing both sides by 3:

x = 8.39

Knowing that Kayla and Rachel raised $8.39 each, to find Francesca's contribution you can either:

A) Subtract Kayla and Rachel's contributions from the total amount:

     35.67 - 8.39 - 8.39 = 18.89

or

B) Add $10.50 to the amount that Kayla and Rachel raised:

     8.39 + 10.50 = 18.89

In a simple linear regression model , if we change the input variable by 1 unit , output variable will change by its slope.

What is linear regression?

According on the value of another variable, a variable's value can be predicted using a linear regression analysis. The dependent variable is the one you're trying to forecast. The term "independent variable" refers to the variable you are using to forecast the value of the other variable.

For linear regression

Y=a + bx + error

If we neglect error

then Y=a + bx.

If x increases by 1

then Y = a +b(x+1) which implies

Y=a + bx + b.

So Y increases by its slope.

Hence their is an increase in the slope in y.

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The length of the hypotenuse is approximately 6.802 units and the length of the adjacent side is approximately 5.5 units in the right triangle where one angle measures 36 degrees and its opposite side measures 4 units.

To find the sides of a right triangle where one angle measures 36 degrees and its opposite side measures 4 units, we can use trigonometric ratios.

Let's label the sides of the triangle:
- The side opposite the angle of 36 degrees is called the opposite side and has a length of 4 units.
- The side adjacent to the angle of 36 degrees is called the adjacent side.
- The hypotenuse is the longest side of the right triangle and is opposite the right angle.

Using the trigonometric ratio for the sine function, we can find the length of the hypotenuse:

sin(angle) = opposite / hypotenuse

Plugging in the values we know:

sin(36 degrees) = 4 / hypotenuse

Now, we can solve for the hypotenuse by isolating it:

hypotenuse = 4 / sin(36 degrees)

Using a calculator, we find that sin(36 degrees) is approximately 0.5878.

hypotenuse ≈ 4 / 0.5878 ≈ 6.802

So, the length of the hypotenuse is approximately 6.802 units.

To find the length of the adjacent side, we can use the Pythagorean theorem:

adjacent^2 + opposite^2 = hypotenuse^2

Plugging in the values we know:

adjacent^2 + 4^2 = 6.802^2

Simplifying the equation:

adjacent^2 + 16 = 46.2496

Subtracting 16 from both sides:

adjacent^2 = 30.2496

Taking the square root of both sides:

adjacent ≈ √30.2496 ≈ 5.5

So, the length of the adjacent side is approximately 5.5 units.

In summary, the length of the hypotenuse is approximately 6.802 units and the length of the adjacent side is approximately 5.5 units in the right triangle where one angle measures 36 degrees and its opposite side measures 4 units.

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The  displacement x of the moving puck is; 0.43 meters

The displacement is defined as the change in position of an object. It is also called a vector quantity and has a direction and magnitude

The parameters given here are;

The polar coordinate initial velocity vector; U = 2.35 m/s, -22°

Final velocity vector; V = 6.42 m/s, +50°

This suggests to us that Cartesian x axis is parallel to angle 0° and y axis is parallel to +90°.

Change of velocity component parallel to +90° =  magnitude*sinθ,.

Thus, the change of that velocity

Δv = |V|sin(50) - |U|sin(-22)

Δv = 6.42sin(50) - 2.35sin(-22)

Δv = 4.9 - (-0.88)

Δv = +5.8 m/s

The equation for displacement is;

s = ut +1/2at^2

where acceleration time t = Δt = 0.215 s

initial velocity u = |U|sin(-22) = -0.88 m/s

acceleration parallel to u is a = Δv/Δt = +5.8/Δt

a = 5.8/t m/s^2

Thus;

s = -0.88t + ¹/₂* 5.8/t * t²

s = -0.88t +2.9t

s = 2.0t

s = 2.0 * 0.215

s = 0.43 m

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Answer:

negative square root 21 over 5.

Step-by-step explanation:

mathGiven that for an angle ,

We are to find the value of  

We know that

Cosine is negative in Quadrant II and Quadrant III.

Tangent is positive in Quadrant 1 and Quadrant III.

So, the given angle  lies in the Quadrant III.

We will be using the following trigonometric identity:

We have

Since the angle  lies in Quadrant III and sine is negative in that quadrant, so

Thus, option (B) is correct.

The range of the function f(x) = |x| is [0,∞)

The function is given as:

f(x) = |x|

The above is the parent equation of an absolute value function.

The above function cannot output any negative value.

This means that:

ƒ(x) >= 0

As an interval notation, we have:

[0,∞)

Hence, the range of the function f(x) = |x| is [0,∞)

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To minimize costs, the optimal distribution schedule for Finnish Furniture would involve shipping 130 units from Reno to Phoenix, 20 units from Denver to Cleveland, and 160 units from Pittsburgh to Chicago. This allocation is determined by using the transportation algorithm, specifically the Vogel's Approximation Method (VAM), which considers the lowest shipping costs per unit for each source-destination combination. By following this approach, the total cost for the distribution is calculated to be $4,360.

To determine the optimal distribution schedule that minimizes costs, we need to allocate the available supplies from the manufacturing facilities to the retail stores based on the shipping costs per unit. We can achieve this by employing the transportation algorithm, such as the North-West Corner Rule or the Vogel's Approximation Method (VAM).

Using VAM, we begin by identifying the lowest shipping cost per unit for each row and column in the given table. We then select the highest difference between the two lowest costs, considering both rows and columns. This difference indicates the most cost-effective allocation.

In this case, the VAM suggests shipping 130 units from Reno to Phoenix since the shipping cost per unit is 10, which is the lowest for the Reno row. For Cleveland, Denver has the lowest cost at 14, so we allocate 20 units from Denver to Cleveland. Lastly, we allocate 160 units from Pittsburgh to Chicago, as the cost per unit is the lowest at 12 for the Pittsburgh column.

Now, let's calculate the total cost. The cost of shipping 130 units from Reno to Phoenix is 130 x 10 = $1,300. Shipping 20 units from Denver to Cleveland costs 20 x 14 = $280. Lastly, shipping 160 units from Pittsburgh to Chicago costs 160 x 12 = $1,920. Adding these costs together gives us a total cost of $1,300 + $280 + $1,920 = $4,360.

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An equation to represent the other lengths, X, of the triangle is 2X+7=23.

An isosceles triangle is one that has two equal-length sides in geometry. The term "equilateral triangle" can refer to a shape with either exactly two sides that are the same length or at least two sides that are the same length, with the latter definition containing the equilateral triangle as an exception. The faces of bipyramids and a few Catalan solids are examples of isosceles triangles, as are the isosceles right triangle, the golden triangle, and others.

Isosceles triangles have been the subject of mathematical research since the time of the Babylonians and the Egyptians.

Given,

Perimeter of an isosceles triangle=23 meters

The base of a triangle=7 meters

P=2X+b

2X+7=23

Therefore, an equation to represent the other lengths, X, of the triangle is 2X+7=23.

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The area A of the region bounded by the functions f(x) = 2x\(x^{2}\)2/3 - x - 4 and g(x) = x\(x^{2}\)2 - 2x/3 - 6 can be calculated using the integral: A = int_[−2, 4] f(x) - g(x) dx. The integral evaluates to A = 65/3 units.

To evaluate the integral, we will first use u-substitution with u = x\(x^{2}\)2/3 and du = 2x/3dx. This substitution simplifies the integral to A = int_[−2\(x^{2}\)3, 4\(x^{2}\)3] (2u/3 - u - 4) du.

Next, we use integration by parts with u = 2u/3 - u - 4 and dv = du. This gives us A = (2u/3 - u - 4)v - int_[−2\(x^{2}\)3, 4\(x^{2}\)3] vdu.

We can now find the integral for v by integrating du, giving us v = u + C. Since v must equal zero when u = −2\(x^{2}\)3, we can set C = -2\(x^{2}\)3 and simplify the integral to A = (2u/3 - u - 4)(u + -2\(x^{2}\)3) - int_[−2\(x^{2}\)3, 4\(x^{2}\)3] (u + -2\(x^{2}\)3)du.

Finally, we can find the integral for u + -2\(x^{2}\)3 by integrating du again, giving us (u + -2\(x^{2}\)3) = 3u\(x^{2}\)2/2 + 2\(x^{2}\)3u + C. We can set C = 0 since u + -2^3 must equal zero when u = −2\(x^{2}\)3, and simplify the integral to A = (2u/3 - u - 4)(u + -2\(x^{2}\)3) - int_[−2\(x^{2}\)3, 4\(x^{2}\)3] (3u\(x^{2}\)2/2 + 2\(x^{2}\)3u) du.

Evaluating this integral gives us A = (2u/3 - u - 4)(u + -2\(x^{2}\)3) - 3(4\(x^{2}\)5/2 + 8\(x^{2}\)4)/2 + 2\(x^{2}\)3(4\(x^{2}\)3 + 8\(x^{2}\)2)/2. Substituting in u = 4\(x^{2}\)3 and u = -2\(x^{2}\)3 gives us A = 65/3 units.

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24 centimeters. Hope this helped!

B seems like the corrects answer because wen dont know how many days and he has 60 dollars

Answer:

B

Step-by-step explanation:

7d is how much money he spends on lunch in all

then you need to subtract from 60 because that is the total amount of money he has

Answer:

c. 141 eighth-grade band students

Part B:

y = 3x

1/3y = x

substitute 140 for 'y', because 'y' is the amount of available cabinets (they need to be available in order for it to be installed).

you have;

140 = 8x + 40

solve for x from here

Answer:

Step-by-step explanation:

To find out how many weeks it will take to fill the high school's order, we need to solve the equation for the number of weeks (x). We can start by plugging in the given value of 104 for y since y represents the number of cabinets, and then solving for x:

y = 8x + 40

104 = 8x + 40

-40           -40

64 = 8x

x = 8

Therefore, it will take 8 weeks to produce enough cabinets to fill the high school's order.

By using the Uniform distribution, we get that the value of standard deviation of weight over a day is 1.15..

The Uniform distribution is a normal continuous probability distribution and it is concerned about an events which are equally likely to occur.

According to question, we have change in water weight are uniformly distributed between -2 and 2 pounds in a day.

let X be random variable on given intervals, U( a,b).

X ~ U(a,b ) where a is lowest value

and b is upper limit of distribution. then a = -2 and b=2

probability function in uniform distribution is

f(x) = 1/ b-a

As we know, the formula of variance in uniform distribution is (b - a)²/ 12

= ( 2-(-2))²/12 = 16/ 12 = 4/3

Now , we shall find out the value of standard deviations for given requirement.

standard deviations = sqrt(variance)

= sqrt( 4/3) = 2√3 / 3 = 1.15

So, we get the required result.

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The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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Answer:

scientific notation

Step-by-step explanation:

This number is shown in scientific notation.

Answer:

0.00000146

Step-by-step explanation:

I took the test

Answer:

Two expressions for the area are;

i) x/3 + 2·y + 6

ii) (1/3) × (x + 6·y + 18)

Step-by-step explanation:

The given dimension of the rectangle are;

The height of the rectangle, h = 1/3

The width of the smallest rectangle, w₁ = x

The width of the med sized rectangle, w₂ = 6·y

The width the large rectangle, w₃ = 18

The area, 'A', of the entire rectangular figure, the big rectangle, can be expressed as follows;

A = A₁ + A₂ + A₃

Where;

A₁ = The area of the smallest rectangle

A₂ = The area of the mid sized rectangle

A₃ = The area of the large rectangle

∴ A = (1/3) × x + (1/3) × 6·y + (1/3) × 18 = x/3 + 2·y + 6

The area of the big rectangle. 'A', can also be found as follows;

A = (1/3) × (x + 6·y + 18)

Therefore, two expressions for the area of the big rectangle are;

x/3 + 2·y + 6 and (1/3) × (x + 6·y + 18).

The measure of angle MNP is 180 - angle MPO - angle NPM = 80 degrees. Perpendicular Bisector Theorem can be used to find the measure of angle NPM.

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Conversely, if a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment. In other words, the perpendicular bisector of a segment is the set of all points that are equidistant from the endpoints of the segment.

We can use the theorem that states "If a line is perpendicular to two intersecting lines at their point of intersection, then it divides the angles into two congruent angles." This theorem is called the Perpendicular Bisector Theorem.

Using this theorem, we know that angle MPO and angle NPM are congruent. We also know that angle MPO and angle NOO are supplementary (since OP is perpendicular to ON). Therefore, we can find the measure of angle NPM as follows:

angle MPO = angle NPM (by the Perpendicular Bisector Theorem)

angle MPO + angle NOO = 180 degrees (by the definition of supplementary angles)

angle NOO = 180 - angle MPO = 180 - 50 = 130 degrees

angle MPO = angle NPM

angle NPM = angle MPO = 50 degrees

Therefore, the measure of angle MNP is 180 - angle MPO - angle NPM = 80 degrees.

We can use the Perpendicular Bisector Theorem to find the measure of angle NPM.

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The distributed computation (e, →) is said to be consistent if all computations lead to the same result, regardless of the order in which the steps are performed.

Let g and h be consistent cuts of a distributed computation (e, →).

We must demonstrate that g ∪ h and g ∩ h are also consistent cuts of (e, →).

Let R be the set of events that are in both g and h. If we remove R from either g or h, we get a consistent cut since the removed events cannot cause a change in the outcome.

By removing R from both g and h, we obtain two new consistent cuts: g − R and h − R.

Thus, we can write:g = (g − R) ∪ R and h = (h − R) ∪ R. Since (g − R) and (h − R) are consistent cuts, it follows that their union, g ∪ h, is also a consistent cut. I

f we let S be the set of events that are in both g and h, then we can write:g = (g ∩ h) ∪ (g − S) and h = (g ∩ h) ∪ (h − S).

Again, (g − S) and (h − S) are consistent cuts, so their intersection, g ∩ h, is also a consistent cut.

Therefore, if g and h are consistent cuts of a distributed computation (e, →), then so are g ∪ h and g ∩ h.

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Answer:

1.) 120

2.)120

Step-by-step explanation:

1.) Do length times width

2.) For the number 120 you don't have to round, so it just stays the same

The mean of the number of drivers expected not to be wearing seatbelts is approximately 4.35, the variance is approximately 15.62, and the standard deviation is approximately 3.95 and they expect to stop approximately 4.35 cars before finding a driver whose seatbelt is not buckled.

a. To find the mean, variance, and standard deviation of the number of drivers expected not to be wearing seatbelts, we can model the situation using a geometric distribution.

Let's define a random variable X that represents the number of cars stopped until the first driver without a seatbelt is found. The probability of a driver not wearing a seatbelt is given as p = 0.23.

The mean (μ) of a geometric distribution is given by μ = 1/p.
μ = 1/0.23 ≈ 4.35

The variance (σ^2) of a geometric distribution is given by σ^2 = q/p^2, where q = 1 - p.
σ^2 = (0.77)/(0.23^2) ≈ 15.62

The standard deviation (σ) is the square root of the variance.
σ = √(15.62) ≈ 3.95


b. The expected number of cars they expect to stop before finding a driver whose seatbelt is not buckled is equal to the reciprocal of the probability of success (finding a driver without a seatbelt) in one trial. In this case, the probability of success is p = 0.23.

Expected number of cars = 1/p = 1/0.23 ≈ 4.35

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In the given graph, the independent variables represent those factors that are manipulated by the researcher. On the other hand, the dependent variable represents the effect of the independent variable(s).Let's first understand the given graph - it shows data from the light-colored soil enclosure.

There is one dependent variable and more than one independent variable on the graph. Based on this information, it can be concluded that the graph represents the result of an experiment where multiple factors were tested to observe their impact on the dependent variable. Now, coming to the question, we need to identify the independent variables from the graph. Unfortunately, the graph is not available here to analyze and provide an accurate answer. Suppose the experiment aimed to study the effect of different factors on the growth of plants in light-colored soil. Some independent variables that could be manipulated by the researcher are:

Amount of water provided to the plants Type of fertilizer used for the soil Temperature of the enclosure Humidity level inside the enclosure Intensity and duration of light exposure. Amount of water provided to the plants, type of fertilizer used for the soil, temperature of the enclosure, humidity level inside the enclosure, intensity, and duration of light exposure.

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The value of angle a and b cannot be determined.

option D.

The value of angle a and b is determined by applying the principle of congruent theorem.

If all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other.

a = 180 - ( 60 + x ) ( sum of angles in a triangle )

b = 180 - ( 40 + y ) ( sum of angles in a triangle )

Since the values of x and y are not know, it is impossible to say what the values of angle a and angle b are.

So, the value of a and b cannot be determined, more information is needed.

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The equation y = x² + 2 is a non linear equation.

Since,

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Here, We have;

The equation is,

y = x² + 2

Since, The degree of x is 2.

Hence, It is a quadratic equation.

Thus, The equation y = x² + 2 is a non linear equation

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Answer:

6 square units

Step-by-step explanation:

Given shape is of a trapezoid:

\(area \: of \: trapezoid \\ = \frac{1}{2} \times (4 + 2) \times 2 \\ \\ = 6 \: {units}^{2} \)

Area of shape = area of square + area of triangle

\( = 2^2 + \frac{1}{2} \times 2\times 2\\

= 4 + 2\\

= 6\: units^2 \\\)

Answer:

7

Step-by-step explanation: