Diego drew a scale drawing of the elementary school. The scale he used was 9 millimeters : 4 meters. In the drawing, the schoolyard is 324 millimeters long. What is the length of the actual schoolyard?

The value of the expression one fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x is 2 - 2/15x.

It should be noted that expressions are simply used to show the relationship that exists between the variables that are given.

In this case, one fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x will be illustrated as:

= 1/5(3x + 10) - (11/15x)

= 3/5x + 2 - 11/15x

= 9/15x + 2 - 11/15x

= 2 - 2/15x

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The expected payback  is mathematically given as

$10

This is further explained below.

Generally, The formula for calculating the anticipated payback is the product of the likelihood times the value.

E(x) = p(x_1)*x_1 + p(x_2)*x_2 + .....

In this particular scenario, we have two distinct options for repayment.

winning

The payback is $2000-$10 = $1990

x_1 = 1990

The probability of winning is one out of 100 (since the choices are 0 to 99)

p(x_1) = 1/100

Losing

The payback is negative $8 since the individual did not win anything, which makes them lose.

x_2 = -10

Because there is only one number that can win, the other 99 numbers are considered to be losing numbers.

p(x_2) = 99/100

Therefore expected payback is

E(x) = p(x_1)*x_1 + p(x_2)*x_2

= (1/100)* 1990+ (99/100)*(-10)

= $10

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CQ

Find the expected payback for a game in which you bet $10 on any number from 0 to 999. If your number comes up, you get $2000

The expected payback is

The base and height of the triangle are 9 cm and 14 cm respectively.

The height of the triangle is 5 centimetres greater than the base.

The area of the triangle is 63 cm².

Therefore,

area of a triangle = 1 / 2 bh

where

Therefore,

h = 5 + b

Hence,

area of a triangle = 1 / 2 × b × (5 + b)

area of a triangle =  1 / 2 × 5b + b²

63 = 5b + b² / 2

cross multiply

126 = 5b + b²

b² + 5b - 126 = 0

b² + 14b - 9b  - 126 = 0

b(b + 14) - 9(b + 14) = 0

(b + 14)(b - 9) = 0

b = -14 or b = 9

Therefore, the base can only be positive .

Hence,

Base of the triangle = 9 cm

height of the triangle = 9 + 5 = 14 cm

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[tex]x \leqslant 48[/tex]

The domain and range of the given inequality graph are; Domain: {x | -2 ≤ x ≤ 2} and Range: {x | -6 ≤ x ≤ 6}

The domain of a function is the set of all possible input values that make a function possible. Meanwhile the range of a function is the set of all possible output values that make a function possible.

Now, when dealing with an inequality graph, it is pertinent to note that a shaded dot implies less than or equal to (≤) or greater than or equal to (≥) while unshaded means less than or greater than.

Now. the range of the graph is closed from y = -6 to y = 6. Thus, the range is; {y| -6 ≤ y ≤ 6}

Meanwhile the domain of the graph is closed from x = -2 to x = 2. Thus, the domain of the graph is;

{x | -2 ≤ x ≤ 2}

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Number 2 is not a function, because we have more that one value of x that is the same

Number 3 is also not a function, we have more than one value of x that is the same

Number 4 is also not a function

Therefore, only number 1 is a function

The perimeter in feet of a rectangle with height 4 1/6 feet and width 3 1/3 is 15 feet.

It should be noted that the perimeter of a rectangle is calculated thus:

Perimeter = 2(Length + Width).

Based on the information, the following can be deduced:

Length = 4 1/6 feet

Width = 3 1/3 feet

Perimeter = 2(Length + Width).

Perimeter = 2(4 1/6 + 3 1/3)

Perimeter = 2(7 1/2)

Perimeter = 15 feet

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Differentiation of the given function f(x)=sinx/(1+tanx)​ is equal to

(cos³x -sin³x) / (cos²x)(1 + tanx)².

As given in the question,

Given function : f(x) = sinx /(1 + tanx )

Let u = sinx , v = ( 1 + tanx)

Differentiate the given function with respect to x

du/dx = cosx

dv/dx = sec²x

         = 1/cos²x

(d/dx)(f(x)) = (d/dx)(sinx /(1 + tanx ))

                = ( d/dx) (u / v)

                = [v (du/dx) -u (dv/dx)] / (v)²

               = [(1+tanx)(cosx) -(sinx)(1/cos²x)] / (1 + tanx)²

               = [cos²x(cosx + sinx) -sinx]/ (cos²x)(1 + tanx)²

               = [cos³x +sinx(cos²x -1)] / (cos²x)(1 + tanx)²

               =  (cos³x -sin³x) / (cos²x)(1 + tanx)²

Therefore, differentiation of the given function f(x)=sinx/(1+tanx)​ is equal to

(cos³x -sin³x) / (cos²x)(1 + tanx)².

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The probability that the person has either had Covid or has been vaccinated and therefore has some protection against Covid is 45%

From the question given, the following data were obtained:

The probability that the person has either had Covid or has been vaccinated and therefore has some protection against Covid can be obtained as follows:

The percentage of person that had Covid and not vaccinated

= 40% - 25%

= 15%

The percentage of person that has been vaccinated and never had Covid

= 55% - 25%

= 30%

The probability that the person has either had Covid or has been vaccinated

= 15% + 30%

= 45%

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There are three main distinctions between AAA, ASA, and SSS:

AAA: A triangle is said to be comparable to another if any two of its three angles are equal to any two of its three angles.

ASA: According to the ASA rule, two triangles are said to be congruent if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and the side located between the angles of the second triangle.

SSS: According to the SSS rule, two triangles are considered to be congruent if all three sides of one triangle are comparable to the corresponding three sides of the other triangle.

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Supposing that the two points are (2,4) and (10,10), the distance between them is given by:

A. 10.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.

For this problem, the two points are (2,4) and (10,10), hence the distance between them is given as follows:

[tex]D = \sqrt{(10 - 2)^2+(10 - 4)^2} = \sqrt{100} = 10[/tex]

Hence the distance is of 10 units and option A is correct.

This problem is incomplete, and I could not find it on any search engine, hence we are going to suppose that the two points are (2,4) and (10,10).

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the vectors are :  (i+5j) , (5i+j)

Here a vector is an object that has both a magnitude and a direction. Geometrically, able to picture a vector as a coordinated line fragment, whose length is the magnitude of the vector, and with an arrow demonstrating the direction. The direction of a vector is from its tail towards its head. Two vectors are the same on the off chance that they have the same magnitude and direction. We signify vectors utilizing boldface as in a or b. In the given graph we can see, for the vector T, it is 1 unit on the x-axis and 5 units on the y-axis, whereas for the vector S its 5 units on the x-axis and 1 unit on the y-axis. Since the unit vectors for the x-axis and y-axis are i and j,

So, the vectors will  i+5j and 5i+j

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Solution:

Given:

To get the precise name of the quadrilateral PQRS, using the coordinates of the points given;

The distance between points P and Q, and points Q and R are the same.

Also the distance between points P and S, and points R and S are also the same.

This means;

Hence, the image is as shown;

By the property of a kite, which says that two pairs of consecutive sides are congruent sides.

Hence, the most precise name for the quadrilateral PQRS is a KITE.

Answer:

[tex]2x^2+23x-10[/tex]

Step-by-step explanation:

1) distribute the parenthesis by multiplying 5 into (x^2 - 2) and -3x into (x - 7)

[tex]5x^2-10 +2x-3x^2+21x\\[/tex]

2) simplify by adding and subtracting like terms

[tex]2x^2+23x-10[/tex]

The x and y values that makes the relation a function are x = -4, y = 0, x = 5, y = -1 and x = 2, y = 8

The ordered pairs are given as

(− 3, 7), (–2, 3), (0, 8), (1, − 1), (x,y)

For a list of ordered pairs to represent a function, the following must be true

The x values must have exactly one y value

Using the above as a guide, we can see that x = -4, y = 0, x = 5, y = -1 and x = 2, y = 8 fits the above description

Hence, the values of x and y are x = -4, y = 0, x = 5, y = -1 and x = 2, y = 8

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The probability that the aircraft is overloaded is 97.98%, which means the pilot should take the action.

In a Normal distribution with mean ц and standard deviation σ, the z-score of a measure x is given by:

Z = X-ц / σ

· It measures how many standard deviations the measure is from the mean.

· After finding Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

· By the Central Limit Theorem, the sampling distribution of sample means of the size n has standard deviation σ

σ = σ / [tex]\sqrt{n}[/tex]    

σ is standard deviation

n is the sample size.

Given that the mean and the standard deviation of the population is 176.1 lb and 35.4 respectively.

⇒ ц = 176.1  and σ = 35.4

For a sample of 43 passengers, we have

n = 43

σ =  [tex]\frac{35.4}{\sqrt{43}}[/tex]

σ = 5.398

Z = X-ц / σ

Z = [tex]\frac{165-176.1}{5.398}[/tex]

Z = -2.05 has p- value of 0.9798

The probability that the aircraft is loaded is

1 - p-value of Z

1 - 0.0202 = 0.9798

The probability that the aircraft is overloaded is 97.98%

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x − 8 =  − 10

Explanation: 9x −13 = − 31 Add 13 to each side.

Answer:

-1

Step-by-step explanation:

3x = 21

Divide both sides by the co efficient of x

3x = 21

3      3

x = 21/3

x = 7

Find x - 8

x = 7

7 - 8

= -1

Answer: 50%

Step-by-step explanation:

when you divide 90 by 2 you get 45 so 45+45=90

Answer: 8% of the students in the sixth grade are girls

Step-by-step explanation:

Step-by-step explanation:

Solve for X for one equation then input that value into the other equation.

x+2y=9

x=9-2y

x-y=3

(9-2y)-y=3

9-3y=3

6=3y

y=2

x=5

The value of the y-coordinate of the system of equations is y=2.

I hope it help

Answer:

Step-by-step explanation:

Total attendance = 500 people

Parents of children in play = 65% of 500

=>0.65 * 500

=> 325

325 were the parents of children in the play.

Equation: h(t) = 96t - 16t²

h(t) = 96t - 16[tex]t^{2}[/tex]

Find the zeros of the given equation:

Factor out the greatest common factor (GCF)

h(t) = 8t (12 - 2t)

The two factors are:

0 = 8t

0 = 12 - 2t

For both factors, solve for t

8t = 0

8t/8 = 0/8

t = 0

12 - 2t = 0

-2t = -12

t = 6

Now we have the x-values (t) of our zeros:

t = 0

(0, 0)

t = 6

(6, 0)

The ball will land on the ground at 6 seconds

Recall that the maximum point of the graph is halfway between the two zeros:

6 + 0 = 6

6 ÷ 2 = 3

The ball will reach its maximum height in 3 seconds

To find this height, substitute t for 3 in the given equation, and solve for h:

t = 3

h(3) = 96(3) - 16(3)²

       = 288 - 16(9)

       = 288 - 144

       = 144

The maximum height the ball will reach is 144 feet

***Refer to the graph below to check your answer:

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

Explanation:

I'll use x in place of t

And use y in place of h(t)

The equation we have is y = 96x - 16x^2

This rearranges to y = -16x^2 + 96x

Compare this to y = ax^2+bx+c to find that

The x coordinate of the vertex is

h = -b/(2a)

h = -96/(2*(-16))

h = 3

Then plug this into the equation to find the value of y

y = -16x^2 + 96x

y = -16(3)^2 + 96(3)

y = 144

The y coordinate of the vertex is k = 144

The vertex is located at (h,k) = (3, 144) to represent the highest point of the parabola.

The max height of 144 feet occurs when the ball is in the air for 3 seconds.

Answer: straight line that makes the right angle (90 degrees) with the other

Step-by-step explanation: In other words, if two lines intersect each other at the right angle, then the lines are perpendicular to each other

After evaluating the limit we have came to find that the limit of   [tex]\lim_{x\rightarrow \infty }-\frac{3x^2}{x^2\ +4}[/tex] as x approaches ∞ is -3

A limit is the value that a function, sequence, or index approaches as an input or index approaches a specified value in mathematics. Limits are required in the definitions of continuity, derivatives, and integrals, which are essential in calculus and mathematical analysis.

The notion of a limit of a sequence is further generalized to include the notion of a limit of a topological network, in addition to being closely related to the concepts of limit & direct limit in category theory.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit we will use L'Hôpital's Rule

Find the derivative

⇒ [tex]\lim_{x\rightarrow \infty }-\frac{3x^2}{x^2\ +4}[/tex]

⇒ [tex]\lim_{x\rightarrow \infty }-\frac{6x}{2x + 0}[/tex]

⇒ [tex]\lim_{x\rightarrow -\infty }\frac{-6x}{2x }[/tex]

Evalúe ∞ as x

⇒ [tex]\frac{-6(\infty)}{2(\infty)} }[/tex]

⇒ -3

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From the triangle given, we are required to solve for x and y.

Since they are similar triangles, let's find x and y below.

For x:

Let's find x, from the equation above.

Cross multiply:

Divide both sides by 8:

For y:

ANSWER:

x = 1.25, y = 1.75

Answer: C=D\A-B THAT IS THE ANSWER

Step-by-step explanation:

It is to be noted that at the equilibrium level, the Equilibrium price/output combination is $4 and 300,000 units respectively. See further calculations and answer below.

Recall that the equilibrium level of the national income is defined as that point where the aggregate supply  (QS) and the aggregate demand (AQD) are the same.

To calculate the market equilibrium price/output combination (EQL:

Step I - Recall the given data

Recall that at EQL, QD = QS

Where:

Qd = 500000 – 50000P; and ....................1

Qs = -100000 + 100000P. ...........................2

Hence, at EQL,

500000 – 50000P = -100000 + 100000P

⇒ 150,000P = 600,000 [divide both sides by 150,000

⇒ P = 600,000/150,000

⇒P = $4

Step II

To get Q, substitute P into (1)

thus, we have:

500,000 – 50000 (4)

500,000 – 200,000

= 300,000 units.

Hence, at EQL, P = $4 and Q = 300,000 units.

B)i What is P = $3?

Recall Step II above,

Simply substitute $3 into  (1)

⇒ 500,000 – 50,000 (3)

= 500,000 – 150,000

= 350,000 units

ii) what is P = $6, just repeat the above steps to get

200,000 units.

C) Price Elasticity of Demand (PED) at Equilibrium Price

The PED is the percentage change in the quantity requested as a result of a 1% change in price. The PED coefficient is often negative, although economists frequently overlook the sign. If the PED coefficient is less than one, demand for an item is generally inelastic (in absolute value).

The formula for demand (PED) at P = 6 is determined using the formula:

PED = %Δ in QD / %Δ in Price..................1

%Δ in QD = (200,000-300,000)/300,000 ..............2

With 300,000 beings (Original Unit at Equilibrium)

Hence %Δ in QD = -0.333

%Δ in Price =  (6-4)/4

= 1/2j or 0.5

PED = -0.333/0.5

PED = |-0.666|

Given that the PED is < 1, we can conclude that the demand for dry cleaning is inelastic.

In a situation where it is greater than 1, then the demand is elastic.

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Using the substitution method, if sum of two numbers is 96 and difference of the two numbers is 42, then the two numbers are 69 and 27

Consider the largest number as x and the smallest number as y

The sum of two numbers is 96

The equation will be

x+y = 96

x = 96-y

The difference of the two numbers 42

x-y = 42

Use the substitution method here

Substitute the value of x in the second equation

x-y =42

(96-y)-y =42

96-2y = 42

-2y = 42-96

-2y = -54

y = 27

Substitute the value of y in the first equation

x+y = 96

x+27 = 96

x = 96-27

x = 69

Hence, using the substitution method, if sum of two numbers is 96 and difference of the two numbers is 42, then the two numbers are 69 and 27

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The new mean is 18.4

According to the question,

The mean of 20 observations is 17

So the total value of all the observations = 20*17

= 340

The new value will be = 340 +40-12

= 368

Then,

The new mean of 20 observations will be= 368÷20

= 18.4

Hence, the new mean is 18.4

Mean is the average of a set of two or more numbers. It is of two types; arithmetic mean and geometric mean. It is part of statistics.

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nswer:

Explanation:

iven the below expression;

We'll follow the below steps to factor the given expression;

tep 1: L

The factors are 12 and 5. We'll go ahead and replace the middle term 17x with these factors as seen below;

tep 2: GG

tep 3: F

tep 4: FW