If 265 students are expected at the prom this year, estimate the maximum dance floor space needed?

Answer:

The unknown number is 2.

Step-by-step explanation:

Let x represent the unknown number.

It is multiplied by 9 then added to 3. Hence, it can be represented by the expression:

[tex]9x + 3[/tex]

The sum is equal to the product of 3 and 7, or 21. Therefore:

[tex]9x + 3 = 21[/tex]

Solve for x. Subtract 3 from both sides:

[tex]9x = 18[/tex]

And divide both sides by 2. Hence:

[tex]x = 2[/tex]

In conclusion, the unknown number is 2.

Answer:

6x-8

Step-by-step explanation:

less  than means it comes after

product of 6 and a number x

6x

8 less than

6x-8

Answer:

2yz/x

Step-by-step explanation:

Given: z/4=x/y

Let's isolate 4 since 8=4(2) which means after isolating 4 we just need to multiply that resulting equation by 2.

Cross multiply:

zy=4x

Divide both sides by x:

zy/x=4

Multiply both sides by 2:

2zy/x=8

Answer:

A = 2 cm²

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the distance between parallel sides and b₁, b₂ , the parallel sides

Here h = 1, b₁ = 3, b₂ = 1 , then

A = [tex]\frac{1}{2}[/tex] × 1 × (3 + 1) = [tex]\frac{1}{2}[/tex] × 4 = 2 cm²

Given the PMF

[tex]P(X=x) = \begin{cases} 0.3 & \text{if } x \in \{-1, 2\} \\ 0.1 & \text{if } x \in \{0, 7\} \\ 0.2 & \text{if } x = 6 \\ 0 & \text{otherwise} \end{cases}[/tex]

(a)

[tex]P(-1 < X \le 2) = P(X = 0) + P(X = 2) = 0.1 + 0.3 = \boxed{0.4}[/tex]

(b) The CDF is defined as [tex]F_X(x) = P(X \le x)[/tex], so that

[tex]F_X(x) = \begin{cases} 0 & \text{if } x < -1 \\ 0.3 & \text{if } -1 \le x < 0 \\ 0.4 & \text{if } 0 \le x < 2 \\ 0.7 & \text{if } 2 \le x < 6 \\ 0.9 & \text{if } 6 \le x < 7 \\ 1 & \text{if } x \ge 7 \end{cases}[/tex]

It follows that

[tex]F(3.2) = \boxed{0.7}[/tex]

(c) Expectation is defined as

[tex]E[X] = \displaystyle \sum_x x\,P(X=x)[/tex]

We have

[tex]E[X] = \displaystyle \sum_{x\in\{-1,0,2,6,7\}} x\,P(X=x) \\\\ E[X] = -P(X=-1) + 2P(X=2)+6P(X=6)+7P(X=7) \\\\ E[X] = -0.3 + 0.6 + 1.2 + 0.7 = \boxed{2.2}[/tex]

(d) First compute the second moment of X, which is defined as

[tex]E[X^2] = \displaystyle \sum_x x^2\,P(X=x)[/tex]

We get

[tex]E[X^2] = (-1)^2P(X=-1) + 2^2P(X=2) + 6^2P(X=6) + 7^2P(X=7) \\\\ E[X^2] = 0.3 + 1.2 + 7.2 + 4.9 = 13.6[/tex]

Variance is defined as

[tex]\mathrm{Var}[X] = E[(X - E[X])^2] = E[X^2] - E[X]^2[/tex]

so it follows that

[tex]\mathrm{Var}[X] = 13.6 - 2.2^2 = \boxed{8.76}[/tex]

(e) Not sure what this part has to do with the rest of the question. At any rate, if Y is a random variable following a Poisson distribution with λ = 3, then Y has a PDF of

[tex]P(Y=y) = \begin{cases}\dfrac{e^{-3}\times3^y}{y!}&\text{if }y\in\{0,1,2,\ldots\}\\\\0&\text{otherwise}\end{cases}[/tex]

Then

[tex]P(Y > 5) = 1 - P(Y \le 5) = 1 - P(Y=0) - P(Y=1) - \cdots - P(Y=5) \\\\ P(Y>5) = \dfrac{5e^3-92}{5e^3} \approx \boxed{0.0839}[/tex]

Answer:

5/12

Step-by-step explanation:

Multiply [tex]\frac{1}{2}[/tex] times [tex]\frac{5}{6}[/tex] by multiplying the numerator times the other numerator and the denominator by the other denominator. Which leaves you with [tex]\frac{5}{12}[/tex].

hope this helps!

Step-by-step explanation:

200m:1.4km

200m:1400m

1:7

Answer:

Step-by-step explanation:

Bonjour,

2^4 * 7^3 => 16* 343 = 5488

21 952 / 5 488 =4

115 248/5 488 =  21

9514 1404 393

Answer:

  2⁴·7³

Step-by-step explanation:

The set of primes that are factors of 21952 is {2, 7}.

The set of primes that are factors of 115248 is {2, 3, 7}.

Common factors are primes that are in the intersection of these sets: {2, 7}. The index associated with the greatest common factor is the smallest index of each of these primes in the prime factorization of those numbers.

The prime 2 is seen to have indices of 6 and 4. 4 is the smallest.

The prime 7 is seen to have indices of 3 and 4. 3 is the smallest.

So, the Highest Common Factor of the two numbers is 2⁴·7³.

Answer:

f(x) = (x + 3)(x − 3)(x − 1)

Step-by-step explanation:

The roots are at -3, -1 and 3 therefore the 3rd option is correct.

Answer:

The answer is D

Step-by-step explanation:

Attatched photo for proof

Answer:

tan 76 = 24/8

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 76 = 24/8

Answer:

(I got your back pal) Your answer is -41/21

Can you give me a brainlest it would help me a lot

Answer:

for the mean you have to do formula efx/n other i dont know

Answer:

yes it is a dilation

Step-by-step explanation:

a dilation makes the size different but shape the same. as we can see the shape is the same meaning this is a non rigid motion or called a dilation.

Answer:

it must be 2983548×2............

Answer:

22/12

Step-by-step explanation:

98-8x=14+12(2-5x)

98-8x=14+24-60x

-8x +60x=10-9

52x=88

x=22/13

Answer:

2/5

Step-by-step explanation:

Use the formula for slope to solve [ y2-y1/x2-x1 ].

7-5/9-4

2/5

Best of Luck!

Answer:

Step-by-step explanations

I don’t know

Answer:

24.64

Method:

You get 10% of the shirt cost, and it on to the 22.40

20×2×÷

2920w0#

393020×22¥3¥

3i839393

Answer:

if we join the angle Z the it will formed as acute angle

if you like ans hit like

thank you

Answer:

y=10

Step-by-step explanation:

y/5+7=9

y/5=9-7

y/5=2

y=2*5

y=10

9514 1404 393

Answer:

  g(f(7/3)) = 4 4/9

Step-by-step explanation:

  g(f(7/3)) = g((7/3)²) = g(49/9) = 49/9 -1 = 40/9

  g(f(7/3)) = 4 4/9

Answer:

Here is your answer. Hope this helps you!

Midpoint has coordinates [tex](x_m,y_m)[/tex] which equal to,

[tex]x_m=\frac{x_1+x_2}{2}[/tex]

[tex]y_m=\frac{y_1+y_2}{2}[/tex]

We know the coordinates of a midpoint as well as the coordinates of [tex]A(x_1,y_1)[/tex] so we should be able to find coordinates of [tex]B(x_2,y_2)[/tex].

First solve both equations for [tex]x_2[/tex] and [tex]y_2[/tex] respectively,

[tex]x_2=2x_m-x_1[/tex]

[tex]y_2=2y_m-y_1[/tex]

Now insert the data,

[tex]x_2=2\cdot1-(-3)=\boxed{5}[/tex]

[tex]y_2=2\cdot2-6=\boxed{-2}[/tex]

The coordinates of B are therefore [tex](5,-2)[/tex].

Hope this helps :)

The midpoint of AB is (1, 2) the coordinates of A are (-3,6) coordinates of B coordinates of point B are (5, -2).

To find the coordinates of point B given that the midpoint of AB is (1, 2) and the coordinates of A are (-3, 6),  use the midpoint formula:

Midpoint formula: M(x, y) = ((x1 + x2) / 2, (y1 + y2) / 2)

Given that M is the midpoint (1, 2) and A is (-3, 6), we have:

(1, 2) = ((-3 + x2) / 2, (6 + y2) / 2)

Solve for x2 and y2:

For x-coordinate:

1 = (-3 + x2) / 2

2 = -3 + x2

x2 = 2 + 3

x2 = 5

For y-coordinate:

2 = (6 + y2) / 2

4 = 6 + y2

y2 = 4 - 6

y2 = -2

To know more about coordinates here

https://brainly.com/question/32836021

#SPJ3

Answer associative

Step-by-step explanation:

Answer:

Sum means addition so you add them together. I don't know why there are a bunch of percentage signs but the answer is 49.

Answer:

x=-14

Step-by-step explanation:

Answer:

one side is 137/4 and other is 3/4

Step-by-step explanation:

all steps are in picture

Answer:

(5,7.5)

Step-by-step explanation:

Hope this helps (:

Answer:

the Highest common factor (HCF)of 8,12,24 is 4