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*see attachment for missing diagram

Answer:

AC = 5 and BC = 5√3

Step-by-step explanation:

Given:

m<A = 60°

m<B = 30°

AB = 10

Required:

AC and BC

Solution:

Recall, SOH CAH TOA

✔️Find AC:

Reference angle (θ) = 30°

Hypotenuse = 10

Opposite = AC

Apply SOH:

Sin θ = Opp/Hyp

Substitute

Sin 30° = AC/10

10*Sin 30° = AC

10*½ = AC (sin 30° = ½)

5 = AC

AC = 5

✔️Find BC:

Reference angle (θ) = 60°

Hypotenuse = 10

Opposite = BC

Apply SOH:

Sin θ = Opp/Hyp

Substitute

Sin 60° = BC/10

10*Sin 60° = BC

10*√3/2 = BC (sin 60° = √3/2)

5*√3 = BC

BC = 5√3

Answer:

D. √2 : 1

Step-by-step explanation:

The hypotenuse = 4√2 (longest side of a right triangle)

The given side = 4

Ratio of the hypotenuse to the given side = 4√2 : 4

Simplify by dividing both numbers by 4

√2 : 1

Question is incomplete, however here's an explanation to solve questions such as this

Answer and explanation:

Probability= number of favorable outcomes/total number of outcomes

The frequency distribution recorded by the professor would show number of times(frequency) each student missed a class day.

We are required to fund the probability that a student would miss class

Probability = number of times the student missed class/ total number of classes missed by all students

Example, if student missed class 20 times in a semester and all students in total missed class 200 times

Probability that the student would miss class=20/200= 1/10

Answer:

x = 2.7

Step-by-step explanation:

The given equation is :

[tex](3x)^2-10=56[/tex]

We need to solve it for x.

It can be rewrite as follows:

[tex]9x^2-10=56[/tex]

Adding 10 to both sides,

[tex]9x^2-10+10=56+10\\\\9x^2=66\\\\x=\sqrt{\dfrac{66}{9}}\\\\x=2.70[/tex]

So, the value of x is equal to 2.7.

Answer:

The general equation for a parabola is:

y = f(x) = a*x^2 + b*x + c

And the vertex of the parabola will be a point (h, k)

Now, let's find the values of h and k in terms of a, b, and c.

First, we have that the vertex will be either at a critical point of the function.

Remember that the critical points are the zeros of the first derivate of the function.

So the critical points are when:

f'(x) = 2*a*x + b = 0

let's solve that for x:

2*a*x = -b

x = -b/(2*a)

this will be the x-value of the vertex, then we have:

h = -b/(2*a)

Now to find the y-value of the vertex, we just evaluate the function in this:

k = f(h) = a*(-b/(2*a))^2 + b*(-b/(2*a)) + c

k =  -b/(4*a) - b^2/(2a) + c

So we just found the two components of the vertex in terms of the coefficients of the quadratic function.

Now an example, for:

f(x) = 2*x^2 + 3*x + 4

The values of the vertex are:

h = -b/(2*a) = -3/(2*2) = -3/4

k = -b/(4*a) - b^2/(2a) + c

=  -3/(4*2) - (3)^2/(2*2) + 4 = -3/8 - 9/4 + 4 = (-3 - 18 + 32)/8 = 11/8

Step-by-step explanation:

The number of cases of a new disease may be modeled by the quadratic regression equation y=-2x^2+44x+8 , what is the best prediction for the number of cases after 20 years ( the carrot symbol (^) means the following number is the exponent)

Explanation:

The result of any absolute value function is never negative. It represents distance on a number line.

The distance from -1.2 to 0 on the number line is exactly 1.2 units.

So that's why |-1.2| = 1.2

In short, we erase the negative sign.

Answer:

12.81 km

Step-by-step explanation:

Pythagoras formula for right-angled triangles.

this scenario just says that Emma is the corner point of that triangle with an angle of 90 degrees.

the distance between Ohenhen and Omusi is the baseline (Hypotenuse c) of that triangle. and the distances to Emma are the sides a and b.

so the formula is

c² = a² + b² = 10² + 8² = 100 + 64 = 164

[tex]c = \sqrt{164} [/tex]

c ≈ 12.81 km (rounded to the nearest hundredth).

Answer:

[tex] {5 x }^{2} +10x[/tex]

Step-by-step explanation:

[tex]5x(x+2)[/tex]

[tex]5x \times x+5x \times 2[/tex]

[tex]5(x \times x)+5x \times 2[/tex]

[tex]5 {x}^{2} +5x \times 2[/tex]

[tex]5 {x}^{2} + 10x[/tex]

Answer:

8:35

Step-by-step explanation:

Answer:

8:35

Step-by-step explanation:

-25+60=35

9h-1h(60 above)=8h

=8:35

Answer:

1/2

Step-by-step explanation:

Convert 2/3 to 4/6

Subtract: 4/6 - 1/6

You get 3/6

Simplify: 1/2

Hope this helps!

Answer: The answer is 1/2

Hi there!

[tex]\large\boxed{\text{Choice 4}}[/tex]

We can look at each function, f(x) and g(x), to determine which is exponential.

Use slope formula: m = y2-y1/x2-x1

f(x) starts off with a slope at about $1800/year, but becomes about $1100/year.

g(x) starts off with a slope of about $1500/year, but becomes about $1874/year.

Thus, g(x) is exponential, because g(x)'s slope is increasing across the interval.

9514 1404 393

Answer:

  372 m²

Step-by-step explanation:

A vertical line down the center of the figure will divide it into two congruent trapezoids, each with bases 13 and 18, and height 12.

The area of one of them is ...

  A = 1/2(b1 +b2)h

So, the area of the two of them together is ...

  A = (2)(1/2)(b1 +b2)h = (b1 +b2)h

  A = (13 m + 18 m)(12 m) = 372 m²

Step-by-step explanation:

If a fraction [tex]f(x)[/tex] is defined as

[tex]f(x) = \dfrac{g(x)}{h(x)}[/tex]

then the derivative [tex]f'(x)[/tex] is given by

[tex]f'(x) = \dfrac{g'(x)h(x) - g(x)h'(x)}{h^2(x)}[/tex]

So the derivative can be calculated as follows:

[tex]f'(x) = \dfrac{d}{dx}\left(\dfrac{4x^3 - 7x + 8}{x} \right)[/tex]

[tex]=\dfrac{(12x^2 - 7)x - (4x^3 - 7x + 8)}{x^2}[/tex]

[tex]= \dfrac{12x^3 - 7x - 4x^3 + 7x - 8}{x^2}[/tex]

[tex]= \dfrac{8x^3 - 8}{x^2}[/tex]

9514 1404 393

Answer:

  (a) max: None; min: -5

  (b) max: 5; min: None

Step-by-step explanation:

a) The upward pointing arrow on the end of the graphed curve tells you that the graph extends upward indefinitely. There is no absolute maximum value.

The solid dot at (-4, -5) is the lowest point on the graph. That tells you the absolute minimum is -5.

__

b) The solid dot at (-4, 5) is the highest point on the graph. That tells you the absolute maximum is 5.

The open dot at (3, -5) is the lowest point on the graph. This means values of the function can be arbitrarily close to -5, but -5 is not one of them. There is no absolute minimum value.

Answer:

Class interval ____, Frequency _ C/frequency

1 - 10 ____________ 1 _________ 1

11 - 20 ___________ 4 _________ 5

20 - 30 __________ 6 _________ 11

31 - 40 ___________3 _________ 14

41 - 50 ___________ 1 _________ 15

51 - 60 ___________ 1 _________ 16

Step-by-step explanation:

Given the data :

35, 26, 31, 17, 46, 30, 28, 21, 26, 34, 15, 27, 7, 18, 16, 57

Class interval ____, Frequency _ C/frequency

1 - 10 ____________ 1 _________ 1

11 - 20 ___________ 4 _________ 5

20 - 30 __________ 6 _________ 11

31 - 40 ___________3 _________ 14

41 - 50 ___________ 1 _________ 15

51 - 60 ___________ 1 _________ 16

The next to highest frequency group has a frequency of 4 and the highest frequency of 6

Total frequency, n = (1 + 4 + 6 + 3 + 1 + 1) = 16

Step-by-step explanation:

4/6

=2/3

That's what I could show you

Answer:

Some demerits of classical probability are provided throughout the following portion.

Step-by-step explanation:

Given:

The domain of function that is translated down 3 is (0, 4), (-5, 8), (4, -2).

To find:

The range of the function.

Solution:

If a function is translated 3 units down, then

[tex](x,y)\to (x,y-3)[/tex]

Using this rule, we get

[tex](0,4)\to (0,4-3)[/tex]

[tex](0,4)\to (0,1)[/tex]

Similarly,

[tex](-5,8)\to (-5,5)[/tex]

[tex](4,-2)\to (4,-5)[/tex]

The range of the given function is (0, 1), (-5, 5), (4, -5).

Therefore, the correct option is A.

Answer:

14x I answered your question thank you for the points appreciate it

Answer:

2x+2x+5x+5x=14x

Ans: 14x

Answer:

[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex] --- set builder

[tex][-21,\infty)[/tex] --- interval notation

Step-by-step explanation:

Given

[tex]-3a - 15 \le -2a + 6[/tex]

Required

Solve

Collect like terms

[tex]-3a + 2a \le 15 + 6[/tex]

[tex]-a \le 21[/tex]

Divide by -1

[tex]a \ge - 21[/tex]

Rewrite as:

[tex]-21 \le a[/tex]

Using set builder

[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex]

Using interval notation, we have:

[tex][-21,\infty)[/tex]

Step-by-step explanation:

As total number of pages in each album is 42 pages, so

➝ Total number of pages in 10 albums = (42 × 10) pages

➝ Total number of pages in 10 albums = 420 pages

Now, as the number of stamps fit on 1 page is 40 stamps, so

➝ Stamps fit on 420 pages = (420 × 40) stamps

➝ Stamps fit on 420 pages = 16,800 stamps

Therefore, 16,800 stamps are in the total collection.

Answer:

16X+134

Step-by-step explanation:

Answer:

1) 6m+8n

4) 21x+14y

7) 14c+16d

10) d+3e

Step-by-step explanation:

Answer:

Step-by-step explanation:

Arrival rate = ∧ = 2.2 customers per hour  

Service rate = u = 5 customers per hour  

1. Probability that one customer is receiving a haircut and one customer is waiting  

P(2 customers)=(∧/u)^2 * (1-∧/u)=(2.2/5)^2 * (1-2.2/5)=0.1936*0.56= 0.108416

2. Probability that one customer is receiving a haircut and two customers are waiting  

P(3 customers)= (∧/u)^3 * (1-∧/u)=(2.2/5)^3 * (1-2.2/5)= 0.085184  

* 0.56= 0.04770304

3. Probability that more than two customers are waiting  

P(more than 3 customers)=1- P(less than 3 customers) =  

1- [P(0)+P(1)+P(2)+P(3)]=  

= 1- [(1-2.2/5) +2.2/5*(1- 2.2/5) + 0.108416+0.04770304]=1-0.9625=0.0375

Answer:

WHAT IS THE FACTOR?

Step-by-step explanation:

Answer:

AAS

Step-by-step explanation:

It will be angle angle side because you are given a side and two angles, and when you put them in the correct order, you will get AAS, or SAA (not the correct way to say it)

Answer:

is that the full question?

Answer:

Solution:-

Given,

ab =perpendicular (p)= 6cm

ac =hypotenuse (h)= 12cm

cd =base (b)= ?

using , Pythagoras theorem we have ,

b²=√h²-p²

or,cd²=√ac²-ab²

= √12²-6²

= √144-36

=√108

=√10.8²

=10.8cm

the length of cd is 10.8 cm

hope it is helpful to you

Answer:

P>-6/5

Step-by-step explanation:

2(P+1)+3(P+2)>2

Use the distributive property to multiply 2 by P+1

2P+2+3(P+2)>2

Use the distributive property to multiply 3 by P+2

2P+2+3P+6>2

Combine 2P and 3P to get 5P

5P+2+6>2

Add 2 and 6 to get 8

5P+8>2

Subtract 8 from both sides

5P>2−8

Subtract 8 from 2 to get −6.

5P>−6

Divide both sides by 5. Since 5 is positive

P>−6/5

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