96 young musicians attended a jazz camp. 30 of them were guitarists. What is the probability that a randomly chosen musician is a guitarist? Write your answer as a fraction or whole number. P(guitarist) =

Answer :-

Step-by-step explanation:

Given :-

To Find :-

Solution :-

According to question,

↠ (x)(x + 2) = 528

↠ x² + 2x = 528

↠ x² + 2x - 528 = 0

↠ x² + 24x - 22x - 528 = 0

↠ x(x + 24) - 22 (x + 24) = 0

↠ (x + 24) (x - 22) = 0

↠ x = -24 or 22

Hence,

Value of two integers are 22 and 24

Step-by-step explanation:

It is given that, The product of 2 consecutive even integers is 528 and we have to find the value of each integers.

Now, As it is stated in the question that the product of 2 consecutive even integers is 528, So

[tex] \\ { \longrightarrow \qquad{ \pmb{ \sf { y(y + 2) = 528 }}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ \pmb{ \sf { {y}^{2} + 2y = 528 }}}} \: \: \\ \\[/tex]

Subtracting both sides by 528 we get :

[tex] \\ { \longrightarrow \qquad{ \pmb{ \sf { {y}^{2} + 2y - 528= 528 - 528 }}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ \pmb{ \sf { {y}^{2} + 2y - 528= 0 }}}} \: \: \\ \\[/tex]

We have to find two numbers such that,

[tex] \\ { \longrightarrow \qquad{ \pmb{ \sf { p + q= 24 }}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ \pmb{ \sf { p \times q= 528 }}}} \: \: \\ \\[/tex]

The two numbers are 24 and 22. So,

[tex] \\ { \longrightarrow \qquad{ \pmb{ \sf { {y}^{2} + (-22y) + 24y - 528= 0 }}}} \\ \\ [/tex]

[tex]{ \longrightarrow \qquad{ \pmb{ \sf { {y}(y -22) + 24(y - 22)= 0 }}}} \\ \\ [/tex]

[tex]{ \longrightarrow \qquad{ \pmb{ \sf { (y -22) (y + 24)= 0 }}}} \\ \\ [/tex]

[tex] \: [/tex]

So, The first consecutive even integer is 22.

Now,

[tex] \\ { \longrightarrow \qquad{ \pmb{ \sf {Second \: consecutive \: even \: integer=y \:+2 \: }}}} \\ \\ [/tex]

[tex]{ \longrightarrow \qquad{ \pmb{ \sf {Second \: consecutive \: even \: integer=2 2+2 \: }}}} \\ \\ [/tex]

[tex]{ \longrightarrow \qquad{ \pmb{ \sf {Second \: consecutive \: even \: integer=24 }}}} \\ \\ [/tex]

Therefore,

Answer:

Step-by-step explanation:

The domain is the set of x-values in the ordered pairs.

So it is {0, 2, 5}

Yes it is a function as for each x value there is  1 y-value  (its a one-to-one function)

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]\frac{x}{a}= \frac{y}{b} =\frac{z}{c}[/tex]

[tex]Let \: \frac{x}{a}= \frac{y}{b} =\frac{z}{c}=m[/tex]

(where m is any constant)

[tex]\implies[/tex]

[tex]\frac{x}{a}=m\implies x =am[/tex]

[tex]\frac{y}{b}=m\implies y =bm[/tex]

[tex]\frac{z}{c}=m\implies z =cm[/tex]

To Prove:

[tex]\frac{ax-by}{(a+b)(x-y)}+\frac{by-cz}{(b+c)(y-z)}=2[/tex]

LHS [tex]=\frac{ax-by}{(a+b)(x-y)}+\frac{by-cz}{(b+c)(y-z)}[/tex]

(Plug the values of x, y and z in the form of am, bm and cm respectively in the LHS)

[tex]=\frac{a(am)-b(bm)}{(a+b)(am-bm)}+\frac{b(bm)-c(cm)}{(b+c)(bm-cm)}[/tex]

[tex]=\frac{a^2m-b^2m}{(a+b)m(a-b)}+\frac{b^2m-c^2m}{(b+c)m(b-c)}[/tex]

[tex]=\frac{m(a^2-b^2)}{m(a+b)(a-b)}+\frac{m(b^2-c^2)}{m(b+c)(b-c)}[/tex]

[tex]=\frac{\cancel{m(a^2-b^2)}}{\cancel{m(a^2-b^2)}}+\frac{\cancel{m(b^2-c^2)}}{\cancel{m(b^2-c^2)}}[/tex]

= 1 + 1

= 2

= RHS

[tex]\implies \purple{\bold{\frac{ax-by}{(a+b)(x-y)}+\frac{by-cz}{(b+c)(y-z)}}}=\red{\bold{2}}[/tex]

Thus proved

Answer:

Part A:

B. rhombus

Part B:

C. Opposite sides are parallel and congruent

Most common is 7

So

Use distributive law to verify

Verified

GCF is 7

Answer:

[tex]u^{2n+1}[/tex]

Step-by-step explanation:

Assuming you mean [tex]u^nu^{n+1}[/tex], then [tex]u^nu^{n+1}=u^{n+n+1}=u^{2n+1}[/tex].

Answer:

[tex]\Longrightarrow: \boxed{\sf{u^2^n+1}}[/tex]

Step-by-step explanation:

This equation can be solved simply by multiplying by the variable to isolate them on one side.

[tex]\Longrightarrow: \sf{u^n*u^n+1}[/tex]

[tex]\sf{u^n*u^n=u^2}\\\\\\\sf{= (u^2)^n}[/tex]

Solve.

[tex]\sf{\left(u^2\right)^n=u^{2n}=\boxed{\sf{u^{2n}+1}}[/tex]

Therefore, the final answer is [tex]\boxed{\sf{u^{2n}+1}}[/tex].

Answer:

(3−5)(+1)

Step-by-step explanation:

I hope this helps you and please mark me as brainliest

Answer:

The answer is ( p + 1 ) ( 3p - 5 )

Step-by-step explanation:

Answer:270

Step-by-step explanation:180/2=90

90*3=270

Hope this helps :)

Answer:

270

Step-by-step explanation:

You can do 180/2 and that gives you 90. Since we know 90:1, we can do 90x3. And that gives 270

Answer:

i³ = -i

Step-by-step explanation:

i³ can be rewritten as i² · i

i² = -1

-1 · i = -i

Hope this helps!

Answer:

[tex] \frac{1}{20} [/tex]

or 5%

Step-by-step explanation:

Explanation:

3/4=15/20

1/5=4/20

So, rest of 'em 1/20

Answer:

1/20.

Step-by-step explanation:

1 - 3/4 - 1/5

= 20/20  - 15/20 - 4/20

= 1/20

Answer:

$ 80.73

Step-by-step explanation:

You can find the complete solution in the given attachment

Answer:

The bench mark values might be 10/120 - 30/80

Step-by-step explanation

Answer:

500,000,000,000 + 800,000,000 + 2,000,000 + 9,000 + 600 + 10 + 2

Step-by-step explanation:

To write a standard form number into an expanded form, we must look at the amount of numbers at each 'place' in the number.

Hundred-Billions --> 5            Hundred-Thousands --> 0

Ten-Billions --> 0                     Ten-Thousands --> 0

Billions --> 0                             Thousands --> 9

Hundred Millions --> 8             Hundreds --> 6

Ten Millions --> 0                      Tens --> 1

Millions --> 2                              Ones --> 2

Answer: five hundred billion eight hundred two million nine thousand six hundred twelve.  

Step-by-step explanation:

500,000,000,000=five hundred billion

800,000,000=eight hundred million

2,000,000=two million

9,000=nine thousand

600=six hundred

10=ten

2=two

Answer:A

Step-by-step explanation: She will still care for people but spend lesser years qualifying

Answer: NURSE

Step-by-step explanation:

Answer:

0.04

Step-by-step explanation:

Have a nice day!

Simply just take 4 divided by 100 -> 4 : 100 = 0.04

Answer:

10: 12 units^2 11: 33 units^2

Step-by-step explanation:

10:

Divide into square and 2 triangles (for simplicity)

square=9

one triangle=3/2

both triangles combined=3

9+3=12

11:

divide into 2 triangles

top triangle: height= 4, base=6

bottom triangle: height= 7, base=6

top=12

bottom=21

Add, 33.

Answer:

72 i think.

Step-by-step explanation:

Answer:

a. 1710 b. 71.25

Step-by-step explanation:

the formula for simple interest is i=prt

2(9500)(0.09)= 1710

to find the monthly payment, divide by the number of months.

1710/24=71.25

Step-by-step explanation:

Angles XVW and XYZ are congruent, and so are angles VWX and XZY by the alternate interior angles theorem.

This means that triangle VWX is similar to triangle YZX.

So, since corresponding sides of similar triangles are proportional, VW/XY = WX / XZ.

120/8 = 15 = WX / 6.

So the width is 90 m.

Answer:

Step-by-step explanation:

x is the adjacent side of 30°

Hypotenuse = 22

[tex]Cos \ 30^ \circ = \dfrac{adjacent \ side}{hypotenuse}\\\\\\0.866 = \dfrac{x}{22}\\\\\\0.866*22 = x\\[/tex]

x = 19.1

Answer:

cosθ=Adjacent/ hypotenuse

[tex] \cos(30) = \frac{x}{22} \\ \\ \frac{ \sqrt{3} }{2} = \frac{x}{22} \\ \\ 2x = 22 \sqrt{3} \\ \\ x = \frac{22 \sqrt{3} }{2} \\ \\ x = 11 \sqrt{3} = 19.05 = 19.1[/tex]

Answer:

A customer purchased a furniture for Rs. 3390 with 13% VAT . Find the cost of the furniture without VAT?

The function h(t) = -16t^2 + 75 is a quadratic function, and the stick hits the ground at about 2.165 seconds

The function is given as:

h(t) = -16t^2 + 75

Next, we plot the graph of the function h(t)

From the graph of the function h(t) (see attachment), we have the following highlight:

t = -2.165 and t = 2.165 when h(t) = 0

Time cannot be negative.

So, we have:

t = 2.165

This means that the stick hits the ground at about 2.165 seconds

Read more about quadratic functions at:

https://brainly.com/question/8649555

Answer:

I think the answer is 6/40

Step-by-step explanation:

Step-by-step explanation:

1.

a. true

b. false (the arc angles are relative to the center of the circle)

c. true (as the central angle of a circle is twice any inscribed angle subtended by the same arc)

d. true (but note that the arc angle of YE is again measured via the center of the circle and twice as large as the angle S)

2.

EGS is an isoceles triangle (that means both legs are equally long).

remember the extended Pythagoras for general triangles :

c² = a² + b² - 2ab×cos(C)

c being the side opposite of the angle C.

let's say c is our long baseline, since we have is opposite angle 124°, and a = b = GE = GS, we have

3.8² = a² + a² - 2aa×cos(124) = 2a² - 2a²×cos(124) =

= 2a²(1 - cos(124))

2a² = 3.8²/(1 - cos(124))

a² = 3.8²/(2(1 - cos(124)))

a = GS = sqrt(3.8²/(2(1 - cos(124)))) =

= 2.151883096... ≈ 2.2 cm

3.

circumference

16pi = 2pi×r

r = 8

area = pi×r² = pi×8² = 64pi

yes, the statement is true.

4.

a half-circle has 180°.

the arc angel AD is a full half-circle (because AD is a diameter), so it is 180°.

the angle ACB is the arc angle AB = 40°. so, the arc angle BD must be the rest of the 180° = 180 - 40 = 140°.

5.

diameter = 50 ft.

so, the radius or distance from the center to the circle arc is 50/2 = 25 ft.

the length of a chord is

c = 2×sqrt(r² - d²)

with r being the radius, d being the distance of the chord from the center.

40 = 2×sqrt(25² - d²)

20 = sqrt(625 - d²)

400 = 625 - d²

-225 = -d²

225 = d²

d = 15 cm

so, the distance of the chord from the center is 15 cm.

6.

the arc angles RE and TS are equal. that means the arc lengths of RE and TS are equal.

and that means the arc lengths of RS and ET are equal. the chords between 2 points on a circle must have the same length, when the arc lengths between these 2 points are the same.

7.

they are equally long.

as we saw in 5., the length of a chord depends on the radius of the circle and the distance of the chord from the center.

since both chords are in the same circle (with the same radius), and they both have the same distance from the center, they can only be equally long, as there is no other element to name them different.

8.

the angle NPE is half of the angle NAE (= the arc angle NE).

the arc angle NE = 63×2 = 126°

the angle PET is half of the angle PAT (= the arc angle PT).

the arc angle PT = 19×2 = 38°

the arcs NP and ET cover the rest of the whole circle circumference (360°).

so, arc angle NP + arc angle ET = 360 - 38 - 126 = 196°

but arc angles NP and ET must be equal (as per the problem definition).

therefore, 2 equal arc angles = 196°

1 arc angle = NP = 196/2 = 98°

Answer:

0.8 meters

Step-by-step explanation:

1 decimeter is 0.1 meters

so,

[tex]\frac{1}{0.1} = \frac{8}{x}\\x = 8*0.1\\x = 0.8[/tex]

Answer:

y > 1/3x - 5/3

x-3y < 5

Step-by-step explanation:

We simplify x-3y=5, to y = 1/3x - 5/3

We notice the boundary line is dotted, we know the inequality must be < or > rather than ≤ or ≥.

The shading is above the line which indicates that in y-intercept form we must use >.

y > 1/3x - 5/3

or x-3y < 5

Either of these show the exact same thing.

B.)

Step-by-step explanation:

area of a 10 inch pizza: A=pi * r^2 = 25 pi

area of a 14 inch pizza : A= 49 pi

the change : 49pi - 25pi = 24 pi or about 75.39822

Answer:

Factoring: [tex]x = -\frac{1}{5}, -3[/tex]

Step-by-step explanation:

A) You can factor the expression [tex]5x^2 + 16x + 3[/tex] into [tex](5x+1)(x+3)[/tex].

5x + 1 = 0 and x + 3 = 0

[tex]x = -\frac{1}{5}, -3[/tex]

B) I would use factoring because you can factor this expression, and you don't have to use completing the square