In a group of 32 pupils, 3 play the flute only. 13 play the piano only. 10 play neither instrument. A student is selected at random. What is the probability the student plays both instruments?

Answer:yˆ=−0.175x2−3.786x+121.119

look at picture

Step-by-step explanation:

The quadratic regression equation for the data set is:

y^ = -0.175x²-3.786x+121.119

Quadratic regression is the process of determining the equation of a parabola that best fits a set of data. This set of data is a given set of graph points that make up the shape of a parabola. The equation of the parabola is y = ax² + bx + c, where a can never equal zero.

According to the given problem,

Let us choose any value of x,

x = 10

For this value of x we can see that the respective value of y= 50

Substituting the value of x in the equations to see which equation satisfies the value of y as 50.

Substituting the value of x in the equation:

y^ = -0.175x²-3.786x+121.119

y^ = 50

Hence, we can conclude that y^ = 0.175x² - 3.786 + 121.119 is the quadratic regression equation for the given data set.

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Answer:

11

Step-by-step explanation:

find the volume

find 80% of whats left

divide by 1.75 (gas price)

sorry if its wrong but im human

will give you the steps but try to do the problem by yourself.  

Start by finding the volume of the tank

Multiply 1.75 ft and 1.25 ft then covert the sum to inches by multiplying it by 12.

Then multiply that amount by the ll inches and you have the volume.

Since the tank is 20% full divide the volume by five, take the number you get from that and subtract it from the origanl volume.

Now you have the amount you need to fill.

Since it is 3.

Divide the amount you need to fill by 77 and you get the cost to fill the tank.

Answer:

Rational

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

Rational.

Step-by-step explanation:

Rational numbers are the numbers that can be expressed in the form of a ratio.

Answer:

Adjacent

Step-by-step explanation:

They are next to each other ^^

Answer:

Prob = 13/1024 = 0.0127

Step-by-step explanation:

Prob {A correct answer} = Correct option / Total options = 1/4

Prob {A wrong answer} = Wrong options / Total options = 3/4

Prob [3 answers correct] = P (3 correct ,& 2 wrong) or P (4 correct ,& 1 wrong) or P (5 correct, & no wrong)

= [ (1/4) x (1/4) x (1/4) x (3/4) x (3/4) ]  +  [ (1/4) x (1/4) x (1/4) x (1/4) x (3/4) ] + [ (1/4) x (1/4) x (1/4) x (1/4) x (1/4) ]

( 9/1024 ) + ( 3/1024 ) + ( 1/1024 )

13/1024 = 0.0127

The Answer Is B

Use proportions to find x% of the children playing on the swings.

[tex] \frac{21}{100} = \frac{5}{x\%} [/tex]

[tex]x = 23.80952380\%[/tex]

Meaning B is correct.

Answer:

12/25=48%

Step-by-step explanation:

total=denominator=12+13=25

numerator=no of cherries=12

12/25=x/100

1200=25x

x=48%

A percentage is a number or ratio that represents a fraction of 100. 

Percentage formula = (Required number / Total number) x 100

The percentage of cherries is 48%.

A percentage is a number or ratio that represents a fraction of 100. 

Example:

50% = 50 /100 = 1/2

25% = 25/100 = 1/4

We have,

Number of cherries = 12

Number of strawberries = 13

The total number of fruits:

= 12 + 13

= 25

Percentage formula = (Required number / Total number) x 100

The percentage of cherries:

= (Number of Cherries / Total number of fruits) x 100

= (12 / 25) x 100

[ 25 x 4 = 100 ]

= 12 x 4

= 48%

Thus,

The percentage of cherries is 48%.

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Answer:

A

Step-by-step explanation:

Here the base (3.2) is greater than 1 and the exponent (t) is positive.  Thus the graph will have shape A.

The correct graph for the given function h(t)=0.6×[tex]3.2^{t}[/tex] will be upward increasing so option (A) will be correct.

A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.

In order to plot the graph, we need to find out y's values corresponding to x's value

After that, we need to substitute the values of x's and y's into the coordinate geometry.

Given function is  h(t)=0.6×[tex]3.2^{t}[/tex]

As t is increasing then the term [tex]3.2^{t}[/tex]  will also go to increase since 3.2 is greater than 1.

Hence the value of the graph will go to increase as x increases so it is clear that option (A) will be correct.

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Answer:

the answer is 6

Step-by-step explanation:

slope = m

y = mx + c

m = 6

Answer:

C.) The fraction is four-sixths.?

Step-by-step explanation:

Answer:

133.33g

Step-by-step explanation:

Let the:

Mass of 1.2g/cm³ of liquid = x

Mass of 1.8g/cm³ of liquid = y

From our Question above, our system of equations is given as:

x + y = 400........ Equation 1

x = 400 - y

1.2 × x + 1.8 × y = 1.6 × 400

1.2x + 1.8y = 640..... Equation 2

We substitute, 400 - y for x in Equation 2

1.2(400 - y) + 1.8y = 640

480 - 1.2y + 1.8y = 640

- 1.2y + 1.8y = 640 - 480

0.6y = 160

y = 160/0.6y

y = 266.67 g

Solving for x

x = 400 - y

x = 400 - 266.67g

x = 133.33g

Therefore, the mass of the liquid of density 1.2g/cm³ is 133.33g

Answer:

640

Step-by-step explanation:

5% of 400 is 20

20 x 12 is 240

400 + 240 = 640

Forgive me if I'm wrong. I suck at math XD

The amount for the month of December is $640.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Gabriel deposits $400 into a savings account in January If he deposits 5% more each month.

The December month deposit is calculated as,

5% of 400 is 20

20 x 12 is 240

400 + 240 = $640

Therefore, the amount for the month of December is $640.

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Answer:

The first one is 140 and the second one is -2.6

Step-by-step explanation:

Your welcome !

just use a calculator lol

Answer:

19 is D

20 is A

Step-by-step explanation:

19. 60+80=140

20. 2.3-4.9=-2.6

Step-by-step explanation:

sin x = 12/16 = 0.75

x = arc sin 0.75 = 48.6°

cos x = 36/40 = 0.90

x= arc cos 0.90 = 25.8°

cos x = 10/15 = 0.6667

x= arc cos 0.6667 = 48.2°

tan x = 30/18 = 1.6667

x = arc tan 1.6667 = 59.0°

Answer: 10

Step-by-step explanation:

10+10 = 20

10 x 10 = 100

mi would do another but i supposed to be in class :P

The two Integers are  [tex]10,10.[/tex]

An Integer number that can be written without a fractional component.

We have,

Sum of two Integers [tex]=20[/tex]

Product of two Integers [tex]=100[/tex]

Now,

Let,

One integer [tex]=x[/tex]

Another integer [tex]=y[/tex]

So,

According to the question,

[tex]x+y= 20[/tex]     [tex].....(i)[/tex]

[tex]x*y=100[/tex]

⇒ [tex]x=\frac{100}{y}[/tex]     [tex].....(ii)[/tex]

Now,

Putting value of x in equation (i),

We get,

[tex]\frac{100}{y}+y= 20[/tex]

[tex]100+y^2=20y[/tex]

[tex]y^2-20y+100=0[/tex]

Using middle term split method,

[tex]y^2-10y-10y+100=0[/tex]

[tex]y(y-10)-10(y-10)=0[/tex]

[tex](y-10) (y-10)=0[/tex]

We get,

[tex](y-10)=0[/tex] and [tex](y-10)=0[/tex]

So, [tex]y=10[/tex]

Now, putting value of y in in equation (i),

[tex]x+10=20[/tex]

[tex]x=10[/tex]

So, two integers are [tex]10,10.[/tex]

Hence, we can say that the two Integers are  [tex]10,10.[/tex]

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Step-by-step explanation:

hope it is helpful to you

Answer:

2√21

Step-by-step explanation:

I basically simplify the radical by breaking the radical up into products of the know factors, assuming the real numbers.

Answer:

Hello! answer:

A: 5

B: 15

C: 61

D: 24

E: 37

F: 10

I believe all of these are correct. when solving remember you do a^2+b^2=c^2

Mean- 26.222222222222

Median- 26

Mode- 24

Range- 7

Hope this helped :D

I am answering this so the other answer can get brainliest since they were the ones who gave you the answer :)

Answer:

Pizza two

Step-by-step explanation:

Given data

Pizza one

Diameter =8in

Cost =$10

Unit price= 10/8= $1.25

Pizza two

Diameter =14in

Cost =$16

Unit price= 16/14= $1.14

The better buy is Pizza two

Step-by-step explanation:

By Basic Proportionality Theorem, the triangles UTV and USR are similar.

Let us consider RV as x.

[tex]\tt{\dfrac{39}{26} = \dfrac{33}{x}}[/tex]

[tex]\rm{x = \dfrac{33 \times 26}{39}}[/tex]

[tex]\sf{ x = 22 }[/tex] is the required answer, after simplifying it.

------------

Or if you want to prove it similar:-

In triangle UTV and USR,

Angle TUV = Angle SUR (common)

Angle UVT = Angle URS (Corresponding angles b/w parallel lines)

By AA similarity,

UTV =~ USR.

Hope it helps :)

Answer:

Step-by-step explanation:

t = 2h-8  

since you didn't put in the equations,  just put in what ever variable is where t is at and any variable other than t for the h   :)

Answer:

Please put equations, so I can able to give you ans

Answer:

Step-by-step explanation:

Circumference (Perimeter) of Circle Formula: The circumference of a circle is determined by the following formula

C

=

D

×

π

where

D

is the length of the diameter of the circle and

π

≈

3.14

.

Circumference (Perimeter) of Circle Formula: The circumference of a circle is determined by the following formula

C

=

2

×

r

×

π

where

r

is the length of the radius of the circle and

π

≈

3.14

.

Area of Circle Formula: The area of a circle is determined by the following formula

A

=

r

×

r

×

π

=

r

2

×

π

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

Explanation:

The diagram shows that PT = 4 and QR = 5. Since QR is a radius of the circle, this means that the other radii segments TR and RS are also 5 units long.

Note how PR = PT+TR = 4+5 = 9, and how this segment is the hypotenuse for the right triangles PQR and PRS.

Picking either triangle, we have one known leg of 5 units (the radius mentioned earlier) and the other is unknown. The unknown leg is tangent to the circle, and recall that a tangent segment is always perpendicular to the radius at the point of tangency. So that's why we have right triangles.

Apply the pythagorean theorem to find the length of PQ and PS (both are the same length)

a^2 + b^2 = c^2

a^2 + 5^2 = 9^2

a^2 + 25 = 81

a^2 = 81 - 25

a^2 = 56

a = sqrt(56)

a = sqrt(4*14)

a = sqrt(4)*sqrt(14)

a = 2*sqrt(14)

The exact length of PQ and PS is 2*sqrt(14) units.

---------

We have enough to find the perimeter of quadrilateral PQRS. We add up the exterior sides. That means we ignore the interior segment PR.

perimeter = PQ+QR+RS+SP

perimeter = 2*sqrt(14)+5+5+2*sqrt(14)

perimeter = 10+4*sqrt(14)

Answer is choice B

Side note: The expression above approximates to roughly 24.966629

Answer:

b

Step-by-step explanation:

Area of a rectangle = length x width

length = 8 + 2 = 10

width = 10 + 2 = 12

10 x 12 = 120

Answer:

a. 120

b. 336

Step-by-step explanation:

hope this helps:)

Answer:

-14

Step-by-step explanation:

-2 x 10 = -20

-20 + 6 = 14

Therefore -2m + 6 = 14

Answer:

35.7% chance

Step-by-step explanation:

First pull is 5/8 chance, but then becasue you don't replace it next pull is 4/7, so you multiply them together