There are 300 teenagers in a park. 32% of them are boys, how
many more girls than boys are there in the park?

The standard form of the parabola is   x = -4/3y² -40/3y -103/3

What is parabola?

A parabola is an approximately U-shaped, mirror-symmetrical planar curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. One way to describe a parabola is with a point and a line.

 x = -4/3(y +5)² -1

Solve for x.

 x = (4y² +40y +103)/(-3)

 x = -4/3y² -40/3y -103/3 . . . . 'standard form' in the US

__

Taking our clues from the graph*, we can write the vertex form equation as ...

 x = -4/3(y +5)² -1 . . . . . . 'standard form' in other places

____

* The vertex is (-1, -5), so for some leading coefficient, the equation will be ...

 x = a(y -(-5))² +(-1) = a(y +5)² -1

The value of 'a' is the scale factor. Here, that is the difference between the parabola value (x = -2 1/3) and the vertex value (x = -1) one unit away from the vertex.

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Answer:

She needs to get at least 96 on the 4th test to earn an average of at least 90 in the class.

Step-by-step explanation:

(97+78+89+?) divided by 4 at\geq 90

It is divided by 4 because it is the average of 4 test scores.

To Solve: (97+78+89+?) divided by 4 at\geq 90

Multiply by 4 on both sides 97+78+89+? at\geq 360

Isolate variable: ? at\geq 96

The probability that an electron will tunnel through a 0.50 nm air gap from a metal to a STM probe if the work function is 4.0 eV is 3.4 × 10^-5

The air gap from a metal to a STM = 0.50 nm

The work function = 4.0 eV

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The probability = Number of favorable outcomes / Total number of outcomes

The value of η = h / [tex]\sqrt{2m(U_0-E)}[/tex]

Substitute the values in the equation

= [tex]\frac{1.05(10^{-34})}{\sqrt{2(9.11(10^{-31})(4(1.6)(10^{-19})} }[/tex]

Do the arithmetic operation

= 0.0972 nm

The probability = exp (-1 / 0.972)

= 3.4 × 10^-5

Therefore, the probability is 3.4 × 10^-5

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When the average distance from Jupiter to the Sun is about 5 x 10^8 miles and the average distance from Venus to the Sun is about 7 x 10^7 miles. The average distance from Jupiter to the Sun is about 7.1 as great as the average distance from Venus to the Sun.

The distances is compare using the mathematical operation called division,

the procedure is done as follows

= (The average distance from Jupiter to the Sun) / (The average

distance from Venus to the Sun)

= 5 x 10^8 miles / 7 x 10^7 miles.

= 7.14285

= 7.1

the comparison showed that the distance from Jupiter to Sun is 7.1 times greater than the distance form Venus to Sun

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send a picture so i know what its asking for

Answer:

x=-24

Step-by-step explanation:

you would solve for x

1) multiply the equation out

2) put x on one side by subtracting and adding on each side (make sure to balance it out)

3) divide or multiple by the number on the number on the x

5/2x + 8 - 3/2x + 12 = -4

5/2 x - 3/2 x  + 8 + 12 = -4

x + 20 = -4

x = -24

Answer:

1.04, 1.4, 1.5 (one and a half), 10, 16

Answer:

1.04, 1.4, 1.5, 1.6

Step-by-step explanation:

1 1 half = 1.5

16 over 10 = 1.6

hope this helps!

Answer:

X-intercept : (-2,0)

Y-intercept : (0,6)

Answer:y-intercept (0,6),x-intercept (-2,0)

Step-by-step explanation:

To find the y-intercept set x=0

-3(0)+y=6

y=6

y-intercept (0,6)

To find the X-intercept set y=0

-3x+0=6

-3x=6

x=-2

x-intercept (-2,0)

Thus, the mass of the frog is 48.6π grams when it is in a hemispherical pod which just floats without sinking into sea water.

The force imposed on a body by a fluid, such as water or air, in which the body is submerged or immersed is known as buoyancy. This force is equivalent to the mass of the fluid that the body has displaced. In mathematics, buoyancy is defined as the sum of the fluid density, gravitational acceleration, and body volume. Archimedes' principle, which asserts that the buoyant force on an item is equal to the weight of the fluid it displaces, is a name for this connection. A key idea in the study of fluid mechanics, buoyancy has many uses, including the construction of boats, planes, and other floating structures.

How to solve?

V = 2/3 * π * r^3,

V = 2/3 * π * 6^3 = 2/3 * π * 216 = 36π.

F = V * d,

F = 36π * 1.35g/c * m^3 = 48.6π g.

F = m + W,

48.6π g = m + 0 g.

m = 48.6π g.

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A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams.

What is radioactive decay?

The release of energy in the form of ionizing radiation occurs during radioactive decay.

                       Ionizing radiation can harm DNA in genes and tissues because it can affect the atoms in living things.

We know that decay behaves exponentially and follows this model

   [tex]m(t) = m_{0} . e^{t/T} \\[/tex]

The time constant can be described in terms of half-life (t1/2), in minutes, through the following expression

     T =  t1/2 /In2

If we know that t1/2 = 8 min , m₀ = 170g and m(t) = 5g then the time needed for the decay is:

τ ≈ 11.541 min

   t = -τ .In m(t)/m₀

t ≈ 40.698 min

A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams.

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The number is 320 and 80 % of the number is 256

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the equation A is

65% of a number is 208 and 15% of the same number is 48

So , 65% of n = 208   be equation (1)

15% of n = 48   be equation (2)

Now , on simplifying the equations , we get

( 15 / 100 ) x n = 48

15n/100 = 48

Multiply both sides by 100 . we get

15n = 4800

Divide by 15 on both sides of the equation , we get

n = 320

The number n can also be determined by

( 65% - 15% ) of n = 208 - 58

50 % of n = 160

So , 100 % on n = 160 x 2

n = 320

Therefore , the number n is 320

Now , the 80 % of the number n is A = 80/100 x 320

A = 320 x 0.8

A = 256

Therefore , the value of A is 256

Hence , The number is 320 and 80 % of the number is 256

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Using mathematical operations, we know that Kona needs a 276 trays to display all her 3308 muffins.

The process of calculating a value using operands and a math operator is known as a mathematical "operation."

The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.

Addition, subtraction, multiplication, division, and modular forms are the five fundamental operations in mathematics.

So, a tray will be needed to display all the cakes:

The total number of muffins is 3308.

Each tray can have 12 muffins.

The total trays needed are:

3308/12

275.66

Rounding off: 276

Therefore, using mathematical operations, we know that Kona needs a 276 tray to display all her 3308 muffins.

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Answer:

Yes, you're right.

Step-by-step explanation:

Just by doing the math, 0.27 times 35 is 9.45.

Plugging it in a calculator also says it's 9.45.

Answer: give me brainliset

(

X

>

42

)

=

P

(

Z

>

−

1.1429

)

=

1

−

P

(

Z

<

1.1429

)

=

1

−

Φ

(

1.1429

)

=

1

−

0.8729

(from tables)

=

0.1271

Step-by-step explanation:

The equation of the line which is perpendicular to 5x - 4y = 16 is  [tex]y = -\frac{4}{5}x -4[/tex].

The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). Finding the distance between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.

Not all crossing lines are parallel ones. If the intersecting lines satisfy the following conditions, they are said to be perpendicular lines. Following are the two primary characteristics of perpendicular lines:

Let's say that lines AB and CD are parallel to one another. Line AB has a slope of m1, whereas line CD has a slope of m2.

If and only if the product of the slopes of the two lines equals negative of unity, two lines are perpendicular to one another.

As a result, the following is the formula for the perpendicular's slope:

m1.m2 = -1

The equation of the line be "y = mx + c".

Equation of the line Perpendicular to the line is 5x - 4y = 16

Therefore,  4y = 5x - 16

⇒ [tex]y = \frac{5}{4}x -4[/tex]

Slope of the line Perpendicular to the required line is [tex]\frac{5}{4}[/tex].

Slope of the required ine be m .

Therefore, m * [tex]\frac{5}{4} = -1[/tex]

⇒ [tex]m = -\frac{4}{5}[/tex].

Equation of the line is ,

[tex]y = -\frac{4}{5}x + c[/tex]

The line passes through (5,-8)

Therefore,

[tex]-8 = \frac{-4}{5}*5 + c[/tex]

⇒ c = -4

The equation of the line is [tex]y = -\frac{4}{5}x -4[/tex].

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There are 22 different ways to organize the word mathematics because no two consecutive letters are the same.

Total number of ways to organize the word "mathematics".

The same letter does not appear twice.

The following word has the letters 2M, 2A, 2T, H, E, I, C, and S.

We will first organize H,E,I,C,S in five different ways;

−H−E−I−C−S−

No, we could arrange 2M, 2T, and 2A as we have 6 gaps;

= 6!/(2!.2!.2!)

So there are a total of;

= 5 x 6!/(2!.2!.2!)

= 22.5

= 22 ways

Thus, there are 22 different ways to organize the word mathematics because no two consecutive letters are the same.

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[tex]4^x=3 \\\\[-0.35em] ~\dotfill\\\\ 4^{2x-2}\implies 4^{2x}\cdot 4^{-2}\implies (4^x)^2\cdot \cfrac{1}{4^2}\implies \cfrac{(4^x)^2}{16}\implies \cfrac{(3)^2}{16}\implies \cfrac{9}{16}[/tex]

Answer:

another root=-2,c=-106

Step-by-step explanation:

let q and r be two roots of eqn 10x²-33x-c=0,--(1)

then,q=5.3

comparing eqn--(1) with ax²+bx+c=0,we get

a=10,b=-33,C=-c

we know,

q+r=-b/c

or,5.3+r=33/10

or,53+10r=33

or,10r=-20

or,r=-2

hence, another root=-2

again,we know

q×r=-C/a

or,5.3×-2=c/10

or,-106=c

hence,c=-106.

The value of x= 93/11 and y=-155/11 when the system of equation are 10x+ 6y=0 and 7x+ 2y=31.

Given that,

The system of equation are 10x+ 6y=0 and 7x+ 2y=31.

We must resolve the equation system.

We know that,

Take the system of equations.

10x+ 6y=0 ------>equation(1)

7x+ 2y=31 ------->equation(2)

Multiply 3 to the equation(2) and subtract with equation(1)

3×(7x+ 2y=31)

21x+ 6y=93

10x+ 6y=0

-----------------         (subtract)

11x+0=93

11x=93                 (divide)

x=93/11

Substitute x=93/11 in equation(1)

10(93/11)+6y=0

930/11+6y=0

6y=-930/11

y=-155/11

Therefore, The value of x= 93/11 and y=-155/11 when the system of equation are 10x+ 6y=0 and 7x+ 2y=31.

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well, let's just divide them anyway and check it out.

hmmm 6.1 ÷ 0.1, well, when dividing decimals, we can first check the decimals on each hmmm 6.1 has one decimal and 0.1 has one decimal, so for the one decimal on 6.1 0.1 gets one "0" and for each decimal on 0.1, 6.1 gets  one "0".

That means we can change the values with no dots to say 610 and 10, so we end up with a division of 610 ÷ 10 = 61.  We can write that as 61.0 hmmm woopsie, the dot moved to the right by one slot.

Given that the drawer includes one pair of brown socks and one pair of white socks, the likelihood of selecting one sock, replacing it, and then selecting another sock is 1/16.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here,

n(s)=4

n(e)=1

Probability of choosing a sock, replacing it, and then choosing another sock,

=1/4*1/4

=1/16

Probability of choosing a sock, replacing it, and then choosing another sock will be 1/16 as the drawer contains one pair of brown socks and one pair of white socks.

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it doesn't have solution

The account balance(i.e. compound amount) will be $5706.84 after 28 years.

What is daily compounded interest?

Daily compounded interest is defined as an interest that is accrued daily and is computed by charging interest on principal plus interest earned daily. Due to the frequent compounding, daily compounded interest is higher than interest compounded on a monthly or quarterly basis.

Given, Principal = $2834

the annual rate = 2.5% = 0.025

time = 28 years

For compounded daily, n = 365

Now, the compound amount is calculated by

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

or, A = [tex]2834(1 + \frac{0.025}{365} )^{365*28}[/tex]

A = $5706.84

Hence, the account balance will be $5706.84 after 28 years.

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The dimensions of a building to be fenced off around a rectangular parcel of land are 10.5 meters and 21 meters.

The Latin word rectus, which meaning "right" or "straight," is the source of the English word "rectangle." The straight sides of a rectangle are a result of its right angles. Rectitude, which refers to moral uprightness, is another term with the same root.

Explanation:

The size of a rectangle

lw = area of rectangle

where,

= length

= width

Thus, perimeter equals 2w plus l.

42 = 2w + l

l = 42 - 2w

Hence,

area = w (42- 2w)

180 = 42w - 2w²

-2w² +42w - 180 = 0

-w² + 21w - 180 = 0

The following is where to find the dimension w;

w = - b / 2a

where

a = -1

b = 21

w = - 21 / 2 × -1

W=10.5 meters.

Then,

l = 42 - 2w

l = 42 - 2(10.5) (10.5)

l=21 meters .Consequently, the measurements are 10.5 meters and 21 meters.

The dimensions of a building to be fenced off around a rectangular parcel of land are 10.5 meters and 21 meters

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Answer:

28.26

Step-by-step explanation:

A=3.14r^2

A=3.14(3)^2

A=3.14(9)

A=28.26

Answer: 28 cm

Step-by-step explanation: Area=π·r² and diameter =2r

So if we need to  find what our radius is. As shown by d=2r our radius is 1/2 our diameter. If our diameter is 6cm our radius is 3cm.

Now plug 3cm into A= 2πr²⇒ A= 2(3.14)(3²) = 28.26

Now round to the nearest whole number ⇒ 28.

Answer:

77.04

Step-by-step explanation:

A=3.14r^2

a=3.14(6)^2

A=3.14(36)

A=77.04

Answer: 113 ft^2

Step-by-step explanation:

The equation of the​ line, in​ slope-intercept form, containing the point ( 5,2. 2) and (9,2. 6) is  y=0.025x+2.375 where 0.025 is the value of slope and 2.375 is the y-intercept.

Take into account the slope-intercept form of the equation y = 6 x + 9 y=6x+9. The x and y intercepts are known. When x = 0, the y-intercept also happens, and when y equals 0, the x-intercept also happens. By setting the value of y to 0, we may find the x-intercept.

The values of the slope and y-intercept reveal details of the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.

To calculate the equation of line containing points (5,2.5) and (9,2.6) we will use the formula y=mx+b

Here, m = (y2-y1)/(x2-x1)

So, m = (2.6-2.5)/(9-5)

m= 1/40

m=0.025

Now finding b by using formula y=mx+b using x= 5 and y= 2.5

2.5=(0.025)(5)+b

2.5=(0.125)+b

b=2.375

so equation of line is y=0.025x+2.375 in slope-intercept form.

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Answer: 21 meters cost $28.5

Step-by-step explanation:

divide 19 by 14 and multiply by 21

21 meters cost $28.5

Answer: g + r = 17

2.5g + 3.5r = 52.5

Step-by-step explanation: Let g be the number of games Nolan played and r be the number of rides Nolan went on. We can write the following system of equations to represent the problem:

g + r = 17

2.5g + 3.5r = 52.5

We can solve this system of equations using elimination, substitution, or graphing.