Evaluate \dfrac32y-3+\dfrac53z 2 3 ​ y−3+ 3 5 ​ zstart fraction, 3, divided by, 2, end fraction, y, minus, 3, plus, start fraction, 5, divided by, 3, end fraction, z when y=6y=6y, equals, 6 and z=3z=3z, equals, 3.

Answer:

the dimensions for the can that will minimize production cost is 9.13 cents

Step-by-step explanation:

The volume of a cylinder  V = π r²h

If we make the height h the subject of the formula; we have :

h = V/ π r²

Given that the volume of the cylinder = 400

Then

h = 400/ π r²

The total cost  will be: 0.02 × 2πrh + 0.07 × 2πr²

= 0.04 (πrh) + 0.14 (πr²)

=  0.04 (πr[tex]\frac{400} {\pi r^2}[/tex]) + 0.14 (πr²)

= 16/r +  0.14 (πr²)

total cost(c)= 16/r +  0.14 (πr²)

(c') = -16/r² +  0.28 (πr)

Let differentiate (c') with respect to zero (0); then:

-16/r² =  - 0.28 (πr)

r³ = 16/0.28 π

r³ = 18.19

r = 2.63 cm

Recall that:

h = 400/ π r²

h =  400/ π (2.63)²

h =  400/21.73

h = 18.41 cm

From;  total cost =  0.04 (πrh) + 0.14 (πr²)

replacing the value of r and h ; we have:

= 0.04 (π×2.63×18.41) + 0.14 (π × 2.63²)

= 0.04 (152.11) + 0.14 ( 21.73)

= 6.0844 + 3.0422

= 9.1266

≅ 9.13 cents

Therefore; the dimensions for the can that will minimize production cost is 9.13 cents

Answer: £4

Step-by-step explanation:

From the question, we are informed that when the normal price of a book is reduced by 30%, then the sale price of the book is £2.80.

Since the normal price of a book is reduced by 30%, that means the book is sold at (100% - 30%) = 70% of its normal price.

Let the normal price of the book be y.

70% of y = £2.80

70/100 × y = £2.80

0.7 × y = £2.80

0.7y = £2.80

y = £2.80/0.7

y = £4

The normal price of the book is £4.

Answer:

y= -4

Step-by-step explanation:

Khan Academy

The equation of a line that is perpendicular to x = 3 will be y = -4.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation is given below.

x = 3

The equation of the line that is perpendicular to the line x = 3 is given as,

y = d

The line is passing through (0, -4), then the equation of the line is given as,

y = -4

The equation of a line that is perpendicular to x = 3 will be y = -4.

More about the equation of a perpendicular line link is given below.

https://brainly.com/question/14200719

#SPJ2

Answer:

$24.

Step-by-step explanation:

Let's say Carlos has $c of money, and Mariame has $m of money.

c = 2.75m

c + m = 90

2.75m + m = 90

3.75m = 90

m = 24

c + 24 = 90

c = 66

So, Mariame has $24 and Carlos has $66.

Hope this helps!

Answer:

$38.64

Step-by-step explanation:

so the equation needed to solve is $56*0.25 and that number is 14. Since it is a coupon you subtract 14 from 56 and end up with 42. Now multiply 0.08*42 and you got your sales tax, $3.36. now subtract that from 42 and you have your answer! Don't forget the dollar sign!

hope this helped! : )

Answer:

40.08%

Step-by-step explanation:

From the given information;

the annual interest rate can be determined using the formula:

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

where;

A = amount

P is the installment per period = $625

r = interest rate

nt = number of installments=  14×(12) =168

i = rate of interest per year

[tex]156700 = 625 \times( 1+ \dfrac{r}{12})^{168}[/tex]

[tex]\dfrac{156700}{625} = {(1+ \dfrac{r}{12})^{168}[/tex]

[tex]250.72 = {(1+ \dfrac{r}{12})^{168}[/tex]

[tex]\sqrt[168]{250.72} = {(1+ \dfrac{r}{12})[/tex]

1.0334 = [tex]{(1+ \dfrac{r}{12})[/tex]

1.0334 -1 = r/12

0.0334 = r/12

r = 0.0334 × 12

r = 0.4008

r = 40.08%

Thus; Karla Harby received an interest rate of 40.08%

Answer:

The function f(x) = IxI works as follows:

if x ≤ 0, then IxI = -x

if x ≥ 0, then IxI = x

notice that if x = 0, then I0I = 0 = -0

Now, we want that:

IxI = x

Then we have that x must be greater or equal than zero:

x ≥ 0.

To represent it in the number line, you should use a black dot in the zero an shade all the right region:

__-2__-1__0__1__2__3__4__5__6__....

Answer:

30%

Step-by-step explanation:

Total population=15,000

kantipur=9000

gorkhapatra= 7500

Both magazine=40%

n(k intersection g)=40% of 15,000

=0.4*15,000

=6,000

n(k) =9000

n(g)=7500

n(A union B)= n(k) + n(g) -n(k intersection g)

=9000+7500-6000

=10,500

Population who do no read= Total population - n(A union B)

=15000-10500

=4500

Percentage population who do not read both magazine

=4,500/15,000 * 100

=0.3 * 100

=30%

Answer: 53x^7

Step-by-step explanation:

Subtracting a negative is like adding.

Answer:

? = 35

Step-by-step explanation:

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

sin ? = opp/ hyp

sin ? = 31/54

Taking the inverse sin of each side

sin ^-1 ( sin ? )= sin ^-1 (31/54)

? = 35.03481479

To the nearest degree

? = 35

Answer:

See below.

Step-by-step explanation:

SQUARE:

The area of the square is:

[tex]9x^2-12x+4[/tex]

Factor it:

[tex]=9x^2-6x-6x+4\\=3x(3x-2)-2(3x-2)\\=(3x-2)(3x-2)\\=(3x-2)^2[/tex]

Remember that all four sides of a square is equal. The area is simply the side squared. Therefore, all four sides of the square measure (3x-2).

RECTANGLE:

[tex]25x^2-16y^2\\[/tex]

Factor it. This resembles the difference of two squares, where:

[tex](x-a)(x+a)=x^2-a^2[/tex]

[tex]25x^2-16y^2\\=(5x)^2-(4y)^2\\=(5x-4y)(5x+4y)[/tex]

This cannot be simplified further. Note that the sides of rectangles doesn't necessarily have to be the same.

The dimensions of the rectangle is:

(5x-4y) by (5x+4y)

Answer:

Step-by-step explanation:

1. the area of square is 9x^2-12x+4 square units

shortcut: (a-b)^2= a^2-2ab+b^2

then simplify 9x^2-12x+4 to (3x-2)^2

area of square = s^2

then side equals sqrt((3x-2)^2)

s = (3x-2) units

2. the area of rectangle is (25x^2-16y^2) square units

shortcut: (a^2-b^2) = (a-b)(a+b)

then simplify (25x^2-16y^2) to (5x-4y)(5x+4y) square units

one side is: (5x-4y) units

one side is (5x+4y) units

Answer: 4

Step-by-step explanation:

Because there are two equal angles, this is an isoceles triangle. Line JP and HP are equal. To find the variable, write the equation which would be 3x-6=x+2. X is 4.

hope this helped:)

Answer: 4 AKA D

Step-by-step explanation:

Well to start off, we must first establish that line JP and line HP are equal because of the red ticks in the corner. So once we figured that out, then 3x-6 = x+2

»Next we add 6 to both side to make 3x = x+8

»Then we subtract x from both sides to equal 2x = 8

»Then we divide both sides by 2 which equals x=4

»So the final answer would be D. 4

Hope i helped

-lvr

This is basically in the form y = mx+b with m = 1/3 as the slope and b = 3 as the y intercept. I'm using f(x) in place of y to indicate function notation.

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

Work Shown:

The goal is to solve for y.

x - 3y = -9

-3y = -9-x ... subtracting x from both sides

-3y = -x-9

y = (-x-9)/(-3) .... dividing both sides by -3

y = -x/(-3) - 9/(-3) ... break up the fraction

y = (1/3)x + 3 .... simplify

f(x) = (1/3)x + 3 .... replace y with f(x)

Answer:

64 in²

Step-by-step explanation:

Given that the two figures are similar, therefore, the ratio of the area areas of both figures is proportional to the ratio of the square of the corresponding side lengths of both figures. This means:

[tex] \frac{100}{x} = \frac{10^2}{8^2} [/tex]

Where x is the area of the other figure.

Solve for x

[tex] \frac{100}{x} = \frac{100}{64} [/tex]

Cross multiply

[tex] 100*64 = 100*x [/tex]

Divide both sides by 100

[tex] \frac{100*64}{100} = \frac{100*x}{100} [/tex]

[tex] 64 = x [/tex]

Area of the other figure = 64 in²

Answer with explanation:

Given: Charlie is laying down mulch in his front yard. It takes Charlie 4 minutes to lay down 11 cubic yards of mulch and  16 minutes to lay down 44 cubic yards of mulch.

Here, Time(Independent variable (x)) is directly proportion to the Volume of mulch(dependent variable (y)) lied by Charlie.

Let k be the constant of proportionality, such that

[tex]k=\dfrac{y}{x}[/tex]

For x= 4 and k= 11, [tex]k=\dfrac{11}{4}[/tex]

Required equation: [tex]y=\dfrac{11}{4}x[/tex]                        

Two points are given in question: (4,11) , (16,44).

Take x= 8 , [tex]y=\dfrac{11}{4}(8)=22[/tex]i.e. point (8,22)

Similarly, for x= 12, y=33 i.e. point (12, 33)

For x= 20 , y= 55 i.e. point (20,55)

Five data points: (4,11) , (16,44), (8,22),  (12, 33), (20,55).

Now, we plot these points on graph and join them

Answer:

Here

Step-by-step explanation:

Answer:

[tex]10[/tex]

Step-by-step explanation:

[tex]f(x)=-x^2+6x+1[/tex]

x coordinate:

[tex]\frac{-b}{2a}[/tex]

[tex]a=-1\\b=6[/tex]

[tex]\frac{-6}{2(-1)} \\\frac{-6}{-2}\\ =3[/tex]

y-coordinate:

[tex]f(3)=-(3)^2+6(3)+1\\f(3)=-9+18+1\\f(3)=10[/tex]

Answer:

10

Step-by-step explanation:

Answer:

Please check explanation

Step-by-step explanation:

Here, we want to do a matching.

We shall be matching the given statements with the features we have on the graph

Hence we shall be looking closely at the graph to answer the questions.

The y-intercept is the point at which the graph touches the y-axis

And it was at -3 degrees celsius at the beginning of the day.

The temperature was above zero between 8am and 8pm. The matching statement is that it is increasing or decreasing interval

We can see that the graph rose from 8am before it finally comes to zero at 8pm

Positive or negative interval matches with it was getting warmer between 2am and 2pm.

While temperature was lowest at 2am, we can see a peak at 2pm.

Answer:

i believe it is c

Step-by-step explanation:

Answer:

[tex]y=\sqrt{55}[/tex]

which agrees with answer A

Step-by-step explanation:

Notice there are three right angle triangles for which we can apply the Pythagorean theorem:

In the small triangle at the bottom we have the Pythagorean theorem rendering:

(a)

[tex]5^2+y^2=x^2\\x^2=25+y^2[/tex]

in the second right angle triangle on top of the previous one, if we call the vertical side on the right side "z", we have:

(b)

[tex]11^2+y^2=z^2\\z^2=121+y^2[/tex]

and finally in the large right angle triangle:

(c)

[tex]z^2+x^2=16^2\\z^2=256-x^2[/tex]

We can combine equations b and c to obtain:

[tex]121+y^2=256-x^2\\x^2+y^2=256-121=135\\x^2=135-y^2[/tex]

and then combine this and (a) to get:

[tex]25+y^2=135-y^2\\2\,y^2=135-25\\2y^2=110\\y^2=55\\y=\sqrt{55}[/tex]

Answer:

[tex] f(x) = x^2 , g(x)= -\frac{2}{3}x^2[/tex]

And we want to compare the two functions.

The minus signs is a reflection around the x axis and the value of 2/3 is a compression of the original function so then the best answer would be:

The graph of g(x) is the graph of f(x) compressed vertically and reflected over the x axis

Step-by-step explanation:

We have the following two function given:

[tex] f(x) = x^2 , g(x)= -\frac{2}{3}x^2[/tex]

And we want to compare the two functions.

The minus signs is a reflection around the x axis and the value of 2/3 is a compression of the original function so then the best answer would be:

d) The graph of g(x) is the graph of f(x) compressed vertically and reflected over the x axis

Answer:

C is the correct answer

Step-by-step explanation:

Answer:

The initial height of the candle is H = 15cm

The rate at which the candle burns is 2.5 cm per hour

Then after one hour, the height of the candle is:

h = 15cm - 2.5cm = 12.5cm

after two hours is:

h = 15cm - 2*2.5cm = 10cm

then, after t hours, the height of the candle is:

h = 15cm - (2.5cm/h)*t

now, the domain of h (or the range of the function) is:

h ∈ [0cm, 15cm]

when t = 0, h(0h) = 15cm

and the maximum value of t will be such that the candle is totally consumed:

h(t) = 0 = 15 - 2.5*t

t = 15/2.5 = 6

Then the domain of the function is:

t ∈ [0h, 6h]

Answer:

12 bags of cookies.

Step-by-step explanation:

Since you already start out with $24, you will have a y-intercept of 24. Your slope will be 3, since each bag sells for $3.

Your equation will be y = 3c + 24.

Your sister does not start out with money, so she will have a y-intercept of 0. Her slope will be 5, as each bag sells for $5.

Her equation will be y = 5c.

Since y = y, you can set the two equations equal to each other.

3c + 24 = 5c

5c = 3c + 24

Subtract 3c from both sides

2c = 24

Divide both sides by 2

c = 12

So, they must sell 12 bags of cookies to raise the same amount of money, $60. Yum!

Hope this helps!

Answer:

The total surface area of cone is 70π cm² or 219.9 cm².

Step-by-step explanation:

Given that the formula of total surface area of cone is T.S.A = πr² + πrl where r represents radius and l is slant height. So you have to substitute the values :

[tex]t.s.a = \pi {r}^{2} + \pi{r}l[/tex]

[tex]let \: r = 5 \: , \: l = 9[/tex]

[tex]t.s.a = \pi {(5)}^{2} + \pi(5)(9)[/tex]

[tex]t.s.a = 25\pi + 45\pi[/tex]

[tex]t.s. a = 70\pi \: or \: 219.9 \: [/tex]

Answer:

piece of wire 8 m long

one piece is bent into square:

the square has four equal sides , so at least 4 m has to be cut from the wire to form a square with side=1 m.

the perimeter of the square =2L+2W=2(1)+2(1)=4 m

that is the max. amount can be cut from the wire, since the other part is bent into a circle.

( note if you cut more, the square will take the whole wire)

Perimeter=2L+2W=2(2)=2(2)=8 m and the area=2*2=4 m²)

Area and perimeter are two crucial characteristics of 2D shapes in mathematics.

The perimeter of the square exists 8 m and the area exists 4 m².

Area and perimeter are two crucial characteristics of 2D shapes in mathematics. The area and perimeter both specify the shape's boundaries and the space they occupy, respectively. Area and perimeter are significant mathematical concepts that are used to daily life. All sizes and shapes, regular or unusual, are covered by this. Each shape's area and perimeter calculations are unique.

Piece of wire is 8 m long and one piece is bent into square:

The square has four equal sides , so at least 4 m has to be cut from the wire to form a square with side = 1 m.

The perimeter of the square = 2L + 2W = 2(1) + 2(1) = 4 m

Which exists the maximum amount that can be cut from the wire, since the other part is bent into a circle.

Perimeter = 2L + 2W =2(2) = 2(2) = 8 m and the area = 2 × 2= 4 m²

To learn more about perimeter and area, refer to:

brainly.com/question/19819849

#SPJ2

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

First find the area of the sector.

For that, use this equation:

area = [tex]\frac{x }{360} * \pi r^{2}[/tex]

where 'x' is the angle and 'r' is the radius

Sub the values in

area = [tex]\frac{56}{360} * \pi15^2[/tex]

Solve:

area = [tex]35\pi[/tex]

It is easier to keep it in terms of pi until the end

Now, calculate the area of the triangle within the sector

area = 1/2 ab x sinC

where 'a' and 'b' are the radius (side lengths) and C is the angle

thus,

area = 1/2(15 x 15) x sin(56)

area = 93.27 (to 2 d.p)

Now subtract the area of the triangle from the area of the sector

[tex]35\pi[/tex] - 93.27 = 16.6857

This would give you a final answer of 16.69 units^2

Have A Nice Day ❤    

Stay Brainly! ヅ    

- Ally ✧    

｡☆✼★ ━━━━━━━━━━━━━━  ☾

Answer:

380.54:1007

Step-by-step explanation:

3.59✖️106=380.54

9.5✖️106=1007

380.54:1007

Answer:

[tex]\huge\boxed{3.779\times10^{11}}[/tex]

Step-by-step explanation:

[tex]\left(3.59\times10^6\right):\left(9.5\times10^{-6}\right)=\dfrac{3.59}{9.5}\times\dfrac{10^6}{10^{-6}}=\dfrac{359}{950}\times10^{6-(-6)}=\dfrac{359}{950}\times10^{6+6}\\\\=\dfrac{359}{950}\times10^{12}\approx0.3779\times10^{12}=3.779\times10^{11}\\\\\text{used}\ \dfrac{a^n}{a^m}=a^{n-m}[/tex]

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

Work Shown:

P = amount deposited = 10000

r = interest rate in decimal form = 0.01

n = compounding frequency = 1 (annual compounding)

t = number of years = 10

--------

A = P*(1+r/n)^(n*t) ... compound interest formula

A = 10000*(1+0.01/1)^(1*10)

A = 11046.221254112

A = 11046.22  rounding to the nearest cent

Answer:

A

Step-by-step explanation:

Kenny scored 13 points, and Micheal scored p points.  They scored a total of 27 points.  This means that 27 is the sum of their scores.  The answer is A.

13 + p = 27

Answer:

It’s b or it’s 13+p=27

Step-by-step explanation: