2/20 : 1/40 as a unit rate

Answer:

£16, £40, £64

Step-by-step explanation:

sum the parts of the ratio, 2 + 5 + 8 = 15 parts

Divide the amount by 15 to find the value of one part of the ratio.

£120 ÷ 15 = £8 ← value of i part of ratio , then

2 parts = 2 × £8 = £16 ← amount Russell gets

5 parts = 5 × £8 = £40 ← amount Sarah gets

8 parts = 8 × £8 = £64 ← amount Terry gets

Answer:

$16, $40, $64

Step-by-step explanation:

The ratio is 2:5:8. Altogether, this adds up to 15. So they divided $120 into 15 portions. 120/15=8.

Russel got 2 portions of 8 dollars, Russel got $16

Sarah got 5 portions of 8 dollars, Sara got $40

Terry got 8 portions of 8 dollars, Terry got $64

Answer:

Step-by-step explanation:

Middle point of AB

x(m) = (6+1)/2 = 7/2

y(m) = (7+4)/2 = 11/2

slope of the line that contains AB

(4-7)/(6-1) = -3/5

eqaution of the perpendicular bisector

y-11/2 = 5/3(x-7/2)

y = 5/3x -35/6 + 11/2

y = 5/3x + (-35 + 33)/6

y = 5/3x -1/3

Middle point of AC

x(m) = (1+5)/2 = 3

y(m) = (7+5)/2 = 6

Slope of the line that contains AC

(5-7)/(5-1) = -1/2

equation of the perpendicular bisector

y-6 = 2(x-3)

y = 2x -6 + 6

y = 2x

Point of intersection

y= 5/3x -1/3

y = 2x

2x = 5/3x - 1/3

6x = 5x - 1

x = -1

y = -2

P(-1,-2)

Answer:

(1,7)

Step-by-step explanation:

Given:

A(1,7)

B(6,4)

C(5,5)

Solution:

Mid point of AB = M((1+6)/2,(7+4)/2) = M(3.5,5.5)

Slope of AB = (4-7)/(6-1) = -3/5

Perpendicular bisector of AB:

L1: y -  11/2 = -(3/5)(x-7/2) ............(1)

Mid point of AC, m= N((1+5)/2,(7+5)/2) = N(3,6)

Slope of AC, n = (5-7)/(5-1) = -2/4 = -1/2

perpendicular bisector of AC:

L2: y-6 = -(1/2)(x-3) ..........."(2)

To find the point of intersection,

(1)-(2)

-5.5 - (-6) = -(3/5)x +12/5 + x/2 - 3/2

1/2 = -x/10 + 6/10

x/10 = 1/10

x = 1

substitute x in (1)

y = 3/2+11/2 =7

Therefore Point of intersection is (1,7)

Answer:

−3x^2+2x /x−2

Step-by-step explanation:

4x−9x^3/ 3x^2−4x−4

=  −9x^3+4x /3x^2−4x−4

=  x(−3x+2)(3x+2) /(3x+2)(x−2)

=  −3x^2+2x /x−2

Answer:

Hey there!

The given equation helps us understand the relationship between Amber's tips earned and the money she earned through her hourly wage. This information will add up to equal a grand total of $69.20.

We know that Amber earns $15.50 in tips during her 6 hour shift. Therefore, this is not considered part of her wage. This would be one of the constants of our equation.

We also know that Amber earns a fixed hourly wage, but we don't know what this wage is. We need to find w.

[tex]6w+15.5=\$69.20[/tex]

Subtract 15.5 from both sides of the equation (and get rid of the currency symbol).

[tex]6w=69.20-15.5\\6w=53.7[/tex]

Divide both sides of the equation by 6.

[tex]\displaystyle \frac{6w}{6}=\frac{53.7}{6}\\\\w=8.95[/tex]

Therefore, Amber's hourly wage is $8.95.

Answer: 4

Step-by-step explanation: bc

Answer:

This is correct.

Step-by-step explanation:

Answer:

Yes...You are right... hope it helps

Answer:

The outcomes produced by A would be greater than B. A further explanation is provided below.

Step-by-step explanation:

Given:

In process A,

Produced units = [tex]32x^{1.5}[/tex]

In process B,

Produced units = [tex]4x^3[/tex]

If the outcomes are equivalent then,

⇒ [tex]32x^{1.5}=4x^3[/tex]

⇒     [tex]x^{1.5} = 8[/tex]

By taking log both  sides, we get

⇒    [tex]log \ 8= 1.5 \ log \ x[/tex]

⇒          [tex]x=3.99[/tex]

Answer: 700

Step-by-step explanation: 3 x 200 + 100

Answer:

c.$700

Step-by-step explanation:

3x+100 3 per chair=3x plus the additional 100 dollar fee

3(200)+100

600+100

700

Answer:

19

Step-by-step explanation:

Conditional probability formula: A|B (A given B)= (A∩B)/B

So cold drink | large (cold drink given large)=  (Cold∩Large)/Large

cold∩large= 5

large= 22+5= 27

5/27=.185185185

which i guess rounds to 19%

Answer:

gal = 663902.4

11 pavers

Step-by-step explanation:

V = l × w × h

V = 164 × 82 × 6.6

V = [tex]88757ft^3[/tex]

**********************************

The Swimming pool is a

rectangular prism. Write

the formula for its volume

and calculate it.

l...length of this prism

w...width of this prism

h...height of this prism

V ...volume

*********************************

To know how many

gallons are in the pool,

multiply the volume by

the number of gallons

in [tex]1ft^3[/tex] gal...number of

gallons

********************************

gal = 88757 × 7.48

gal = 663902.4

********************************

First to not confuse

anybody on this, we need

to convert the meters into

centimeters.

Rule: 1 m = 100 cm

        3 m = 300 cm

        2.5 m = 250 cm

********************************

so for every meter, we

multiply 100 to get the

amount of centimeters

********************************

so then add the

centimeters of 3 m and

2.5 m

Answer: 550 cm

so then now compare

the measurings...

3 m = 300 cm

50cm × y = 300cm

50cm × 6 = 300cm

y = 6

2.5 m = 250 cm

50cm × y = 250cm

50cm × 5 = 250cm

y = 5

6 + 5 = 11 pavers

so Oliver will need 11 pavers

Answer:

m∠B = 94º

Step-by-step explanation:

Supplementary angles total 180

(8x + 6) + ( 7x + 24) = 180

Combine like terms

15x + 30 = 180

15x = 150

x = 10

m∠B = 7x + 24

m∠B = 7(10) + 24

m∠B = 94º

Answer:

-.985

Step-by-step explanation:

Given:

[tex]PQRS\sim TUVW[/tex]

In the given figure, PS=x, RS=35, UV=20, VW=25 and TW=15

To find:

The scale factor from PQRS to TUVW.

Solution:

We have,

[tex]PQRS\sim TUVW[/tex]

We know that the corresponding sides of similar figures are proportional. The scale factor is the ratio of one side of image and corresponding side of preimage.

The scale factor is:

[tex]k=\dfrac{VW}{RS}[/tex]

[tex]k=\dfrac{25}{35}[/tex]

[tex]k=\dfrac{5}{7}[/tex]

Therefore, the scale factor from PQRS to TUVW is [tex]k=\dfrac{5}{7}[/tex].

Answer:

Our two numbers are:

[tex]2+4\sqrt{2} \text{ and } 4\sqrt{2}-2[/tex]

Or, approximately 7.66 and 3.66.

Step-by-step explanation:

Let the two numbers be a and b.

One positive real number is four less than another. So, we can write that:

[tex]b=a-4[/tex]

The sum of the squares of the two numbers is 72. Therefore:

[tex]a^2+b^2=72[/tex]

Substitute:

[tex]a^2+(a-4)^2=72[/tex]

Solve for a. Expand:

[tex]a^2+(a^2-8a+16)=72[/tex]

Simplify:

[tex]2a^2-8a+16=72[/tex]

Divide both sides by two:

[tex]a^2-4a+8=36[/tex]

Subtract 36 from both sides:

[tex]a^2-4a-28=0[/tex]

The equation isn't factorable. So, we can use the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = 1, b = -4, and c = -28. Substitute:

[tex]\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-28)}}{2(1)}[/tex]

Evaluate:

[tex]\displaystyle x=\frac{4\pm\sqrt{128}}{2}=\frac{4\pm8\sqrt{2}}{2}=2\pm4\sqrt{2}[/tex]

So, our two solutions are:

[tex]\displaystyle x_1=2+4\sqrt{2}\approx 7.66\text{ or } x_2=2-4\sqrt{2}\approx-3.66[/tex]

Since the two numbers are positive, we can ignore the second solution.

So, our first number is:

[tex]a=2+4\sqrt{2}[/tex]

And since the second number is four less, our second number is:

[tex]b=(2+4\sqrt{2})-4=4\sqrt{2}-2\approx 3.66[/tex]

Answer:

[tex]2+4\sqrt{2}\text{ and }4\sqrt{2}-2[/tex]

Step-by-step explanation:

Let the large number be [tex]x[/tex]. We can represent the smaller number with [tex]x-4[/tex]. Since their squares add up to 72, we have the following equation:

[tex]x^2+(x-4)^2=72[/tex]

Expand [tex](x-4)^2[/tex] using the property [tex](a-b)^2=a^2-2ab+b^2[/tex]:

[tex]x^2+x^2-2(4)(x)+16=72[/tex]

Combine like terms:

[tex]2x^2-8x+16=72[/tex]

Subtract 72 from both sides:

[tex]2x^2-8x-56=0[/tex]

Use the quadratic formula to find solutions for [tex]x[/tex]:

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] for [tex]ax^2+bx+c[/tex]

In [tex]2x^2-8x-56[/tex], assign:

Solving, we get:

[tex]x=\frac{-(-8)\pm \sqrt{(-8)^2-4(2)(-56)}}{2(2)},\\x=\frac{8\pm 16\sqrt{2}}{4},\\\begin{cases}x=\frac{8+16\sqrt{2}}{4}, x=\boxed{2+4\sqrt{2}} \\x=\frac{8-16\sqrt{2}}{4}, x=\boxed{2-4\sqrt{2}}\end{cases}[/tex]

Since the question stipulates that [tex]x[/tex] is positive, we have [tex]x=\boxed{2+4\sqrt{2}}[/tex]. Therefore, the two numbers are [tex]2+4\sqrt{2}[/tex] and [tex]4\sqrt{2}-2[/tex].

Verify:

[tex](2+4\sqrt{2})^2+(4\sqrt{2}-2)^2=72\:\checkmark[/tex]

Answer:

d

Step-by-step explanation:

on edge

Answer:

D!!

Step-by-step explanation:

Got it right

Answer:

36.87°

Step-by-step explanation:

Given the right angle triangle :

To obtain the value of Cosθ ; we use the trigonometric relation :

Cosθ = Adjacent / Hypotenus

The adjacent angle isn't given :

Opposite = 9 ; hypotenus = 15

Adjacent = √(hypotenus ² + opposite ²)

Adjacent = √(15² - 9²)

Adjacent = √(225 -81)

Adjacent = √144 = 12

Hence,

Cos θ = 12/15

θ = Cos^-1(12/15)

θ = 36.87°

Answer:

1, -3.5

Step-by-step explanation:

Answer:(0.5,-3.5)

Step-by-step explanation:

(-2+3/2)/2, (-5-2)/2

0.5,-3.5

Answer:

Box Dimensions:

L  = 15.15 ul

W = 7.15 ul

h = x = 2.43 ul

V(max) =    263.22 cu

Step-by-step explanation:

We call x the length of the square to be cut in the corners then:

Are of the base of the box is:

(20 - 2*x)  is the future length of the box and

(12 - 2*x) will be the width

The heigh is x  then the volume of the box is:

V = ( 20 - 2*x )* ( 12 - 2*x ) * h

And the volume as a function of x is:

V(x) = ( 20 - 2*x) * ( 12 - 2*x ) * x     or   V(x) = (240 -40*x -24*x + 4*x²) * x

V(x) =  240*x - 64*x² + 4*x³

Taking derivatives on both sides of the equation we get:

V´(x) = 240 - 128*x + 12*x²

V´(x)  =  0              240 - 128*x + 12*x²  = 0    or     60 - 32*x + 3*x²

3*x²  -  32*x  +  60  = 0

Solving:

x₁,₂  =  32  ± √ (32)² - 4*3*60 ]/ 2*3

x₁,₂  =  32  ± √ 1024 - 720 )/6

x₁,₂  = ( 32  ± √ 304 )/6

x₁,₂  = ( 32  ± 17.44 )/6

x₁  =  8.23      ( we dismiss this solution because is not feasible 2*x > 12

x₂ = 2.43  u.l ( units of length)

Then

L  =  20 - 2*x      L  = 20  - 4.85     L  = 15.15 ul

W =  12 - 2*x      W = 12 - 4.85      W = 7.15 ul

h  =  2.43 ul

V = 2.43*7.15*15.15  cubic units

V =  263.22 cu

To see if when x = 2.43   function V has a maximum we go to the second derivative

V´´(x)  = - 128  + (24)*2.43

V´´(x) = - 69.68      as        V´´(x)  < 0   then we have a maximum for V(x) in the point x = 2.43

Answer:

ANSWER IS 12

Step-by-step explanation:

Answer:

42

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

x = 6

7x

Step 2: Evaluate

Answer:

Step-by-step explanation:

volume of reqd. figure=10×5×1+3×3×1=50+9=59 cm³

Answer:B

Step-by-step explanation:

simple, there is one point of intersection or where the lines meet

Answer:

B:  One solution

Step-by-step explanation:

The graphs show that the two lines intersect at one point.  This point represents the ONE solution of this system of equations.

If the lines did not intersect, the system would have no solution.

If the lines coincide, the system would have infinitely many solutions.

Answer:

last term is 1536

Value of the geometric series is 3,069

Step-by-step explanation:

took one for the team

There are 10 terms in the geometric series.

And, The first term of the series is, 3

We know that;

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The geometric series is,

⇒ S₁₀ = ∑ 3 (2)ⁿ⁻¹

Where, n is from 1 to 10.

Thus, We get;

There are 10 terms in the geometric series.

And, For first term;

Put n = 1;

⇒ S₁₀ = ∑ 3 (2)ⁿ⁻¹

⇒ S₁₀ = ∑ 3 (2)¹⁻¹

⇒ S₁₀ = ∑ 3 (2)⁰

⇒ S₁₀ = ∑ 3 × 1

⇒ S₁₀ = 3

Thus, The first term of the series is, 3

Learn more about the geometric sequence visit:

https://brainly.com/question/25461416

#SPJ7

Answer:

[tex]-\infty < x < \infty[/tex]

Step-by-step explanation:

Given

[tex]y = \sqrt[3]{x - 1}[/tex]

Required

The domain

The given function is cubic root; there are no restrictions on cubic root functions

Hence, the domain is:

[tex]-\infty < x < \infty[/tex]

Answer:

153

Step-by-step explanation:

[tex]other \: number = \frac{9 \times 459}{27} \\ \\ = \frac{459}{3} \\ \\ = 153[/tex]

Answer:

Other number is 153

Step-by-step explanation:

Usually, the product of the HCF and LCM will be the product of the 2 numbers in question.

The HCF and LCM are given as 9 and 459.

While one of the numbers used to find the HCF & LCM was 27.

Let the other number be y.

Thus;

27y = 459 × 9

y = 459 × 9/27

y = 153

Answer:

4 + (1/3)w + w = 24

subtract 4 from both sides

(1/3)w + w = 20

multiply both sides by 3 to clear the fraction

w + 3w = 60

4w = 60

Divide both sides by 4

w = 15

Solution :

It is given that a company named  "Sugary Sweet" wishes to test about the sweet and the flavorful that their participants like the candy.

There are Two levels of the flavor and three levels of sugar.

Thus it is a Two Way ANOVA test.

A two-way ANOVA test is used to test the effect of any two independent variables on the dependent variable.

[tex]$H_{01} : \text{Mean effect of the sugar are equal}$[/tex]

[tex]$H_{02} : \text{Mean effect of the flavor are equal}$[/tex]

[tex]$H_{01} : \text{There is no interaction between the sugar and the flavor}$[/tex]

Answer:

Step-by-step explanation:

This is a positive parabola so it opens upwards. The equation for the directrix of this parabola is y = k - p. k is the second number in the vertex of the parabola which is (0, 0), but we need to solve for p.

The form that the parabola is currently in is

[tex]y=a(x-h)^2+k[/tex] so that means that [tex]a=\frac{1}{8}[/tex]. We can use that to solve for p in the formula

[tex]p=\frac{1}{4a}[/tex] so

[tex]p=\frac{1}{4(\frac{1}{8}) }[/tex] which simplifies to

[tex]p=\frac{1}{\frac{1}{2} }[/tex] which gives us that

p = 2. Now to find the directrix:

y = k - p becomes

y = 0 - 2 so

y = -2, choice A.

Answer and Step-by-step explanation:

You are being asked to find the area of a trapezoid. The area of a trapezoid is:

[tex]\frac{a+b}{2}[/tex] × h

Where:

a = Top base

b = Bottom base

h = Height

Plug in the values given to you via from the page.

[tex]\frac{7+11}{2} (3)\\\\\\\frac{18}{2}(3)\\\\(9)(3) = 27[/tex]

The answer (the area) is 27 [tex]cm^2[/tex].

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