Rectangle TUVW is dilated by a scale factor of 3
3 to form rectangle T'U'V'W'. Side U'V' measures 93
93. What is the measure of side UV?

[tex]\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=x\\b=2\\r+1=5\Rightarrow r=4\\n=7\\T_5=\binom{7}{4}x^{7-4}2^4\\T_5=\dfrac{7!}{4!3!}\cdot x^3\cdot16\\T_5=16\cdot \dfrac{5\cdot6\cdot7}{2\cdot3}\cdot x^3\\\\T_5=560x^3[/tex]

Answer:

[tex]\large \boxed{560x^3}[/tex]

Step-by-step explanation:

[tex](x+2)^7[/tex]

Expand brackets.

[tex](x+2) (x+2) (x+2) (x+2) (x+2) (x+2) (x+2)[/tex]

[tex](x^2 +4x+4) (x^2 +4x+4) (x^2 +4x+4)(x+2)[/tex]

[tex](x^4 +8x^3 +24x^2 +32x+16)(x^3 +6x^2 +12x+8)[/tex]

[tex]x^7 +14x^6 +84x^5 +280x^4 +560x^3 +672x^2 +448x+128[/tex]

The fifth term is 560x³.

THIS IS THE COMPLETE QUESTION BELOW

The demand equation for a product is p=90000/400+3x where p is the price (in dollars) and x is the number of units (in thousands). Find the average price p on the interval 40 ≤ x ≤ 50.

Answer

$168.27

Step by step Explanation

Given p=90000/400+3x

With the limits of 40 to 50

Then we need the integral in the form below to find the average price

1/(g-d)∫ⁿₐf(x)dx

Where n= 40 and a= 50, then if we substitute p and the limits then we integrate

1/(50-40)∫⁵⁰₄₀(90000/400+3x)

1/10∫⁵⁰₄₀(90000/400+3x)

If we perform some factorization we have

90000/(10)(3)∫3dx/(400+3x)

3000[ln400+3x]₄₀⁵⁰

Then let substitute the upper and lower limits we have

3000[ln400+3(50)]-ln[400+3(40]

30000[ln550-ln520]

3000[6.3099×6.254]

3000[0.056]

=168.27

the average price p on the interval 40 ≤ x ≤ 50 is

=$168.27

Step-by-step explanation:

2 cups of water used with 4 packs

therefore for 12 we use x cups of water

2:4

X :12

therefore 6'cups of water?

Answer:

B

Step-by-step explanation:

we take the only point we know

(0,20)

in A when x =0

[tex]f(x)=e^{20x} =e^{20*0}=1[/tex]

in B when x=0

[tex]f(x)=20e^x=20e^0=20*1=20[/tex]

fits

in C

[tex]f(x)=20^x=20^0=1[/tex]

in D

[tex]f(x)=20^{20x}=20^{20*0}=20^0=1[/tex]

so the only choice is B

Answer:

Hello,

Answer A

Step-by-step explanation:

if x=0 then sin(2*0)=sin(0)=0

if x= π/4 then sin(π/2)=1

if x= π/2 then sin(π)=0

The equation of the sinusoid will be y=Sin(2x)

It is defined as the relation between two variables, for a sinusoidal wave the equation will be in the form of Sin or Cos.

if x=0 then sin(2*0)=sin(0)=0

if x= π/4 then sin(π/2)=1

if x= π/2 then sin(π)=0

Hence the equation of the sinusoid will be y=Sin(2x)

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[tex]\\ \sf\longmapsto XY+YZ=XZ[/tex]

[tex]\\ \sf\longmapsto 7a+5a=6a+24[/tex]

[tex]\\ \sf\longmapsto 12a=6a+24[/tex]

[tex]\\ \sf\longmapsto 12a-6a=24[/tex]

[tex]\\ \sf\longmapsto 6a=24[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{24}{6}[/tex]

[tex]\\ \sf\longmapsto a=5[/tex]

Value of a is 4 and value of YZ is 20 units

Step-by-step explanation:

Given:

Y is between point X and Z

Value of line XY = 7a

Value of line YZ = 5a

Value of line XZ = 6a + 24

Find:

Value of "a" and line YZ

Computation:

We know that

XY + YZ = XZ

So,

7a + 5a = 6a + 24

12a = 6a + 24

6a = 24

a = 4

Value of a = 4

So,

Value of line YZ = 5a

By putting value of a

Value of line YZ = 5(4)

Value of line YZ = 20 units

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Answer:

a) 952

b) 136

Step-by-step explanation:

Ratio of b:g = 3:4, based on this we have:

Number of spectacle wearers:

Number of those not wearing spectacles:

And this number equals to 612, then we can find the value of x:

a) Total number of pupils:

b) The difference in the number of boys and girls:

Answer:

total number of students: 952

number of girls more than boys :136 more girls

Step-by-step explanation:

1/3 of boys +3/8 girls= spectacles

612 people do not wear spectacles

3:4= boys: girls

total number of students

3+4=7

boys + girls = total ratio

7= total ratio

1/3×3=1 3/8×4=3/2

1+3/2=5/2

7-5/2=9/2 9/2=612 students

If 9/2=612 Then 7=?

7= 7÷ 9/2×612

=952 people

Girls more than boys

if 7= 952

3= 3/7 × 952=408 boys

if 7 = 952

4= 4/7 ×952=544girls

Girls - boys

544- 408 = 136 girls

Answer:

The [tex]L_{ACL}[/tex] of the player is  [tex]L_{ACL} = 56.82 \ mm[/tex]

Step-by-step explanation:

From the question we are told that

       The relationship between the length [tex]L_{ACL}[/tex] to the height is  

            [tex]L_{ACL} = 0.04606h - (41.29 \ mm)[/tex]

       The height of the basketball player  is  [tex]h = 2.13 \ m = 2130 \ mm[/tex]

Substituting the value of height of the basket ball player in to the model we have the [tex]L_{ACL}[/tex] of the player is

          [tex]L_{ACL} = 0.04606 (2130) - (41.29 ) \ mm[/tex]

         [tex]L_{ACL} = 56.82 \ mm[/tex]

Rewrite f in terms of the unit step function:

[tex]f(t)=\begin{cases}5&\text{for }0\le t<7\\-3&\text{for }t\ge7\end{cases}[/tex]

[tex]\implies f(t)=5(u(t)-u(t-7))-3u(t-7)=5u(t)-8u(t-7)[/tex]

where

[tex]u(t)=\begin{cases}1&\text{for }t\ge0\\0&\text{for }t<0\end{cases}[/tex]

Recall the time-shifting property of the Laplace transform:

[tex]L[u(t-c)f(t-c)]=e^{-cs}L[f(t)][/tex]

and the Laplace transform of a constant function,

[tex]L[k]=\dfrac ks[/tex]

So we have

[tex]L[f(t)]=L[5u(t)-8u(t-7)]=5L[1]-8e^{-7s}L[1]=\boxed{\dfrac{5-8e^{-7s}}s}[/tex]

In this exercise you have to find the laplace transform:

[tex]L[f(t)]=\frac{5-8e^{-7s}}{s}[/tex]

Rewrite f in terms of the unit step function:

[tex]f(t)=\left \{ {{5, for 0\leq t\leq 7} \atop {-3, for t\geq 7}} \right. \\f(t)= 5(u(t)-u(t-7)-3u(t-7)=5u(t)-8u(t-7)[/tex]

Where:

[tex]u(t)= \left \{ {{1, t\geq 0} \atop {0, t<0}} \right.[/tex]

Recall the time-shifting property of the Laplace transform:

[tex]L[u(t-c)f(t-c)]= e^{-cs}L[f(t)][/tex]

and the Laplace transform of a constant function,

[tex]L[k]=\frac{k}{s}[/tex]

So we have:

[tex]L[f(t)]= L[5u(t)-8u(t-7)]= 5L[1]-8e^{-7s}L[1]= \frac{5-8e^{-7s}}{s}[/tex]

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Answer:

0.9719

Step-by-step explanation:

Find the mean and standard deviation of the sampling distribution.

μ = 5.1

σ = 1.1 / √49 = 0.157

Find the z score.

z = (x − μ) / σ

z = (4.8 − 5.1) / 0.157

z = -1.909

Use a calculator to find the probability.

P(Z > -1.909)

= 1 − P(Z < -1.909)

= 1 − 0.0281

= 0.9719

The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values.

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

Given,

Mean = 5.1 inches

Standard deviation = 1.1 inches

Sample size = 49

New mean = 4.8

Z score = Difference in mean /(standard deviation / [tex]\sqrt{sample size}[/tex])

Z score = [tex]\frac{4.8-5.1}{1.1/\sqrt{49} }=-1.909[/tex]

Z score = -1.909

Then the probability

P(Z>-1.909)

=1-P(Z>-1.909)

=1-0.0281

=0.9719

Hence, The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719

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Answer:

x = 9

this is a ratio problem. You can see that 12/6 = 2, so you can also take 18/2 to get 9.

Answer:

the answer is 6

Step-by-step explanation:

Because 6 and x are corresponding angle so that means no matter what ( if u want the answer to how long the line is or what degree the angle is ) the answer is always going to be the same as the one above ( which is 6 )

Hop this helpssss

Answer:

D) (-4,8)

Step-by-step explanation:

Multiply both coordinates by -2

Answer:

(-4,8)

Step-by-step explanation:

I found a school pdf with the answer key to this exact equation and thats the answer

We have [tex]f\left(f^{-1}(x)\right) = x[/tex] for inverse functions [tex]f(x)[/tex] and [tex]f^{-1}(x)[/tex]. Then if [tex]f(x) = 2x+5[/tex], we have

[tex]f\left(f^{-1}(x)\right) = 2f^{-1}(x) + 5 = x \implies f^{-1}(x) = \dfrac{x-5}2[/tex]

Then

[tex]f^{-1}(8) = \dfrac{8-5}2 = \boxed{\dfrac32}[/tex]

Answer:

Step-by-step explanation:

[tex]4 + \frac{4}{4} [/tex]

= 4 + 1

= 5 (Ans)

Answer:

Perimeter= 29.12 unit

Step-by-step explanation:

Perimeter of the triangle is the length of the three sides if the triangle summef up together

Let's calculate the length of each side.

For (-4,-6),(3,3)

Length= √((3+4)²+(3+6)²)

Length= √((7)²+(9)²)

Length= √(49+81)

Length= √130

Length= 11.40

For (-4,-6),(7,2)

Length= √((7+4)²+(2+6)²)

Length= √((11)²+(8)²)

Length= √(121+64)

Length= √185

Length= 13.60

For (3,3),(7,2)

Length=√( (7-3)²+(2-3)²)

Length= √((4)²+(-1)²)

Length= √(16+1)

Length= √17

Length= 4.12

Perimeter= 4.12+13.60+11.40

Perimeter= 29.12 unit

Answer:

the Sum

hope this helps

the answer is: combation

Your question is not complete but I guess you want to know the total price to be paid. This will be:

= $145 + (5.5% × $145)

= $145 + (0.055 × $145)

= $145 + $7.975

= $152.975

Answer:

5 a) Total = 20.83 hrs = 20 hrs and 50 mins  (1250mins total)

5 b) Total = 96 meters. = 0.096km in 8 hrs.

Step-by-step explanation:

1km = 1000 meters

5 mins = 4 meters

1000/4 = 250 multiplier

250 x 5mins = 1250 minutes

1250/60 = 20hrs + 50 minutes

50 / 60 =  0.83 = 20.83hrs

b)  8 hrs = 8 x 60 = 480 minutes

480/5 = 24 multiplier of 4 meters

24 x 4 = 96 meters

Answer:

the next one is .857 I hope this helps you :)

Answer:

5.3 days

Step-by-step explanation:

Let us assume the loss of ability to recall a learned material = 100%

Formula to calculate number of days = time(t) =

t = t½ × Log½(Nt/No)

Nt = Ending Amount

No = Beginning Amount

t½ = Half life

t = Time elapsed

Therefore, we have the following values from the questions:

Half life (t½)= 35 days

Initial or beginning amount = 100%

Ending amount = 90%

t = t½ × Log½ (Nt/No)

t = 35 × Log ½(90/100)

t = 5.3201082705768 days

Approximately = 5.3 days

Answer:

n=39/5

Step-by-step explanation:

24=5(n-3)

24=5n-15

-5n= -15-24

-5n=39

n= 39/5

Answer:

Step-by-step explanation:

y varies with the square of x:

y = kx²

y equals 24 when x equals 10

24 = k·10²

constant of proportionality k = 0.24

when x = 20, y = 0.24·20² = 96

"select two answers"  —where are the choices?

Question:

A research center poll showed that 78% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?

The probability that someone does not believe that it is morally wrong to not report all income on tax returns is . (Type an integer or a decimal.)

Answer:

[tex]q = 0.22[/tex]

Step-by-step explanation:

Given

Let p represent the given proportion

p = 78%

Required

Determine the probability that someone holds a contrary belief

Start by converting the given proportion to decimal

[tex]p = 78\%[/tex]

[tex]p = \frac{78}{100}[/tex]

[tex]p = 0.78[/tex]

In probability, the sum of opposite probability is equal to 1

Represent the probability that someone holds a contrary belief with q

So;

[tex]p + q = 1[/tex]

Make q the subject of formula

[tex]q = 1 - p[/tex]

Substitute 0.78 for p

[tex]q = 1 - 0.78[/tex]

[tex]q = 0.22[/tex]

Hence, the probability that someone does not believe is 0.22

Answer:

Step-by-step explanation:

L = 9 mm

W =  9 mm

H = 10 mm

volume = LWH/3 = 9·9·10/3 = 270 mm³

Answer:

I don't know what you think about it is not going to be a great day of school and I don't know what you think about it is not going to be a great day of school

Answer:

p=0,83641536

Step-by-step explanation:

Let's calculate the probability that all 4 marbles are yellow:

p=26/40*25/39*24/38*23/37 ( no replacement)

=0,1635846372688....

probability that at least one of the marbles is green= 1-p

=0,83641536...

Answer:

We have the magnitude, M, and the angle A.

(The angle is always measured from the +x-axis)

Then we have that:

x = M*cos(A)

y = M*sin(A)

in this case:

M = 9m

A = -80°

x = 9m*cos(-80°) = 1.562

y = 9m*sin(-80) = -8.86m

Now, the component parallel to the x axis is:

x = 9m*cos(-80°) = 1.562 m

And the slope of something parallel to the x-axis is always zero, as this is a constant line.