Which expression is equivalent to [tex]10\sqrt{5}[/tex] ?

Giving 20 points

$ (20b + 80) is the cost to buy a frame for the panting given that measures b meters by 4 meters and charges $10 per meter for a wooden frame. This can be obtained by finding the perimeter of the painting and multiplying with the cost of wood per meter.

Given that,

length of the painting (l) = b meters

width of the painting (b) = 4 meters

Perimeter of the painting = 2(l+b)

                                          = 2(b+4)

                                          = 2b + 8

Cost of the frame = (2b + 8)× $10 per meter

                             = $ (20b + 80)

Hence $ (20b + 80) is the cost to buy a frame for the panting given that measures b meters by 4 meters and charges $10 per meter for a wooden frame.

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Answer:

The runner in first place is 16 meters ahead of the runner in last place

Step-by-step explanation:

There are 4 boys racing - Pete, Nick, Manny, and Oliver.

Pete is 11 meters ahead of Nick, Oliver is 10 meters ahead of Manny, and Oliver is ahead of Pete by 5 meters.

This means Oliver is ahead of the other three racers, putting him in first place, and Manny is between Nick and Pete.

So in order to find out the distance between the racer in first place (Oliver) and the racer in last place (Nick), add the distance between Oliver and Pete and the distance between Pete and Nick.

Add the distances: 5 + 11

Therefore, the runner in first place (Oliver) is 16 meters ahead of the runner in last place (Nick).

Answer:

$1150 will be the weekly wage

Step-by-step explanation:

184 = 16%*x

184 = 0.16*x

184/0.16 = x

x = $1150

Here, "x" is her weekly wage.

Answer:

arc TBU = 268°

Step-by-step explanation:

the measure of the tangent- chord angle TUV is half the measure of its intercepted arc UT , then

UT = 2 × 46° = 92°

the sum of the arcs in a circle = 360° , that is

TBU + UT = 360°

TBU + 92° = 360° ( subtract 92° from both sides )

TBU = 268°

Answer:

(x+3)^3 exponent is 3

An equation is formed of two equal expressions. The value of x is -28/9.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given expression can be simplified as,

[tex]2 \frac17+\dfrac37(3x-5)=-4\\\\\dfrac{15}{7} + \dfrac{9x-15}{7} = -4\\\\ \dfrac{15+9x-15}{7} = -4\\\\9x = -28\\\\x = \dfrac{-28}{9}[/tex]

Hence, the value of x is -28/9.

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Since intersection means the element in set A that are also in set B, hence (A ∩ B) = {3, 7}

Sets are arrangements of elements in a specific order. Given the following sets.

A = {1, 3, 7, 8, 11}

B = {2, 3, 6, 7, 12}

Determine the intersection of A and B

Since intersection means the element in set A that are also in set B, hence;

(A ∩ B) = {3, 7}

Hence the elements of (A ∩ B) is {3, 7}

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Answer:

D) (3,7)

Step-by-step explanation:

P(AnB) mean intersection, which is (3,7)

P(AUB) mean Union

However. if the question was asking this "What are the elements of P(AUB) then the answer would be A) {1, 2, 3, 6, 7, 8, 11, 12}.

But the question was asking for P(AnB) which is D) (3,7)

Step-by-step explanation:

Let the consecutive positive integer be x , x+1

now, we know that there product is less then 10000

so, x(x+1) = 10000

x² + x - 10000 = 0

On solving the quadractic equation,

we get the roots = (-100.50124999219 ), (99.501249992188)

since we are asked for less then 10000 we can approximate the answer to x = 99.5

Answer:

99.5

Step-by-step explanation:

Let the consecutive positive integer be n , n+1

now, we know that there product is less then 10000

so, n(n+1) = 10000

So, the question asked " Less than 10,000 " so, we get the roots = (-100.50124999219 ), (99.501249992188)

n² + n - 10000 = 0

Let's solve this equation together!

n approximate number is 99.5.

The maximum volume of the cylinder is 27147.355 at the maximum point  [tex]r = \frac{50}{\sqrt{3} }[/tex] .

The formula for the volume of the cylinder v = [tex]\pi[/tex][tex]r^{2}[/tex]h, To find the maximum volume of the cylinder we apply the condition of maxima  [tex]\frac{\mathrm{d} v}{\mathrm{d} r}[/tex] = 0.

Let r cm be the radius and h cm be the height of the closed cylinder.

Then, Total surface area of the cylinder = [tex]2\pi r(r+h)[/tex]

                                                        [tex]5000[/tex] = [tex]2\pi r^{2} +2\pi rh[/tex]

                                                             [tex]h[/tex] =   [tex]\frac{5000-2\pi r^{2} }{2\pi rh}[/tex] .............(1)

Volume of the cylinder v = [tex]\pi r^{2} h[/tex]

Substitute the value of [tex]h[/tex] in the above equation

[tex]\Rightarrow[/tex]                                       = [tex]\pi r^{2}[/tex] × [tex]\left [ \frac{5000-2\pi r^{2}}{2\pi r} \right ][/tex]

[tex]\Rightarrow[/tex]                                      = [tex]\frac{r}{2}[/tex] ×  [tex](5000-2\pi r^{2} )[/tex]

[tex]\Rightarrow[/tex]                                    v = [tex]2500r-\pi r^{3}[/tex] ..............(2)

Now, for the maximum volume of the cylinder  [tex]\frac{\mathrm{d} v}{\mathrm{d} r}[/tex] = 0

[tex]\Rightarrow[/tex]                                                            [tex]\frac{\mathrm{d} (2500r-\pi r^{3})}{\mathrm{d} r} = 0[/tex]

[tex]\Rightarrow[/tex]                                                                      [tex]3\pi r^{2} = 2500[/tex]

[tex]\Rightarrow[/tex]                                                                          [tex]r^{2} = \frac{2500}{3\pi }[/tex]

[tex]\Rightarrow[/tex]                                                                          [tex]r = \frac{50}{\sqrt{3\pi } }[/tex]

Volume is maximum for  [tex]r = \frac{50}{\sqrt{3\pi } }[/tex]  

Then, v = [tex]2500r-\pi r^{3}[/tex]

[tex]\Rightarrow[/tex]              =  [tex]2500 \frac{50}{\sqrt{3\pi } } -\pi (\frac{50}{\sqrt{3\pi } } )^{3}[/tex]                              

[tex]\Rightarrow[/tex]             = [tex]\frac{125000}{\sqrt{3\pi } } - \frac{125000}{3\sqrt{3\pi } }[/tex]

[tex]\Rightarrow[/tex]             = [tex]\frac{125000}{\sqrt{3\pi } }[/tex]×[tex]\frac{2}{3}[/tex]

[tex]\Rightarrow[/tex]             = [tex]\frac{250000}{3\sqrt{3\pi } }[/tex]                                                              

[tex]\Rightarrow[/tex]          v = 27147.355

Hence, The maximum volume of the cylinder is 27147.355 at the maximum point  [tex]r = \frac{50}{\sqrt{3} }[/tex] .                                                

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Fewer births and increased survival rates are changing the shape of the population from a pyramid to a(n): Rectangle

It is given that fewer births and increased survival rates are changing the shape of the population from a pyramid.

Survival rates is the percentage of people in a study or treatment group who are still alive for a certain period of time after they were diagnosed with or started treatment for a disease, such as cancer.

A population pyramid is a way to visualize two variables: age and sex. They are used by demographers, who study populations. A population pyramid is a graph that shows the distribution of ages across a population divided down the center between male and female members of the population.

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Answer:

a.

Step-by-step explanation:

a= y-k/ (x-h)^2

Answer:

in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. Given : ABCD is a quadrilateral in which ∠A = ∠C and ∠B = ∠D . We know that the sum of the angles of a quadrilateral is 360o. Hence, ABCD is a parallelogram.

Answer:

2/5

Step-by-step explanation:

To find the slope of a line segment, find the difference in y and divide by the difference in x (delta y / delta x)

Delta y: -7 - (-13) = 6

Delta x: 15 - 0 = 15

Slope = delta y / delta x

Slope = 6/15 = 2/5

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The values of a and b of the given sequence are; a = 6 and b = -15

We are given the formula for nth term of a sequence as;

an² + bn

We are given that;

Third term = 9

Sixth term = 126

Thus;

a₃ = 9 = a(3)² + b(3)

9a + 3b = 9    ------(1)

Similarly for the 6th term;

a(6)² + b(6) = 126

36a + 6b = 126    ------(2)

Multiply eq 1 by 2 to get;

18a + 6b = 18    ------(3)

Subtract eq 3 from eq 2 to get;

18a = 108

a = 6

18(6) + 6b = 18

6b = 18 - 108

6b = -90

b = -90/6

b = -15

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The area of the square LMNP is 50 square units

The circumference of the circle is given as:

C = 10π

Circumference is calculated as:

C = 2πr

So, we have:

2πr = 10π

Divide by 2π

r = 5

This represents the length OM

The length PM is calculated as:

PM = 2 * OM

This gives

PM = 2 * 5

PM = 10

The length (PN) of the square is then calculated as:

PM = PN√2

This gives

10 = PN√2

Square both sides

100 = PN^2 * 2

Divide by 2

50 = PN^2

Rewrite as:

PN^2 = 50

Hence, the area of the square LMNP is 50 square units

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Answer:

3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

28 - 12 = 16

28 / 35 = 16 / 4x

28 = 4 * 7

35 = 5 * 7

16 = 4 * 4

4x = 4 * x

( 4 * 7 ) / ( 5 * 7 ) = ( 4 * 4 ) / ( 4 * x )

( 4 / 5 ) = ( 4 / x )

Cross multiply,

4 * x = 5 * 4

Divide 4 on both sides,

x = 5

Answer:

ABCD is a parallelogram/Given

Line AB is parallel to line DC/Opposite sides of a parallelogram are equal

Line FD is congruent to Line FD/Reflexive property

Line BE is congruent to line BE/Reflexive property

Line AC is congruent to Line AC/Reflexive Property

Angle A is congruent to Angle BCD by Alternate Interior Angle Theorem

Angle BCD is congruent to Angle FCE by Vertical Angles Theorem

Angle A is congruent to Angle BCD by Transitive Property

Answer:

80 - 30

Step-by-step explanation:

I'm just guessing

The percentages for each acid are:

Here we just need to use the given formula:

[tex]percent\ disolved = \frac{initial\ mass - \ final \ mass}{initial \ mass}*100 \%[/tex]

For the 0% acid, the initial and final mass are the same:

initial mass = final mass = 10.3g

Then the percent dissolved is:

[tex]percent\ disolved = \frac{10.3g - 10.3g}{10.3g}*100 \% = 0 \%[/tex]

For the 33% acid we have:

Then:

[tex]percent\ disolved = \frac{10.1g - 10g}{10.1g}*100 \% = 1 \%[/tex]

For the 66% acid:

[tex]percent\ disolved = \frac{10g - 9.8g}{10g}*100 \% = 2 \%[/tex]

for the 100% acid:

[tex]percent\ disolved = \frac{9.9g - 9.5g}{9.9g}*100 \% = 4.2 \%[/tex]

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The price of flowers in September exists $1.25.

Total money released in October = $420.

The class gained more money in September and they gained $30 better than in October.

Part A

Let the cost of flowers in September be x, then

(100 + 20)/100 [tex]*[/tex] x = $1.50

120/100 [tex]*[/tex] x = $1.50

1.2x = $1.50

x = $1.50/1.2 = $1.25

The price of flowers in September exists $1.25

Part B

Total money released in September = $1.25 [tex]*[/tex] 900 = $1,125

40% earned = 0.4 [tex]*[/tex] $1,125 = $450

Total money released in October = $1.50 [tex]*[/tex] 700 = $1,050

40% earned = 0.4 [tex]*[/tex] $1,050 = $420

The class gained more money in September and they gained $30 better than in October.

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The sum of the first ten prime numbers is 129.

The prime numbers are those numbers that have only one factor namely 1 and the number itself.

The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

Their sum is

2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29

= 129

Hence, the sum of the first ten prime numbers is 129.

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Answer:

1/40 or 0.025

Step-by-step explanation:

the weight of baby el is 200

the weight of mama el is 8000

take 200/8000 and simplify.

if you divide the top by 200 then divide the bottom by 200

200 divided by 200 is 1

8000 divided by 200 is 40

so the simplest fraction is 1/40

if you type this in to a calculator, you will find that it equals 0.025

4 and 8 will equal the same since they are corresponding angles

So since 8 and 7 make a line they equal 180

180= 132+"7

Subtract both sides by 132

48=angle 7.



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The data can be shown in the frequency table with only 4 intervals and the histogram is shown in the picture.

It is defined as the depiction of numerical data in a graph using a bar with no space. The histogram depicts the approximate distribution of the data.

We have data:

6, 5, 4, 3, 0, 7, 1, 5, 4, 4, 3, 2, 2, 3, 2, 4, 3, 4, 0, 7

Intervals   Frequency

 0 - 3     6

 3 - 6     11

 6 - 9     3

 9 - 12     0

The histogram is shown in the attached picture.

Thus, the data can be shown in the frequency table with only 4 intervals and the histogram is shown in the picture.

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Answer:

3rd option : 5

Step-by-step explanation:

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its a slope question

f(x) is y

y2-y1/x2-x1

-10+25/-1+4

15/3

5

Since we know that the equation of a line in slope-intercept form is: , where, m= Slope and b= y-intercept.

Upon substituting m = 5 in slope-intercept form of equation we will get,

Now let us find y-intercept by substituting coordinates of one point in our given line.

So the equation of given line will be,

Now let us find value of n by substituting x = n and y = 20 in our equation.

Therefore, the value of n is 5.

Answer:

Step-by-step explanation:

Horizontal translation of the graph of a function is accomplished by replacing x with (x-h) for translation h units to the right. Vertical translation of the graph is accomplished by adding the amount of translation to the function value: f(x)+k translates the graph k units upward.

Reflection of a function over the x-axis is accomplished by changing the sign of every function value: -f(x).

We observe that f(x) has been transformed by ...

The effect of these transformations is (correspondingly) ...

__

The attached graph shows a function f(x) (red) and the transformed function (blue).

Answer:

[tex]\frac{\sqrt{3} }{3} or \frac{1}{\sqrt{3} }[/tex]

Step-by-step explanation:

We can break the problem into three parts,

tan45 = sin(45)/cos(45)=[tex]\frac{\frac{\sqrt{2}}{2} }{\frac{\sqrt{2}}{2} } =1[/tex]

[tex]tan^{2}30 =(tan30))^{2}=(sin30/cos30)^2=((1/2)/(\sqrt{3}/2))^2 =(1/\sqrt{3})^2[/tex]

[tex]tan60=sin60/cos60=\frac{\sqrt{3}/2 }{1/2} =\sqrt{3}[/tex]

Then, [tex]tan45*tan^230*tan60=1*(1/sqrt(3))^2*sqrt(3)=1/sqrt(3)=sqrt(3)/3[/tex]

Therefore, the solution is sqrt(3)/3