Tyler is 8 years old. His sister Olivia is 4 years less than twice his age.
Write a numerical expression for Olivia's age in the box below.

The total cost is $245.31.

Given,

Volume = 10[tex]m^{3}[/tex]

Width = w

Length = 2w

Base area = Length x Width = [tex]2w^{2}[/tex]

Cost of base = $15

Cost of sides = $9

Since the volume is 10[tex]m^{3}[/tex],

Volume = Base Area x Height

Height = [tex]\frac{10}{2w^{2} }[/tex] = [tex]\frac{5}{w^{2} }[/tex]

Cost of making such a container:

Cost of base =  [tex]2w^{2}[/tex] x 15 = $[tex]30w^{2}[/tex]

Cost of sides = [(2 x 2w x  [tex]\frac{5}{w^{2} }[/tex]) + (2 x w x  [tex]\frac{5}{w^{2} }[/tex])] x $9 = $[tex]\frac{270}{w}[/tex]

Overall Cost = Cost of Base + Cost of Sides

f(x) = [tex]30w^{2} + \frac{270}{w}[/tex] = [tex]30(w^{2} + \frac{9}{w})[/tex]

To get the minimum cost, we will have to find the derivative of f(x) and equate it to zero.

d(f(x))/dx = 0

[tex]2w - \frac{9}{w^{2} } = 0\\w^{3} = 4.5 \\w = 1.651m[/tex]

Putting the value of w in f(x),

f(x) = $245.31 (after calculations)

Therefore, the final answer is $245.31.

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Answer:

1262(2)^x

Step-by-step explanation:

3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).

Given that,

The perimeter of a triangle 12cm.if the lengths of the three sides are all integers (in cm).

We have to find how many such difference triangle are possible.

We know that,

Perimeter of the triangle is 12cm.

p=12

a+b+c=12

a+b≥c

b+c≥a

So,

a+b+c≥2c

12≥2c

c≤6

So,

a≤6,b≤6,c≤6

We get,

a=6,b=3,c=3

a=5,b=4,c=3

a=4,b=4,c=4

Therefore, 3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).

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Answer:

[tex]\frac{141}{a^{2} }[/tex]

Step-by-step explanation:

[tex]\frac{6}{a^{2} } + \frac{5a^{-2} }{3^{-3} }[/tex]

[tex]\frac{141}{a^{2} }[/tex]

Answer: A.

Step-by-step explanation:

Most of the function f(x) has a domain (- infinity, positive infinity), and the function in the picture is the same. So, the answer is A

The entire surds are √128, √225,√180, √117 respectively

An entire surd is a surd in which the entire number is under the root sign.

Given here are 8√2,5√9,6√5,3√13

thus their entire roots are  8√2 =√2×64

                                                   = √128

again, 5√9 = √9×25

                   = √225

          6√5=√5×36

                 = √180

Similarly 3√13= √117

Hence, the respective entire surds are √128, √225,√180, √117

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Answer:

7.5

Step-by-step explanation:
100% = 75
100% divided by 10 is 10%
75 divided by 10 is 7.5

Answer:

88√2 = 124.5 (nearest tenth)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Dot Product of two vectors}\\\\$a \cdot b=|a||b| \cos \theta$\\\\where:\\ \phantom{ww}$\bullet$ $|a|$ is the magnitude of vector a. \\ \phantom{ww}$\bullet$ $|b|$ is the magnitude of vector b. \\ \phantom{ww}$\bullet$ $\theta$ is the angle between $a$ and $b$. \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the dot product formula:

[tex]\begin{aligned}\implies u \cdot v &=|u||v| \cos \theta\\\\&=8 \cdot 22 \cdot \cos \left(\dfrac{\pi}{4}\right)\\\\&=176 \cdot \dfrac{\sqrt{2}}{2}\right)\\\\&=88\sqrt{2}\\\\&=124.5\; \sf (nearest\;tenth)\end{aligned}[/tex]

Answer: 1. Given two sides

If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root: a = √(c² - b²)

If leg b is unknown, then: b = √(c² - a²)

For hypotenuse c missing, the formula is: c = √(a² + b²)

Answer:

Law of Sines

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

[tex]\sqrt{16}[/tex] = 4

The side lengths of the square is 4.

Area = Length times width

Area = 4 x 4

Are = 16

The perimeter of the given composite figure is; 5¹/₂ cm

To get the perimeter of the given composite figure, what we will do is to dd up the given segment side lengths and we are given the following;

AE + DC = 1¹/₅ cm

AB = 1 ³/₄ cm

DE = 1 ¹/₄ cm

BC = 1 ³/₁₀ cm.

Thus, we can say that the Perimeter is;

Perimeter = AE + DE + DC + BC + AB

Perimeter  = (AE + DC) + DE + BC + AB

= 1¹/₅ + 1 ¹/₄ + 1 ³/₁₀ + 1 ³/₄

= (1²/₁₀ + 1³/₁₀) +(1¹/₄ + 1³/₄)

= 2⁵/₁₀ + 3

= 5¹/₂ cm

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Answer:

23 purple marbles

115 yellow marbles

Step-by-step explanation:

Let y represent the yellow marble

Let p represent the purple marbles

So, we have the equations

y = 5p

Therefore, y + p = 138

5p + p = 138

6p = 138

p = 23 marbles

Now let's put 23 in for the p in the equation to find the number of yellow marbles

y = 5(23)

y = 115 marbles

Angle B D E measure 228 degrees in the irregular pentagon A B D E C.

Polygons that lack equal sides and angles are referred to as irregular polygons. Polygons that are irregular are not regular, in other words. Closed two-dimensional shapes known as polygons are created by connecting three or more line segments. Regular and irregular polygons are two different forms of polygons.

As we know, the Sum of the interior angles of an irregular polygon =

(n − 2) × 180°

{ 'n' = the number of sides of a polygon.}

As given, A B D E C is a pentagon, so

n= 5

The sum of interior angles=

3 X \180= 540

As AB and CE are parallel to each other:

angle BAC=y

angleECA= 180-y

=>the sum of interior angles:

104+x+28+180-y+y= 540

104+x+28+180=540

x+312=540

=> x=228

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Answer:

1.5 groups.

Step-by-step explanation:

1 divided by 8/12 is 1.5

Answer:

1 1/2

Step-by-step explanation:

The figure shows a large rectangle that is divided into 12 parts of equal size.

Think of the entire rectangle as 1.

Each small rectangle is 1/12 of 1.

Now count 8 small rectangles starting at the left.

When you divide 1 by 8/12, you can fit 1 full 8/12 (8 small rectangles) and another half of 8/12 (another 4 small rectangles.

Since you can fit 1 1/2 groups of 8 small rectangles,the result is 1 1/2.

Answer: 1 ÷ 8/12 = 1 1/2

Answer:

[tex]83\frac{1}{3} miles[/tex]

Step-by-step explanation:

90/100=75/x

90x=100(75)

90x=7500

/90.  /90

x=83 1/3 miles

Hopes this helps

[tex] \Large{\boxed{\sf 2x - y = 18}} [/tex]

[tex] \\ [/tex]

We will try to write the given linear equation in standard form.

[tex] \Large{\left[ \begin{array}{c c c} \underline{\tt Standard \ Form \ of \ a \ linear \ equation \text{:}} \\ ~ \\ \tt Ax + By = C \end{array} \right] } [/tex]

Where:

[tex] \\ [/tex]

Given linear equation:

[tex] \sf y + 4 = 2(x - 7) [/tex]

[tex] \\ [/tex]

First, expand the right side of the equation:

[tex] \sf y + 4 = 2 \cdot x + 2 \cdot (-7) \\ \\ \sf y + 4 = 2x - 14 [/tex]

[tex] \\ [/tex]

Subtract 2x from both sides of the equation:

[tex] \sf y + 4 - 2x = 2x - 14 - 2x \\ \\ \sf -2x + y + 4 = -14 [/tex]

[tex] \\ [/tex]

Subtract 4 from both sides of the equation:

[tex] \sf -2x + y + 4 - 4 = -14 - 4 \\ \\ \sf -2x + y = -18 [/tex]

[tex] \\ [/tex]

Since the coefficient of x (-2) has to be positive, multiply both sides of the equation by -1:

[tex] \sf -1 \cdot (-2x + y) = -1 \cdot (-18) \\ \\ \sf -1 \cdot (-2x) + (-1) \cdot y = 18 \\ \\ \boxed{\boxed{\sf 2x - y = 18 }} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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The mass and center of mass of the lamina is [tex]\frac{8}{15} k, (0, \frac{4}{7} )[/tex]

The mass of a homogenous lamina is given by [tex]$m=\iint_R \delta(x, y) d A$[/tex]

We can rewrite the equation using the limits of integration as [tex]$$m=\int_a^b \int_c^d \delta(x, y) d y d x$,[/tex] where a ≤ x ≤ b and c ≤ y ≤ d.

The objective is to find the mass and center of mass of the lamina that occupies the region D.

From the given equations, we get the limits of integration as -1 ≤ x ≤ 1 and  0 ≤ x ≤ 1-[tex]x^{2}[/tex]. Substitute the known values in the equation.

[tex]$$\begin{aligned}& m=\int_{-1}^1 \int_0^{1-x^2} k y d y d x \\& =\int_{-1}^1 \frac{1}{2} k\left(1-x^2\right)^2 d x \\& =\frac{1}{2} k \int_{-1}^1\left(1+x^4-2 x^2\right) d x \\& =\frac{k}{2}\left[x+\frac{x^5}{5}-2 \frac{x^3}{3}\right]_{-1}^1 \\\\\end{aligned}$$[/tex]

[tex]& =\frac{k}{2}\left[1+\frac{1}{5}-\frac{2}{3}+1+\frac{1}{5}-\frac{2}{3}\right] \\\\& =\frac{k}{2}\left[\frac{16}{15}\right] \\\\& =\frac{8}{15} k[/tex]

Hence, the mass of the lamina as [tex]\frac{8}{15} k[/tex].

The center of mass of the lamina is given by[tex]$(\bar{x}, \bar{y})$[/tex], where [tex]$$\begin{gathered}\bar{x}=\frac{1}{m} \iint_R x \delta(x, y) d A \text { and } \\\bar{y}=\frac{1}{m} \iint_R y \delta(x, y) d A .\end{gathered}$$[/tex]

First, find [tex]$\bar{x}$[/tex] as follows:

[tex]$$\begin{aligned}\bar{x} & =\frac{1}{\frac{8}{15} \mathrm{k}} \int_{-1}^1 \int_0^{1-x^2} k x y d y d x \\& =\frac{1}{\frac{8}{15} \mathrm{k}} \int_{-1}^1 \frac{1}{2} k x\left(1-x^2\right)^2 d x \\= & \frac{15}{8 k} \cdot \frac{k}{2} \int_{-1}^1 x\left(1+x^4-2 x^2\right) d x \\= & \frac{15}{16}\left[\frac{x^2}{2}+\frac{x^6}{6}-2 \frac{x^4}{4}\right]_{-1}^1 \\= & 0\end{aligned}$$[/tex]

Thus, the  [tex]$\bar{x}$[/tex]-coordinate of the center of gravity as 0 .

Now, evaluate [tex]$\bar{y}$[/tex].

[tex]& \bar{y}=\frac{1}{\frac{8}{15}} \int_{-1}^1 \int_0^{1-x^2} k y^2 d y d x \\\\& =\frac{1}{\frac{8}{15}} \int_{-1}^1 \frac{1}{3} k\left(1-x^2\right)^3 d x \\\\& =\frac{15}{8 k} \cdot \frac{k}{3} \int_{-1}^1\left(1-x^6-3 x^2+3 x^4\right) d x \\\\& =\frac{15}{24}\left[x-\frac{x^7}{7}-3 \frac{x^3}{3}+3 \frac{x^5}{5}\right]_{-1}^1 \\\\& =\frac{15}{24} \times \frac{32}{35} \\\\& =\frac{4}{7}[/tex]

Hence, the center of gravity of the lamina is ([tex]0, \frac{4}{7}[/tex]).

Therefore,  the mass and center of mass of the lamina that occupies the region D is [tex]\frac{8}{15} k[/tex], [tex](0, \frac{4}{7} )[/tex]

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The value of r'(1) and s'(4) is 0 that can be interpreted with the help of the graph that is given in the question.

Derivative in mathematics, the rate of change of a characteristic with recognize to a variable. Derivatives are essential to the answer of troubles in calculus and differential equations. The essence of calculus is the by-product. The by-product is the immediately price of extrade of a characteristic with recognize to certainly considered one among its variables. This is equal to locating the slope of the tangent line to the characteristic at a point

[tex]r(x) = f(g(x))[/tex]therefore the derivative of r is given by [tex]r'(x) = f'g(x)\times g'(x)[/tex]

[tex]r'(1) = f'(g(1))\times g'(1)[/tex] from the graphs

r'(1) = f'4 \times g'1 = (5/4) \times(0) = 0

Similarly s'(1) = g'(f(1))\times f'(1) from the graphs

 f(1)=1.5, f'(1)

=\dfrac{ (3-0)}{(0-2)}

= -3/2 , g'(3/2) = 0

s'(4) = g'(3/2) \times f'(4) = 0(-1.5) = 0

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Complete question:

let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. find r'(1) and s'(4).

Answer:

36 = 2h

Step-by-step explanation:

Here h represents the heigh

We know that the height of the door was twice the height of the window so that the equation will be

36 = 2h

Answer:330

Step-by-step explanation:

Set up cross multiplication:

33/x    10/100

Cross multiply

10*x   100*33

Divide sums

3,300/10x

Answer:

330 total cards

The score of the 60th percentile on the test is 84.

The definition of percentile is the percentage that a certain percentage falls beneath. Ben is the fourth-tallest child in a group of 20 kids, whereas 80% of the kids are shorter than you.

Given:

58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96

Calculate the percentile of score 71 as shown below,

[tex]Percentile = n / N \times 100[/tex]

Here, n is the number of scores below the score of 60th percentile and N is the total number of scores,

60 = n / 15 × 100

n / 15 = 60 / 100

n = 0.6 ×  15

n = 9

Thus, the 9th term = 84  is the score of the 60th percentile,

Therefore, the score of the 60th percentile on the test is 84.

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Answer:

b). parameter

Step-by-step explanation:

A parameter is a fixed value in the model that is not a decision variable and is not changed during the optimization process. It is used to represent known quantities that are used in the model but are not being optimized. For example, in a linear programming model, the cost of a product may be represented by a parameter, as the cost is not a decision variable and is fixed.

a) The velocity of particle at t=2s is 5m/s

b) The velocity of particle at t=4s is 20m/s

To obtain the function of velocity from the graph we need to find the equation of accleration- time graph

so the equation of accleration is :

a= [tex]\frac{10-0}{4-0}[/tex]t

a= 5/2t

and we know that :

a= [tex]\frac{dv}{dt}[/tex]

=> dv= adt

=> dv= [tex]\frac{5}{2}[/tex] t dt

integrating both side we get:

v= [tex]\frac{5}{4}[/tex][tex]t^2[/tex]  +c

where c is constant

it is given that at t=0s it starts from rest so

v=0 at t=0

=> 0 = 0+c

=>c=0

so v=[tex]\frac{5}{4}t^2[/tex] ---- (i)

a) as we have got the equation of velocity with respect to time

 we have to find velocity at t=2s

putting t=2s we get

 v = 5/4 *4

 so velocity of particle at t=2s is 5m/s

b) as we have got the equation of velocity with respect to time

 we have to find velocity at t=4s

putting t=4s we get

 v = 5/4 *16

 so velocity of particle at t=2s is 20m/s

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equation of simple straight line

Complete question:

the figure shows the acceleration graph for a particle given that particle starts from rest at t=0.

determine the velocity of partice at

a)2s

b)4s

Answer:

- [tex]\frac{65}{12}[/tex]

Step-by-step explanation:

let the number to be found be n , then

n + [tex]\frac{9}{2}[/tex] = - [tex]\frac{11}{12}[/tex]

multiply through by 12 ( the LCM of 2 and 12 ) to clear rhe fractions

12n + 54 = - 11 ( subtract 54 from both sides )

12n = - 65 ( divide both sides by 12 )

n = - [tex]\frac{65}{12}[/tex]

Answer:

send the complete question . there are some missing signs .

False. The margin of error only accounts for sampling variability (the fact that my sample will be different that many other people's and therefore provide different statistics.

Statistics is a technique for interpreting, analyzing, and summarizing data in mathematics. In light of these characteristics, the various statistical types are divided into: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as through graphs, bar graphs, or tables.

Inferential statistics, which draws conclusions from information using statistical tests like the student's t-test, is one of the two main statistical methods used in data analysis. Descriptive statistics presents data using indices like mean and median.

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Lauren's reasoning does not make sense because the LCM of 2 and 8 is not 16, the LCM will be equal to 8.

The Least Common Multiple is the meaning of the acronym LCM. The smallest number that both numbers can divide by is known as the least frequent multiple (LCM) for two numbers.

It can also be computed for several different numbers.

As per the given information in the question,

Lauren says that the LCM of 2 and 8 is 16.

Now, let's check whether it is correct or not.

Let's make a factor of both numbers,

2 = 2 × 1

8 = 2 × 2 × 2

So, the LCM will be: 2 × 2 × 2 = 8

It means that the LCM of 2 and 8 is not 16, the LCM is 8.

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The given polygon IJKL is a rectangle. Therefore, option C is the correct answer.

Given that, the polygon IJKL if IJ≅KL, JK≅LI, IJ⊥JK, JK⊥KL, KL⊥LI and LI⊥IJ.

A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.

Here, the opposite sides IJ and KL are equal and the opposite sides JK and LI are equal.

Since, all the sides are perpendicular to each other makes an angle 90°

The given polygon IJKL is a rectangle. Therefore, option C is the correct answer.

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Both automobiles' lines have the equation "y = 3x," and their respective gas mileage is 3 miles per gallon. Wyatt's automobile gets more miles per gallon of gas than Camden's vehicle does.

We must compute the mileage (the distance driven per gallon of fuel) for each automobile using the provided information to determine the difference between the ranges of travel for Camden's and Wyatt's vehicles.

We can determine the miles for Wyatt's automobile using the data points (5, 15) and (7, 21). The equation for the slope of the line connecting these two locations is

(y2 - y1) / (x2 - x1) = (21 - 15) / (7 - 5) = 6/2 = 3

"Y = mx + b" is the equation for the line connecting these two points, where m denotes the line's slope and b its y-intercept. We may determine the equation of the line by adding the values of m as well as the dimensions of one of the endpoints into this equation:

y = 3x + b

15 = 3(5) + b

15 = 15 + b

0 = b

"Y = 3x" is the equation for the line passing thru the points (5, 15) and (7, 21).

We can determine the miles for Camden's automobile using the data points (10, 30) and (14, 42). The equation for the slope of the line connecting these two locations is

(y2 - y1) / (x2 - x1) = (42 - 30) / (14 - 10) = 12/4 = 3

"Y = mx + b" is the equation for the line connecting these two points, where m denotes the line's slope and b its y-intercept. We may determine the equation of the line by incorporating the values of m as well as the dimensions of one of the endpoints into this equation:

y = 3x + b

30 = 3(10) + b

30 = 30 + b

0 = b

"Y = 3x" is the equation for the line passing through the points (10, 30) & (14, 42).

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The question is -

Computes the miles per gallon of your car via the miles traveled and the number of gallons used. Also, if you enter the cost per gallon and how many miles you drive a day, it will estimate your monthly and yearly gas expenses with data points (5, 15) and (7, 21).