Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 3 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 63 ?

Answer:

F.  31.4 ft

Step-by-step explanation:

The distance around the edge of a circle is called the circumference.

Formula for the circumference of a circle

[tex]\sf Circumference\:of\:a\:circle=2 \pi r[/tex]

(where r is the radius)

Given values:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \sf circumference & = \sf 2 \cdot 3.14 \cdot 5\\ & = \sf 31.4\:ft \end{aligned}[/tex]

Therefore, the distance around the edge of the circular patio is 31.4 ft.

The distance around the edge of the patio is 31.4 feet, which is determined by the circumference of a circle. The correct answer is option (F).

To find the distance around the edge of the circular patio, we need to calculate the circumference of the circle.

The formula for the circumference of a circle is given by:

Circumference = 2 × π × radius

Given that the radius of the patio is 5 feet and using the approximate value of π as 3.14, we can now calculate the circumference:

Circumference = 2 × 3.14 × 5

Circumference = 31.4 feet

Therefore, the distance around the edge of the patio is 31.4 feet.

Hence, the correct answer is option (F).

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If the scale factor is 1/2. Then the coordinate of the pre-image will be (-1, 1), (0, 1), (1, 0), (0, -1), and (-1, -1).

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Dilation does not change the shape, but changes the size of the geometry.

On a coordinate plane, an image has points (-2, 2), (0, 2), (2, 0), (0, -2), and (-2, -2).

The scale factor is 1/2. Then the coordinate of the pre-image will be

(-1, 1), (0, 1), (1, 0), (0, -1), and (-1, -1).

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Answer:D (-4) (-4)

Step-by-step explanation:

Answer:

B.a numerical expression

Answer:

[tex] {( \sqrt{ {x}^{ - 3} }) }^{5} = ({( {x}^{ - 3}) }^{ \frac{1}{2} } ) ^{5} \\ \\ = {x}^{ - 3 \times \frac{1}{2} \times 5} = {x}^{ - \frac{15}{2} } = \frac{1}{ {x}^{ \frac{15}{2} } } [/tex]

Or ;

[tex] {( \sqrt{ {x}^{ - 3} } )}^{5} = {( \sqrt{ \frac{1}{ {x}^{3} }} })^{5} = ( { \frac{ \sqrt{1} }{ \sqrt{ {x}^{3} } } })^{5} \\ \\ = ( { \frac{1}{ \sqrt{x} \sqrt{ {x}^{2} } } })^{5} = ({ \frac{1}{ x\sqrt{x} }})^{5} \\ \\ = ( \frac{ {(1)}^{5} }{ {x}^{5} ( \sqrt{x} )^{5} } ) = \frac{1}{ {x}^{5} \times {x}^{ \frac{1}{2} \times 5 } } \\ \\ = \frac{1}{ {x}^{5} \times {x}^{ \frac{5}{2} } } = \frac{1}{ {x}^{5} \sqrt{ {x}^{5} } } \\ \\ = \frac{1}{ {x}^{5} \sqrt{ {x}^{4} {x}^{1} } } = \frac{1}{ {x}^{5} \sqrt{x} \sqrt{( { {x}^{2} })^{2} } } \\ \\ = \frac{1}{ {x}^{5} {x}^{2} \sqrt{x} } = \frac{1}{ {x}^{7} \sqrt{x} } = \frac{ \sqrt{x} }{ {x}^{8} } [/tex]

Answer:

∠A ≅ ∠D

Step-by-step explanation:

When writing a triangle congruency like ΔABC ≅ ΔDEF, the angles are congurent based on the orders listed. For example the first angle A is congruent with the first angle of the other triangle D.  

∠A ≅ ∠D

∠B ≅ ∠E

∠C ≅ ∠F

Using the z-distribution, it is found that 3,007 passengers must be surveyed.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

In this problem, we desired a margin of error of M = 0.015, with no prior estimate, hence [tex]\pi = 0.5[/tex], then we solve for n to find the minimum sample size.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.015 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.015\sqrt{n} = 1.645(0.5)[/tex]

[tex]\sqrt{n} = \frac{1.645(0.5)}{0.015}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.645(0.5)}{0.015}\right)^2[/tex]

n = 3007.

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Answer:

1650 Cubic Centimeters

Step-by-step explanation:

To get the volume of the cereal boxes, you must multiply their 3 dimensions together.

Box A:

25×20=500

500×9=4500

Box B:

25×19=475

475×6=2850

Now, to find the difference of these volumes, you want to subtract the smaller volume from the larger volume.

4500-2850=1650

The answer is 1650 cubic centimeters.

Answer:

16.19

Step-by-step explanation:

Use the cosine rule:

[tex]\sqrt{a^{2} +b^{2} -2abcosy} \\\\\sqrt{16^{2} +20^{2} -(2)(16)(20)cos(52)} \\\\\\= 16.19cm[/tex]

Answer:

4/2 is the wrong answer

Step-by-step explanation:

because it is

Answer:

[tex]1)\text{ Friday}\\2)\text{ }7:00\\3a)\text{ }0\\3b)\text{ }4\\3c)\text{ }0\\4a)\text{ }6\\4b)\text{ }4\\4c)\text{ }2[/tex]

Answer:

[tex]=\frac{4y^2}{x^2}[/tex]

Step-by-step explanation:

[tex]\frac{(8x^2y^3)}{(2x^4y)}[/tex]

[tex]=\frac{(8x^2y^3)}{(2x^4y)}\\[/tex]

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

[tex]=\frac{4y^2}{x^2}[/tex]

I Hope This helps :)

Answer: 2

Step-by-step explanation:

[tex]g(-2)=-2\\\\g(1)=4\\\\\frac{g(-2)-g(1)}{-2-1}=\frac{-2-4}{-3}=\boxed{2}[/tex]

Answer:

A. $60.25

B. 76 miles

C. 216 miles

Step-by-step explanation:

x is miles

y is total amount spent

For A, 57 miles is the x value. Plug that in to x.

y= 46 + .25(57)

y= 60.25

For B, the total is the y. So plug 65 in for y.

65 = 46 + .25x   Subtract 46 from both sides

19 = .25x             Divide by .25

76 = x

For C, the maximum you can spend is $100. Plug that in for y.

100 = 46 + .25x   Subtract 46 from both sides

54 = .25x             Divide by .25

216 = x

The answer for part a is $60.25, for part b the answer is 76 miles, and for part c the answer is 216 miles.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The equation to represent the cost would be y=46+0.25x

x is the number of miles.

a) What is your cost if you travel 57 miles?

Plug x = 57 in the above equation:

y = 46 + 0.25(57)

y = $60.25

b) If your cost was $65.00, how many miles were you charged for traveling?

Plug y = 65 in the equation:

65 = 46 + 0.25x

x = 76 miles

c) Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel?

Plug y = 100 in the equation:

100 = 46 + 0.25x

x = 216 miles

Thus, the answer for part a is $60.25, for part b the answer is 76 miles, and for part c the answer is 216 miles.

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Answer:

C

Step-by-step explanation:

a = 4

b = 5

c = 2

C = arccos((a² + b² - c²) / 2ab)

C = arccos((16 + 25 - 4) / 2(4)(5))

C = arccos(37 / 40)

C = 22.33°

2abcosC

2(4)(5)cos(22.33)

40(0.925)

37

Option C is correct, if the law of cosines is a² + b² - 2abcosC = c² then the value of 2abcosC is 37.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We have from law of cosines that a² + b² - 2abcosC = c²

We have to find the value of 2abcosC.

Now let us find the value of C

C = arccos((a² + b² - c²) / 2ab)

C = arccos((16 + 25 - 4) / 2(4)(5))

C = arccos(37 / 40)

C = 22.33°

Now plug in the value of C in  2abcosC.

2abcosC

=2(4)(5)cos(22.33)

=40(0.925)

=37

Hence, option C is correct, if the law of cosines is a² + b² - 2abcosC = c² then the value of 2abcosC is 37.

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The value of the height of the prism is 8.68 inches

The surface area is the sum of the area of the faces.

The formula for calculating the surface area of the pyramid is;

TSA  = [tex]a^2+2a\sqrt{\frac{a^2}{4} + h^2}[/tex]

where

a is the side length. = 7in

h is the height

Substitute

[tex]189=7^2+2(7)\sqrt{\frac{7^2}{2} + h^2} \\189=49+14\sqrt{\frac{49}{2} + h^2}\\140=14\sqrt{\frac{49}{2} + h^2}\\10=\sqrt{\frac{49}{2} + h^2}\\[/tex]

Square both sides to have

100 = 49/2 + h²

h² = 100 - 49/2

h² = 151/2

h² = 75.5

h = 8.68in

Hence the value of the height of the prism is 8.68 inches

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The process of Graphing a exponential decay function is shown in detail below.

There are two types of exponential equations: exponential decay and exponential growth. The fundamental shape of an exponential function and its corresponding graphs must be understood in order to fully comprehend the distinctions between exponential growth and decay. The fundamental distinction between the two is that in an exponential decay connection, the output values rise quickly as the input value rises, but in an exponential growth relationship, the output rises noticeably faster as the input value rises. Furthermore, neither of the two functions is linear, hence their rate of change is not constant. What distinguishes one equation from the other when they both have the same precise form, y = abx?

The value of the constant "b" is the fundamental factor in deciding whether the exponential function is one of growth or decay:

In this way we can graph a exponential decay function

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Answer:

Total Miles he  drives first day      = 8 miles

Total Miles he drive second day   = 12miles

Total Miles he drives third day    =    18miles

Total Miles he drives fourth day    =  27 miles

Step-by-step explanation:

This is a problem of linear equations in 1 variable:

The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.

It is given in the question that ,

This week his goal is to drive bike about 65 total miles over four days. Each day, he wants to ride 1.5 times as far as he rode the day before.

Let, on the first day, he drives x miles. On second day, he drives 1.5x. On the third day, he drives 1.5(1.5x) and on the fourth day, he drives 1.5(1.5(1.5x)).

So the equation is :

x +1.5x + 1.5(1.5x) + 1.5(1.5(1.5x)) = 65miles

x + 1.5x + 2.25x + 3.375x   = 65miles

            8.125x   =    65 miles

                  x   =  65/8.125  miles

                  x   = 8 miles

so after solving the equation we get, on the first day Gavin drives 8 miles

similarly, on the second day he drives 12miles

               on third day 18 miles

   and     on the fourth day  27miles

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Answer:

A. 4/5

Step-by-step explanation:

Answer:

4/5  (option a)

Step-by-step explanation:

by following the exponent rule of [tex]a^1 = a[/tex], we know that

[tex](\frac{4}{5} )^1[/tex] = [tex]\frac{4}{5}[/tex]

So, the value of

[tex]\frac{4}{5}^{1}[/tex]  is  4/5

My theorems include the Pythagoras theorem, midpoint theorem, and angle bisector theorem.

The Pythagoras theorem is used to find the length in a right angle.

The midpoint theorem states that the line segment in a triangle is parallel to the third side and is half the length.

The angle bisector theorem is concerned with the lengths of the two segments that the triangle side is divided into by a line which bisects the opposite angle.

I like them because they're important when solving triangle related problems.

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The graph is shown below:

A graph is a mathematical diagram which shows the relationship between two or more sets of numbers or measurements.

Given function: f(x) = x

We have to draw the graph for the function ,f(x) =x with two cases.

For x<2 and for x ≥ 2

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Answer:

m=0 , b=41

Step-by-step explanation:

Using a trigonometric identity, it is found that the equivalent expression is given by 1.

Relating sine and cosine, we have that:

[tex]\sin^{2}{\beta} + \cos^{2}{\beta} = 1[/tex]

Then:

[tex]\cos^{2}{\beta} = 1 - \sin^{2}{\beta}[/tex]

For the tangent, we have that:

[tex]\tan{\beta} = \frac{\sin{\beta}}{\cos{\beta}}[/tex].

For the secant, we have that:

[tex]\sec{\beta} = \frac{1}{\cos{\beta}}[/tex].

In this problem, the expression is:

[tex]\frac{(1 - \sin{\beta})(1 + \sin{\beta})}{\cos^{2}{\beta}} = \frac{1 - \sin^2{\beta}}{\cos^2{\beta}} = \frac{\cos^2{\beta}}{\cos^2{\beta}} = 1[/tex]

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The equation of the line that passes through the given points is            y= -4x+23.

A line can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:

a= the slope

b=constant term that represents the y-intercept.

From the stardard form equation:

Solving the system for equations 1 and 2.

3=5a+b

-13=9a+b * (-1)

3=5a+b

13=-9a-b * (-1)

16= -4a

4= -a

a= -4

If a= -4 from equation 1, you have

3= 5 * (-4)+b

3= -20+b

b=23

Therefore, the line equation is y= -4x+23.

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The flux is 9.

Flux is the presence of a force field in a specified physical medium, or the flow of energy through a surface.

Given:

2x+2y+z= 1

F = 2i+2j + 2k

Now,

r = xi + yj + z( 1-2x-2y) K

dr/dx= i - 2k

dr/dy = j-2k

dr/dx* dr/dy

= ( i - 2k) * (j-2k)

= 2i + 2j + k

F(x)= 2i+2j + 2k

F(x). da = 4 +4 +2 = 10 dxdy

Hence, flux

= [tex]\int\limits^1_0 {\int\limits^{1-2y}_0 {10 } \, dx dy } \,[/tex]

=  [tex]\int\limits^1_0[/tex]  10(1-2y) dx

= [tex]\int\limits^1_0[/tex] 10-2y

= 10(1) - (1)²

=9

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The plane has intercepts (1/2, 0, 0), (0, 1/2, 0), and (0, 0, 1). Parameterize [tex]S[/tex] by the vector function

[tex]\vec s(u,v) = \dfrac{(1-u)(1-v)}2 \, \vec\imath + \dfrac{u(1-v)}2 \, \vec\jmath + v \,\vec k[/tex]

with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. (More explicitly, we have the parameterization

[tex]\vec s(u,v) = (1-v)((1-u) p_1 + u p_2) + v p_3[/tex]

where [tex]p_i[/tex] denote the given points.)

The normal vector to [tex]S[/tex] is

[tex]\vec n = \dfrac{\partial\vec s}{\partial u} \times \dfrac{\partial\vec s}{\partial v} = \dfrac{1-v}2\,\vec\imath + \dfrac{1-v}2\,\vec\jmath + \dfrac{1-v}4\,\vec k[/tex]

Then the flux of [tex]\vec F = 2\,\vec\imath+2\,\vec\jmath+2\,\vec k[/tex] across [tex]S[/tex] is given by the surface integral,

[tex]\displaystyle \iint_S \vec F \cdot d\vec\sigma = \iint_S \vec F \cdot \vec n \, dA[/tex]

[tex]\displaystyle = \int_0^1 \int_0^1 \left(2\,\vec\imath+2\,\vec\jmath+2\,\vec k) \cdot \left(\frac{1-v}2\,\vec\imath + \frac{1-v}2\,\vec\jmath + \frac{1-v}4\,\vec k\right) \, du \, dv[/tex]

[tex]\displaystyle = \frac52 \int_0^1 \int_0^1 (1-v) \, du \, dv[/tex]

[tex]\displaystyle  = \frac52 \int_0^1 (1-v) \, dv = \boxed{\frac54}[/tex]

Answer:

A

Step-by-step explanation:

[tex]s=\frac{a+b+c}{2}[/tex]

multiply both sides by 2

[tex]2s = a + b +c[/tex]

substract b and c from both sides to get a by itself

[tex]a = 2s - (b + c)\\a = 2s - b - c[/tex]

so the answer is A.

Adding 2x to both sides, we get [tex]\boxed{2x+y=5}[/tex]

Probability helps us to know the chances of an event occurring. The probability of pulling a green or red card is 9 / 100.

Probability helps us to know the chances of an event occurring.

P =  [tex]\dfrac{Desired \ outcomes}{Posiible \ outcomes}[/tex]

The probabilities of different color cards being pulled are 1/25 for red, 1/20 for green, 1/15 for purple, and 1/10 for black Therefore, the probability of pulling  a green or red card is,

Probability = 1/20 + 1/25

                 = (5 + 4) /100

                 = 9 / 100

Hence, the probability of pulling a green or red card is  9 / 100.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: x = 25°[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 4x - 13 = 2x + 37[/tex]

[ Alternate Exterior Angle ]

[tex]\qquad \tt \rightarrow \: 4x - 2x = 37 + 13[/tex]

[tex]\qquad \tt \rightarrow \: 2x = 50[/tex]

[tex]\qquad \tt \rightarrow \: x = \cfrac{50}{2} [/tex]

[tex]\qquad \tt \rightarrow \: x = 25 \degree[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

It's +2

Step-by-step explanation:

As the positive occurs on the right side of the negatives in the number line so if we keep extending on the right side so we get +2