The perimeter of a football field is 1040 feet. The length of the field is 120 feet less than 3 times the width. What are the dimensions of the field?

Applying the central angle theorem, we have:

a. angle BAC.

b. arc BEC

c. arc BC

d. Measure of arc BEC = 260°

e. Measure of arc BC = 100°

According to the central angle theorem, the central angle that is suspended at the center of a circle by two line segments (usually radii) have a measure that is equal to the measure of the intercepted arc. That is:

Measure of central angle = measure of intercepted arc.

A major arc have a measure that is greater than 180 degrees or half a circle, while minor arcs have a measure that is less than 180 degrees or half a circle.

a. A central angle in the image given is: angle BAC.

b. One major arc in the given circle is arc BEC (greater than half a half a circle/180 degrees).

c. One minor arc in the given circle is arc BC (less than half a half a circle/180 degrees).

d. m∠BEC = 360 - 100

m∠BEC = 260°

m∠BEC = measure of arc BEC [central angle theorem].

Measure of arc BEC = 260°

e. Measure of arc BC = m∠BAC [central angle theorem].

Measure of arc BC = 100°

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Answer:

16

Step-by-step explanation:

By the trapezoid midsegment theorem,

[tex]\frac{ST+6}{2}=11 \\ \\ ST+6=22 \\ \\ ST=16[/tex]

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

We can use Trapezoid midsegment property:

[tex] \qquad❖ \: \sf \: \dfrac{ST + QR}{2} = LM[/tex]

[tex] \qquad❖ \: \sf \: \dfrac{ST + 6}{2} = 11[/tex]

[tex] \qquad❖ \: \sf \: {ST + 6} =2 \times 11[/tex]

[tex] \qquad❖ \: \sf \: {ST + 6} =22[/tex]

[tex] \qquad❖ \: \sf \: {ST } =22 - 6[/tex]

[tex] \qquad❖ \: \sf \: {ST } =16[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

thanks for your support of the personal information on the direction of economics class

Answer:

0.7

Step-by-step explanation:

Each increment is 0.1, so count the approximate number of increments needed to get from the orange circle on the left and the one on the right and multiply by 0.1 to get the difference.

Answer:

  170

Step-by-step explanation:

The given relations can be used to write and solve an equation for the number of stickers Peter has.

Let p represent the number of stickers Peter has. That is twice as many as Joe, so Joe has (p/2) stickers. Joe has 40 more stickers than Emily, so the number of stickers Emily has is (p/2 -40).

The total number of stickers is 300:

  p +p/2 +(p/2 -40) = 300

  2p = 340 . . . . . . . . . . . . . . add 40, collect terms

  p = 170 . . . . . . . . . . . divide by 2

Peter has 170 stickers.

__

Additional comment

Joe has 170/2 = 85 stickers. Emily has 85-40 = 45 stickers.

We could write three equations in three unknowns. Solving those using substitution would result in substantially the same equation that we have above. Or, such a system of equations could be solved using a calculator's matrix functions, as in the attachment.

  p +j +e = 300

  p -2j +0e = 0

  0p +j -e = 40

The number of specimens should be tested is 1352.

According to the statement

we have to given that the in testing of wine specimens, lead levels ranging from 47 to 660 parts per billion were recorded. and we have to find the number specimen should be tested.

so,

Using the uniform and the z-distribution, it is found that 1353 specimens should be tested.

For an uniform distribution of bounds a and b, the standard deviation is given by:

σ = [tex]\sqrt{\frac{(b-a^{2})}{12} }[/tex]

and put the values a= 50 and b= 700 then the

standard deviation is 187.64

And here the critical value become 1.6 then

We want the sample for a margin of error of 10, thus, we have to solve for n with the help of value of m is 100.

Then n is 1352.

So,  The number of specimens should be tested is 1352.

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Answer:

12 walls

Step-by-step explanation:

Let's take everyone paints a different wall and there are no overlaps.

Given information from the question:

1.5 hours = 1 wall

1 hour =

[tex] \frac{1}{1.5} \\ = \frac{2}{3} walls[/tex]

per person.

From the information above, we can deduce:

6 people =

[tex] \frac{2}{3} \times 6 \\ = \frac{12}{3} \\ = 4 \: walls[/tex]

Since we know 6 people can paint 4 walls in an hour,

3 hours =

[tex]3 \times 4 \\ = 12 \: walls[/tex]

Answer:

45:315

Step-by-step explanation:

Add up the ratio to get the total ratio.

1+7=8

Divide the 360 by the total ratio.

360÷8=45

The number 45 tells you how many times to multiply both sets of the ratio to get a total of 360.

1×45=45

7×45=315

so,

45:315

Hope this helped. Comment below if you need more assistance! :)

Answer:

3rd grade

Step-by-step explanation:

Given that the values are different types (fractions, decimals, and percentages), it would be helpful to convert them to the same type of value.

Converting everything to percentages seems more convenient.

Since 61.24% is already a percentage, we simply have to convert 0.52, 25/36, and 0.5274444 (I wrote 0.5274 like this since the 4 is a repeating value).

To convert 0.52, we simply multiply by 100:

0.52 * 100 = 52%

For 25/36, we need to know its decimal form and multiply by 100 to find the percentage:

25 / 36 = 0.6944 * 100 = 69.44%

For 0.5274444, we also multiply by 100:

0.5274444 * 100 = 52.74444

Thus, we have 52% (2nd grade), 69.44% (3rd grade), 61.24% (4th grade), and 52.74444% (5th grade).

3rd grade has the highest portion of students

Using the arrangements formula, it is found that 1680 arrangements can be made with these numbers.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

When there are repeated elements, repeating [tex]n_1, n_2, \cdots, n_n[/tex] times, the number of arrangements is given by:

[tex]A_n^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]

For the number 28535852, we have that:

Hence the number of arrangements is:

[tex]A_8^{3,2,2} = \frac{8!}{3!2!2!} = 1680[/tex]

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Answer:

To solve the problem we have to take 4 percent of 5000 and multiply it by 8 years and the final result is 1600 dollars, which would be the final result.

The behavior of the graph with the equation y=x66x5+50x3+45x2108x108 at each of its zeros will be as follows: two of them will resemble a quadratic function, while one of them will resemble a linear function.

This is further explained below.

Generally, a diagram that illustrates the relationship between variable quantities, usually consisting of two variables, with each variable being measured along one of a pair of axes that are intersected at right angles.

In conclusion, At each of its zeroes, the graph y=x66x5+50x3+45x2108x108 will exhibit one linear behavior and two behaviors that resemble quadratic functions.

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Answer: 1:52 PM

Step-by-step explanation:

PAULA: 2:14PM FINISHED THE RACE

BEATRICE: FINISHED 22 MINUTES EARLIER THEN PAULA

YOU TAKE 2:14PM AND SUBTRACT THE 22 MINS BEATRICE RAN TO GET YOU ANSWER.

SO 2:14 -14 MINS=2:00PM 14+8=22 (THE MINS BETRICE FINISHED)

2:00-8 MINS ( REMAINING FROM THE 22 ) THEN 2:00-8 MINS =1:52

ANSWER:1:52PM

Answer:

6 * (5 + n)

Explanation:

Sum = addition

Difference = subtraction

Product = multiplication

Quotient = division

Answer:

13

Step-by-step explanation:

The range of the data set can be defined as: max-min, and in a sorted data  set, the min should be the first value, and the max should be the last value. We don't necessarily need to sort the data here, since we're just looking for two values which we can easily compare to other numbers without having them in order. Although it's important to note when looking for stuff like the median, first, and third quartile you should sort the data.

With that being said, let's look for the min and max! So by looking at the data set, you should be able to determine that the min (minimum) value is 17, and that the max (maximum) value is 30.

This means the range is defined as: 30 - 17 = 13

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads....}[/tex]

[tex]\text{Find the range for the set of data 24, 30, 17, 22, 22}[/tex]

[tex]\huge\textbf{What does \boxed{range} mean in math?}[/tex]

[tex]\boxed{Range}\rightarrow\text{is the DIFFERENCE between the biggest number and the}\\\text{smallest number.}[/tex]

[tex]\huge\textbf{How do you find the \boxed{range}?}[/tex]

[tex]\text{You find the biggest number \& subtract it from the smallest number.}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\text{24, 30, 17, 22, 22}[/tex]

[tex]\huge\textbf{The \boxed{\mathsf{\mathsf{biggest}}} number }\huge\boxed{\downarrow}[/tex]

[tex]\text{30}[/tex]

[tex]\huge\textbf{The \boxed{\mathsf{\mathsf{smallest}}} number }\huge\boxed{\downarrow}[/tex]

[tex]\text{17}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\rm{30 - 17}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\large\text{Start at 30 and go DOWN 17 spaces to the \boxed{left} and you will}\\\large\text{have your answer. }[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{13}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The most efficient measurements of the box should be 4cm long, 1cm wide and 2cm high so that its cost is $129.2

To calculate the measurements of the rectangular box we must take into account the following condition:

According to the above, we can establish that the most appropriate measurement for the bottom and top should be 1cm (width) × 4cm (length). Additionally we can establish that the height of the box would be 2cm.

To find the volume of the box we must use the following formula:

The areas of this box are:

The total price of this box is as follows:

Top and bottom:

Sides:

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Answer:

See below

Step-by-step explanation:

237/50   =    4    R 37

37/20     =     1     R 17

17 / 10     =     1     R 7

7 / 1         =     7    R 0

4   50gm's      1     20gm       1   10gm       and   7    1g wts

The required number of weights used in chemical balance to weigh 237g is 4,1,1,7 respectively.

What is mathematical expression?

A mathematical expression expression in mathematical is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Here, it is given that :

A chemical balance needs to weigh 237g using weights of 50g, 20g, 10g and 1g.

Now, let us find the number of weights for each weight type :

For 50g weight the maximum number of weights needed will be 4 that is :

50g x 4 = 200g

Now, for 20g weight the maximum number of weights needed will be 1 that is :

20g x 1 = 20g

Now, for 10g weight the maximum number of weights needed will be 1 that is :

10g x 1 = 10g

Now, for 1g weight the maximum number of weights needed will be 7 that is :

1g x 7 = 7g

Adding all the weights we get :

200g + 20g + 10g + 7g = 237g;

which is the required weight and the number of weights used is 4,1,1,7 respectively.

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The expression, [tex](-243)^{-3/5}[/tex] on simplification using the laws of the exponent can be written as - (1/27).

Exponents are of the form aˣ, read as " a to the power x", function as a multiplied by itself x number of times, and are used in a numerical and algebraic expression.

To simplify these expressions, we use the following laws of the exponents:

[tex]1. a^m.a^n = a^{m + n}\\2.\frac{a^m}{a^n} = a^{m-n}\\ 3. (a^m)^n = a^{mn}\\4. a^{-m} = \frac{1}{a^m}\\5. a^0 = 1[/tex]

In the question, we are asked to simplify the expression, [tex](-243)^{-3/5}[/tex].

The expression can be solved using the laws of exponent as follows:

[tex](-243)^{-3/5}\\[/tex]

= [tex]((-3)^5)^{-3/5}[/tex]

= [tex](-3)^{-3}[/tex] {Using the law of exponent: [tex](a^m)^n = a^{mn}[/tex]}

= [tex]\frac{1}{-3^3}[/tex] {Using the law of exponent: [tex]a^{-m} = \frac{1}{a^m}[/tex]}

= 1/(-27)

= - (1/27).

Thus, the expression, [tex](-243)^{-3/5}[/tex] on simplification using the laws of exponent can be written as - (1/27).

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Answer:

your question is not correct i can not find the answer

The initial amount in the sample and the amount remaining after 40 hours are 2400 grams and 331 grams respectively.

From the information given, we have the function to be;

a(t)=2400(1/2)^t/14

Where

To determine the initial amount, we have that t = 0

Substitute into the function, we have

[tex]A(t) = 2400[/tex] × [tex]\frac{1}{2} ^\frac{0}{14}[/tex]

[tex]A (t) = 2400[/tex]  × [tex]\frac{1}{2} ^0[/tex]

[tex]A (t) = 2400[/tex]

The initial amount is 2400 grams

For the amount remaining after 40 years, t = 40 years

A(t)=2400(1/2)^t/14

Substitute into the function, we have

[tex]A(t) = 2400[/tex] × [tex]\frac{1}{2} ^\frac{40}{14}[/tex]

[tex]A(t) = 2400[/tex] × [tex](0. 5) ^2^.^8^5^7[/tex]

[tex]A(t) = 2400[/tex] × [tex]0. 1380[/tex]

A(t) = 331. 26

A(t) = 331 grams in the nearest gram

Thus, the initial amount in the sample and the amount remaining after 40 hours are 2400 grams and 331 grams respectively.

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Answer:

-5^x + 3x - 2.

Step-by-step explanation:

(f - g) (x) = f(x) - g(x)

=  -5^x - 4 - (-3x - 2)

= -5^x - 4 + 3x + 2

= -5^x + 3x - 2.

Answer:

[tex]y=\dfrac{8}{7}x - \dfrac{23}{7}[/tex]

Step-by-step explanation:

Rearranging the terms, we get [tex]7y=8x-23[/tex]. Dividing both sides by 7, we get [tex]\dfrac{7y}{7} = \dfrac{8x-23}{7}[/tex], so [tex]\boxed{y=\dfrac{8}{7}x - \dfrac{23}{7}}[/tex]

Answer:

y = [tex]\frac{8}{7}[/tex]x -[tex]\frac{23}{7}[/tex]

Step-by-step explanation:

You are changing this to the slope-intercept form of a line.

y = mx + b

8x -7y = 23  Subtract 8x from both sides of the equation

-7y = -8x + 23  Divide both sides of the equation by -7

y = [tex]\frac{-8}{-7}[/tex]  - [tex]\frac{23}{7}[/tex]  

[tex]\frac{-8}{-7}[/tex] is the same as [tex]\frac{8}{7}[/tex]

y = [tex]\frac{8}{7}[/tex]x - [tex]\frac{23}{7}[/tex]

The attached figure represents the array for 237 x 43

The array is given as:

237 x 43

An array is represented as:

Row x Column

This means that:

Row = 237

Column = 43

i.e. the array has 237 rows and 43 columns

The numbers are large, so the cells would be small when the arrays are drawn

See attachment for the array

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The number of kilometres travelled by the satellite in discuss in which case, the satellite makes 8 revolutions around the earth is; C = 177,271.8 km.

Given from the task content, the earth's diameter is; 6371 km and since, the height at which the satellite orbits the earth is; 343km, it follows that the diameter of orbit if the satellite in discuss is;

D = 6371 + (343)×2

Hence, we have; diameter, D = 7057 km.

Hence, the distance travelled after 8 revolutions is;

C = 8 × πd

C = 8 × 3.14 × 7057

C = 177,271.8 km.

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The value of surface integral using the Divergence Theorem is [tex]729\pi[/tex] .

Divergence Theorem states that the surface integral of a vector field over a closed surface, is equal to the volume integral of the divergence over the region inside the surface. Mathematically the it can be calculated using the formula:[tex]\int\int\int\limit{ }_V(\delta \cdot F)=\int\int(F \cdot n)dS[/tex]

The divergence of F is

[tex]div F=\frac{d}{dx}(2x^{3}+y^{3})+\frac{d}{dy}( y^{3} +z^{3})+\frac{d}{dz}3y^{3} z[/tex]

[tex]div F=6x^{2}+3y^{2}+3y^{2}[/tex]

Let E be the region [tex]{(x,y,z):0\leq z\leq 9-x^{2} -y^{2}[/tex] then by divergence theorem we have [tex]\int \int\limits^{}_s {F\cdot n\times dS} =\int\int\int\limits^{}_E divFdV=\int\int\int\limits^{}_E(6x^2+6y^2)dV[/tex]

Now we find the value of the integral:

[tex]=\int\limits^{2\pi}_0\int\limits^3_0\int\limits^{9-r^2}_0(6r^2)rdzdrd{\theta}\\=\int\limits^{2\pi}_0 \int\limits^3_0(9-r^2)6r^3drd{\theta}\\=2\pi\int\limits^3_0 {(54r^3-6r^5)} dr\\[/tex]

[tex]=2\pi\times \frac{729}{2}\\=729\pi[/tex]

Thus we can say that the value of the integral for the surface around the paraboloid is given by [tex]729\pi[/tex].

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

The straight angles are angles that form a straight line, and their measure = 180°

In the given figure, the Straight angles is :

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

arithmetic sequence formula: first term + (n - 1)common difference

9 + (n - 1)-2

9 + -2n + 2

= -2n + 11

The standard form of the equation whose graph is the line through (1, -2) and (-5, 6) is 3y = -4x -2.

According to the question,

The standard form of the equation whose graph is the line through (1, -2) and (-5, 6). Now first to find slope of the equation using below formula,

Slope of the equation (m)= (change in y axis) / (change in x axis)

= (6- (-2))/(-5 - 1)

= 8/-6

=-(4/3)

Slope of the equation (m) = -4/3. whose graph is the line through (1, -2) and (-5, 6).Formula to find Standard form of the equation is y = mx + c.

-2 = -(4/3) 1 + c

c = -2 +(4/3)

c = -2/3

The standard form of the equation whose graph is the line through (1, -2) and (-5, 6) is 3y = -4x -2. y = -(4/3)x -(2/3).

⇒  3y = -4x -2.

Hence, the standard form of the equation whose graph is the line through (1, -2) and (-5, 6) is 3y = -4x -2.

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The histogram that correctly shows the data in the table is the histogram number four.

This a type of graph that allows people to visually represent data by using bars and gathering the data they have in different categories.

This data can be represented using ranges of temperature and the number o elements or substances in these ranges.

This data matches the fourth graph

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