A javelin throwing arena is illustrated
alongside. It has the shape of a sector of
a circle of radius 100 m. The throwing
line is 5 m from the centre. A white line
is painted on the two 95 m straights and
on the two circular arcs.
a Find the total length of the painted
white line.
b If the shaded landing area is grassed,
what is the total area of grass?

An additional information that is needed to prove the triangles are congruent by the SAS Postulate is: D. ∠BAC ≅ ∠DAC.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce that ∆BAC is congruent to ∆DAC when the angles A (∠A) are congruent by the reflexive property.

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The value of x would be,

⇒ x = 15

We have to given that;

A figure with QC is parallel to BR

Now, We can formulate that,

Triangle BDR and triangle CDQ are similar.

Hence, By using proportionality we get;

⇒ BD / DR = QD / CD

Substitute all the values we get;

⇒ (24 + 40) / (15 + x) = 40 / x

Solve for x,

⇒ 64 / (15 + x) = 40 / x

⇒ 64x = 40 (15 + x)

⇒ 8x = 5 (15 + x)

⇒ 8x = 45 + 5x

⇒ 8x - 5x = 45

⇒ 3x = 45

⇒ x = 15

Thus, The value of x would be,

⇒ x = 15

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Answer:

A. mBC = 71

B. mAB = 142

C. AD = 30

D. BD = 30

E. YD = 16

F. DC = 18

Step-by-step explanation:

A. mBC = mAC = 71

B. mAB = mBC + mAC = 71 + 71 = 142

C. AD = AB/2 = 60/2 = 30

D. BD = AD = 30

E. YA^2 = YD^2 + AD^2

YD^2 = YA^2 - AD^2 = 34^2 - 30^2 = 1156 - 900 = 256

YD = √256 = 16

F. DC + YD = YC

DC = YC - YD = 34 - 16 = 18

"The set of all functions from X to Y" refers to the collection of all possible functions that can be defined from a set X to a set Y. This set is denoted as Y^X or X→Y.

Each element of the set Y^X is a function that maps each element of set X to a unique element of set Y. The notation for such a function f is f: X → Y.

Given,

f is a function from X to Y .

Note:

The cardinality (size) of the set Y^X is given by |Y^X| = |Y|^|X|. In other words, if the set X has m elements and the set Y has n elements, then the set of all functions from X to Y has n^m elements.

It is often used to describe the space of all possible solutions to a given problem or equation.

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Answer:

x= -3

Step-by-step explanation:

x-3

-----------

x+3

This expression is undefined when the denominator is zero.

x+3 =0

x= -3

Applying the angle of intersecting secants theorem, the measure of arc LN in the circle is: 56°.

Given the circle in the image above where the two secants intersect outside the circle, the angle of intersecting secants theorem states that:

external angle formed = 1/2 * (the measure of arc KP - the measure of arc LN)

Plug in the values:

20 = 1/2 * (96 - m(LN))

2 * 20 = 96 - m(LN)

40 = 96 - m(LN)

m(LN) = 96 - 40

m(LN) = 56°

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The Surface area of Triangular Prism is 132 cm².

We have have the dimension of prism as

Sides = 3 cm, 4 cm, 5 cm

and, l = 10 cm

and, b= 4 cm

Now, Surface area of Triangular Prism as

= (sum of sides) l + bh

= (3 + 4 + 5)10 + 4 x 3

= 12 x 10 + 12

= 120 + 12

= 132 cm²

Thus, the Surface area of Triangular Prism is 132 cm².

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The equation of the circle is (x - 2)² + (y - 3)² = 36

From the question, we have the following parameters that can be used in our computation:

The circle

Where, we have

Center = (a, b) = (2, 3)

Radius, r = 6 units

The equation of the circle is represented as

(x - a)² + (y - b)² = r²

So, we have

(x - 2)² + (y - 3)² = 6²

Evaluate

(x - 2)² + (y - 3)² = 36

Hence, the equation is (x - 2)² + (y - 3)² = 36

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Answer:

domain= [-5,5]

range= [-3,3]

Step-by-step explanation:

the domain is with the x axis you have to look for the farthest x axis which would be - 5 in this case and the closest axis which is 5 so the x can be anywhere between - 5 and 5

then for the range is with the y axis you would look for the farthest y axis which is - 3 and the closes which is 3 so the y can be anywhere in between - 3 and 3

Answer:

y=3x+5

Step-by-step explanation:

you do 4 times 3 then subtract that from 17

The graph of the solution of the inequality is attached

From the question, we have the following parameters that can be used in our computation:

x - 4 < 5

Add 4 to both sides of the inequality

So, we have

x - 4 + 4 < 5 + 4

Evaluate the like terms

So, we have

x < 9

This means that the solution of the inequality is x < 9

See attachment for the graph

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The dollar value of total revenue at each price is $[tex]0[/tex], $[tex]10[/tex], $[tex]12[/tex], $[tex]12[/tex], $[tex]10[/tex], and $[tex]6[/tex]. Total revenue will be the greatest at a price of $[tex]4[/tex], with [tex]3[/tex] units sold.

To find the dollar value of total revenue at each price, we can multiply the price by the corresponding quantity in the demand schedule:

Price: $[tex]6[/tex]

Quantity: [tex]0[/tex]

Total Revenue: $[tex]6 \times 0[/tex] = $[tex]0[/tex]

Price: $[tex]5[/tex]

Quantity: [tex]2[/tex]

Total Revenue: $[tex]5 \times 2[/tex] = $[tex]10[/tex]

Price: $[tex]4[/tex]

Quantity: [tex]3[/tex]

Total Revenue: $[tex]4 \times 3[/tex] = $[tex]12[/tex]

Price: $[tex]3[/tex]

Quantity: [tex]4[/tex]

Total Revenue: $[tex]3 \times 4[/tex] = $[tex]12[/tex]

Price: $[tex]2[/tex]

Quantity: [tex]5[/tex]

Total Revenue: $[tex]2 \times 5[/tex] = $[tex]10[/tex]

Price: $[tex]1[/tex]

Quantity: [tex]6[/tex]

Total Revenue: $[tex]1 \times 6[/tex] = $[tex]6[/tex]

To determine at which price the total revenue will be the greatest, we observe that the highest total revenue occurs at the price with the highest quantity sold. In this case, the price with the highest quantity is $[tex]3[/tex], and the corresponding quantity sold is [tex]4[/tex] units.

Therefore, at a price of $[tex]3[/tex], the total revenue will be the greatest, with [tex]4[/tex] units sold.

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The expression -2(5 + 7x) + 5(x + 5) is equivalent to the expression -9x + 15. So, the answer is option B: 15 - 9x.

To simplify the expression -2(5 + 7x) + 5(x + 5), we can distribute the coefficients and simplify further.

Starting with the expression -2(5 + 7x):

-2(5 + 7x) = -2 × 5 - 2 × 7x

= -10 - 14x

= -14x - 10

Now let's simplify the expression 5(x + 5):

5(x + 5) = 5 × x + 5× 5

= 5x + 25

Finally, combining the two simplified expressions:

-14x - 10 + 5x + 25

Combining like terms:

(-14x + 5x) + (-10 + 25)

-9x + 15

Therefore, the expression -2(5 + 7x) + 5(x + 5) is equivalent to the expression -9x + 15.

So, the answer is option B: 15 - 9x.

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Step-by-step explanation:

To multiply the polynomials (8v - 5)(v + 7), we can use the distributive property:

(8v - 5)(v + 7) = 8v(v + 7) - 5(v + 7)

Now we can simplify by multiplying each term:

8v(v + 7) - 5(v + 7) = 8v^2 + 56v - 5v - 35

Finally, we can combine like terms to get the simplified expression:

8v^2 + 51v - 35

Therefore, (8v - 5)(v + 7) = 8v^2 + 51v - 35.

Answer:

-4

Step-by-step explanation:

i jus did this question

The rule used to determine the term value from its position in the sequence is often referred to as the "nth term" rule.

The nth-term rule involves identifying a pattern or relationship between the position (n) of a term in the sequence and the value of that term.

By analyzing the pattern, such as the common difference or common ratio, the nth-term rule allows us to express the value of any term in the sequence based on its position.

This rule provides a formula or equation that relates the position of a term to its corresponding value in the sequence.

Mathematically, the rule is:

T(n) = a + (n - 1) * d

where:

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The frequency distribution that matches the data {3,8,5,6,4,3,7,8,9,5,5,6,4,12,14,10,8} is C.

Number

of Shoes   Frequency

3-5                   7

6-8                  6

9-11                 2

12-14              2

A frequency distribution is a frequency table or chart that visually displays the actual number of observations in each range or class or the percentage of the observations.

In this frequency distribution, the group 3-5 has the highest frequency of 7 followed by 6-8 with 6 frequencies.

3,8,5,6,4,3,7,8,9,5,5,6,4,12,14,10,8

Number

of Shoes   Frequency

3-5              IIIIIII        7

6-8              IIIIII         6

9-11             II             2

12-14           II             2

Total                        17

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The expression which is equivalent to -32^3/5 is  -32768 / 125.

We are given that;

Expression=-32^3/5

Now,

To find an equivalent expression for -32^3/5 is to use the property of exponents that says [tex](a/b)^n = a^n / b^n.[/tex] Applying this property, we get:

-32^3/5 = (-32)^3 / 5^3

Now we can simplify the numerator and denominator by cubing them:

-32^3/5 = -32768 / 125

This is an equivalent expression for -32^3/5. There may be other ways to find equivalent expressions, such as factoring or using common denominators.

Therefore, by the expression the answer will be -32768 / 125.

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To solve the compound inequality 2y + 3 ≥ -9 or -3y < -15, we'll solve each inequality separately and then combine the solutions.

First, let's solve the first inequality: 2y + 3 ≥ -9.

Subtract 3 from both sides:

2y ≥ -12

Divide both sides by 2 (note that dividing by a positive number does not change the inequality direction):

y ≥ -6

Next, let's solve the second inequality: -3y < -15.

Divide both sides by -3 (remember to reverse the inequality direction when dividing by a negative number):

y > 5

Now, let's combine the solutions. We have y ≥ -6 or y > 5.

In interval notation, we can express the solution as (-∞, -6] ∪ (5, ∞). This means that the solution includes all real numbers less than or equal to -6, as well as all real numbers greater than 5.

Answer:

When an exponent of the power is an even number and the base is a negative number, the value is always positive.

The mean weekly expense, after correcting the incorrectly recorded week, is $81.25.

Given that Taylor recorded the past 16 weeks' expenses, excluding the incorrect recording of $90 as $38, we have 15 correct expense values.

Sum of correct expenses = $83.20 * 15 = $1248

Now we need to include the corrected expense of $90 instead of $38.

New sum of expenses = $1248 - $38 (incorrectly recorded) + $90 (corrected) = $1300

Finally, we calculate the mean by dividing the new sum by the total number of weeks, which is 16.

Mean weekly expense = $1300 / 16 = $81.25

Therefore, the mean weekly expense, after correcting the incorrect recording, is $81.25.

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Answer:

[tex]\textsf{a)} \quad T_n=-n^2+n+20[/tex]

[tex]\textsf{b)} \quad T_{12}=-112[/tex]

[tex]\textsf{c)} \quad \sf 8th\;term[/tex]

a)  Second difference is 2.

b)  First term is 10.

Step-by-step explanation:

The given number pattern is:

To determine the type of sequence, begin by calculating the first differences between consecutive terms:

[tex]20 \underset{-2}{\longrightarrow} 18 \underset{-4}{\longrightarrow} 14 \underset{-6}{\longrightarrow}8[/tex]

As the first differences are not the same, we need to calculate the second differences (the differences between the first differences):

[tex]-2 \underset{-2}{\longrightarrow} -4 \underset{-2}{\longrightarrow} -6[/tex]

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

As the second difference is -2, the coefficient of the n² term is -1.

Now we need to compare -n² with the given sequence (where n is the position of the term in the sequence).

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}\sf operation&+21&+22&+23&+24\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}[/tex]

We can see that the algebraic operation that takes -n² to the terms of the sequence is to add (n + 20).

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}+n&0&-2&-6&-12\\\cline{1-5}+20&20&18&14&8\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}[/tex]

Therefore, the expression to find the the nth term of the given quadratic sequence is:

[tex]\boxed{T_n=-n^2+n+20}[/tex]

To find the value of T₁₂, substitute n = 12 into the nth term equation:

[tex]\begin{aligned}T_{12}&=-(12)^2+(12)+20\\&=-144+12+20\\&=-132+20\\&=-112\end{aligned}[/tex]

Therefore, the 12th term of the number pattern is -112.

To find the position of the term that has a value of -36, substitute Tₙ = -36 into the nth term equation and solve for n:

[tex]\begin{aligned}T_n&=-36\\-n^2+n+20&=-36\\-n^2+n+56&=0\\n^2-n-56&=0\\n^2-8n+7n-56&=0\\n(n-8)+7(n-8)&=0\\(n+7)(n-8)&=0\\\\\implies n&=-7\\\implies n&=8\end{aligned}[/tex]

As the position of the term cannot be negative, the term that has a value of -36 is the 8th term.

[tex]\hrulefill[/tex]

Given terms of a quadratic number pattern:

We know the first differences are negative, since the difference between the second and third terms is -7. Label the unknown differences as -a, -b and -c:

[tex]T_1 \underset{-a}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-b}{\longrightarrow}T_4 \underset{-c}{\longrightarrow} -14[/tex]

From this we can create three equations:

[tex]T_1-a=1[/tex]

[tex]-6-b=T_4[/tex]

[tex]T_4-c=-14[/tex]

The second differences are the same in a quadratic sequence. Let the second difference be x. (As we don't know the sign of the second difference, keep it as positive for now).

[tex]-a \underset{+x}{\longrightarrow} -7\underset{+x}{\longrightarrow} -b \underset{+x}{\longrightarrow}-c[/tex]

From this we can create three equations:

[tex]-a+x=-7[/tex]

[tex]-7+x=-b[/tex]

[tex]-b+x=-c[/tex]

Substitute the equation for -b into the equation for -c to create an equation for -c in terms of x:

[tex]-c=(-7+x)+x[/tex]

[tex]-c=2x-7[/tex]

Substitute the equations for -b and -c (in terms of x) into the second two equations created from the first differences to create two equations for T₄ in terms of x:

[tex]\begin{aligned}-6-b&=T_4\\-6-7+x&=T_4\\T_4&=x-13\end{aligned}[/tex]

[tex]\begin{aligned}T_4-c&=-14\\T_4+2x-7&=-14\\T_4&=-2x-7\\\end{aligned}[/tex]

Solve for x by equating the two equations for T₄:

[tex]\begin{aligned}T_4&=T_4\\x-13&=-2x-7\\3x&=6\\x&=2\end{aligned}[/tex]

Therefore, the second difference is 2.

Substitute the found value of x into the equations for -a, -b and -c to find the first differences:

[tex]-a+2=-7 \implies -a=-9[/tex]

[tex]-7+2=-b \implies -b=-5[/tex]

[tex]-5+2=-c \implies -c=-3[/tex]

Therefore, the first differences are:

[tex]T_1 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}T_4 \underset{-3}{\longrightarrow} -14[/tex]

Finally, calculate the first term:

[tex]\begin{aligned}T_1-9&=1\\T_1&=1+9\\T_1&=10\end{aligned}[/tex]

Therefore, the first term in the number pattern is 10.

[tex]10 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}-11 \underset{-3}{\longrightarrow} -14[/tex]

Note: The equation for the nth term is:

[tex]\boxed{T_n=n^2-12n+21}[/tex]

Answer:

Step-by-step explanation:

32 60 68

The length of the radius of the circle of equation (x + 3)² + (y - 7)² = 289 is given as follows:

b) 17.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by the equation presented as follows:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The equation for the circle in this problem is given as follows:

(x + 3)² + (y - 7)² = 289.

Hence the center and the radius are obtained as follows:

Hence option B is the correct option for this problem.

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Rounded to the nearest hundredth, the value of y at [tex]x = 7[/tex] is approximately [tex]12.78[/tex], according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form [tex]y = mx + b[/tex], where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

[tex]\[ y = 1.3642x + 3.2324 \][/tex]

To find the value of [tex]y[/tex] at [tex]x = 7[/tex], we substitute [tex]x = 7[/tex] into the equation:

[tex]\[ y = 1.3642(7) + 3.2324 \][/tex]

Simplifying the equation, we get:

[tex]\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \][/tex]

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is [tex]y = 1.3642x + 3.2324[/tex]. By substituting [tex]x = 7[/tex] into the equation, we find that the estimated value of y is approximately [tex]12.78[/tex]. This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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The values are x = 2 and NS = 3.5.

Given is a circle with center S, we need to find the missing measure,

K = 16, MP = 8, LP = 2x+4, and PS = 3.5, we need to find the measures of x and NS.

We know that the perpendicular drawn from the center of a circle bisect the chords into two halves,

And the perpendiculars are congruent.

Therefore,

MP = PL

2x+4 = 8

x+2 = 4

x = 2

Also,

NS = PS

So, NS = 3.5

Hence the values are x = 2 and NS = 3.5.

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The area of the right triangle is 18.02 cm².

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sum of angles in a triangle is 180 degrees.

Therefore, let's find the area of the right angle triangle as follows;

let's find the height and base of the triangle.

using trigonometric ratios,

cos 75 = adjacent / hypotenuse

cos 75 = base / 12

base = 3.10582854123

Therefore,

sin 75 = opposite / hypotenuse

sin 75 = h / 12

height = 11.5911099155

height = 11.59

Therefore,

area of the triangle = 1 / 2 × 3.11 × 11.59

area of the triangle = 36.0483518371 / 2

area of the triangle = 18.0241759186

area of the triangle = 18.02 cm²

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Answer:

I am confident the answer is H.

Based on the information, A. There is a 99% chance that the proportion of students who eat cauliflower on Jane's campus is between 5.03% and 17.83%.

Calculate the sample proportion:

= x / n = 4 / 35

= 0.1143

Calculate the Agresti and Coull's adjustment factor:

zα/2 = z(1 - α/2) = z(1 - 0.99/2)

= 2.576

Calculate the margin of error:

= 2.576 √(0.1143(1 - 0.1143) / 35)

= 0.064

Calculate the confidence interval:

= 0.1143 ± 0.064

= (0.0503, 0.1783)

We are 99% confident that the true proportion of students who eat cauliflower on Jane's campus is between 5.03% and 17.83%.

In other words, if we were to repeat this study many times, we would expect to obtain a confidence interval that includes the true proportion of students who eat cauliflower on Jane's campus 99% of the time.

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