The circumference of a circle is 15π in. What is the area, in square inches? Express your answer in terms of \piπ.

Answer:

[tex]\sf \tan\left(c_2\right)=\dfrac{OD}{OC}=\dfrac{2\sqrt{66}}{19}[/tex]

Step-by-step explanation:

**Please note that if the segment AO = 3.8 cm then the 50° angle on the given rhombus is incorrect. It should be 49.46° (2 d.p.)**

In a rhombus, all four sides are equal in length.  Therefore:

Diagonals bisect each other at 90°.  Therefore:

Therefore, triangle COD is a right triangle.

To find the tangent ratio of angle c₂, first find the length of OD using Pythagoras Theorem:

[tex]\implies OC^2+OD^2=CD^2[/tex]

[tex]\implies 3.8^2+OD^2=5^2[/tex]

[tex]\implies 14.44+OD^2=25[/tex]

[tex]\implies OD^2=10.56[/tex]

[tex]\implies OD^2=\dfrac{1056}{100}[/tex]

[tex]\implies OD^2=\dfrac{1056 \div 4}{100 \div 4}[/tex]

[tex]\implies OD^2=\dfrac{264}{25}[/tex]

[tex]\implies OD^2=\dfrac{4 \cdot 66}{25}[/tex]

[tex]\implies OD=\sqrt{\dfrac{4 \cdot 66}{25}}[/tex]

[tex]\implies OD=\dfrac{\sqrt{4 \cdot 66}}{\sqrt{25}}[/tex]

[tex]\implies OD=\dfrac{2\sqrt{66}}{5}[/tex]

[tex]\boxed{\begin{minipage}{6 cm}\underline{Tan trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}[/tex]

Given:

Substitute the values into the tan ratio:

[tex]\implies \sf \tan\left(c_2\right)=\dfrac{OD}{OC}[/tex]

[tex]\implies \sf \tan\left(c_2\right)=\dfrac{\frac{2\sqrt{66}}{5}}{3.8}[/tex]

Rewrite 3.8 as 19/5:

[tex]\implies \sf \tan\left(c_2\right)=\dfrac{\frac{2\sqrt{66}}{5}}{\frac{19}{5}}[/tex]

[tex]\implies \sf \tan\left(c_2\right)=\dfrac{2\sqrt{66}}{19}[/tex]

The diagram that shows the C intercept D would be = diagram B. That is option B.

A universal set is defined as the set that contains all the values that makes up a data.

The universal set contains the following:

A = ( yellow corn)

B = ( yellow corn with variety kernel)

C = ( white corn)

D= ( white corn with variety butter and sugar).

The C intercept means the contents that are in C that can be found in D. The diagram that represents this form is diagram B.

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Answer:

-----------------------------------------

Use the coordinates to determine the function.

Point (0, 2):

The function becomes:

It has a multiplier of 0.8, so b = 0.8, so the function is:

Use the first point:

Use the second point:

The function is:

Answer:

[tex]\textsf{a)} \quad y=2(0.8)^x[/tex]

[tex]\text{b)} \quad y=3.5(3)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given:

Substitute the values of a and b into the exponential function formula:

[tex]\implies y=2(0.8)^x[/tex]

The y-intercept is when x = 0.  Therefore, given the function passes through point (0, 3.5), the y-intercept is 0.35 ⇒ a = 3.5.

Substitute the found value of a and given point (2, 31.5) into the exponential function formula and solve for b:

[tex]\implies 31.5=3.5b^2[/tex]

[tex]\implies b^2=9[/tex]

[tex]\implies b=3[/tex]

Substitute the values of a and b into the exponential function formula:

[tex]\implies y=3.5(3)^x[/tex]

The inequality that can be used to find the number of windows is d + r ≤ 235 and 250r + 220d ≥ 55000

An equation is an expression that shows how two or more numbers and variables are related to each other. Types of equations can either be linear, quadratic or cubic

Inequalities are used to show the nonequal comparison of two or more numbers and variables

Let r represent the regular price and let d represent the discounted price.

Gerald company has an inventory of 235 windows, hence:

d + r ≤ 235   (1)

Also, the regular price is $250 and the discounted price is $220. The sales goal is $55000, hence:

250r + 220d ≥ 55000   (2)

The inequality is d + r ≤ 235 and 250r + 220d ≥ 55000

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The numerical length of TU is TU = 26.

What is the numerical length?

The formula states that the base-numerical length of a number is the number of digits in the base-numeral for where is the floor function. An -digit's length is another name for its multiplicative persistence.

Given:

ST=4x-4,   TU=4x-10,   and SU =5x+1

We have to find the numerical length of TU.

Here,

SU = ST + TU

5x + 1 = 4x - 4 + 4x - 10

Simplifying,

5x + 1 = 8x - 14

Subtract 1 on both sides,

5x + 1 - 1 = 8x - 14 - 1

        5x = 8x - 15

Subtract 5x on both sides,

5x - 5x = 8x - 15 - 5x

        0 = 3x - 15

      3x = 15

        x = 5

⇒ TU = 5(5) + 1 = 25 + 1 = 26

Hence, the numerical length of TU is TU = 26.

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Answer: 87

Step-by-step explanation:

The cost per pint of juice $0.63875.

What is division?

Division, or the process by which two or more numbers are joined together to generate a new number, is one of the four basic arithmetic operations. Addition, subtraction, and multiplication make up the remaining operations.

Weight of juice for a classroom party is 5 gallons.

Total price is $25.55.

We know that 1 US liquid pint = 0.125 US liquid Gallon

=> 0.125 US liquid Gallon = 1 US liquid pint

Therefore, 5  US liquid Gallon = 5/0.125 US liquid pint

=> 5  US liquid Gallon = 8*5 US liquid pint

=> 5  US liquid Gallon = 40 US liquid pint

Now, the required price is 25.55/40 = $0.63875

Hence, the cost per pint of juice $0.63875.

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Answer: OC. x = -8 is not in the domain of the function f(x) = √x - 8 because the square root of a negative number is not a real number. Therefore, the only value of x that is in the domain of the function is x ≥ 0.

Step-by-step explanation:

The solution to the system of equations is

The number of ducks D = 8 ducks

The number of cows C = 6 cows

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of ducks be D

Let the number of cows be C

Now , the total number of animals = 14

So , D + C = 14   be equation (1)

And , the total number of legs = 40

Number of legs for ducks = 2 legs

Number of legs for cows = 4 legs

And , the total number of legs = 2D + 4C = 40

So , 2D + 4C = 40   be equation (2)

On simplifying the equations , we get

Multiply equation (1) by 2 , we get

2D + 2C = 28   be equation (3)

Subtracting equation (3) from equation (2) , we get

2C = 40 - 28

2C = 12

Divide by 12 on both sides of the equation , we get

C = 6 cows

Substituting the value of C in equation (1) , we get

D = 14 - 6

D = 8 ducks

Therefore , the value of C and D is 6 and 8 respectively

Hence , the number of cows is 6 and number of ducks is 8

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Answer:

the first box is 3 and the second box is 25

Step-by-step explanation:

Answer: Box 1: 3 Box 2:  25

Step-by-step explanation:

Box 1:

Since the top is divided by 3, you have to do the same to the bottom

9 / 3 = 3

Box 2:

The bottom is multiplied by 1 ⅔, so you do the same to the bottom

1 ⅔ x 15 = 25

Answer:

3rd one is 100.6⁰F I think... not sure

Answer: B

Step-by-step explanation: 100.7 is current. In the past, it was lower so we have to subtract. We know how much we subtract (2.5). In B, if we subtract 2.5 we are taking 2.5 away from his current temp to get yesterday's temp.

Answer:

10

Step-by-step explanation:

180-140=20

20÷2=10

×=10

y=10

there is no question!

The length of the mid-segment of the trapezoid for these problems is given as follows:

28. n + 12 = 17.

29. 2n + 11 = 27.

The length of the mid-segment of a trapezoid is half the sum of the lengths of the bases.

Hence the value of n for item 28 is given as follows:

n + 12 = 1/2(2n - 2 + 4n + 6)

n + 12 = 0.5(6n + 4)

n + 12 = 3n + 2

2n = 10

n = 5.

Hence the length of the mid-segment is of:

n + 12 = 5 + 12 = 17.

The value of n for item 29 is given as follows:

2n + 11 = 1/2(5n - 2 + n + 8)

2n + 11 = 0.5(6n + 6)

2n + 11 = 3n + 3

n = 8.

Hence the length of the mid-segment is of:

2n + 11 = 16 + 11 = 27.

(replacing n = 8 into 2n + 11).

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The perimeter of the triangle having vertices (0,1),(3,6), and (4,1) will be 10.83 units.

Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape.

Any polygon's perimeter is equal to the sum of its side lengths. Considering a triangle

The sum of the three sides equals the perimeter.

Units are always a part of the ultimate response. The final solution should be given in centimeters if the triangle's sides are in that unit.

Because the y values between U and V differ, the distance is equal to the x value difference.

Because the x values of V and W differ, the distance equals the difference between their y values.

The hypotenuse of a right triangle, or U to W, equals sqr (sum of squares on the other two sides)

Perimeter = sum of the 3 sides

[tex]= \sqrt{34} + \sqrt{26}+ \sqrt{16}= 5.83 + 5.1 + 4 = 10.83\:units[/tex]

As the value of 34 is 5.83 squared,  26 is 5.1 squared,  16 is about 4 squared.

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The total distances add up to the triangle's perimeter is 10.00

The triangle's perimeter may be calculated by summing the distances between its three vertices. Use the distance formula to calculate the separation between the points:

d = √((x2 - x1)2 + (y2 - y1)2)

The distances between the points are as a result for the triangle with vertices (0,1), (3,6), and (4,1)

Utilizing the distance formula, determine the separation between (0,1) and (3,6):

d = √((x2 - x1) 2 + (y2 - y1) 2) = √((3-0) 2 + (6-1) 2) = √(32 + 52) = √45

Utilizing the distance formula, determine the separation between (3,6) and (4,1):

d = √((x2 - x1) 2 + (y2 - y1) 2) = √((4-3) 2 + (1-6) 2) = √(12 + 52) = √25

Utilizing the distance formula, determine the separation between (4,1) and (0,1):

d = √((x2 - x1) 2 + (y2 - y1)2) = √((0-4) 2 + (1-1) 2) = √(42 + 02) = √16

The triangle's perimeter is calculated by adding the three distances together:

Perimeter = √45 + √25 + √16 = 10.00.

Hence, the perimeter of the triangle is 10.00, rounded to the closest hundredth.

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Answer:

£202

Step-by-step explanation:

It is import that you read ratios from left to right - the subjects/names and the ratio itself. In this case the "subjects" are Starksy and Hutch. So Starsky = 3, Hutch = 1.

Use cross multiplication:

S(Starksy):H(Hutch)

      3       :      1

     606.  :       ?

(606 * 1) divided by 3 = your answer = 202

Reply if you are unfamiliar with the cross multiplication method

Answer:

202

Step-by-step explanation:

Ratios

Starsky : Hutch

3           :           1

Starsky has 606  so divide 606 by 3

606/3 = 202

Multiply each term by 202

Starsky : Hutch

3*202  :   1*202

Starsky : Hutch

606     :   202

The solution for the system of linear equations is (1,-3)

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: -4x+5y=-19

                     -x-2y=5

Solving for x we get y equal to -3

Thus putting y=-3 in equation 1 we get x=1

Hence, The solution for the system of linear equations is (1,-3)

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It's worth noting that to solve for T2 you need to have the values of other variables such as K1, K2, Ea, R and T1

What is the Arrhenius Equation?

The Arrhenius equation is a mathematical equation that describes the relationship between the rate constant (K) of a chemical reaction and the temperature (T) of the reaction. The equation was first proposed by Svante Arrhenius in 1889 and it states that the rate constant of a chemical reaction is directly proportional to the exponential of the negative activation energy (Ea) of the reaction, divided by the gas constant (R) and the absolute temperature (T). The equation can be written as:

K = A * e^(-Ea / (R*T))

The Arrhenius Equation Two-point form is a mathematical equation that describes the relationship between the rate constant (K) of a chemical reaction, the activation energy (Ea) of the reaction, the universal gas constant (R), and the temperature (T) of the reaction.

Given the equation K2/K1 = Ea / R (1/T1 - 1/T2)

a. To solve for K2, we can multiply both sides of the equation by

K1: K2 = K1 * Ea / R (1/T1 - 1/T2)

b. To solve for K1, we can divide both sides of the equation by

Ea / R (1/T1 - 1/T2): K1 = K2 / Ea / R (1/T1 - 1/T2)

c. To solve for Ea, we can multiply both sides of the equation by

R (1/T1 - 1/T2): Ea = K2/K1 * R (1/T1 - 1/T2)

d. To solve for T2, we can use the equation 1/T2= 1/T1 - Ea/R * K1/K2

It's worth noting that to solve for T2 you need to have the values of other variables such as K1, K2, Ea, R and T1.

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The length of the curve is given by the integral of the magnitude of the velocity vector, which is the derivative of the position vector. Taking the derivative of the position vector, we get the velocity vector as follows:

v(t) = 6i + 24t1/2j + 12tk

The magnitude of this vector is

√(6²+ 24²t + 12²t²)

= √(36 + 576t + 144t²).

To find the length of the curve, we need to integrate this magnitude from t=0 to t=1. This is given by the integral:

L = ∫0² √(36 + 576t + 144t²)dt

This evaluates to L = 18.75. Therefore, the length of the curve is 18.75.

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To solve the equation 6x - 7y = 18 for y, you can start by isolating y on one side of the equation. To do this, you can add 7y to both sides of the equation:

6x - 7y + 7y = 18 + 7y

6x = 18 + 7y

Next, divide both sides of the equation by 7:

6x/7 = 18/7 + 7y/7

x = 3 + y

So the solution is y = 3 - x

This is the final solution for y in the equation 6x - 7y = 18

The rate of change for the interval between –6 and –3 on the x-axis is; 2

To find the rate of change  for the interval between –6 and –3 on the x-axis, the first step is to locate the ordered pairs at those two points. Locating the two ordered pairs from the graph is seen to be (3, -2) and (6, 4).

Applying the slope formula with those two points, we can find the rate of change as;

slope; m = (y₂ - y₁)/(x₂ - x₁)

m = (4 + 2)/(6 - 3)

m = 6/3

m = 2

This value of m represents the rate of change

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Answer:

A (x,y) becomes A'(y,-x)

Step-by-step explanation:

this means we switch x and y to make x a negative

We can see here that the missing proof is option D: ΔBPQ ∼ ΔDRS Reason: SSA.

A proof is a logical argument that demonstrates the truth of a statement or theorem. In mathematics, a proof is a sequence of logical steps that shows that a statement is true by using a combination of logical reasoning, definitions, established facts, and accepted rules of inference.

In other fields, such as computer science, a proof may refer to a demonstration that a program or algorithm is correct or that a system has a certain property.

We see here that the option selected above is actually the missing step in the proof.

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The probability that the student finishes the inquiry in less than 1.5 hours is 0.45.

Mean= 4/3 and standard deviation= √(11/90)

a) To find the probability that the student finishes the inquiry in less than 1.5 hours, we need to find the area under the probability density function (PDF) of f(x) between the lower limit of 1 and the upper limit of 1.5.

This is given by the definite integral of f(x) from 1 to 1.5:

∫f(x)dx from 1 to 1.5

= ∫(2/5(x + 1))dx from 1 to 1.5

= (2/5)∫(x + 1)dx from 1 to 1.5

= (2/5)[x^2/2 + x] from 1 to 1.5

= (2/5)[(1.5)^2/2 + 1.5 - (1)^2/2 - 1]

= (2/5)[2.25/2 + 1.5 - 1/2 - 1]

=(2/5)[2.25/2]

=0.45

b) To find the mean, we need to use the formula:

Mean = ∫x*f(x)dx from a to b

In this case:

Mean = ∫x*(2/5(x + 1))dx from 1 to 2

= (2/5)∫x(x + 1)dx from 1 to 2

= (2/5)[x^3/3 + x^2/2] from 1 to 2

=(2/5)[(2)^3/3 + (2)^2/2 - (1)^3/3 - (1)^2/2]

= (2/5)[8/3 + 4/2 - 1/3 - 1/2]

=(2/5)[7/3 + 3/2]

=(2/5)[(20)/6]

=4/3

=1.333

To find the standard deviation, we need to use the formula:

Standard deviation^2 =(∫(x-μ)^2*f(x)dx) from a to b

Where μ is the mean

In this case,

Standard Deviation ^2= ∫(x-μ)^2(2/5)(x+1) dx from 1 to 2

=(2/5)∫(x-μ)^2(x+1) dx from 1 to 2

Simplifying, we get,

(x-μ)^3*(3x+μ+4)/30 from 1 to 2

=[(2-μ)^3*(6+μ+4)-(1-μ)^3*(3+μ+4)]/30

=[(2-μ)^3*(10+μ)-(1-μ)^3*(7+μ)]/30

Substituting the value of μ,

=[(2-4/3)^3*(10+4/3)-(1-4/3)^3*(7+4/3)]/30

=11/90

Therefore, Standard Deviation= √(11/90)

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Critical F value with 8 numerator and 29 denominator degree of freedom at α = 0.01 is 3.20

The critical F value with 8 numerator degrees of freedom (also known as the numerator degrees of freedom or the numerator df) and 29 denominator degrees of freedom (also known as the denominator degrees of freedom or the denominator df) at a significance level of 0.01 can be found using a table of F-distribution values or by using a calculator or a software that can compute the F-distribution function.

The critical F value with 8 numerator degrees of freedom (df1) and 29 denominator degrees of freedom (df2) at a significance level of 0.01 can be found using the following formula:

F_critical = F(1 - alpha, df1, df2)

where F(1 - alpha, df1, df2) is the inverse of the cumulative distribution function (CDF) of the F-distribution, alpha is the significance level (0.01 in this case), and df1 and df2 are the numerator and denominator degrees of freedom, respectively.

For this case, the critical F value can be found using the inverse cumulative distribution function with 1- alpha = 0.99, df1 = 8 and df2 = 29

F(0.99,8,29) = 3.17

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The  correct option is  the root of auxiliary equation are 0 and6

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Running made Ava’s heart beat faster.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

While playing basketball, Ava’s heartbeat is 80 times in 30 seconds.

And, While running, her heartbeat was 60 times in 20 seconds.

Clearly, Ava's heartbeat is faster when he was running.

So, Running made Ava’s heart beat faster.

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If a quantity increases or decreases as per the increase or decrease in other quantity, the two quantities are said to be in a proportional relationship.

And here, the graph representing the proportional relationship is the one with positive slope (2nd graph)

Answer:

[tex]x > 11[/tex]

Step-by-step explanation:

Greetings!!

Given equation

[tex]x + 2 > 13[/tex]

subtract 2 from both sides

[tex]x + 2 - 2 > 13 - 2[/tex]

simplify

[tex]x > 11[/tex]

[tex]solution \: \: x > 11 \\ interval \: notation \: (11, \infty )[/tex]

Hope it helps!!