Write an equation in standard form of the circle with the given center and radius.

center (1,1) , radius 1.5 .

Answer:

Step-by-step explanation:

Hello! Here are the steps to solve 4x - 8 = 3x + 13

4x - 8 = 3x + 13
    + 8         + 8
____________

4x       = 3x + 21
-3x        -3x
____________
x = 21

There is one solution because there is only one possibility for x.  Let's check the answer.

4(21) - 8 = 3(21) + 13
84 - 8 = 63 + 13
76 = 76

x = 21, x does equal 21 and the answer that there is only one solution is correct.

No solutions would mean that after you solved the equation, you would get something like 9 = 7, 2 = 5, etc. which is not true.  No solutions would mean that you would receive a false equation.

Infinite solutions would mean that after you solved an equation, such as 2x = 2y, you would get x = y.  There are infinite solutions for this because you can substitute infinite numbers in for x and y.  1 = 1, 2 = 2, 3 = 3, 4 = 4, 5 = 5, etc.

The area of the shaded region in the given shapes is determined as 0.544 in².

The area of the shaded region is calculated by subtracting the area of the inscribed hexagon from the area of the circle.

Let's start by finding the side length of the regular hexagon inscribed in the circle.

The distance from the center of the circle to any vertex of the hexagon is equal to the radius of the circle, which is 1 inch.

In a regular hexagon, all sides are equal in length, so each side of the hexagon is also equal to 1 inch.

The area of the regular hexagon can be found using the formula:

Area of a regular hexagon = (3√3/2) x (side length)²

Substituting the side length of 1 inch, we get:

Area of regular hexagon = (3√3/2) x (1 inch)^2

= (3√3/2) square inches

= 2.598 in²

Now, to find the area of the circle, we can use the formula:

Area of a circle = π x (radius)²

Substituting the radius of 1 inch, we get:

Area of circle = π x (1 inch)²

= π square inches

= 3.142 in²

Area of the shaded region = area of circle - area of hexagon

= 3.142 in² - 2.598 in²

= 0.544 in²

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Answer:

x=4, y=5

Step-by-step explanation:

System of Equations

Given triangles ABC and DEC are congruent, then:

3y + 1 = 4x

4y - 6 = 2x + 6

We need to solve the system of equations above.

Rearranging both equations:

-4x + 3y = -1       [1]

-2x + 4y = 12      [2]

Multiplying [2] by -2:

4x - 8y = -24      [3]

Adding [1] and [3]:

-5y = -25

Dividing by -5:

y = 5

Substituting in [1]:

-4x + 3(5) = -1

-4x + 15 = -1

Subtracting 15:

-4x = -16

Dividing by -4:

x = 4.

Solution: x=4, y=5

A symmetrical distribution of exam scores in a college course indicates that the student's scores are evenly distributed across the entire range of scores. This suggests that about an equal number of students had relatively high and relatively low scores.

Correct answer will be b) About an equal number of students had relatively high and relatively low scores.

And that there is no single group that overwhelmingly outperformed or underperformed the others. Furthermore, it indicates that there were a substantial number of students who achieved high scores, as well as a substantial number who achieved low scores.

This type of even distribution of scores is often seen when students are equally prepared, and when the exam is designed to be neither too difficult nor too simple.

In conclusion, a symmetrical distribution of exam scores suggests that the students were similarly prepared and that the exam was appropriately challenging.

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Zeros of P(x) = x^4 + 4x^2: The zeros of this polynomial are x = 0 and x = ±2i, where i is the imaginary unit.

Zeros of P(x) = x^3 - 2x^2 + 2x: The zero of this polynomial is x = 0.

Zeros of P(x) = x^4 + 2x^2 + 1: The zeros of this polynomial are x = ±i, where i is the imaginary unit.

Factorization:

Factorization of P(x) = x^4 + 4x^2: We can factor this polynomial as P(x) = x^2(x^2 + 4). The factorization is now complete.

Factorization of P(x) = x^3 - 2x^2 + 2x: This polynomial does not factor further as a product of linear factors.

Factorization of P(x) = x^4 + 2x^2 + 1: We can factor this polynomial as P(x) = (x^2 + 1)^2. The factorization is now complete.

For P(x) = x^4 + 4x^2, we can solve for the zeros by setting the polynomial equal to zero and factoring: x^4 + 4x^2 = 0. Taking out the common factor of x^2, we get x^2(x^2 + 4) = 0. Setting each factor equal to zero gives us x^2 = 0 and x^2 + 4 = 0. Solving these equations, we find x = 0 and x = ±2i, respectively.

For P(x) = x^3 - 2x^2 + 2x, we set the polynomial equal to zero and attempt to factor: x^3 - 2x^2 + 2x = 0. However, this polynomial does not have any rational zeros or factors, so x = 0 is the only real zero.

For P(x) = x^4 + 2x^2 + 1, we can factor it using the identity for the sum of squares: a^2 + 2ab + b^2 = (a + b)^2. Applying this to our polynomial, we rewrite it as (x^2 + 1)^2 = 0. Taking the square root of both sides, we find x^2 + 1 = 0, which leads to x = ±i.

For the polynomial P(x) = x^4 + 4x^2, the zeros are x = 0 and x = ±2i. The factorization of P(x) is x^2(x^2 + 4).

For the polynomial P(x) = x^3 - 2x^2 + 2x, the only zero is x = 0. It does not factor further.

For the polynomial P(x) = x^4 + 2x^2 + 1, the zeros are x = ±i. The factorization of P(x) is (x^2 + 1)^2.

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Therefore, the directional derivative of \(f(x, y) = x^3y - y^2\) at the point (1, 2) in the direction of θ = 5π/6 is -3(√3 + 1/2).

To find the directional derivative of the function \(f(x, y) = x^3y - y^2\) at the point (1, 2) in the direction of θ = 5π/6, we first need to find the unit vector corresponding to the θ direction.

The unit vector u in the direction of θ is given by:

u = (cos(θ), sin(θ)) = (cos(5π/6), sin(5π/6))

Evaluate the values:

u = (-√3/2, -1/2)

Now, we can calculate the directional derivative D_uf(x, y) using the gradient operator ∇f(x, y) and the unit vector u:

D_uf(x, y) = ∇f(x, y) ⋅ u

Calculate the partial derivatives of f(x, y):

∂f/∂x\(= 3x^2y\)

∂f/∂y\(= x^3 - 2y\)

Evaluate the gradient at the point (1, 2):

∇f(1, 2) = (∂f/∂x(1, 2), ∂f/∂y(1, 2))

\(= (3(1)^2(2), (1)^3 - 2(2))\)

= (6, -3)

Now, calculate the directional derivative:

D_uf(1, 2) = ∇f(1, 2) ⋅ u

= (6, -3) ⋅ (-√3/2, -1/2)

= 6(-√3/2) + (-3)(-1/2)

= -3√3 - 3/2

= -3(√3 + 1/2)

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Answer:

No, I do not think the sample is biased.

Step-by-step explanation:

Well, Theo is surveying people randomly, he has no way of knowing who'll be the fourth person.

Answer:67%

Step-by-step explanation:

Answer: 157 in2

Step-by-step explanation:

The formula for the surface area of a cylinder is given by 2πr(r+h), where r is the radius of the base and h is the height of the cylinder. From the given net of the cylinder, we can see that the radius of the base is 5 inches and the height of the cylinder is 4 inches.

Substituting these values into the formula, we get:

Surface area = 2 x 3.14 x 5 x (5 + 4)

Surface area = 157 in2

Therefore, the surface area of the cylinder is 157 in2.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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The given number 1,000,000 can be written in words as

Ten Lakhs only.

Given, a number 1,000,000

we have to write the given number in words.

now to write any number in words, we have to know the place value of the digits of the given number

As, the place value of the digit 1 is tenth lakh and remaining digits in the number are all zeros.

So, the number 1,000,000 can be written in words as

Ten Lakhs only.

Hence, the given number 1,000,000 can be written in words as

Ten Lakhs only.

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Answer:

Step-by-step explanation:

\( \frac{26}{25} \times ( - \frac{16}{63} )\)

Multiplying a positive and a negative equals a negative\(( + ) \times ( - ) = ( - )\)

\( = - \frac{26}{25} \times \frac{16}{63} \)

Multiply the fractions:

\( = - \frac{416}{1575} \)

Hope this helps..

Best regards!!

Answer:

D. 29

Step-by-step explanation:

just did the test and got it correct. Edmentum, Plato.

Answer:

Step-by-step explanation:

he should put $81 into savings because 30% of 270 is 81.

Answer:=-3

Step-by-step explanation: trust the processe

-3x-3<6

   +3 l+3

  -3x  > 9

  -3x  -3x

  x=-3

The appropriate hypotheses for testing whether the average level of radon gas is greater than the safe level of 4pCi/L are:

H0: μ ≤ 4.0 (null hypothesis)
HA: μ > 4.0 (alternative hypothesis)

So, the answer is (a).

The null hypothesis (H0) is the default assumption that there is no significant difference or effect between two groups or variables. In this case, the null hypothesis is that the average concentration of radon gas in the classroom is less than or equal to the safe level of 4pCi/L.

The alternative hypothesis (HA) is the opposite of the null hypothesis, and it represents the possibility of a significant difference or effect. In this case, the alternative hypothesis is that the average concentration of radon gas in the classroom is greater than the safe level of 4pCi/L.

Therefore, we want to test whether the data provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

To perform this test, we can use a one-sample t-test, where we compare the sample mean (4.4pCi/L) to the hypothesized population mean (4pCi/L) while taking into account the sample standard deviation (1pCi/L) and the sample size (36).

If the calculated t-statistic is greater than the critical value from the t-distribution with 35 degrees of freedom (df = n-1), we can reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the average concentration of radon gas in the classroom is greater than the safe level of 4pCi/L.

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\(\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=\cfrac{ns^2}{4}\cot\left( \frac{180}{n} \right) ~~ \begin{cases} n=\stackrel{sides'}{number}\\ s=\stackrel{side's}{length}\\[-0.5em] \hrulefill\\ n=9\\ s=4 \end{cases}\implies A=\cfrac{(9)(4)^2}{4}\cot\left( \frac{180}{9} \right) \\\\\\ A=36\cot(20^o)\implies A\approx 98.91~m^2\)

Make sure your calculator is in Degree mode.

Step-by-step explanation:

Area = 1/2 apothem × perimeter

Area = 1/2 apothem × perimeter A= 1/2 r cos(20) × N × S

Area = 1/2 apothem × perimeter A= 1/2 r cos(20) × N × S we need to find radius so

Area = 1/2 apothem × perimeter A= 1/2 r cos(20) × N × S we need to find radius so s = 2rsin(180/90)

Area = 1/2 apothem × perimeter A= 1/2 r cos(20) × N × S we need to find radius so s = 2rsin(180/90)4 = r ( 2 sin(20) )

Area = 1/2 apothem × perimeter A= 1/2 r cos(20) × N × S we need to find radius so s = 2rsin(180/90)4 = r ( 2 sin(20) )r = 4/ ( 2 sin(20)

Area = 1/2 apothem × perimeter A= 1/2 r cos(20) × N × S we need to find radius so s = 2rsin(180/90)4 = r ( 2 sin(20) )r = 4/ ( 2 sin(20)r = 5.847 approximate to 6

when we go back

A = 1/2( 6 × cos(180/n) )×9×4

A = 1/2( 6 × cos(180/n) )×9×4A = 1/2( 6 × cos(180/9) )×9×4

A = 1/2( 6 × cos(180/n) )×9×4A = 1/2( 6 × cos(180/9) )×9×4A = 101.486m2 app|ozximate to 102 m2

Using equations the answers to both subparts are shown:

(A) The equation: (500x + 5600)/x = C

(B) Cost per person (C) = $1,060

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2.

When two or more components must be taken into account collectively in order to comprehend or describe the overall situation, this is known as an equation.

So, (A) the equation would be:

C is the cost per person and x is the number of people.

(500x + 5600)/x = C

(B) Cost per person if 10 people are traveling.

x = 10

(500x + 5600)/x = C

(500*10 + 5600)/10 = C

(5000 + 5600)/10 = C

10600/10 = C

$1,060 = C

Therefore, using equations the answers to both subparts are shown:

(A) The equation: (500x + 5600)/x = C

(B) Cost per person (C) = $1,060

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When designing a 3x3 factorial study design with a within-subjects design and when 10 participants are assigned for each cell, the number of participants we require in total is 10.

Therefore, the answer is 10.

In a n×m factorial study design, the number of factors is the number of numbers, that is here 2 and the first factor is of n levels and second factor is of m levels.

So in 3x3 factorial study we have two factors each with 3 levels and the number of groups is 3 × 3 = 9.

In a within-subject design, all the participants take part in every group. So if there are 10 participants in a cell, these 10 participants are part of all groups. So we require only 10 participants in total for this study.

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Answer:

Erosion

Step-by-step explanation:

Erosion is the movement of sediment from one place to another. Erosion is the mechanical process of wearing or grinding somethin down. It condition in which the earth’s surface is worn away by the action of water and wind.

Therefore, the answer is erosion.

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Answer:

3 miles

Step-by-step explanation:

to find the amount of miles it is to the library you have to find how many miles it is when the minutes are zero

so when x = 0 what is y

0 + 7y = 21

7y = 21

y is 3

so that means the library is 3 miles away from his house

Step-by-step explanation:

Let the number be x

The number is multiplied by 4

That's

4 × x = 4x

One is added to it

= 4x + 1

The whole result is squared

That's

Hope this helps you

Answer:

\(\huge \boxed{(4x+1)^2 }\)

Step-by-step explanation:

\(\sf Let \ the \ number \ be \ x.\)

\(\sf x \ is \ multiplied \ by \ 4.\)

\(x \times 4\)

\(\sf 1 \ is \ added.\)

\(4x+1\)

\(\sf The \ result \ is \ squared.\)

\((4x+1)^2\)

Answer:

3 rows of  3  then 2 roes of 2

Step-by-step explanation:

Answer:

it is (0,0)

Step-by-step explanation:

hope it helps

The total area of the surface of the pool is 32x + 256

The area of a shape is defined as the amount of space the shape occupies

The pools have the shape of a rectangle, and their dimensions are given as:

The areas of both pools is calculated as:

\(A_1 = (8 + x) \times 25\)

\(A_2 = 7 \times (8 + x) \)

The total area of the surface of the pool is then calculated as:

\(A =A_1 + A_2\)

So, we have:

\(A = (8 + x) \times 25 + 7 \times (8 + x)\)

Expand

\(A = 200+ 25x + 56 + 7x\\ \)

Collect like terms

\(A = 25x + 7x+200 + 56\)

\(A = 32x+256\)

Hence, the total area of the surface of the pool is 32x + 256

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Answer:

Step-by-step explanation:

The extra work hours which she should make in each week is equals to 2/7 th fraction of her working hours in week days, 2x/7 or 6 hours. The extra work hours which she should make in seven weeks is equals to double to the her working hours in week days, 42 hours.

We have Amy has a chance to work some extra hours on the weekends.

Number of extra hours she will work at each week = 6 hours

number of weeks she have for doing extra hours work at weekends = 7 weeks

Let amy works 'x hours' in each week. So, her working rate is x/7 hours/day. As we know very well that weekend consists two days ( Saturday and Sunday). So, she will make extra work each week = extra work in weekend ( 2 days)

The extra work that she will do in weekend or each week= 2(x/7) = 2x/7 hours = 6 hours

Now, The extra work hours that she make in seven weeks = Multiplication of 7 by the extra work hours that she make in each week

= 7(6) hours = 42 hours

Hence, required value of hours is 42 ( that is double of her working hours in week days).

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The sum of the diagonals of a rectangle = 223.6 cm if the area of the rectangle is 5000 cm².

Area can be defined as the quantum of material of a given consistence needed to make a model of the shape, or the quantum of makeup needed to cover the face with a single fleece. It's the two- dimensional fellow of the length of a wind or the volume of a solid.

Given,

Area of a cube = 5000 square cm

Also given that length is two times of the range also,

l = 2w

Area = l × w

5000 = 2w × w

2w ² = 5000

w ² = 2500

w = 50

also, l = 100

thus, l = 100 cm, w = 50 cm

Sum of the inclinations of a cube = √ l ² w ²

= √ 100 ² 50 ²

√ 10000 2500

= √ 12500

= 111.8 cm

In a cube, we've two inclinations

So, The sum of the inclinations of a cube = 111.8111.8 = 223.6 cm

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Answer:

Auto repair labor rates vary widely across the country, and even within the same city. As of January 17, 2017, auto repair shops in the AAA Approved Auto Repair network charged between $47 and $215 per hour, based primarily on the shop's cost of doing business.