HELPPPPPPP plz will mark brainliest and 25 pts
Write the standard form of the equation for the circle that passes through the points (2, 31), (–15, 14), (33, 0). Then identify the center and radius.

Question 4 options:

a. (x – 6)2 + (y – 5)2 = 625; center (6, 5), r = 25
b. (x – 9)2 + (y – 7)2 = 625; center (7, 10), r = 5
c. (x+ 7)2 + (y + 10)2 = 25; center (9, 7), r = 25
d. (x + 7)2 + (y + 10)2 = 25; center (7, 10), r = 5

Answer:

-5

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Answer:

339.3 cm. squared

Step-by-step explanation:

The expressions are given as;

1. The factored form of g(x) is g(x) = 1/(x-6)

2. The LCD of g(x) and h(x) is (x-6)(x+8)

3. The LCD of h() and p(x) is (x-6)(8x + 32)

Functions are simply defined as laws, equations or rules showing the relationship between two variables.

These variables are termed;

From the information given, we have that;

g(x) = (x + 8)/x² + 2x - 48

Factorize the denominator of the function;

x²+ 8x - 6x - 48

group in pairs

x(x + 8) - 6(x + 8)

Then,

g(x) = x + 8/(x-6)(x+ 8)

g(x) = 1/(x-6)

The lowest common denominator of the functions g(x) and h(x) is;

g(x) = x + 8/(x-6)(x+ 8)

h(x) = 6x - 36/x-6

LCD = (x-6)(x+8)

The LCD of h(x) and p(x) is given as;

p(x) = x² - x - 20/8x + 32

= (x-6)(8x + 32)

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Answer:

35 as a fraction is 7/20

Step-by-step explanation:

Answer:

11/35

Step-by-step explanation:

14.59 in the equation represents the predicted bfi when triceps is 0 mm. This is also known as the bfi intercept.Therefore, both the answers are correct so, the correct option is option  is c) All of the above.

A regression line is an estimate of the line that describes the true, but unknown, linear relationship between the two variables.

In a regression line, the equation is typically written in the form y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

In this case, bfi is the dependent variable and triceps is the independent variable. The slope of the line is 0.74, and the y-intercept is 14.59.

Therefore, 14.59 represents the predicted bfi when triceps is 0 mm, or the point at which the regression line crosses the y-axis. This is also known as the bfi intercept.

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a) The forecasted number of disk drives to be made next year is 210.

b) The mean squared error (MSE) when using linear regression is 160.

c) The mean absolute percent error (MAPE) when using linear regression is approximately 7.51%.

Let's calculate the linear regression line using the given data points. We will use the least squares method to find the equation of the line:

Year (x)     Disk Drives (y)

1                   140

2                 160

3                 190

4                 200

5                210

Now calculate the means of x and y:

X = (1 + 2 + 3 + 4 + 5) / 5 = 3

Y= (140 + 160 + 190 + 200 + 210) / 5 = 180

The deviations from the means (dx and dy):

dx = (1 - 3, 2 - 3, 3 - 3, 4 - 3, 5 - 3) = (-2, -1, 0, 1, 2)

dy = (140 - 180, 160 - 180, 190 - 180, 200 - 180, 210 - 180)

= (-40, -20, 10, 20, 30)

The sums of squares (Sxx and Sxy):

Sxx = Σ(dx²) = (-2)² + (-1)² + 0² + 1² + 2² = 10

Sxy = Σ(dx × dy) = (-2× -40) + (-1 × -20) + (0 × 10) + (1 × 20) + (2× 30)

= 100

Now find the slope (b):

b = Sxy / Sxx = 100 / 10 = 10

Find the intercept (a):

a = Y - (b × X) = 180 - (10 × 3)

= 180 - 30

= 150

Now we have the equation of the regression line:

y = a + bx

y = 150 + 10x

To forecast the number of disk drives to be made next year (year 6), we substitute x = 6 into the equation:

y = 150 + 10×6

y = 150 + 60

y = 210

Therefore, the forecasted number of disk drives to be made next year is 210.

b) To compute the mean squared error (MSE) when using linear regression.

we need to calculate the residuals (differences between the actual and predicted values) for each data point, square them, and find the average.

Let Year (x), Disk Drives (y), Predicted (Y), Residual (d = y - Y), Residual Squared (d²)

X        y         Y          d            d²

1       140      160        -20      400

2      160      170        -10        100

3       190     180         10         100

4       200    190         10         100

5        210    200        10         100

MSE = Σ(d²) / n

= (400 + 100 + 100 + 100 + 100) / 5

= 800 / 5

= 160

(c)To compute the mean absolute percent error (MAPE), we need to calculate the absolute percent error for each data point, find the average, and express it as a percentage.

Year  Disk Drives  Predicted  Absolute Error  Percent Error

1              140               160             20                     14.29%

2             160               170             10                       6.25%

3             190               180             10                       5.26%

4             200              190             10                       5.00%

5             210              200             10                        4.76%

MAPE = Σ(|d| / y × 100) / n

= (14.29% + 6.25% + 5.26% + 5.00% + 4.76%) / 5

= 7.51%

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Answer: 130

Step-by-step explanation:

Answer:

  A, B, C, E, F

Step-by-step explanation:

Integers are numbers that can be written in decimal without a fractional part. 7 is an integer. (A)

Real numbers are numbers that do not have an imaginary part. 7 is a real number. (B)

Natural numbers are the numbers we count with. They are positive numbers. 7 is a natural number. (C)

Irrational numbers are numbers that cannot be expressed as the ratio of two integers. Written in decimal, they have an infinite-length, non-repeating decimal fraction. 7 is not irrational.

Rational numbers are numbers that can be expressed as the ratio of two integers. 7 = 7/1 is a rational number. (E)

Whole numbers are non-negative integers. They are all the natural numbers together with zero. 7 is a whole number. (F)

Answer:

C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

i have the same question

When measuring wind speed with a cup anemometer on a sailboat trip across the Atlantic Ocean, there are a few situations that may arise, as shown below:1. When the bearing of the axle is old, the type of error that occurs is systematic error. To reduce or overcome this error, you would need to replace the bearing to avoid it.

2. When there is turbulent flow, the type of error that occurs is random error. To overcome this error, you would have to wait for the wind to stabilize or take an average of many measurements.  3. When there is icing on the cups, the type of error that occurs is also random error.

To overcome this error, you would need to remove the ice or wait for it to melt before continuing the measurement.4. When there is strong tumbling of the sailboat, the type of error that occurs is systematic error. To overcome this error, you would need to find a way to stabilize the boat or take measurements when the boat is less unstable.

It is not well posed to use a cup anemometer to measure in-cabin air flow in a quiet environment because the device is not sensitive enough. The device needs a minimum wind speed to provide accurate readings, and it is not designed to measure low wind speeds. Therefore, it may not be the right tool for the job, and a different instrument may be more appropriate.

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The power series solution of the differential equation about x0 = 1 has a radius of convergence of 1.

To find the minimum radius of convergence R of power series solutions about the ordinary point x0 = 1 for the given differential equation, we need to use the Cauchy-Hadamard formula. The formula states that the radius of convergence R is given by:

R = 1/lim sup(|an|)^(1/n)

where an is the nth coefficient of the power series solution.

First, we need to find the power series solution of the differential equation about x0 = 1. We can assume that the solution is in the form of a power series:

y(x) = ∑ an (x-1)^n

We can differentiate this power series to find the derivatives needed to substitute into the differential equation. After substituting and simplifying, we get:

∑ (n+2)(n+1)an (x-1)^n + ∑ (n+1)an (x-1)^n + 4∑ an (x-1)^n = 0

Next, we need to find the coefficients an. We can do this by equating the coefficients of each power of (x-1) to zero. The first few coefficients are:

a0 = y(1)

a1 = y'(1)

a2 = y''(1)/2!

Substituting these coefficients into the formula for R, we get:

R = 1/lim sup(|(n+2)(n+1)/2!|^(1/n) + |(n+1)/1!|^(1/n) + |4/0!|^(1/n))

Taking the limit as n approaches infinity, we get:

lim sup(|(n+2)(n+1)/2!|^(1/n) + |(n+1)/1!|^(1/n) + |4/0!|^(1/n)) = 1

Therefore, the minimum radius of convergence R is:

R = 1/1 = 1

So the power series solution of the differential equation about x0 = 1 has a radius of convergence of 1.

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The length and width of the plot that will maximize the area is 60 meters by 120 meters. The largest area that can be enclosed is 7200 square meters.

To maximize the area of the rectangular plot, Farmer Ed must use 9000 meters of fencing to enclose three sides of the plot. The fourth side, which borders the river, does not need to be fenced. To find the length and width of the plot that will maximize the area, the 9000 meters of fencing must be divided into two sides of equal length, with the remaining fencing used for the third side. This results in a length of 120 meters and a width of 60 meters, which maximizes the area of the plot. The largest area that can be enclosed is 7200 square meters.

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The Frequency will be "266.14 Hz" and the number of loops are "60".

For the given question-

The formula for the linear velocity is given as;

Linear density; μ = mass/length

Put the values,

μ = 4.5 x 10⁻³/0.6

μ = 7.5 x 10⁻³ kg/m

The formula for the fundamental frequency is;

F = (1/2L)√(T/ μ)      

F = (1/2x0.6)√(765/ 7.5 x 10⁻³)      

F = 266.14 hz

The number of loops  is;

n = f'/f

n = 16000/266.14

n = 60

Thus, a person who can hear frequencies up to f = 16 kHz would be able to hear the highest harmonic with number n equal to 60.

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The complete question is-

A piano tuner stretches a steel piano wire with a tension of 765 N . The steel wire has a length of 0.600 m and a mass of 4.50g .

What is the frequency (f_1) of the string's fundamental mode of vibration?

What is the number n of the highest harmonic that could be heard by a person who is capable of hearing frequencies up to f = 16 kHzc?

Answer:

12 miles

Step-by-step explanation:

Total miles = Length of trail ×

Number of times she rode

Total miles = 3 miles × 4 times

Total miles = 12 miles

Mika traveled a total of 12 miles.

Answer:

$2.46

Step-by-step explanation:

7.38/3 = 2.46

2.46 x 3 = 7.38

To find the length of the segment between the given points, we can use the distance formula. The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:
\[d = \sqrt{{(x_2 - x_1)^2 + (y_2 - y_1)^2}}\]

Let's apply this formula to the given points: $(2a, a-4)$ and $(4, -1)$.

The distance between these two points is $2\sqrt{10}$ units. So we have:
\[2\sqrt{10} = \sqrt{{(4 - 2a)^2 + (-1 - (a-4))^2}}\]

Simplifying the equation, we get:
\[4\sqrt{10} = \sqrt{{(4 - 2a)^2 + (-5 - a)^2}}\]

Squaring both sides of the equation, we have:
\[160 = (4 - 2a)^2 + (-5 - a)^2\]

Expanding the equation, we get:
\[160 = 16 - 16a + 4a^2 + 25 + 10a + a^2\]

Combining like terms, we have:
\[0 = 5a^2 - 6a + 1\]

Now, we can solve this quadratic equation for the possible values of $a$.

Factoring the equation, we have:
\[0 = (5a - 1)(a - 1)\]

Setting each factor equal to zero and solving for $a$, we get:

\[5a - 1 = 0 \quad \Rightarrow \quad a = \frac{1}{5}\]
\[a - 1 = 0 \quad \Rightarrow \quad a = 1\]

Therefore, the possible values for $a$ are $\frac{1}{5}$ and $1$. The product of these values is:
\[\left(\frac{1}{5}\right) \cdot 1 = \frac{1}{5}\]

So, the product of all possible values for $a$ is $\frac{1}{5}$.

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The Vieth-Müller Circle is an imaginary circle that passes between both retinae and the fixation point.

The Vieth-Müller Circle is an ophthalmology concept that depicts an imaginary circle that passes across the foveas (the primary points of the retinae that are responsible for acute, detailed vision) and the fixation point (the point at which the eyes are directed).

The Vieth-Müller Circle is significant because it helps to explain the phenomenon of binocular vision, which is the ability to perceive depth and three-dimensional space using both eyes together. The circle aids in the definition of the equivalent locations on the two retinae, which are sites that receive visual field information and are critical in combining the images from the two eyes into a single, three-dimensional perception.

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The imaginary circle that passes through both retinae and the fixation point is called the horopter. The horopter is important in visual perception as it represents the set of points in space that stimulate corresponding points on each retina, which is necessary for binocular vision and depth perception.

The Horopter is an imaginary circle that passes through both retinae and the fixation point. In this context:

1. "Imaginary" refers to the fact that the Horopter is a theoretical concept rather than a physical object.
2. "Retinae" are the light-sensitive layers at the back of both eyes, which play a crucial role in processing visual information.
3. "Fixation" is the point where both eyes are focused on a single object in the visual field.

In brief, the Horopter represents a collection of points in the 3D space that are perceived as having the same depth or distance as the fixation point. It helps in understanding binocular vision and depth perception, as points on the Horopter contribute to forming a single, fused image from both eyes.

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Answer:

6/5

Step-by-step explanation:

Answer:

1) x = 22.5

Step-by-step explanation:

4/9 = 10/x

4 × x = 10 × 9

4x = 90

4x/4 = 90/4

x = 22.5

Answer:

2) 2.4

Step-by-step explanation:

5/2 = 6/x

5 × x = 6 × 2

5x = 12

5x/5 = 12/5

x = 2.4

Answer:

3) x = 0.8

Step-by-step explanation:

5/2 = 2/x

5 × x = 2 × 2

5x = 4

5x/5 = 4/5

x = 0.8

hope it helps!! (I'll add other answers too)

tell me if any of my answers are wrong

Answer:

\(y = 17\).

Step-by-step explanation:

In general, the equation of a line in a cartesian plane may be written as \(y = m\, x + b\), where \(m\) and \(b\) are constants: \(m\!\) is the slope of this line, and \(b\!\) is the \(y\)-intercept of this line.

A point \((x_{0},\, y_{0})\) is on a given line if and only \(x := x_{0}\) and \(y := y_{0}\) (setting \(x\) to \(x_{0}\) and \(y\) to \(y_{0}\)) would satisfy the equation of that line.

That is: \(y_{0} = m\, x_{0} + b\).

A line in a cartesian plane is horizontal if and only if its slope is \(0\). That is: \(m = 0\). The equation of this line would be in the form \(y = b\) for some constant \(b\).

The point \((-5,\, 17)\) is on the line in this question. Thus, \(x := -5\) and \(y := 17\) should satisfy the equation of this line. That is: \(17 = b\).

Hence, the value of the constant \(b\) would be \(17\) for this particular line. The equation of the line would be \(y = 17\).

Answer:

x=-5

Step-by-step explanation:

trust me i do rsm its correct

The p-value for testing H0 (null hypothesis) versus Ha (alternative hypothesis) is 0.0038. We need to determine whether H0 would be rejected at different significance levels: α = 0.10, α = 0.05, α = 0.01, and α = 0.001.

To make the decision, we compare the p-value with the chosen significance level. If the p-value is less than or equal to the significance level, we reject H0. Otherwise, we fail to reject H0.

At α = 0.10: Since the p-value (0.0038) is less than 0.10, we reject H0.

At α = 0.05: Since the p-value (0.0038) is less than 0.05, we reject H0.

At α = 0.01: Since the p-value (0.0038) is greater than 0.01, we fail to reject H0.

At α = 0.001: Since the p-value (0.0038) is greater than 0.001, we fail to reject H0.

In summary:

H0 would be rejected at α = 0.10 and α = 0.05.

H0 would not be rejected at α = 0.01 and α = 0.001.

Please note that the decision to reject or fail to reject the null hypothesis depends on the chosen significance level, and different levels of significance can lead to different conclusions.

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By applying the exponent rule of division, the equivalent expression to  \(r^m \div r^n\) is: A. \(r^{m - n}\).

Given the expression, \(r^m \div r^n\), we can find the expression that is equivalent to it by rewriting the expression as shown below:

r^m ÷ r^n

According to the exponent rule of division, if we are to divide two bases together that have the same same base but different exponents, what we only need to do is to subtract their powers.

We would apply this same rule in this given problem.

Applying the exponents rule of division, we would subtract the powers:

r^m ÷ r^n = r^(m - n)

Therefore, by applying the exponent rule of division, the equivalent expression to  \(r^m \div r^n\) is: A. \(r^{m - n}\).

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Answer:

Step-by-step explanation:

x + 12 = y

x = y - 12

Answer:

98

Step-by-step explanation:

7x+4 = 88 because they are vertical angles and vertical angles are equal

7x = 88-4

7x = 84

Divide by 7

7x/7 = 84/7

x = 12

<1 and 7x-2 are supplementary angles since they form a line

<1 + 7x-2 = 180

<1 + 7(12) -2 = 180

<1 +84-2 =180

<1 +82 = 180

<1 = 180-82

<1 = 98

Answer-

98

step by step explanation -

7x+4=88

7x=84

x=12

7x-12=7*(12)-2=82

angle 1=180-82 =

She needs to deposit of amount  $92,421.48 today to do this.

We need to find out the present value of $1,000 per month for the next 10 years by considering the interest rate and compounding period given. We are given,Anita wants to withdraw $1,000 per month for the next 10 years.The bank pays interest at 6% compounded monthly.We can calculate the present value of $1,000 per month for the next 10 years by using the formula for Present Value of Annuity. The formula for Present Value of Annuity is given by:PVA= A((1- (1+r)^-n)/r), wherePVA = Present Value of AnnuityA = Amountn = Number of Periodsr = Interest Rate per PeriodFirst, we calculate the interest rate per period as follows:r = 6% per annum/ 12 monthsr = 0.5% per monthNumber of periods (n) = 10 years x 12 months per year = 120 months Amount of Annuity (A) = $1,000Using the above values, we can calculate the present value of the annuity as follows:PVA = 1000 * ((1- (1+0.5%)^-120)/(0.5%))PVA = $92,421.48Therefore, she needs to deposit $92,421.48 today to do this. Therefore, the correct option is $92,421.48.

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the volume of Prism N is 7/9733 of the volume of Prism M, or approximately 0.000719 in decimal form. Rounded to the nearest hundredth, the answer is 0.01, or 1/100.

Since Prism M is a dilation of Prism N, the ratio of their heights is equal to the ratio of their volumes.

Let x be the height of Prism N. Then,

x/2 = V(N)/V(M)

Substituting the given values, we get:

x/2 = V(N)/683

Multiplying both sides by 683 and simplifying, we get:

V(N) = (683/2) * x

To find the volume of Prism N, we need to find the value of x.

We can use the fact that the ratio of the volumes of similar figures is equal to the cube of the ratio of their corresponding side lengths.

Since Prism M is a dilation of Prism N, their corresponding side lengths are proportional. Let k be the proportionality constant. Then:

height of Prism M / height of Prism N = k

43 / 2 = k

k = 21.5

Therefore, the ratio of the volumes of Prism M to Prism N is:

(k)^3 = (21.5)^3 = 9733.375

So we have:

V(N) / 683 = 1 / 9733.375

Multiplying both sides by 683 and simplifying, we get:

V(N) = 683/9733.375

Expressing this as a mixed number in simplest form, we get:

V(N) = 0 7/9733

Therefore, the volume of Prism N is 7/9733 of the volume of Prism M, or approximately 0.000719 in decimal form. Rounded to the nearest hundredth, the answer is 0.01, or 1/100.

So the answer is 100.

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Answer:

$12,000

Step-by-step explanation:

Kabore wants to make $700 this week. We can subtract 100 from that amount because his base pay is $100.

700 - 100 = 600

This leaves us with 600. Kabore has to make $600 from his sales. However, he only gets paid 5% of his sales. So, 600 is worth 5% of his sales. This can be represented in an equation, where x represents his sales and 0.05 is 5% in decimal form:

\(\frac{600}{x}\) = 0.05

Multiply both sides of the equation by x to isolate it on one side:

600 = 0.05x

Divide both sides by 0.05 to find the value of x:

12000 = x

Kabore needs to sell $12,000 worth of product if he wants to make $700 this week.

Hope this helps :)

Using it's formula, the distance between these two points is given by:

\(\sqrt{97}\).

Suppose that we have two points, \((x_1,y_1)\) and \((x_2,y_2)\). The distance between them is given by:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

For this problem, the points are:

(2,4) and (6,-5).

Hence the distance is given by:

\(D = \sqrt{(6 - 2)^2+(-5 - 4)^2} = \sqrt{97}\)

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