In the figure below, the segments AB and AC are tangent to the circle centered at O. Given that AC=9 and OA= 10.6, find OB.

Step-by-step explanation:

Find Object Volume Rotation

Suppose That \( R \) Is The Finite Region Bounded By \( Y=X, Y=X+1, X=0 \), And \( X=3 \). find the exact value of the volume of the object we obtain when rotating about the -axis.

The region R is a triangular region defined by the lines y = x, y = x + 1, x = 0, and x = 3. To find the volume of the object obtained by rotating this region about the x-axis, we can use the method of cylindrical shells.

The height of the cylindrical shell is given by the difference between y = x and y = x + 1, or 1 unit. The radius of the cylindrical shell is given by x. Therefore, the volume of the object is given by:

\begin{align*}

V &= \int_{x=0}^{x=3} \pi x^2 \cdot 1, dx \

&= \pi \int_{x=0}^{x=3} x^2, dx \

&= \pi \left[ \frac{x^3}{3} \right]_{x=0}^{x=3} \

&= \pi \left( \frac{27}{3} - \frac{0}{3} \right) \

&= 9\pi

\end{align*}

So the volume of the object is equal to 9π cubic units.

Answer:

Magnitude of force is [tex]||v||\approx16.12\text{ lbs}[/tex]

Step-by-step explanation:

[tex]||v||=\sqrt{x^2+y^2}\\||v||=\sqrt{(-8)^2+(14)^2}\\||v||=\sqrt{64+196}\\||v||=\sqrt{260}\\||v||\approx16.12\text{ lbs}[/tex]

Answer:

The 9th term is 30

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

Use nth term equation:

We have:

And we need to find the 9th term.

Write the given terms as below and solve for d:

Subtract the first equation  from the second:

The first term is:

Find 9th term:

Answer:

The 9th term is 30

Step-by-step explanation:

The required slope of the line is -1/4 which passes through points (1,-1) and (5,-2).

The slope of the line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

Given,

Let

x₁ = 1 , y₁ = -1

x₂ = 5, y₂ = -2

∵ Slope m = (y₂ - y₁)/(x₂ -x₁  )

Substitute values in the formula, and we get

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

m = (-2 + 1)/(4)

m = -1/4

Thus, the required slope of the line is -1/4.

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Step-by-step explanation:

Ted is correct

When you multiply exponents, they actually add.

Note**

[tex]4x = {4x}^{1} [/tex]

Looking at pearl, when she did

[tex] {2x}^{2} \times 4 {x}^{1} [/tex]

It should have equaled

[tex]8 {x}^{3} [/tex]

Pearl's did not, but Ted's did

The smallest integer is 10, the middle integer is 11, and the largest integer is 12.

What is the consecutive integers in algebra?

In algebra, consecutive integers are a sequence of numbers that follow each other in order, where each number is one more than the previous number.

Let's call the smallest integer "x". Then, the middle integer is "x + 1" and the largest integer is "x + 2".

Now, using the given information, we can set up an equation:

x + 2(x + 1) = 56 - 3(x + 2)

Expanding the equation and simplifying:

3x + 2 = 56 - 3x - 6

6x = 62

x = 10

So, the three consecutive integers are 10, 11, and 12.

Hence, The smallest integer is 10, the middle integer is 11, and the largest integer is 12.

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Answer: Para encontrar el denominador que falta, podemos utilizar una regla de tres simple. En este caso, queremos encontrar el valor de la segunda fracción, por lo que podemos escribir:

2/7 = 10/x

Para despejar x, podemos multiplicar ambos lados de la ecuación por x y luego dividir por 2:

2/7 * x = 10

x = 10 * 7 / 2

x = 35

Por lo tanto, el denominador que falta en la segunda fracción es 35. La fracción completa es:

2/7 = 10/35

Standard deviation is the square root of the variance. A mean of squared differences the square root of the variance unit-free the covariance.

The standard deviation is a measure of variance from the mean that includes spread, dispersion, and spread. The standard deviation displays a "typical" deviation from the mean. It is a well-liked measure of variability because it retains the original units of measurement from the data set. There is a small variation when data points are near the mean, and a large variation when they are far from the mean. The values' distance from the mean is determined by the standard deviation. The most common method of measuring dispersion is standard deviation, which is based on all values.

Hence, standard deviation is the square root of the variance.

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Answer: 6.3%

Step-by-step explanation:

The probability that the same song is played twice = Number of favourite outcomes / Total outcomes.

= 1 / 6

= 0.0625

in per cent = 6.25%

Probability to the nearest tenth of % = 6.3%

.: Probability - Probability is a number that reflects the chance or likelihood that a particular event will occur.
Probability can be expressed as proportional that ranging from 0 to 1.

They can also be expressed as percentages ranging from 0% to 100%.

Answer:

you are right

Step-by-step explanation:

Answer: The correct answer is D, X^2 - 1.

A prime polynomial is a polynomial that has no real or complex roots (i.e., no solutions), except for 0. X^2 - 1 has two roots, -1 and 1, both of which are not 0. Hence, it is a prime polynomial.

Step-by-step explanation:

Sorina's chronological age is 8.

What is Intelligence Quotient?

The Intelligence Quotient (IQ) is an intelligence test that measures the intellectual abilities that a person has, that is to say, that it measures intelligence. To obtain a person's IQ, we divide the mental age by the chronological age and multiply the result by 100.

In this case, we have the IQ score, which is 125, and the mental age, which is 10, so we have to clear C (chronological age) to find the chronological age.

(mental age)/( chronological age) X 100 = IQ .  

(10/C) X100 =125

10 X100 =125 X C

1000 = 125C

1000125 = C

8=C

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Sorina's chronological age is 8.

What is Intelligence Quotient?

The Intelligence Quotient (IQ) is an intelligence test that measures the intellectual abilities that a person has, that is to say, that it measures intelligence. To obtain a person's IQ, we divide the mental age by the chronological age and multiply the result by 100.

In this case, we have the IQ score, which is 125, and the mental age, which is 10, so we have to clear C (chronological age) to find the chronological age.

(mental age)/( chronological age) X 100 = IQ .  

(10/C) X100 =125

10 X100 =125 X C

1000 = 125C

1000125 = C

8=C

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The measure of ZPQR is approximately 113°. This can be solved usiing the concept of geometry.

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects. A geometer is a mathematician who specializes in geometry.

Therefore, to find the measure of ZPQR, we would follow the following steps:

Let x= measure of <PQR

Hence, the measure of <PQR

296 = x/360 x 3.14 x 2 x 150

Hence, x = 113.12 °

Approximately, the measure of ZPQR is 113 °

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The tape diagram is attached in the solution.

A tape diagram is a rectangular visual model resembling a piece of tape, that is used to assist with the calculation of ratios and addition, subtraction, and commonly multiplication.

Given is an equation x+4 = 17,

We need to draw a tape diagram for the same,

So, for that, since we have x + 4 which is equal to 17, so, we will draw a box, divide into two parts one will show the x part and ine will show the 4 part, and collectively it will show 17.

The value of the x+4 and 17 is the same, because, according to the diagram, the quantity x+4 collectively showing 17, therefore, they have same values.

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The required, given expression is completely factored as  (4y -5)(3x - 5).

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

To factor the expression 12xy - 15x - 20y + 25, we can use the distributive property to factor out a common factor from each of the first two terms and the last two terms:

12xy - 15x - 20y + 25

= (12x)(y) - (15x)(1) - (20)(y) + (5)(5)

= (3x)(4y) - (5)(3x) - (4)(5y) + (5)(5)

= 3x(4y - 5) - 5(4y - 5)

= (4y -5)(3x - 5)

So, the expression is completely factored as, (4y -5)(3x - 5).

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a) From the given information, [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

be a random sample of size 5 from a normal population with mean 0 and variance 1. Hence,

[tex]W=(\sum_{i=1}^5 Y_{i}^2)\sim X_{5}^2[/tex]

b) From the given information, the random variable is   [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

and  [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables. Hence,

.[tex]U=(\sum_{i=1}^5 (Y_{i} - \bar{Y})^2) \sim X_{5}^2[/tex]

c) From the given information,[tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables and moreover, [tex]Y_{6}[/tex]

is independent standard normal variable. Hence,  [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2\sim X_{5}^2[/tex]

and

.[tex]Y_{6}^2\sim X_{1}^2[/tex]

What is Chi-square distribution?

Chi-square distribution with k degrees of freedom is defined as the sum of the k standard normal variables. This is also defined as the square of the deviations taken from the mean. Chi-square distribution is used for testing goodness of fit and independence in contingency tables.

• If  [tex]z_{1}, z_{2},...........z_{k}[/tex]

are independent standard normal variables, then

[tex]\sum_{i=1}^k z_{i}^2\sim X_{k}^2[/tex]

• If   [tex]X\sim X_{m}^2[/tex]

and   [tex]Y\sim X_{n}^2[/tex]

, then

[tex](X+Y)\sim X_{m+n}^2[/tex]

Step: 1

(a)

The distribution of    [tex]\sum_{i=1}^5 Y_{i}^2[/tex]

is obtained below:

From the given information, [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

be a random sample of size 5 from a normal population with mean 0 and variance 1. Hence,

[tex]W=(\sum_{i=1}^5 Y_{i}^2)\sim X_{5}^2[/tex]

The random variable,  [tex]W=\sum_{i=1}^5 Y_{i}^2[/tex]

representing the sum of squares of standard normal variables and hence, the distribution of   [tex]W=\sum_{i=1}^5 Y_{i}^2[/tex]

is identified as chi-square distribution.

Hint:

Use chi-square distribution to find the distribution of

.[tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

Step: 2

(b)

From the given information, the random variable is   [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

and  [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables. Hence,

.[tex]U=(\sum_{i=1}^5 (Y_{i} - \bar{Y})^2) \sim X_{5}^2[/tex]

The random variable    [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

representing the sum of squares of deviations taken from the mean for 5 standard normal variables and hence, the distribution of
[tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

is chi-square distribution with 5 degrees of freedom.

Hint:

Use       [tex](X+Y)\sim X_{m+n}^2[/tex]  

to find the distribution of

[tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2+Y_{6}^2[/tex]

Step: 3

(c)

From the given information,[tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables and moreover, [tex]Y_{6}[/tex]

is independent standard normal variable. Hence,  [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2\sim X_{5}^2[/tex]

and

.[tex]Y_{6}^2\sim X_{1}^2[/tex]

Therefore,

[tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2+Y_{6}^2\sim X_{5+1}^2[/tex]

[tex]\sim X_{6}^2[/tex]

The distribution of    [tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2+Y_{6}^2[/tex]

is identified as chi-square distribution with degrees of freedom is obtained by adding the degrees of freedom of[tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

and the degrees of freedom of   [tex]Y_{6}^2[/tex].

The distribution of   [tex]W=\sum_{i=1}^5 Y_{i}^2[/tex]

is chi-square distribution with 5 degrees of freedom.

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The value of M when r = 12 and the value of r when M = 224 are 504 and 8 respectively.

Direct proportionality is expressed as;

M ∝ r²

Hence; M = kr²

Where k is the proportionality constant.

Given that;

First, we determine the proportionality constant.

M = kr²

k = M/r²

Plug in r = 2 and M = 14

k = 14 / (2)²

k = 14/4

k = 7/2

Now, a) the value of M when r = 12 will b;

M = kr²

M = (7/2) × ( 12 )²

M = (7/2) × 144

M = 504

Next, b) the value of r when M = 224

M = kr²

r = √(M/k)

r = √( 224 ÷ 7/2 )

r = 8

Therefore, the values of M and r are 504 and 8 respectively.

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The rate for a ratio of the two different quantities would be 13 over 2 puppies per litter. That is option D.

The total number of puppies that Mallory's Border Collie has = 13 puppies.

The number of litters that the puppies are being placed = 2 litters.

Therefore, the rate of puppies per litter is calculated as follows:

13 puppies = 2 litters

X puppies = 1 litter

Make X the subject of formula;

X = 13×1/2

X= 13/2 puppies per litter

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Answer:Alex has a collection of vehicle models. He built 8 model airplanes, 4 model trains, and 12 model cars. Write a ratio to represent the ratio of cars to trains.

Step-by-step explanation:3/1 ur welcome

Answer:

15 and 8

Step-by-step explanation:

Let the legs be a, b

a+b=23

ab=120

Then, 23b-b^2=120. so b^2-23b+120=0. Thus (b-8)(b-15)=0. Thus b=8,15, and if b=8, then the other length a is 15.

Answer:

C

Step-by-step explanation:

The shorter the angle, the shorter the side that lies across from it

In angle order it's 33, 71, 76

The lines across in that order are LK, LJ, JK

Answer:

the answer is A

Step-by-step explanation:

use the formula y=mx+b

25.95 is the slope because its a constant arte of change and 50 is the y-intercept because you gain $50 in addition to the slope

Answer:

y=25.95x+50

Step-by-step explanation:

25.95 is the dependent variable, so it is the coefficient. The starting amount, or the y-intercept, is 50. This makes the equation y=25.95x+50.

Answer:

  x = 22

  y = 59

Step-by-step explanation:

You want the values of x and y as shown in the figure where angles (2x)° and (y-15)° are vertical angles, and (2x)° and (2x+2)° are complementary.

Two angles are complementary when their sum is 90°.

  (2x)° +(2x+2)° = 90°

  4x = 88 . . . . . . . . . . . divide by °, subtract 2

  x = 22

Vertical angles have the same measure:

  (2x)° = (y -15)°

  2·22 = y -15 . . . . . . divide by °, substitute for x

  59 = y . . . . . . . . .  add 15

The value of x is 22.

The value of y is 59.

Answer: (x^3 - 3x^2 + 5x - 3)/(x^2 - 2)

Step-by-step explanation:

It says the volume equals the height multiplied by the base area, or base area x height = volume. Because we are given the volume and the base area, we can plug in the values to get (x^2 - 2) x height = (x^3 - 3x^2 + 5x - 3). Finally, we can divide both sides by (x^2 - 2) to get height = (x^3 - 3x^2 + 5x - 3)/(x^2 - 2).

Answer:

12x^2 + 12

Step-by-step explanation:

1. Remove the parentheses:

x^4 + 8x^2 + 16 - x^4 + 4x^2 - 4

2. Cancel out terms:

8x^2 + 16 + 4x^2 - 4

3. Combine like terms:

12x^2 + 12

Answer:

35

Step-by-step explanation:

The formula for the variance of a sample is:

Variance = Σ (x - average)^2 / (n - 1)

Where n is the sample size and x is each data point.

We are given the variance as 544 and the standard deviation as 4, and we know that:

Standard deviation = sqrt(Variance)

So,

Variance = Standard deviation^2

Variance = 4^2

Variance = 16

Now we have the variance and can find the sample size:

544 = 16 * (n - 1)

n - 1 = 544 / 16

n - 1 = 34

The sample size is n = 35.

Answer:2 one

Step-by-step explanation:

The correct answer to the statement is A. True. The equation Ax= b is referred to as a vector equation because it consists of scalars multiplied by vectors.

The matrix A multiplies the input vector x, which results in the output vector b.

In other words, each element of the output vector is a scalar multiple of the corresponding element of the input vector.

Thus, the equation represents a vector equation, which describes the relationship between two vectors.

he equation Ax= b is a fundamental concept in linear algebra and is widely used in various mathematical and scientific fields.

It represents the relationship between a linear transformation represented by the matrix A, the input vector x, and the output vector b.

In this equation, the matrix A acts as a set of coefficients that scale the elements of x to produce the elements of b.

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Answer:

[tex]\textsf{LCM}=(x+3)^3(x-3)^2[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6cm}\underline{Difference of Two Squares Formula}\\\\$a^2-b^2=\left(a+b\right)\left(a-b\right)$\\ \end{minipage}}[/tex]

Factor x² - 9 by applying the Difference of Two Squares formula:

[tex]\begin{aligned}\implies x^2-9&=x^2-3^2\\&=(x+3)(x-3)\end{aligned}[/tex]

Rewrite each of the given expressions as an expansion of their factors:

[tex]\bullet \quad (x-3)^2=(x-3)(x-3)[/tex]

[tex]\bullet \quad x^2-9=(x+3)(x-3)[/tex]

[tex]\bullet \quad (x+3)^3=(x+3)(x+3)(x+3)[/tex]

Therefore, we can see that each expression has a factor of (x - 3), (x + 3) or both (x - 3) and (x + 3).

The least common multiple (LCM) of a, b, and c is the smallest multiplier that is divisible by a, b and c.

Therefore, to find the LCM of the given expressions, multiply each factor with the highest power:

17) The number of miles that the car will travel with 90%, 30%, and 50% probability on a full tank of gas is:

90% probability: 420.5 + (1.645 x 50) = 545.25 miles

30% probability: 420.5 - (1.645 x 50) = 295.75 miles

50% probability: 420.5 miles

18) The upper and lower values for the interval of miles traveled on a full tank of gas around the mean that includes approximately 68% of miles for this car is:

Upper value: 420.5 + (1 x 50) = 470.5 miles

Lower value: 420.5 - (1 x 50) = 370.5 miles

19) The upper and lower values for the interval of miles traveled on a full tank of gas around the mean that includes approximately 95% of miles for this car is:

Upper value: 420.5 + (2 x 50) = 520.5 miles

Lower value: 420.5 - (2 x 50) = 320.5 miles

20) The upper and lower values for the interval of miles traveled on a full tank of gas around the mean that includes approximately 99.7% of miles for this car is:

Upper value: 420.5 + (3 x 50) = 570.5 miles

Lower value: 420.5 - (3 x 50) = 270.5 miles

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

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