Find the Area if the circle.

The two values with the same value as 18 ones and 302 thousandths, given their place values, are:

Place value describes the position or place of a digit in a number, which determines its numerical value.

Place values form the basis of the number system because the position occupied by a digit in a number shows its value.

The place values on the left of the decimal point include Billions, Hundred Millions, Ten Millions, Millions, Hundred Thousands, Ten Thousands, Thousands, Hundreds, Tens, and Ones.

After the decimal point, on the right, the place values include tenths, hundredths, and thousandths.

18 ones and 302 thousandths

= 1 ten + 8 ones + 3 tenths + 2 thousands

= (1 x 10) + (8 x 1) + (3 x 1/10) + (2 x 1/1,000)

Thus, 18 ones and 302 thousandths share the same place values as Options B and D.

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Answer:

0.9995

Step-by-step explanation:

10% = 0.10

1 - 0.10 = 0.9

n = number of light bulbs = 7

we calculate this using binomial distribution.

p(x) = nCx × p^x(1-p)^n-x

our question says at most 4 is defective

= (7C0 × 0.1⁰ × 0.9⁷) + (7C1 × 0.1¹ × 0.9⁶) + (7C2 × 0.1² × 0.9⁵) + (7C3 × 0.1³ × 0.9⁴) + (7C4 × 0.1⁴ × 0.9³)

= 0.478 + 0.372 + 0.1239 + 0.023 + 0.0026

= 0.9995

we have 0.9995 probability that at most 4 light bulbs are defective.

Jenny's Average swimming speed is 1.5 km/h.

Jenny's average swimming speed as S (in km/h). We can then use the given information to set up equations and solve for S.

We know that Jenny swam for 1 hour, so the distance she swam is given by the formula: Distance = Speed * Time.

Thus, the distance she swam is S * 1 = S km.

Next, we know that her average running speed is 8 times her average swimming speed. Therefore, her average running speed is 8S km/h.

Since she ran for 1 hour, the distance she ran is 8S * 1 = 8S km.

Furthermore, we are given that her average bicycling speed is 2 times her average running speed. Therefore, her average bicycling speed is 2 * 8S = 16S km/h.

She biked for 1.75 hours, so the distance she biked is 16S * 1.75 = 28S km.

The total distance of the triathlon is the sum of the distances for each segment: Distance(swimming) + Distance(running) + Distance(biking) = 55.5 km.

Therefore, we can write the equation:

S + 8S + 28S = 55.5.

Simplifying the equation, we get:

37S = 55.5.

To solve for S, we divide both sides of the equation by 37:

S = 55.5 / 37 = 1.5.

Thus, Jenny's average swimming speed is 1.5 km/h.

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The coordinates of vertex D in the parallelogram are (-7, -10).

We have,

To find the coordinates of vertex D of the parallelogram, we need to use the properties of a parallelogram.

One of these properties states that opposite sides of a parallelogram are parallel and have equal lengths.

Given that A = (8, 2), B = (6, -4), and C = (-5, -4), we can find the coordinates of D as follows:

Find the vector representing one of the sides of the parallelogram.

We can use the vector AB.

Vector AB = (x-coordinate of B - x-coordinate of A, y-coordinate of B - y-coordinate of A)

= (6 - 8, -4 - 2)

= (-2, -6)

Add this vector to point C to find the coordinates of D.

Coordinates of D = (x-coordinate of C + x-coordinate of AB, y-coordinate of C + y-coordinate of AB)

= (-5 - 2, -4 - 6)

= (-7, -10)

Therefore,

The coordinates of vertex D are (-7, -10).

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Answer:

The correct answer is B

Step-by-step explanation:

The balance in the account after 20 years is 24347914754cents when if you deposit $2,000 in a savings account with a 6% annual percentage yield that pays simple interest.

Given that,

If you deposit $2,000 in a savings account with a 6% annual percentage yield that pays simple interest.

We have to find what will the balance be after 20 years.

The formula for calculating simple interest is

SI = PRT

P is the amount invested = $2000

R is the rate (in decimal) = 6% = 0.06

T is the time in years = 20 years

We get the simple interest

SI = 2000 × 0.6 × 20

SI = $24,000

The balance after 20 years will be $2,000 + $24,000 = $26,000

The compound amount formula is expressed as:

A = P(1 + r/t)ⁿˣ

A = 2000(1+0.6/12)^12(20)

A = 2000(1+0.05)^240

A = 2000(1.05)^240

A = 24347914754cents

Therefore, The balance in the account after 20 years is 24347914754cents when if you deposit $2,000 in a savings account with a 6% annual percentage yield that pays simple interest.

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Answer:

Explanation:

The terms with x add up with terms with x. The same for y.

Then:

The angle sum property of a triangle and the angle formed between a tangent and a radius of a circle indicates.

m∠ADC = 58°

A tangent to a circle is a straight line which touches the circumference of a circle at only one point.

The vertical angles theorem indicates that we get;

∠1 ≅ ∠2

Therefore; m∠1 = m∠2

The tangent to a circle indicates that we get;

The angle formed at vertex B and Q are 90 degrees angles and the triangles ABP and AQP are right triangles, which indicates that the acute angles of each of the right triangles are complementary, therefore;

m∠1 + 26° = 90°

m∠1 = 90° - 26° = 64°

Therefore, m∠2 = m∠1 = 64°

m∠2 = m∠CAD = 64°

The segments AC and AD are radial lengths therefore, the triangle ΔACD is an isosceles triangle.

m∠ADC ≅ m∠ACD (Base angles of an isosceles triangle)

The angles ∠ADC and ∠ACD are therefore;

m∠CAD + m∠ADC + m∠ACD = 180° (Angle sum property of a triangle)

m∠CAD + m∠ADC + m∠ADC = 180°

m∠CAD + 2 × m∠ADC = 180°

64° + 2 × m∠ADC = 180°

m∠ADC = (180° - 64°)/2 = 58°

m∠ADC = 58°

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the answer is D no solution

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Thus, the answer is D

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

159.410 is greater than 159.399 with 0.011

11.0 is the same as 11.000

and so on

Answer:

6.5 and 2.5

Step-by-step explanation:use midpoint formula

The coordinates of point {T} is (6.5, 2.5).

Two rays intersect to form a angle. The point of intersection is called the vertex point.

Given is a parallelogram PQRS with P(3,1), Q(8,1), R(10,4), S(5,4).

The diagonals of the parallelogram bisect each other. So, we can write the coordinates of point {T} using the section formula as -

{x, y} = {(3 + 10)/2 , (4 + 1)/2}                               {m : n = 1 : 1}

{x, y} = (6.5, 2.5)

Therefore, the coordinates of point {T} is (6.5, 2.5).

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===================================================

Explanation:

For now I'll use x in place of t.

Two points on that line segment are: (15,190) and (25,170)

Use the slope formula to get the following

\((x_1,y_1) = (15,190) \text{ and } (x_2,y_2) = (25,170)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{170 - 190}{25 - 15}\\\\m = \frac{-20}{10}\\\\m = -2\\\\\)

The slope is -2.

A slope of -2 means we go down 2 each time we move to the right 1.

In short: "down 2, right 1".

Now use point-slope form to determine the equation

\(y - y_1 = m(x - x_1)\\\\y - 190 = -2(x - 15)\\\\y - 190 = -2x + 30\\\\y = -2x + 30 + 190\\\\y = -2x + 220\\\\\)

The last step to do is replace x with t and we get y = -2t+220 which is the final answer.

---------

Check:

Plugging in t = 15 should lead to y = 190.

y = -2t + 220

y = -2(15) + 220

y = -30 + 220

y = 190

So far so good.

Now we need to check if t = 25 leads to y = 170.

y = -2t + 220

y = -2(25) + 220

y = -50 + 220

y = 170

That works as well.

We have confirmed the points (15,190) and (25,170) are on this equation. The answer is confirmed.

The conditional probability for this problem is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have that 5 students play soccer, and of those, 2 play basketball, hence the conditional probability is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

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Answer:

it can't be simplified

Step-by-step explanation:

If Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

To show that x is also an eigenvector of QT, we need to demonstrate that QT * x is a scalar multiple of x.

Given that Q is an orthogonal matrix, we know that QT * Q = I, where I is the identity matrix. This implies that Q * QT = I as well.

Let's denote x as the eigenvector corresponding to the eigenvalue λ1 This means that Q * x = λ1 * x.

Now, let's consider QT * x. We can multiply both sides of the equation Q * x = λ1 * x by QT:

QT * (Q * x) = QT * (λ1 * x)

Applying the associative property of matrix multiplication, we have:

(QT * Q) * x = λ1 * (QT * x)

Using the fact that Q * QT = I, we can simplify further:

I * x = λ1 * (QT * x)

Since I * x equals x, we have:

x = λ1 * (QT * x)

Now, notice that λ1 * (QT * x) is a scalar multiple of x, where the scalar is λ1. Therefore, we can rewrite the equation as:

x = λ2 * x

where λ2 = λ1 * (QT * x).

This shows that x is indeed an eigenvector of QT, with the eigenvalue λ2 = λ1 * (QT * x).

In conclusion, if Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

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Answer:

Step-by-step explanation:

45° is 1/8 of a circle, so the area of the sector is 1/8 the area of the circle.

Area of circle = 8*50 = 400 sq ft

πr² = 400

r = √(400/π) = 20/√π ≈ 11.3 ft

In spherical coordinates, the region R is the set

\(R = \left\{ (\rho, \theta, \varphi) \, : \, 0 \le \rho \le 3, \, 0 \le \theta \le 2\pi, \, \dfrac\pi6 \le \varphi \le \pi\right\}\)

Then the volume of R is

\(\displaystyle \iiint_R dV = \int_0^3 \int_0^{2\pi} \int_{\frac\pi6}^\pi \rho^2 \sin(\varphi) \, d\varphi \, d\theta \, d\rho\)

The integrand is free of \(\theta\), so we can immediately compute that integral and pull out a factor of 2π :

\(\displaystyle \iiint_R dV = 2\pi \int_0^3 \int_{\frac\pi6}^\pi \rho^2 \sin(\varphi) \, d\varphi \, d\rho\)

and the remaining double can be factorized as

\(\displaystyle \iiint_R dV = 2\pi \left(\int_0^3 \rho^2 \, d\rho\right) \left(\int_{\frac\pi6}^\pi \sin(\varphi) \, d\varphi\right)\)

The single integrals are trivial:

\(\displaystyle \int_0^3 \rho^2 \, d\rho = \frac13 (3^3 - 0^3) = 3^2 = 9\)

\(\displaystyle \int_{\frac\pi6}^\pi \sin(\varphi) \, d\varphi = -\cos(\pi) - \left(-\cos\left(\frac\pi6\right)\right) = 1 + \frac{\sqrt3}2\)

So, the volume of R is

\(\displaystyle \iiint_R dV = 2\pi \cdot 9 \cdot \left(1 + \frac{\sqrt3}2\right) = \boxed{9(2+\sqrt3)\pi}\)

Answer:

C) -2/9

Step-by-step explanation:

\(\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}\)

Answer:

Hence, Option (C) - 2/9 is the Answer:

Step-by-step explanation:

-1/6 [3 -15(1/3)^2]

-1/6(3 -15)(1/9))

-1/6(3 - 5/3)

-1/6 (4/3)

Hence, Option (C) - 2/9 is the Answer:

I hope it helps!

Understanding statistical questions and data distributions is an important concept in data analysis and statistics. A statistical question is one that can be answered by collecting and analyzing data.

These questions typically ask about a population or group of individuals and are often related to trends or patterns.

Data distributions refer to the way data is spread out or distributed within a dataset. This can include measures like the mean, median, and standard deviation. Understanding data distributions is important for making accurate interpretations and predictions based on the data.

To practice understanding statistical questions and data distributions, it's important to work with real-world datasets and ask questions that can be answered using statistical analysis.

This can involve looking at trends and patterns in the data and interpreting the results in a meaningful way. By building these skills, you can become better equipped to analyze and interpret data in a variety of settings.

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The discrete data is (b) while the continuous data are (a) and (d)

These are data that can be represented using positive whole numbers.

Using the above definition as a guide, the discrete data is (b) The number of books in your apartment

These are data that can be represented using decimal numbers.

Using the above definition as a guide, the continuous data are (a) The weight of cows  and (d) The ounces of water that you drink each day

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Answer:

-119

Step-by-step explanation:

Answer:

-8.4

Step-by-step explanation:

-7 x 1.2

The true statement about the axis of rotation is the option;

It is parallel to a side of the equilateral triangle, but is separate from the equilateral triangle.

The axis of rotation is a straight line around which all points on a rotating body rotates.

The diagram shows a figure with a hollow cylindrical cross section and triangular cross section on the left and right, which indicates that the figure is created by the rotation of the equilateral triangle about height of the cylinder, such that the axis of rotation is a vertical line through the center of the hollow cylinder. Therefore, the axis of rotation is parallel to the height of the cylinder, and therefore, it is parallel to the base of the equilateral triangle, but it it seperate from walls of the cylinder, and therefore, separate from the equilateral triangle

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Answer: x<4

Given the inequality:

We want to solve the inequality for x.

First, distribute the bracket on the right side of the inequality.

Next, subtract 10x from both sides of the inequality.

Add 24 to both sides of the inequality.

Divide both sides of the inequality by 6.

The solution to the inequality is x<4.

The following answers are given as:

2.1)

2 teaspoons of vinegar are needed for 5 teaspoons of olive oil.

2.2)

8 teaspoons of vinegar are needed for  20 teaspoons of olive oil.

2.3)

There are 12 teaspoons of vinegar and 30 teaspoons of olive oil in the 42 teaspoons of salad.

2.4)

There are 4 teaspoons of vinegar and 10 teaspoons of olive oil in the 14 teaspoons of salad.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

6 teaspoons of vinegar = 15 teaspoons of olive oil.

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Now,

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 2 on both sides.

2 teaspoons of vinegar = 5 teaspoons of olive oil.

Now,

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 8 on both sides.

8 teaspoons of vinegar = 20 teaspoons of olive oil.

Now,

Total number of teaspoons = 42

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 12 on both sides.

12 teaspoons of vinegar = 30 teaspoons of olive oil.

12 + 30 = 42 teaspoons

Now,

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 4 on both sides.

4 teaspoons of vinegar = 10 teaspoons of olive oil.

4 + 10 = 14 teaspoons

Thus,

2 teaspoons of vinegar are needed for 5 teaspoons of olive oil.

8 teaspoons of vinegar are needed for  20 teaspoons of olive oil.

There are 12 teaspoons of vinegar and 30 teaspoons of olive oil in the 42 teaspoons of salad.

There are 4 teaspoons of vinegar and 10 teaspoons of olive oil in the 14 teaspoons of salad.

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Answer:

its yes

Step-by-step explanation:

Answer:

[6, 8).

Step-by-step explanation:

When we are looking for the range of a function by just looking at the graph, we have to define from what point to what point the graph move vertically. On the other hand, if we were looking for the domain, we would state from where to where the graph moves horizontally.

In this case we have to analyze the graph vertically, since we are looking for the range of the function. Therefore, if we take a look at the line we can notice that it goes from y=6 to y=8. Therefore the range should be from 6 to 8.

Now, this result must be expressed in interval notation, meaning that we have to state whether the values of each end are contained or not by the function. The graph already tells us about it., because it marks it with the closed or open dots. In the case of the number 6, we have a closed dot, means that the function contains the number 6. For the other end we have an open dot, means that the function doesn't contain the number 8.

Applying internal notation, the range of this function is:

[6, 8).

Learn more about interval notation here:

1. https://web.nmsu.edu/~kberver/Unit1/Unit18.html#:~:text=An%20interval%20is%20closed%20if,used%20for%20an%20open%20endpoint.

2. https://brilliant.org/wiki/interval-notation/#:~:text=Interval%20notation%20is%20a%20way,inequality%20or%20system%20of%20inequalities.