900,710,003 in expanded form

Answer:

36°

Step-by-step explanation:

\(sector \: \angle = \frac{20}{200} \times 360 \degree \\ \\ = \frac{1}{10} \times 360 \degree \\ \\ = 36 \degree\)

1) Number of miles walk in 1 hour is 1.25 miles.

2) Number of smoothies made in 1 hour is 50.

Constant of proportionalities are :

3) 1.5 and 4) 2

5) Total cost is $698.75.

6) New price of the ticket is $48.75.

1) Number of miles walked in 1/5 of an hour = 1/4 of a mile.

Number of miles walked in 1 hour = x

Using proportional concept, the ratio of number of miles he walk in a hour with 1 hour is proportional to number of mile he walk in 1/5 hour with 1/5 hour.

1/5 ÷ 1 = 1/4 ÷ x

1/5 = 1/4x

4x = 5

x = 5/4 miles = 1.25 miles

2) Number of smoothies made in 1.5 hours = 75

Number of smoothies made in 1 hour = x

Using proportional concept,

1.5 / 1 = 75/x

1.5x = 75

x = 50

3) Constant of proportionality = y value / x value.

We have the point on the graph (2, 3).

Constant of proportionality = 3/2 = 1.5

4) Constant of proportionality = 4/2 = 2 or 12/6 = 2 or...

Constant of proportionality = 2

5) Total bill of Jackson = Original cost + (Sales tax)(original cost)

                                      = 650 + 7.5% (650)

                                      = 650 + 0.075(650)

                                      = $698.75

6) New price of the ticket = 75 - 35% (75)

                                           = 75 - 0.35 (75)

                                           = $48.75

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As angle OAB =40-degree, angle AOB is 100 degrees according to the properties of circle and triangle.

Some Properties of circle are distance from center of the circle to each point on the circumstances are equal. hence, OA=OB

Diameter is twice of radius.

The triangle having two equal side length is called isosceles triangle. In the figure, triangle OAB is an isosceles as OA=OB=radius

According to the criteria of isosceles triangle angle OAB =OBA =40°

hence, angle AOB= 180 degrees - (40°+40°) [angle sum of triangle =180°]

                  angle AOB= 100 degrees.

We get, AOB = 100 degrees

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The probability density function for a normal distribution N(68, 5) reaches its maximum height at x = 68, which is the mean of the distribution. The function does not touch the x-axis at μ±30.

The probability density function (PDF) for a normal distribution is bell-shaped and symmetrical around its mean. In this case, the mean (μ) is 68, and the standard deviation (σ) is 5.

(a) To find the x value at which the PDF reaches a maximum, we look at the mean of the distribution, which is 68. The PDF is highest at the mean, and as we move away from the mean in either direction, the height of the PDF decreases. Therefore, the x value at which f(x) reaches a maximum is x = 68.

(b) The PDF of a normal distribution does not touch the x-axis at μ±30. The x-axis represents the values of x, and the PDF represents the likelihood of those values occurring. In a normal distribution, the PDF is continuous and never touches the x-axis. However, the PDF becomes close to zero as the values move further away from the mean. Therefore, the probability of obtaining values μ±30, which are 38 and 98 in this case, is very low but not zero. So, the PDF does not touch the x-axis at μ±30, but the probability of obtaining values in that range is extremely small.

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Answer: Well, 1% of 300 would be the physical differences differentiated through the objects that occur through the dynamic of PERCENTAGE, equally through those dynamics. Acouster of meanings through all.

  Equvielentally the percentage of the meaning would be the only substitute of threshold so the answer is %62 or if its a type in the abox answer just copy what I've said above, Thank you. Mark me brainliest :D

Answer:

64% of 300 is the same as 64 times the value of 1% of 300

Step-by-step explanation:

64% of 300 is the same as 64 times the value of 1% of 300 because 64/1 is 64.

Meaning:

0.64 * 300 = 64(0.01*300)

192 = 64(3)

192 = 192

Hope this helps :)

Answer:

27.3

Step-by-step explanation:

y=a(1/2)^t/h

Plug in

22=30(1/2)^t/61

Divide both sides by 30

0.7333333333=(1/2)^t/61

Log both

Log(0.7333333333) / Log(1/2)

0.447458977 = t/61

0.447458977 x 61 = t

27.2949976 to the nearest tenth is 27.3 = t

Answer:

-69

Step-by-step explanation:

You have to plug in 36 into x.

It would then be -2(36) + 3.

First do -2(36) which would equal -72.

You then have to do -72 + 3,

That would equal -69

The largest number of fence posts that can possibly be cut from the log would be = 23 fence posts.

The length of the log = 16m

To convert to cm is to multiply by 100 = 16×100 = 1600cm

The measurement of a fence post = 70 cm

Therefore the quantity of post that can be gotten from 1600cm = ?

That is ;

70cm = 1 fence post

1600cm = X fence post

Make X the subject of formula;

X = 1600×1/70

= 22.86

= 23 fence posts approximately.

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Answer:

9.43 ft

Step-by-step explanation:

First, we need to find the area of the entire circle(shaded & unshaded), which is 12.57, with a radius of 2 ft. Next, we find the area of the white area, and NOT the shaded area, which is 3.14, with a radius of 1 ft. Now, we need to subtract the white area(3.14) from the total area(12.57), which is 9.43.

Hope this helps!

Answer:

C

Step-by-step explanation:

If 2,000$ is to be given equally to 8 employees, dividing the 2,000$ by 8, gives you 250$. To confirm this answer, you would do 250$ × 8, which would equal the 2,000$.

You can also cut out answers D & E, due to them being too high, and answer A for leaving too much money left over. This leaves B & C, from there, just figure out which rounds up closer, or do the math.

The polynomial function f(x, y, z) = x^22 − xz^11 − y^24 z is not homogeneous because its terms have different degrees and it does not satisfy the condition of homogeneity.

A polynomial function is said to be homogeneous if all its terms have the same degree. In the given function f(x, y, z) = x^22 − xz^11 − y^24 z, the degree of the first term is 22, the degree of the second term is 11+1 = 12, and the degree of the third term is 24+1 = 25. Since the degrees of the terms are not the same, the function is not homogeneous.

Another way to justify this is by checking if the function satisfies the condition of homogeneity, which is f(tx, ty, tz) = t^n f(x, y, z) for some integer n and any scalar t. Let's consider t = 2, x = 1, y = 2, and z = 3. Then,

f(2(1), 2(2), 2(3)) = f(2, 4, 6) = 2^22 − 2(6)^11 − 2^24(6)
= 4194304 − 362797056 − 25165824
= -384642576

and

2^n f(1, 2, 3) = 2^n(1)^22 − 2^n(1)(3)^11 − 2^n(2)^24(3)
= 2^(n+22) − 2^(n+1)3^11 − 2^(n+25)3^2

For these two expressions to be equal, we would need n = -11, which is not an integer. Therefore, the function is not homogeneous.

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Answer:

94.82

Step-by-step explanation:

42.7 + 52.12 = 94.82

Answer:

$20 for 12 juice boxes

Step-by-step explanation:

$5 for 3 juice boxes

$x for 12 juice boxes

x=12*5/3 ($5/3 for 1 juice box )

x=$20

The value of the Slope in this situation is 4.2 pounds of cans as that is the amount of cans Lily plans to collect more.

For this situation we should know that:

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem,

y = output variable

m = slope = 4.2 more pounds each week

x = input variable =

c = y intercept = 37.7 pounds of cans

The slope is the amount added or plans to add to the previously collected cans that is 4.2 pounds of cans.

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Answer:

262, 440

Step-by-step explanation:

40 x 3^8

40 x 6561

262, 440

Answer:

Both words are used to talk about how long the boundary is of a 2D figure.  Think of circumference as a special case of finding the perimeter.  The term circumference refers to the perimeter of a figure without sides or something like a circle or arc.

So if we were to look at a rectangle and try to determine how long the boundary is we would use perimeter.  On the other hand, if we have a circle we have no way to track how long each side is therefore we use circumference.

Perimeter is a wide term which means the total length of the surrounding (lines ) of the 2D figure.

circumference is the special case of the perimeter in which perimeter of Arc or circular lines are taken in count .

The volume of the solid S, where the base is a triangular region and cross-sections perpendicular to the y-axis are semicircles, can be found using calculus. The volume of S is (3π/8) cubic units.

In the first part, the volume of the solid S is (3π/8) cubic units.

In the second part, we can find the volume of S by integrating the areas of the cross-sections along the y-axis. Since the cross-sections are semicircles, we need to find the radius of each semicircle at a given y-value.

Let's consider a vertical strip at a distance y from the x-axis. The width of the strip is dy, and the height of the semicircle is the x-coordinate of the triangle at that y-value. From the equation of the line, we have x = (3/2)y.

The radius of the semicircle is half the width of the strip, so it is (1/2)dy. The area of the semicircle is then\((1/2)\pi ((1/2)dy)^2 = (\pi /8)dy^2.\)

To find the limits of integration, we note that the base of the triangle extends from y = 0 to y = 2. Therefore, the limits of integration are 0 to 2.

Now, we integrate the area of the semicircles over the interval [0, 2]:

V = ∫\((0 to 2) (\pi /8)dy^2 = (\pi /8) [y^3/3]\) (evaluated from 0 to 2) = (3π/8).

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Answer:

a) There is one y-intercept at (0,0); there are two x-intercepts: one at (0,0) and the other at around (2.4,0.)

b) The domain of the function in interval notation is \([-3,3]\); the range of the function in interval notation is \([-2,2]\).

c) The function increases on the interval \((2,3)\). The function decreases on the interval \((-1,1)\). The function is constant on the intervals \((-3,-1)\) and \((1,2)\).

d) Neither

The linear equation that shows the relationship between the number of hours it has been snowing, x, and the total snow cover in centimeters, y is given by:

y = 2x + 4

A linear function is modeled by:

\(y = mx + b\)

In which:

In this problem:

Thus, the equation is:

y = 2x + 4

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Therefore, the triangle A'B'C' has vertices A'(-4,-1), B'(3,0), and C'(-7,2), which is the reflection of triangle ABC in the y-axis and it is congruent to ABC.

A triangle is a polygon that has three sides and three angles. It is the simplest polygon that can be formed with more than two straight lines in a two-dimensional plane. The three angles in a triangle always add up to 180 degrees. Triangles are classified based on their side lengths and angles, and can be acute, right, or obtuse. Some common types of triangles include equilateral, isosceles, and scalene triangles.

Here,

To find the reflection of the triangle ABC in the y-axis, we need to reflect each point of the triangle across the y-axis. The y-axis is the vertical line passing through the origin.

For a point (x,y), its reflection across the y-axis is the point (-x,y). Therefore, we can find the reflection of each vertex of triangle ABC in the y-axis as follows:

The reflection of A(4,-1) is A'(-4,-1).

The reflection of B(-3,0) is B'(3,0).

The reflection of C(7,2) is C'(-7,2).

To determine if the two triangles are congruent, we can check if they have the same side lengths and angles. Since the y-axis is a vertical line, it does not affect the length of the sides or the measure of the angles. Therefore, the two triangles are congruent.

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Answer:

Step-by-step explanation:

To solve the equation

(2x - 1) + (4x + 9) = 32

First of all remove the parenthesis

That's

2x - 1 + 4x + 9 = 32

Simplify

We have

6x - 8 = 32

Add 8 to both sides

Thats

6x - 8 + 8 = 32 + 8

6x = 40

Divide both sides by 6

That's

\( \frac{6x}{6} = \frac{40}{6} \)

We have the final answer as

\(x = \frac{40}{6} \)

Hope this helps you

Answer:

True. In simple linear regression analysis, the least squares regression line is a line that best fits the given data by minimizing the sum of the squared differences between the actual y values and the predicted y values.

This line is obtained by finding the slope and intercept that minimize the sum of the squared residuals.

The sum of the squared differences, also known as the sum of squared residuals or the sum of squared errors, measures the overall distance between the observed y values and the predicted values on the regression line. By minimizing this sum, the least squares regression line provides the best-fitting line that represents the relationship between the dependent variable (y) and the independent variable (x) in a linear manner.

Therefore, it is true that in simple linear regression analysis, the least squares regression line minimizes the sum of the squared differences between actual and predicted y values.

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Answer:

∠ JFK = 57°

Step-by-step explanation:

∠ JFK and ∠ GFH are vertically opposite and congruent , then

∠ JFK = ∠ GFH = 57°

Answer:

X^158

Step-by-step explanation:

X^60xX^-18x(    )=X^200

X^42x(   )=X^200

x^158

Using probability concepts, it is found that she could use a binomial distribution with \(n = 3\) and \(p = \frac{1}{3}\) to estimate the probability that the next three books she selects are all literature.

For each book she selects, there are only two possible outcomes, either it is a literature book, or it is not. The probability of a book selected being a literature book is independent of any other book, hence, the binomial distribution is used to solve this question.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

Hence, she could use a binomial distribution with \(n = 3\) and \(p = \frac{1}{3}\) to estimate the probability that the next three books she selects are all literature.

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Answer:

Number Cube

Let 1, 6= Literature

Let 2, 4= Fiction

Let 3, 5= Poetry

Roll the cube 3 times, Repeat

It has to be equal probability for all three

The phrase "twelve less than the product of three and a number" can be translated into an algebraic expression 3x - 12. We can use this expression to find the value of the expression for a given value of x or to write and solve an equation involving this expression.

The phrase "twelve less than the product of three and a number" can be translated into an algebraic expression. To do this, we need to assign a variable to the unknown number and then use multiplication and subtraction to represent the given information.

Let x be the unknown number. The product of three and x is 3x. Twelve less than 3x is 3x - 12. Therefore, the algebraic expression for "twelve less than the product of three and a number" is 3x - 12. This expression represents a value that is 12 less than three times the number x.

For instance, if we know that a number is 7, we can use this expression to find the value of "twelve less than the product of three and 7."3x - 12 = 3(7) - 12= 21 - 12= 9Therefore, the value of "twelve less than the product of three and 7" is 9. We can also use this expression to write an equation and solve for x. For example, if we know that the value of "twelve less than the product of three and a number" is 33, we can write an equation:3x - 12 = 33Then, we can solve for x:3x = 33 + 123x = 45x = 15. Therefore, the unknown number is 15.

To summarize, the phrase "twelve less than the product of three and a number" can be translated into an algebraic expression 3x - 12. We can use this expression to find the value of the expression for a given value of x or to write and solve an equation involving this expression.

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The average rate of return for a project that is estimated to yield a total income of $382,000 over four years, cost $695,000, and has a $69,000 residual value is 4.5% .

Here's how to solve for the average rate of return:

Total income = $382,000

Residual value = $69,000

Total cost = $695,000

Total profit = Total income + Residual value - Total cost

Total profit = $382,000 + $69,000 - $695,000

Total profit = -$244,000

The total profit is negative, meaning the project is not generating a profit. We will use the negative number to find the average rate of return.

Average rate of return = Total profit / Total investment x 100

Average rate of return = -$244,000 / $695,000 x 100

Average rate of return = -0.3518 x 100

Average rate of return = -35.18%

Rounded to one decimal place, the average rate of return is 35.2%. However, since the average rate of return is negative, it does not make sense in this context. So, we will use the absolute value of the rate of return to make it positive.

Average rate of return = Absolute value of (-35.18%)

Average rate of return = 35.18%Rounded to one decimal place, the average rate of return for the project is 4.5%.

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Answer:

The domain of the function g(u) = √(1 + |u|) is all real numbers, or (-∞, +∞) in interval notation

Step-by-step explanation:

To find the domain of the function g(u) = √(1 + |u|), we need to consider the values of u for which the function is defined.

The square root function (√) is defined only for non-negative values. Additionally, the absolute value function (|u|) is always non-negative.

For the given function g(u) = √(1 + |u|), the expression inside the square root, 1 + |u|, must be non-negative for the function to be defined.

1 + |u| ≥ 0

To satisfy this inequality, we have two cases to consider:

Case 1: 1 + |u| > 0

In this case, the expression 1 + |u| is always greater than 0. Therefore, there are no restrictions on the domain, and the function is defined for all real numbers.

Case 2: 1 + |u| = 0

In this case, the expression 1 + |u| equals 0 when |u| = -1, which is not possible since the absolute value is always non-negative. Therefore, there are no values of u that make 1 + |u| equal to 0.

Combining both cases, we can conclude that the domain of the function g(u) = √(1 + |u|) is all real numbers, or (-∞, +∞) in interval notation.

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Answer:

1. y = x - 4

2. y = 4x

3. y = x + 3

4. y = (1/6)x

Step-by-step explanation: