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1) 3,500 rounded to the nearest ten thousand is 0.

2) 462,183.5062749 rounded to the nearest tenth is 462,183.5.

3) 6 + (-3) - 5 is equal to -2.

QUESTION 1:The given number is 3,500. To round it to the nearest ten thousand, we need to see which ten thousand is closest to the number. In this case, 3,500 is between 0 and 10,000. Since 0 is closer, we round down to 0. So, 3,500 rounded to the nearest ten thousand is 0.

QUESTION 2: To round the given number, 462,183.5062749, to the nearest tenth, we need to look at the digit in the hundredths place (the second digit after the decimal point), which is 0. Since 0 is less than 5, we round down the digit in the tenths place to 3.

Therefore, 462,183.5062749 rounded to the nearest tenth is 462,183.5.

QUESTION 3:We have to evaluate 8 to the 8th power. That means we have to multiply 8 by itself 8 times. Using a calculator, we can find that 8^8 is equal to 16,777,216.

QUESTION 4:When solving the expression 6 + (-3) - 5, we should follow the order of operations, which is: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Since there are no parentheses or exponents in this expression, we can simply perform addition and subtraction from left to right.

6 + (-3) = 3, then 3 - 5 = -2.

Therefore, 6 + (-3) - 5 is equal to -2.

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Answer:

D) C': ( -3, -2), D': ( -4, 1), E': ( -1, -2)

Step-by-step explanation:

Formula for this equation:

(x - 5, y - 3)

C:

(2, 1)

(x - 5, y - 3)

C': ( -3, -2)

E:

(4, 1)

(x - 5, y - 3)

E': ( -1, -2)

D:

(1, 4)

(x - 5, y - 3)

D': ( -4, 1)

The line should be perpendicular to x = -4

x= -4 is a vertical line crossing the x axis at x= -4

The slope is undefined in x =-4

For an equation in slope intercept form, the general form is ;

y= mx + b where m is the slope and b is the y-intercept

So for any y value, x is always -4

Thus the slope for line x = -4 is not defined

A line perpendicular to x = -4 will thus be a horizontal line with slope 0

For the equation of this line

0= y--5/x-4

0 = y+5 /x-4

0{x-4} = y +5

0 = y+5

y= - 5

Answer: A + 7 = 28

Step-by-step explanation:

In the polar coordinate system, the region R corresponds to 0 ≤ r ≤ (2 - 9sin(θ))/(9cos(θ) + 9sin(θ)) and 0 ≤ θ ≤ π/2.

To evaluate the given iterated integral ∫∫R (1 - y²)/(9(x + y)) dA, where R is the region in the xy-plane bounded by the curves x = 0, y = 1, and 9(x + y) = 2, we can convert it to polar coordinates for easier computation.

In polar coordinates, we have x = rcos(θ) and y = rsin(θ), where r represents the distance from the origin and θ is the angle measured counter clockwise from the positive x-axis.

The integral becomes ∫∫R (1 - r²sin²(θ))/(9(rcos(θ) + rsin(θ))) r dr dθ. In the polar coordinate system, the region R corresponds to 0 ≤ r ≤ (2 - 9sin(θ))/(9cos(θ) + 9sin(θ)) and 0 ≤ θ ≤ π/2.

In the given integral, we substitute x and y with their respective polar coordinate representations. The numerator becomes 1 - r²sin²(θ), and the denominator becomes 9(rcos(θ) + rsin(θ)). Multiplying the numerator and denominator by r, we have (1 - r²sin²(θ))/(9(rcos(θ) + rsin(θ))) = (1 - r²sin²(θ))/(9r(cos(θ) + sin(θ))). We then rewrite the double integral as two separate integrals: the outer integral with respect to θ and the inner integral with respect to r. The limits of integration for θ are 0 to π/2, while the limits for r are determined by the curve 0 = (2 - 9sin(θ))/(9cos(θ) + 9sin(θ)).

We can simplify this curve to 2cos(θ) - 9sin(θ) = 9, which represents an ellipse in the xy-plane. The limits of r correspond to the radial distance within the ellipse for each value of θ. By evaluating the double integral using these limits, we can determine the result of the given iterated integral.

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Answer:

B

Step-by-step explanation:

Area = length x width

Total surface area

=2(8*3) + 2(10*3) + 2(10*8)

=48+60+160

=268

Answer:

\(\frac{1}{2x-3}\)

Step-by-step explanation:

(\(\frac{f}{g}\) )(x)

= \(\frac{f(x)}{g(x)}\)

= \(\frac{x+1}{2x^2-x-3}\) ( factorise the denominator )

= \(\frac{x+1}{(2x-3)(x+1)}\) ← cancel the common factor (x + 1) on numerator/ denominator

= \(\frac{1}{2x-3}\)

Total surface area of cuboid is 56 sq.units.

Total surface area is the total space covered by an object. It includes both top and bottom of an objects.

Let a be the side of the cube, a=2.

The cube with 2 units are placed adjacent to each other it forms cuboid.

The dimensions of cuboid are,

length, l = a + a + a ⇒ 2+2+2=6 units.

breadth, b = a=2 units.

height, h =a=2 units.

Total surface area of cuboid = 2(lb+bh+hl) sq. units

                                               = 2(6*2+2*2+2*6)

                                               = 56 sq.units.

Hence, the total surface area of the cuboid thus formed is 56 sq.units.

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Answer:

341

STEPS:

an = a1 + (n-1) d

a1 is the first number

d = is the difference between each number = 6

a11 = 1 + (11 - 1)6

a11 = 61

Sn = n (a1 + an)/2

S11 = 11 (1 + 61)/ 2

S11 = 682/2

S11 = 341 = answer

The 11th partial sum of the arithmetic sequence {1, 7, 13, 19, …} = 341

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.

\(a_{n} = a_{1} + (n-1)d\\\\\)

Given : {1, 7, 13, 19.....}

\(a_{1} = 1\\\\d = a_{2} - a_{1} = 7 - 1 = 6\\\\a_{n} = 1 + 6(n-1) = 1 + 6n - 6 = 6n -5\\\\a_{11} = 6*11 -5 = 61\\\\S_{n} = \frac{n(a_{1} + a_{n})}{2} \\\\S_{11} = \frac{11(1+ 61)}{2} = 11 * 31 = 341\)

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The hypothesis that is typically used to test the claim is the null hypothesis, which asserts that the average time spent by students studying for a midterm exam is indeed 3 hours. The alternative hypothesis would be that the average time spent is either greater or less than 3 hours.

The null hypothesis is usually denoted as H0 and the alternative hypothesis as Ha. In this case, we can write:

H0: The average time spent by students studying for a midterm exam is 3 hours.

Ha: The average time spent by students studying for a midterm exam is not 3 hours.

To test this hypothesis, a statistical test can be performed, such as a t-test or a z-test, depending on the sample size and the population parameters. The results of the test will determine whether the null hypothesis can be rejected or not. If the null hypothesis is rejected, it means that there is evidence to suggest that the average time spent studying is different from 3 hours. If the null hypothesis is not rejected, it means that there is not enough evidence to suggest that the average time spent studying is different from 3 hours.

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a) .25

b) .6

c) .875

d) 3.3125

e) .06

f) 19.425

Answer:

3x(2x - 3)

Step-by-step explanation:

Given

y = 6x² - 9x ← factor out 3x from each term

  = 3x(2x - 3)

We estimate that there are approximately 43 horse beads in the bag.

We can use the method of proportion to estimate how many horse beads are in the bag. We know that Neil randomly selected 14 beads out of a total of 200 beads, which represents 7% of the total.

We can assume that the proportion of horse beads in the bag is the same as the proportion of horse beads in the sample of 14 beads that Neil selected.

Out of the 14 beads that Neil selected, 3 were horse beads. Therefore, we can estimate that the proportion of horse beads in the bag is:

3/14 = 0.214

To estimate how many horse beads are in the bag, we can multiply the proportion by the total number of beads:

0.214 * 200 = 42.8

Rounding to the nearest whole number, we estimate that there are approximately 43 horse beads in the bag.

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Answer: 350

Step-by-step explanation: So they are selling the sofa for 50 more than what they bought times 2, so to get that you subtract 750-50. Then to find the two times you divide 700 by 2. Hope this helps!

The plant utilization for brat would be 77.5% if Baldwin is producing 2,325 units of brat next year.

The plant utilization for brat would depend on the capacity of the plant and the production level achieved. Without knowing the capacity of the plant, it is difficult to provide an accurate calculation. However, assuming that the plant has a capacity of 3,000 units and Baldwin is producing 2,325 units, the utilization would be calculated as follows:

Utilization = (Actual Production / Maximum Production Capacity) x 100
Utilization = (2,325 / 3,000) x 100
Utilization = 77.5%

Therefore, the plant utilization for brat would be 77.5% if Baldwin is producing 2,325 units of brat next year.

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Answer:

You would start with 00.-6 and stop a-5954

Step-by-step explanation:

Answer:

\(Area = 26478cm^2\)

Step-by-step explanation:

Given

See attachment for desk

Required

The area

First, calculate the area of the semicircular cutout

\(Area = \frac{\pi r^2}{2}\)

Where

\(r = 60cm\)

So:

\(A_1 = \frac{3.14 * 60^2}{2}\)

\(A_1 = \frac{11304}{2}\)

\(A_1 = 5652cm^2\)

Next, the area of the complete trapezium

\(Area= \frac{1}{2}(a + b) * h\)

Where

\(a = 300\)

\(b = 2 * r = 2 * 60 = 120\)

\(h = 153\)

So:

\(A_2 = \frac{1}{2} * (300 + 120) * 153\)

\(A_2 = \frac{1}{2} * 420 * 153\)

\(A_2 = 32130cm^2\)

The area of the desk is:

\(Area = A_2 - A_1\)

\(Area = 32130cm^2 - 5652cm^2\)

\(Area = 26478cm^2\)

Answer:

20mph

Step-by-step explanation:

because you have to divide 240 by 12 and the answer is 20

The slope of the line c is - 92.

The points via which the line b passes are:

(-20, 4) and (-21, 96).

The slope of the line is given by:

m = (y₂ - y₁) / (x₂ - x₁)

Slope of the line b passing through these points are:

m = (96 - 4) / (- 21 + 20)

m = (92) / (-1)

m = - 92

Since, line b is parallel to line c,

Slope of line b = slope of line c

So, the slope of line c is also:

m' = - 92

Therefore, we get that, the slope of the line c is - 92.

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Answer:

120

Step-by-step explanation:

280 divided by 7= 40. 40*3=120

therefore 120 is the answer

Answer:

288 cubic feet

Step-by-step explanation:

6x6= 36 that is for one base now multiply by 8 and get 288

Answer:

f=1

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

If you find area of base then you can multiply by height and divide by 3. So first find the area of the base

An octant's main features are :

An octant is formed by three perpendicular axes, labeled X, Y, and Z. These axes intersect at a common point called the origin. Each octant contains both positive and negative values along the X, Y, and Z axes. The positive region is located on one side of each axis, while the negative region is on the other side.

Each of the three axes divides an octant into two quadrants. These quadrants are numbered from 1 to 8, with quadrant 1 being in the positive X, Y, and Z regions and quadrant 8 being in the negative X, Y, and Z regions.

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Answer:

Step-by-step explanation:

y = mx + b

"m" is slope or rate ;

"b" is y-intercept ( value of "y" when x = 0 ) or flat fee.

~~~~~~~~~~~

b).

$4.95 person pays even he/she download 0 e-books, and monthly pay will be increased by $3.99 for each downloaded e-book.

c = 4.95 + 3.99 b

d). Graph is discrete, because person buys whole e-book and not the parts of the e-books.

Using the given logarithmic values, we can evaluate the logarithms of different numbers. The calculations include finding the logarithms of 18, 81, 6, √2, 1.5, and 4.5.



a) To find loga(18), we need to express 18 as a power of a. Since 18 is not a power of 3 or 2, we can't directly determine the value. We need additional information about the relationship between a and the given logarithms.

b) To find log, (81), we can express 81 as a power of 3: 81 = 3^4. Now we can use the properties of logarithms to evaluate it. Since log(3) = 0.53, we can rewrite log, (81) as (4 * log(3)). Therefore, log, (81) = 4 * 0.53 = 2.12.

c) Similarly, to find log, (6), we need to express 6 as a power of 2 or 3. Since 6 is not a power of 2 or 3, we cannot directly evaluate log, (6) without additional information.

d) To find log, (√2), we can rewrite it as log, (2^(1/2)). By applying the property of logarithms, we get (1/2) * log(2). Since log(2) = 0.33, we can calculate log, (√2) as (1/2) * 0.33 = 0.165.

e) To find log, (1.5), we do not have enough information to directly evaluate it without additional information about the relationship between a and the given logarithms.

f) Similarly, to find log, (4.5), we cannot evaluate it without additional information about the relationship between a and the given logarithms.

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Solution

67)

68)

Draw a right angle triangle:

Answer:

The absolute value of point B on the number line is 2.2.

Step-by-step explanation:

A number line is given with point A at coordinate negative 2.2, point B at coordinate negative 1.6, and point C at coordinate 1.2.

So, on the number line, all the points having negative value are on the left side of zero.

Position of the point A is -2.2,

Position of the point B is -1.6,

Position of the point C is -1.2.

The absolute value of any point on the number line is the distance of that point from zero.

So, the absolute value of point B on the number line is the distance of point B from zero which is |-2,2|=2.2.