Find the vectors that join the center of a clock to the hours 1:00, 2:00, and 3:00. Assume the clock is circular with a radius of 1 unit.
at
1:00
2:00
3:00

The approximate volume of the solid is 1.6 × 10^23 π cubic feet.

The approximate volume of the solid is 8.17 × 10^20 π cubic inches.

We have,

1.

The volume V of a cylinder is given by V = πr²h,

where r is the radius and h is the height.

Substituting r = 2.0 × 10^7 feet and h = 4.0 × 10^5 feet.

V = π (2.0 × 10^7)² (4.0 × 10^5)

Simplifying,

V = 1.6 × 10^23 π cubic feet (using scientific notation and leaving the answer in terms of π)

2.

The volume of a cone is given by V = 1/3πr²h,

where r is the radius, h is the height, and we are given the diameter (d = 2r).

Substituting,

d = 1.0 × 10^7 inches, r = d/2 = 5.0 × 10^6 inches, and

h = 5.0 × 10^5 inches, we get:

V = 1/3 π (5.0 × 10^6)² (5.0 × 10^5)

Simplifying,

V = 2.6 × 10^20 π cubic inches

(using scientific notation and leaving the answer in terms of π)

Rounding to the nearest hundredth,  

V = 8.17 × 10^20 π cubic inches.

Thus,

The approximate volume of the solid is V = 1.6 × 10^23 π cubic feet.

The approximate volume of the solid is V = 8.17 × 10^20 π cubic inches.

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The probability of a simple event is the likelihood or chance of that event occurring. The formula is P(A) = Number of favorable outcomes / Total number of possible outcomes.

It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The formula for the probability of a simple event is:

P(A) = Number of favorable outcomes / Total number of possible outcomes

For example, if we toss a fair coin, the probability of getting heads is:

P(Heads) = 1 (number of favorable outcomes) / 2 (total number of possible outcomes)

So, the probability of getting heads is 0.5 or 50%.

A simple event is an event that has only one possible outcome. For instance, rolling a specific number on a dice, drawing a specific card from a deck of cards, or picking a specific colored ball from a bag of balls are all examples of simple events.

In summary, the probability of a simple event is the ratio of the number of ways the event can happen to the total number of possible outcomes.

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The values of the exponential function are calculated below and as x increases, the exponential function increases.

In the table of function given, we can calculate the value of f(x) as it relates to x.

The given exponential function is ;

f(x) = 2ˣ

Substituting the values;

f(-4) = 2⁻⁴ = 1/2⁴ = 1/16

f(-3) = 2⁻³ = 1/2³ = 1/8

f(-2) = 2⁻² = 1/2² = 1/4

f(-1) = 2⁻¹ = 1/2

f(0) = 2⁻⁰ = 1/2⁰ = 1

As the value of x increases, the exponential function increases.

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Answer:

4/5 ×400

0.8 × 400

=320 freshmen study algebra.

I had used fraction method.

Answer:

a) m || n

b) p || q, and m must be perpendicular to both p and q.

c) p || q

d) p || q

e) m || n and p || q

The values of lengths are:  AE = 30, GF = 10, GD = 5 for the given ΔABC.

Point at which all three medians of a particular triangle meet is called as a centroid. Median also called as a line segment which connects the vertex of a triangle to the midpoint.

Since G is the centroid of ΔABC, it divides each median in the ratio  of 2:1. That is,

AG:GE = 2:1,     BG:GF = 2:1,     CG:GD = 2:1

First, we know, AG/GE = 2/1         (given, AG = 20)

20 / GE = 2/1

GE = 10

So, given in the median of ΔABC is,

AE = AG + GE      (put the values)

AE = 20 + 10

AE = 30

Now, we can use the fact that BG:GF = 2:1 to find the length of GF:

we know, BG/GF = 2/1         (given, BF = 30 = BG + GF)

BG = 2GF

(BF - GF) = 2GF                     (here, BG = BF - GF)

30 - GF = 2GF

GF = 10

Now, we can use the fact that CG:GD = 2:1 to find the length of GD:

we know, CG/GD = 2/1         (given, CG = 10)

10 / GD = 2/1

GD = 5

Therefore, we get the values are:  AE = 30, GF = 10, GD = 5

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In ΔDEF, the measure of angle D = 38.4°

Here in triangle DEF the measure of angle F = 90°

This means that ΔDEF is a right triangle and DE is the hypotenuse.

We need to find the measure of angle D.

Consider the tangent of angle D.

tan(D) = opposite side/ adjacent side

tan(D) = EF / FD

Here, EF = 2.3 feet, and FD = 2.9 feet.

So above equation becomes,

tan(D) = 2.3 / 2.9

tan(D) = 0.79310

D = arctan(0.7931)

D = 38.42°

Therefore, the measure of ∠D = 38.4°

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The statement " A(n) method is like a blueprint, or template, for all the objects within a class" is true because methods define the behavior or operations that an object can perform and are defined within a class, acting as a blueprint or template for creating objects in object-oriented programming.

A method in object-oriented programming is a set of instructions that defines the behavior or operations that an object can perform. It is a part of a class, which acts as a blueprint or template for creating objects. When an object is created from a class, it can access and use the methods defined within that class.

Methods can be used to perform tasks, manipulate data, or interact with other objects. They are an essential aspect of encapsulation in object-oriented programming, as they allow for data to be accessed and manipulated in a controlled manner. Overall, methods are a crucial tool for developers to create robust and scalable applications.

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The length of curve DE, which is 5% longer than line segment AB, is 10.5 units.

To calculate the length of curve DE, we first need to determine the length of line segment AB. Let's say, for example, that line segment AB has a length of 10 units. To find the length of curve DE, we need to add 5% of line segment AB's length to line segment AB.

To calculate 5% of line segment AB's length, we can multiply the length of line segment AB by 0.05. This gives us:

5% of 10 = 0.05 x 10 = 0.5

So, 5% of line segment AB's length is 0.5 units. To find the length of curve DE, we need to add 0.5 units to the length of line segment AB. This gives us:

Length of curve DE = Length of line segment AB + 5% of Length of line segment AB

= 10 + 0.5

= 10.5 units

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Complete Question:

You are trying to help Matt understand the concept of a 5% slack in the line. You explain that having a 5% slack means that the length is 5% longer than it would be if it were completely straight. You compare ABC to Figure DEF, where curve DE is 5% longer than line segment AB.

Enter the length of curve DE given that the curve is 5% longer than line segment AB.

The remainder of the f(x) = 3x³ + 6x² - 3x + 2 and divisor x + 3 applying synthetic division is equal to -16.

Use synthetic division and the remainder theorem to find the remainder of f(x) when divided by x- c,

Set up the synthetic division table with c on the left side, and the coefficients of f(x) on the top row.

Bring down the first coefficient of f(x) into the first box below the horizontal line.

Multiply c by the number in the first box and write the result in the second box.

Add the number in the second box to the coefficient in the second column, and write the result in the third box.

Repeat steps 3 and 4 until you reach the last box. The number in the last box is the remainder.

Check if the remainder is zero. If it is zero, then x -c is a factor of f(x),

and g(x) = (x- c) is a factor of f(x).

Dividend is equal to,

f(x) = 3x³ + 6x² - 3x + 2

Divisor is equal to,

g(x) = x + 3

Synthetic division is attached in the figure.

Expressed in remainder theorem

3x² -3x + 6 + ( -16 / x + 3 )

Therefore, the remainder of the synthetic division for the given dividend and divisor is equal to -16.

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The expression that is equivalent by the Distributive Property is A 3x+12

this is the only answer that actually uses the distributive property.

The Distributive Property is a mathematical rule that applies to operations such as multiplication and addition or subtraction. It states that when you multiply a number by a sum or difference of two or more numbers, you can distribute the multiplication over each of the individual terms in the sum or difference.

3 can be multiplied by both x and 4 to get 3x+12 (which is using the distributive property)

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Answer:

k = 30

Step-by-step explanation:

an equation of proportionality has the form

y = kx ← k is the constant of proportionality

y = 30x ← is in this form

with k = 30

An equation of the line that passes through the point (6,2) and has a slope of -1/2 is y = -1/2(x) + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (6, 2) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = -1/2(x - 6)  

y - 2 = -1/2(x) + 3

y = -1/2(x) + 3 + 2

y = -1/2(x) + 5

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The length of the diagonal of the door is approximately 14.308 feet. Rounding to the nearest whole number, the answer is 14 feet.

The lengths of the trim pieces that make an X on the door form the legs of a right triangle, and the diagonal of the door forms the hypotenuse of the right triangle. Using the Pythagorean theorem, we can find the length of the hypotenuse:

a^2 + b^2 = c^2

where a and b are the lengths of the trim pieces and c is the length of the hypotenuse.

Each trim piece forms a right triangle with the height of the door (7 feet) and one half of the width of the door (1.5 feet). Using the Pythagorean theorem, we can find the length of each trim piece:

a^2 + b^2 = c^2

where a = 7 feet and b = 1.5 feet

c = sqrt(a^2 + b^2) = sqrt((7 feet)^2 + (1.5 feet)^2) = sqrt(49 + 2.25) = sqrt(51.25) ≈ 7.154 feet

The length of each trim piece is approximately 7.154 feet. Since there are two trim pieces that intersect at the center of the door, the length of the hypotenuse is twice this length:

2 * 7.154 feet ≈ 14.308 feet

Therefore, the length of the diagonal of the door is approximately 14.308 feet. Rounding to the nearest whole number, the answer is 14 feet.

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The diameter of the balloon is increasing at a rate of approximately 0.79 ft/min when the diameter is 1.5 feet.

We can use the formula for the volume of a sphere to relate the rate of change of volume with the rate of change of diameter

V = (4/3)πr^3 = (1/6)πd^3,

where V is the volume, r is the radius, and d is the diameter.

Taking the derivative with respect to time t, we get

dV/dt = (1/2)πd^2 (dd/dt),

where dd/dt is the rate of change of diameter.

We are given that dV/dt = 2.8 ft^3/min and d = 1.5 ft, so we can solve for dd/dt

dd/dt = (2dV/dt)/(πd^2) = (2(2.8))/(π(1.5)^2) ≈ 0.79 ft/min.

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Answer:

-18.67.

Step-by-step explanation:

If you think math is boring, think again. Here is a fun way to learn how to find the rational number that we need to divide -15/56 by to get -5/7. It's like a puzzle, but with fractions!

First, we need to make -15/56 look nicer. How do we do that? By dividing both the top and the bottom by -1. That's like flipping the sign. So we get 15/56. Much better!

Next, we need to find a mystery number that makes -5/7 and 15/56 equal when we multiply them. That's like finding a missing piece of a jigsaw puzzle. How do we do that? By cross-multiplying! That's when we multiply the top of one fraction by the bottom of the other and set them equal. So we get:

-5 times 56 equals 15 times mystery number

Now we just need to solve for the mystery number. How do we do that? By dividing both sides by 15. That's like cutting a cake into equal slices. So we get:

Mystery number equals (-5 times 56) divided by 15

Now we just need to simplify. How do we do that? By using a calculator or our brains. Either way, we get:

Mystery number equals -18.67

And that's it! We found the rational number that we need to divide -15/56 by to get -5/7. It's -18.67. Isn't math fun?

We can rewrite the following logarithms to common logarithms as follows:

1. 2.3768

2. 3.8173

To rewrite the logarithms in the common format we can use the following formula.

loga b = log10 b / log10 a

So, we have:

log5 46 = log10 46 / log10 5

Using a calculator, we find that log10 46 ≈ 1.66276 and log10 5 ≈ 0.69897, so:

log5 46 ≈ 1.66276 / 0.69897 ≈ 2.3768

For the second one, we can approach the problem this way:

loga b = log10 b / log10 a

So, we have:

log3 66 = log10 66 / log10 3

Using a calculator, we find that log10 66 ≈ 1.81954 and log10 3 ≈ 0.47712, so:

log3 66 ≈ 1.81954 / 0.47712 ≈ 3.8173

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Answer:

y=-0.5x+3

Step-by-step explanation:

The equation of a line is

y=mx+b, with m being the slope, and b being the y-intercept

The slope is -0.5, and the y intercept is 3

so:

y=-0.5x+3

Answer:

y= -1/2x+3

Expiation:

you can find the equation between two points by using the slope formula and the slope intercept form which is y=mx+b.

The estimated area is about 22.5 square units

To estimate the perimeter of a patio, you need to measure the length of each side and then add those lengths together.

Here's a step-by-step guide to help you:

Determine the shape of your patio: Before you can estimate the perimeter, identify whether your patio is a rectangle, square, circle, or any other shape. The method for calculating the perimeter will vary depending on the shape.

Measure the sides:

a. For rectangular or square patios: Measure the length (L) and width (W) of the patio using a measuring tape. Ensure that the measurements are taken in the same unit (e.g., feet, meters, etc.).

b. For circular patios: Measure the diameter (D) or radius (R) of the patio. The radius is the distance from the center of the circle to any point on its edge.

c. For irregularly-shaped patios: Break the patio down into smaller, regular shapes (like rectangles, squares, or triangles), and measure each side of these smaller shapes.

Calculate the perimeter:

a. For rectangular or square patios: Use the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

b. For circular patios: Use the formula P = 2πR or P = πD, where P is the perimeter, R is the radius, and D is the diameter. π (pi) is approximately 3.14159.

c. For irregularly-shaped patios: Add up the side lengths of each smaller shape that you've broken the patio into. The sum of these lengths will give you the total perimeter.

(look at the image)

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Lateral surface area = 2H(L + W)

Total surface area = 2 LW + 2 WH + 2 HL

We need to know the prism's dimensions in order to determine its lateral and total surface area for a rectangular base prism. The rectangular prism's length, width, and height are assumed to be L, W, and H, respectively.

The sum of the areas of the rectangular prism's four lateral faces determines its lateral surface area. Since every sidelong face is a square shape with a level of H and a width of one or the other L or W, the parallel surface region is given by:

Lateral Surface Area = 2H(L + W)

The sum of the areas on each of the six faces creates the rectangular prism's total surface area. This incorporates the four sidelong faces, as well as the top and base faces, which are additionally square shapes with aspects L x W. Consequently, the all out surface region is given by:

Total Surface Area = 2(LW + LH + WH)

So, if you know the dimensions of the rectangular prism, you can use these formulas to find its lateral and total surface area.

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If for an arithmetic-sequence, the terms are t₅ = -154 and t₉ = -274, then the first-three terms are t₁ = -274, t₂ = -244 and t₃ = -214.

An "Arithmetic-Sequence" is defined as a sequence of numbers in which the difference between any two consecutive terms is always the same, which is called the "common-difference".

To find first 3 terms of an "arithmetic-sequence" given the values of t₅ and t₉, we use formulas for "nth-term" of an arithmetic sequence, which is

⇒ tₙ = t₁ + (n - 1)d,

where tₙ = nth term, t₁ = first term, n = position of term in sequence, and d = common-difference,

Given that t₅ = -154 and t₉ = -274,

So,

⇒ t₅ = t₁ + (5 - 1)d = -154,

⇒ t₉ = t₁ + (9 - 1)d = -274,

We first find the "common-difference" by subtracting "t₁" from both sides of first equation and "t₉" from both sides of second-equation,

We get,

⇒ 4d = -154 - t₁,

⇒ 8d = -274 - t₁,

Simplifying further,

We get,

⇒ 4d = 120,

⇒ d = 30,

Now, we substitute it in "4d = -154 - t₁",

We get,

⇒ 4(30) = -154 - t₁,

⇒ 120 = -154 - t₁,

⇒ t₁ = -154 - 120,

⇒ t₁ = -274

So, the first term is = -274;

Now we use "d = 30" to find second and third terms of sequence,

We get,

⇒ t₂ = t₁ + (2 - 1)d = -274 + 30 = -244,

⇒ t₃ = t₁ + (3 - 1)d = -274 + 60 = -214,

Therefore, first three-terms of arithmetic sequence are -274, -244, and -214.

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The given question is incomplete, the complete question is

Find the first 3 terms of arithmetic sequence if t₅ = -154 and t₉ = -274. Find t₁, t₂, t₃.

The side length of the juice box is given as follows:

5 cm³.

The volume of a cube of side length a is given by the cube of the side length, as follows:

V(a) = a³.

The total volume of the box in this problem is given as follows:

55 + 40 + 30 = 125 cm³.

Hence the side length of the juice box is given as follows:

a³ = 125

a³ = 5³

a = 5 cm.

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The total surface area of a gift box is  42.06 square feet

We know that the formula for the surface area of rectangular prism is:

A = 2(lw + wh + lh)

where l is the length

w is the width

and h is the height

The box shaped like a rectangular prism is 3.2 feet long and 2.1 feet wide and 2.7 feet high.

⇒ l = 3.2 ft,

w = 2.1 ft

and h = 2.7 ft

Using above formula the total surface area of the box would be,

A = 2(lw + wh + lh)

A = 2 × [(3.2 × 2.1) + (2.1 × 2.7) + (3.2 × 2.7)]

A = 2 × 21.03

A = 42.06 square feet

Therefore, the required area is  42.06 square feet

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Answer:

There are 2 answers:

Step-by-step explanation:

110 = c²

√110 = √c²

±10.5 = c

Solve for c:

[tex]110=c^2[/tex]

Take the square root of 110

[tex]10.48\thickapprox10.5[/tex]

[tex]\longrightarrow \boxed{\bold{c=10.5}}[/tex]

[tex]\text{so} \ \boxed{110=\bold{10.5^2}}[/tex]

Answer:

They are length, thickness and temperature

Answer: $34,828.59

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

A = P(1 + r)^t

where:

P = the principal (in this case, $14,275)

r = the annual interest rate (6%, or 0.06 as a decimal)

t = the number of years (18)

Plugging in the values we know, we get:

A = $14,275(1 + 0.06)^18

A = $14,275(1.06)^18

A = $34,828.59 (rounded to the nearest penny)

Therefore, the value of the investment after 18 years, rounded to the nearest penny, is $34,828.59

The 6 steps for inferential statistics to test researchers question can be:

It is the branch of statistics that is concerned with obtaining information about a population from a sample of that population. It is used to make inferences, that is, draw conclusions and make predictions about the population based on the information obtained from the sample.

These assertions are based on hypothesis tests, confidence intervals and statistical models.

Therefore, the goal of inferential statistics is to make accurate and reliable statements about the population using limited sample information.

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The length of the hypotenuse in the given right-angle triangle is 7.5 feet.

According to Pythagoras' theorem, "the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides." Perpendicular, Base, and Hypotenuse are the names given to the triangle's sides. The hypotenuse is the longest side in this case since it is opposite the angle of 90°.

It is a right-angle triangle.

[tex]c = \sqrt{6^{2} +4^{2} } \\c = \sqrt{36 + 16}\\ c = \sqrt{56}\\ c = 7.48[/tex]which is nearly equal to 7.5

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Complete question:

Answer:

225

Step-by-step explanation:

1 1/4 can be put into decimal form:

1.25

So the equation would now be

1.25 times 180

use a calculator:

225

Answer: 225

1 1/4 x 180 = 225