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Answer:

Step-by-step explanation:

If diameter is 5, then the radius is 2.5 cm.

Area of circle = πR²

Area = 3.14 * 2.5^2 = 3.14 * 6.25 = 19.625

Circumference = π * Diameter

Circumference = 3.14 * 5 = 15.7

Answer:

Step-by-step explanation:

Objective: find the circumference and area of a circle.

Given values; diameter: 5cm, pie: 3.14.

Step one:

Circumference: pie x diameter

= 3.14 x 5cm = 15.7 cm (circumference)

Step two:

Area: ( pie x radius to the power of 2)

= 3.14 x 6.25 cm

= 19.625 (area)

Answer:

67 inches

Step-by-step explanation:

Step-by-step explanation:

A³B = 4T

A³=4T/B

A = cbrt 4T/B. or

³√(4T/B)

hope this helps.

Answer:

Please see the attached picture for the full solution.

9514 1404 393

Explanation:

Substituting the cut line into the curve equation, we have ...

  x(x+10) = 11x +5

In standard form this is ...

  x^2 -x -5 = 0

The sum of the two roots of this equation is the opposite of the x-coefficient*, so is -(-1) = 1. Then the midpoint between the points of intersection has an x-coordinate of ...

   (root sum)/2 = 1/2

__

The midpoint y-coordinate will be the y-value on the cut line, so is ...

  y = x + 10 = (1/2) +10 = 10.5

Then the midpoint of AB is C(0.5, 10.5). This is easily shown to lie on the line ...

  x + y = 11

  0.5 + 10.5 = 11

_____

* The factored form of a monic polynomial can be expanded to show this:

  (x -a)(x -b) = x^2 -(a+b) +ab

That is, the sum of the roots a and b is the opposite of the x-coefficient.

Answer:

QR=2x=16

Step-by-step explanation:

2x+8= 3x

8=3x-2x

8=x

QR=2x= 8*2=16

Answer:

The area of the room is 37.5 square inches.

Step-by-step explanation:

Consider that the room is rectangular in shape.

The dimensions of the rooms are:

Length (l) = 7.5 inches

Breadth (b) = 5 inches

The area of a rectangle is:

Area = l × b

Compute the area of the room as follows:

Area = l × b

        \(=7.5\times 5\\=37.5\)

Thus, the area of the room is 37.5 square inches.

The volume of the given shape above would be = 32cm³

The volume of the shape can be calculated by the addition of volume of a cube and a rectangle cube.

The formula for the volume of a rectangular cube = Length × width × height

Where,

Length = 6m

width = 2m

height = 2m.

Volume = 6×2×2 = 24cm³

The volume of cube = a³

where a = 2

Volume = 2³ = 8cm³

Therefore the volume of the shape = 24+8 = 32cm³

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The five elements to be assessed during sample selection in audit sampling are Sapmlinf Frame, Sample Size, Sampling Method, Sampling Interval, Sampling Risk.

1. Sampling Frame: The sampling frame is the list or source from which the sample will be selected. It is important to ensure that the sampling frame represents the entire population accurately and includes all relevant elements.

2. Sample Size: Determining the appropriate sample size is crucial to ensure the sample is representative of the population and provides sufficient evidence for drawing conclusions. Factors such as desired confidence level, acceptable level of risk, and variability within the population influence the determination of the sample size.

3. Sampling Method: There are various sampling methods available, including random sampling, stratified sampling, and systematic sampling. The chosen sampling method should be appropriate for the objectives of the audit and the characteristics of the population.

4. Sampling Interval: In certain sampling methods, such as systematic sampling, a sampling interval is used to select elements from the population. The sampling interval is determined by dividing the population size by the desired sample size and helps ensure randomization in the selection process.

5. Sampling Risk: Sampling risk refers to the risk that the conclusions drawn from the sample may not be representative of the entire population. It is important to assess and control sampling risk by considering factors such as the desired level of confidence, allowable risk of incorrect conclusions, and the precision required in the audit results.

During the sample selection process, auditors need to carefully consider these elements to ensure that the selected sample accurately represents the population and provides reliable results. By assessing and addressing these elements, auditors can enhance the effectiveness and efficiency of the audit sampling process, allowing for meaningful generalizations about the population.

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Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

The region in the plane consists of all points with polar coordinates (r,θ) such that 0 ≤ r < 7 and π ≤ θ ≤ 3π/2 is the shaded region in the fourth quadrant bounded by the circle with radius 7 and the positive x-axis extended to the origin.

In polar coordinates, a point in the plane is represented by its distance from the origin (r) and the angle it makes with the positive x-axis (θ). The given conditions are 0 ≤ r < 7 and π ≤ θ ≤ 3π/2.

The condition 0 ≤ r < 7 means that the points must be inside the circle of radius 7 centered at the origin. The condition π ≤ θ ≤ 3π/2 means that the points must be in the fourth quadrant and lie between the angles π and 3π/2 measured from the positive x-axis.

Therefore, the shaded region in the fourth quadrant bounded by the circle with radius 7 and the positive x-axis extended to the origin is the region in the plane consisting of all points with polar coordinates (r,θ) such that 0 ≤ r < 7 and π ≤ θ ≤ 3π/2.

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Answer:

13 1/3 pounds

Step-by-step explanation:

Hi! Each bad weighs 2 2/3 pounds. There were 5 bags bought so we multiply. Here is the expression:

2 2/3 x 5 = x

Now we need to convert 2 2/3 into an improper fraction, which is 8/3.

Easy! Now

8          5         40

-      x    -     =    -

3           1          3

*I tried to set it up like fractions.*

Simplify 40/3 and you get 13 1/3

Step-by-step explanation:

Given

5e = 45

e = 45 / 5

e = 9

Hope it will help :)

Answer: When viewed from the side, the spire forms an isosceles triangle m, the area of the isosceles triangle is equal to  1/4b√4a²-b².

Step-by-step explanation:

What is isosceles triangle?

A triangle with two equal-length sides is said to be isosceles. The triangle's third side is referred to as the base, while the triangle's two equal sides are known as the legs. The triangle's legs are usually shorter than the base, which is usually the triangle's longest side.

To determine if the spire on top of a building forms an isosceles triangle when viewed from the side, we first need to define the three sides of the triangle. Let's call the two sides that are equal in length "s" and the third side "l".

Next, we need to determine if the triangle satisfies the definition of an isosceles triangle. The two sides "s" of the spire must therefore be of equal length for the spire to create an isosceles triangle.

To confirm this, we can measure the length of the sides "s" and compare them to each other. If they are equal in length, then the spire forms an isosceles triangle. If they are not equal in length, then the spire does not form an isosceles triangle.

For example, if the base of the triangle is 10 feet and the length of the two equal sides is 10 feet, then the triangle is isosceles. Therefore, the spire on the top of the building forms an isosceles triangle when viewed from the side.

Therefore, if the two sides "s" of the spire are equal in length, then the spire forms an isosceles triangle when viewed from the side.

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An isosceles triangle is a triangle with two sides of equal length and two equal angles.

What is isosceles triangle?

An isosceles triangle is a type of triangle that has two sides of equal length and two angles of equal measure. The two sides of equal length are the two legs of the triangle, while the third side is called the base. The angles opposite the two equal sides are equal in measure, while the angle opposite the base is the third angle. Isosceles triangles are classified according to the measure of their angles. An equilateral triangle is an isosceles triangle with all angles equal to 60°. An isosceles triangle with two angles equal to 45° is called an isosceles right triangle. An isosceles triangle with two angles equal to less than 45° is referred to as an acute isosceles triangle, while an isosceles triangle with two angles equal to more than 45° is referred to as an obtuse isosceles triangle. Isosceles triangles have many practical uses in engineering and architecture. For example, buildings and bridges often feature isosceles triangles in their roofs and arches in order to provide strength and stability.

When viewed from the side, the spire on the top of a building forms an isosceles triangle because it has two equal sides (the sides running up the spire) and two equal angles (the angles at the base of the spire).

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There are a total of 212 pounds of berries, and the number of friends sharing the berries is equal to 4.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

The total amount of berries = 212 pounds

The number of berries received by each one = 54 pounds

Then, the number of friends sharing the berries is:

212/54 = 3.92 ≈ 4 friends.

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Answer:

31

Step-by-step explanation:

7, 10, 12, 16, 19, 22, 25, 28, 31

Adding by 3

Hope this works

Answer:

5

combine like terms, simplify, add or subtract all answers are 5.

Answer:

Step-by-step explanation:

= -5

Step-by-step explanation:

b.) 8/7≈ 1.1

Final.) and then using the exponential decay formula, 18.1 will be left after

Answer:Ming pays $25.96 to the cab driver.

Step-by-step explanation:

Ming took a cab across town, his fare of cab = $22.00

He leaves a tip of 18% of total fare = 18% of $22.00

Total amount = (18% of $22) + $22.00

( 18/100× 22) + 22.00

= (0.18 × 22) + 22.00

= 3.96 + 22.00

= $25.96

Ming pays $25.96 to the cab driver.

The y-intercept of g(x) is -23. Since f(x) is an even function, we know that f(-x) = f(x) for all x.

Therefore, we can conclude that f(6) = f(-6).
And since f(6) = -8, we can also say that f(-6) = -8.
Now, we can use the given equation for g(x) to find its y-intercept:
g(x) = 2f(x-6) - 7
To find the y-intercept, we need to set x = 0:
g(0) = 2f(0-6) - 7
g(0) = 2f(-6) - 7
g(0) = 2(-8) - 7
g(0) = -23
Therefore, the y-intercept of g(x) is -23.
An even function satisfies the condition f(-x) = f(x). Given that f(6) = -8 and g(x) = 2f(x-6) - 7, we can find the y-intercept of g(x) by substituting x = 0.
g(0) = 2f(0-6) - 7 = 2f(-6) - 7
Since f(x) is an even function, f(-6) = f(6) = -8.
g(0) = 2(-8) - 7 = -16 - 7 = -23
So, the y-intercept of g(x) is -23.

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The mass of the solid is 7π/2 units.

The task is to calculate the mass of the solid.

Step-by-step solution: The solid occupies the region between the unit sphere at the origin and a sphere of radius 2 with the center at the origin. The spherical coordinates in 3D space are (r,θ,φ), where:r = radius, θ = polar angle, φ = azimuthal angle.

The equations of the given sphere are r=1 for the unit sphere and r=2 for the second sphere.

Using spherical coordinates, the solid can be defined as 1≤r≤2, 0≤θ≤2π, 0≤φ≤π.

The density is equal to the distance from the origin, i.e. ρ = r.

The mass of the solid is given by the triple integral ρ dV taken over the solid, where dV is the volume element in spherical coordinates.dV = r²sin φ dφdθdr

The limits for the triple integral are: 0 ≤ θ ≤ 2π, 0 ≤ φ ≤ π, and 1 ≤ r ≤ 2.M = ∭ρ dV = ∭r(r²sin φ) dφdθdr= ∫[0,2π]∫[0,π]∫[1,2] r³sin φ drdφdθ= ∫[0,2π]∫[0,π] -cos φ [r⁴/4]₁ ₂ drdφdθ= ∫[0,2π]∫[0,π] 7/4 cos φ dφdθ= ∫[0,2π] 7sin φ/4 ]₀  π dθ= 14π/4= 7π/2 units.

The mass of the solid is 7π/2 units.

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Answer:

Triangle 1 : isosceles triangle

Triangle 2 : Right Triangle

Step-by-step explanation:

The value of PQ is 1.

Given is a right triangle PQR, where ∠P and ∠R = x° and PR (hypotenuse) = √2, We need to find the value of PQ,

Since the angles P and R are equal so the sides PQ and QR are equal by the definition of postulate of triangles,

Therefore,

Using the Pythagoras theorem,

PQ² + QR² = PR²

PQ² + PQ² = √2²

2PQ² = 2

PQ² = 1

PQ = 1

Hence the value of PQ is 1.

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Using Excel, the probability that at least 35 of the 154 randomly selected vehicles exceed 110 kilometers per hour when 17.7% of vehicles exceed this speed on the expressway is approximately 0.0027, rounded to four decimal places.

To solve this problem in Excel, we can use the binomial distribution function. In this case, the probability of success (a vehicle exceeding 110 kilometers per hour) is p = 0.177, and the number of trials (vehicles selected) is n = 154.

We want to find the probability of at least 35 successes (vehicles exceeding 110 kilometers per hour), which can be calculated using the formula:

=1-BINOM.DIST(34,154,0.177,TRUE)

This formula gives a probability of 0.0027, which is the probability that at least 35 of the selected vehicles exceed 110 kilometers per hour. Therefore, the answer is 0.0027, rounded to four decimal places.

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Answer:

G should be at the sum of y and x combined but x is not given

Step-by-step explanation:

Answer:

(0,-2)

Step-by-step explanation:

The graph intercepts through the y axis, G.

You can get these coordinates b solving the equation like so:

y=3x-2

move the x varible to the left side and the y to the left....

-3x+y=-2        

 -3x=-2-y

divided both sides by 3 to isolate x

x= 2/3+ 1/3y

when you graph that equation you get the points (0,-2)

The equation of the line with a slope of −1/4 that passes through the point (4, 5) is y = - x/4 + 6.

The slope of the line is given as a tangent angle made by line with horizontal. i.e. m = tanx where x in degrees.

Here,

The slope of the line is given as,

m = -1/4

The equation of the line passing through point t (4, 5), is given as

y - y₁ = m (x - x₁)

y -5 = -1/4 (x - 4)
y = -x/4 +1 + 5
y = - x/4 + 6

Thus, the equation of the line is y = - x/4 + 6.

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Answer:

false

Step-by-step explanation:

Answer:

false

Step-by-step explanation: