could someone please help me? thank you!​

To determine whether the actual fit is an interference fit or a clearance fit, you need to measure the actual sizes of the shaft and hole and compare them to the tolerance limits specified by the H8 and p7 designations.

In a transition fit, such as φ50 H8/p7, the fit allows for both interference and clearance depending on the actual sizes of the shaft and hole.

To determine whether the actual fit formed by the actual shaft and hole is an interference fit or a clearance fit, we need to compare the actual sizes of the shaft and hole with the tolerance limits specified by the H8 and p7 designations.

In this case, the H8 tolerance for the hole indicates a basic hole size with a relatively tight tolerance, while the p7 tolerance for the shaft indicates a basic shaft size with a looser tolerance. The "φ50" specification specifies the nominal size of the fit as 50 mm.

If the actual shaft size falls within the upper limit of the p7 tolerance and the actual hole size falls within the lower limit of the H8 tolerance, the fit will be a clearance fit. This means that there will be a gap or clearance between the shaft and the hole, allowing for easy assembly and potential movement or play between the parts.

On the other hand, if the actual shaft size falls within the lower limit of the p7 tolerance and the actual hole size falls within the upper limit of the H8 tolerance, the fit will be an interference fit. This means that the shaft will be larger than the hole, resulting in a tight fit where the parts are pressed or forced together. This can create friction and require more force for assembly.

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The answer is 3√5 units.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

With the given vertices value of the triple integral is 0.

To evaluate the triple integral of the function f(x, y, z) = xyz over the given tetrahedron T with vertices (0,0,0), (1,0,0), (1,1,0), and (1,0,1), follow these steps:

1. Set up the limits of integration: The tetrahedron T is bounded by the planes x=0, y=0, z=0, x+y+z=1. We need to find the limits for x, y, and z.

- For x, the range is between the points (0,0,0) and (1,0,0), so 0 ≤ x ≤ 1.
- For y, given a fixed value of x, the range is between the points (x,0,0) and (x,1-x,0), so 0 ≤ y ≤ 1-x.
- For z, given fixed values of x and y, the range is between the points (x,y,0) and (x,y,1-x-y), so 0 ≤ z ≤ 1-x-y.

2. Write the triple integral with the determined limits of integration:
⌡⌡⌡(xyz dV) = ∫(from 0 to 1) ∫(from 0 to 1-x) ∫(from 0 to 1-x-y) xyz dz dy dx.

3. Integrate with respect to z:
∫(from 0 to 1) ∫(from 0 to 1-x) [(1/2)xyz²] (from 0 to 1-x-y) dy dx
= ∫(from 0 to 1) ∫(from 0 to 1-x) (1/2)xyz(1-x-y)² dy dx.

4. Integrate with respect to y:
∫(from 0 to 1) [(1/6)x(1-x)³] (from 0 to 1-x) dx
= ∫(from 0 to 1) (1/6)x(1-x)³ dx.

5. Integrate with respect to x:
[(1/24)(1-x)⁴] (from 0 to 1)
= (1/24)(1-1)⁴ - (1/24)(1-0)⁴
= 0.

Therefore, the value of the triple integral is 0.

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The probability that the customer will default. is 0.2337.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

P(missing one month payment | not default) = 0.21

P(missing one month payment | default) = 1

P(missing one month payment) = P(missing one month payment | default) * P(default) + P(missing one month payment | not default) * P(not default)

= 1 * 0.03 + 0.21 * 0.97

= 0.2337

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Hello!

Answer:

A. The theoretical probability of flipping 3 heads on one flip of three coins is (1/2) * (1/2) * (1/2) = 1/8. Since you flipped three heads 7 times out of 50, the experimental probability of flipping 3 heads is 7/50.

B. To calculate the theoretical probability of flipping less than 3 heads, we can calculate the probability of flipping 0, 1, or 2 heads and add them together. The probability of flipping 0 heads is (1/2) * (1/2) * (1/2) = 1/8, since all three coins must come up tails. The probability of flipping 1 head is (1/2) * (1/2) * (1/2) * 3 = 3/8, since there are three ways to get one head (HTT, THT, TTH). The probability of flipping 2 heads is (1/2) * (1/2) * (1/2) * 3 = 3/8, since there are three ways to get two heads (HHT, HTH, THH). Therefore, the theoretical probability of flipping less than 3 heads is:

1/8 + 3/8 + 3/8 = 7/8.

So the theoretical probability of flipping less than 3 heads is 7/8.

Answer:

X = add 25  Y =add 3 see 3 ,3+3=6  so i think y is 3

Step-by-step explanation:

Answer:

87.8

Step-by-step explanation:

87 + 80 + 96 + 94 + 88 = 439

439 ÷ 5 = 87.8

If you have a required return of 6% per year, compounded monthly, and you are offered an investment that will pay you $800 a month for 40 years, you would be willing to pay approximately $206,595.71 for this investment.

To determine the value you would be willing to pay for this investment, we can use the concept of present value. The present value of an investment is the current worth of the future cash flows it will generate. In this case, the investment will pay you $800 a month for 40 years.

To calculate the present value, we can use the formula:

\(PV = CF / (1 + r)^n\)

Where PV is the present value, CF is the cash flow, r is the required return per period, and n is the number of periods.

In this case, the cash flow is $800 per month, the required return is 6% per year (or 0.06/12 = 0.005 per month), and the number of periods is 40 years * 12 months = 480 months.

Plugging these values into the formula, we have:

PV = $800 / \((1 + 0.005)^(480)\)

Calculating this expression, we find that the present value is approximately $206,595.71. Therefore, you would be willing to pay approximately $206,595.71 for this investment to achieve your required return of 6% per year, compounded monthly.

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Answer:

It is its tenth value

Step-by-step explanation:

The 4 in .487 is the tenths value

Answer:

\(\frac{4}{12}\) or \(\frac{1}{3}\)

Step-by-step explanation:

\(\frac{1}{4} + \frac{1}{12} = \frac{3}{12} + \frac{1}{12} = \frac{4}{12}\)

Answer:

Domain: [-1, 5]

Range: [-1, 2]

Step-by-step explanation:

Answer:

25×124/100=31

120×175/100=210

35×160/100=56

72×165/100=118.8

Answer:

5) 31

6) 210

7) 14

8) 25.2

Step-by-step explanation:

25+6=31

120+90=210

35-21=14

72-46.8=25.2

Answer:

Hence option C is correct...hope this helps you:)

The length CF in the circle is 12.12 units

From the question, we have the following parameters that can be used in our computation:

TM = 14

This is the diameter of the circle

So, it means that

OC = OF = 14/2

OC = OF = 7

The length CF is then calculated as

sin(60) = (1/2 CF)/OC

This gives

sin(60) = (1/2 CF)/7

So, we have

1/2CF = 7 * sin(60)

Multiply by 2

CF = 2 * 7 * sin(60)

Evaluate

CF = 12.12

Hence, the segment is 12.12 units long

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There are 144 possible sequences of chip colors.

We can solve this problem by counting the number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7.

Let's consider all the possible sequences of chips that can be drawn from the bag. The first chip can be any of the 6 chips in the bag. For each chip color, there are different scenarios that can happen after drawing the first chip:

Therefore, the total number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7 is: 2 x 32 + 1 x 32 + 3 x 16 = 144

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Answer:

113

Step-by-step explanation:

96+17=113

180-113=67

67+x=180

x=180-67

x=113

Answer:

y = x + 5

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes, so the line will have a slope of 1.

Then, plug in the slope and given point into y = mx + b to solve for b:

y = mx + b

-4 = 1(-9) + b

-4 = -9 + b

5 = b

Plug in the slope and b into y = mx + b:

y = 1x + 5

y = x + 5

So, the equation of the line is y = x + 5

Using the formula of compound interest and simple interest, the investment option that is better is at interest rate of 3.99% which is compounded monthly

To compare the investment options, you need to calculate the future value of each investment after 8 years. Here's a breakdown of each option:

A. 3.99% compounded monthly: This option earns interest every month and compounds, meaning the interest is added to the principal, so future interest is earned on the increased principal amount. This type of interest compound is the most advantageous to the investor. The formula for calculating the future value for this option is:

FV = P * (1 + r/n)^(nt)

FV = 12000(1 + 0.0399 / 12) * (12 * 8)

FV = $16,503.58

where P is the principal ($12,000), r is the annual interest rate (3.99%), n is the number of times the interest is compounded in a year (12 times), t is the number of years invested (8 years).

B. 4% compounded quarterly: This option earns interest every quarter and compounds. The formula for calculating the future value is the same as option A, with the only difference being the number of times the interest is compounded in a year (n=4).

Substituting the values into the formula;

FV = $16,499.29

C. 4.175% compounded annually: This option earns interest once a year and compounds. The formula for calculating the future value is the same as options A and B, with the only difference being the number of times the interest is compounded in a year (n=1).

Substituting the values into the formula

FV = $16,645.21

D. 4.2% simple interest: This option earns interest once a year based on the original principal amount and does not compound. The formula for calculating the future value for this option is:

FV = P(1 + rt)

FV = 12000 (1 +  0.042 * 8)

FV = $16032

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Answer:

7x(3+2)=35x

add:

3+2=5

multiply:

7x(5)=35x

just using the distributive property, nothing more

Answer:

35x

Step-by-step explanation:

you just use the distributive property and the combine like terms and thats it.

a. The coordinates of the new triangle's points after a dilation with a scale factor of 2 are A'(-5, -9), B'(13, 7), and C'(-13, 5).

b. The coordinates of the new triangle's points after a dilation with a scale factor of 1/2 are A"(-1/2, 0), B"(4, 4), and C"(-5/2, 7/2).

a. If the scale factor is 2, the coordinates of the new triangle's points A', B', and C' can be found by applying the dilation formula:

For point A:

x-coordinate of A' = (scale factor) * (x-coordinate of A) + (1 - scale factor) * (x-coordinate of center)

y-coordinate of A' = (scale factor) * (y-coordinate of A) + (1 - scale factor) * (y-coordinate of center)

Using the given values:

x-coordinate of A' = 2 * (-2) + (1 - 2) * 1 = -4 + (-1) = -5

y-coordinate of A' = 2 * (-3) + (1 - 2) * 3 = -6 + (-3) = -9

So, the coordinates of point A' are (-5, -9).

Following the same formula, we can find the coordinates of B' and C':

For point B:

x-coordinate of B' = 2 * 7 + (1 - 2) * 1 = 14 + (-1) = 13

y-coordinate of B' = 2 * 5 + (1 - 2) * 3 = 10 + (-3) = 7

So, the coordinates of point B' are (13, 7).

For point C:

x-coordinate of C' = 2 * (-6) + (1 - 2) * 1 = -12 + (-1) = -13

y-coordinate of C' = 2 * 4 + (1 - 2) * 3 = 8 + (-3) = 5

So, the coordinates of point C' are (-13, 5).

b. If the scale factor were 1/2, the coordinates of the new triangle's points A", B", and C" can be found using the same dilation formula:

For point A:

x-coordinate of A" = (scale factor) * (x-coordinate of A) + (1 - scale factor) * (x-coordinate of center)

y-coordinate of A" = (scale factor) * (y-coordinate of A) + (1 - scale factor) * (y-coordinate of center)

Using the given values:

x-coordinate of A" = (1/2) * (-2) + (1 - 1/2) * 1 = -1 + 1/2 = -1/2

y-coordinate of A" = (1/2) * (-3) + (1 - 1/2) * 3 = -3/2 + 3/2 = 0

So, the coordinates of point A" are (-1/2, 0).

Following the same formula, we can find the coordinates of B" and C":

For point B:

x-coordinate of B" = (1/2) * 7 + (1 - 1/2) * 1 = 7/2 + 1/2 = 4

y-coordinate of B" = (1/2) * 5 + (1 - 1/2) * 3 = 5/2 + 3/2 = 4

So, the coordinates of point B" are (4, 4).

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The distance from City Hall to 2nd Street along Cedar Road is 5.4 miles

The scale factor is the size by which the shape is enlarged or reduced. It is used to increase the size of shapes like circles, triangles, squares, rectangles, etc.

From City Hall to 1st St. form a triangle. Also, City Hall to 2nd St. form a triangle.

We can use the ratio of the distances along Aspen road (scale factor) of the triangles to find the required distance. That is:

scale factor =  (2.8 + 3.5)/2.8 = 6.3/2.8 = 2.25

Let the distance from City Hall to 1st St. be x. Thus:

scale factor = (x + 3.0)/x

2.25 = (x + 3.0)/x

2.25x = x + 3.0

2.25x -x = 3.0

1.25x = 3.0

x = 3.0/1.25

x = 2.4 miles

distance from City Hall to 2nd Street along Cedar Road = x + 3.0

distance from City Hall to 2nd Street along Cedar Road = 2.4 + 3.0 = 5.4 miles

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Answer:

725.51

Step-by-step explanation:

Integer -17 represents Rudy's score for 2 weeks.

Rudy's scores:

Then, add 15 and -32 as follows:

Therefore, integer -17 represents Rudy's score for 2 weeks.

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Answer:

B. h(x) = -3x + 4.

Step-by-step explanation:

I am assuming that the vertical shift is upwards,

A refection in the x axis gives -3x

Vertical shift upwards of 4 gives -3x + 4.

The width of the tank, which has a length 4 feet longer than its width, the height is 2 feet more than the width which is three feet.

The Hit and Trial Method is a very useful to solve the roots in a equation. In this , substituting different values of the variable and checking the equality of LHS and RHS is the trial and error method.

We have a tank ( cuboid shape) with

length, width and height and volume of tank is 105 cubic feet. Let length , width and height of tank be "l" feet , "w " feet and "h" feet.

lenght, l = w + 4

height, h = w + 2

Volume of tank , V = l× h × w

=> (w + 4 )×w × (w + 2) = 105

=> w ( w² + 6w + 8) = 105

=> w³ + 6 w²+ 8 w = 105

Using the hit and trial method to solve the above cubic equation in one variable, w.

We get, w = 3

So, the required width is 3 feet .

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Answer:

two real, unequal  roots

Step-by-step explanation:

This is a quadratic equation.  The quadratic formula can be used to determine how many and what kind of roots may exist:  

Find the discriminant, which is defined as b^2 - 4ac, if ax^2 + bx + c = 0.  In this case, a = 1, b = -2 and c  = -8, so that the discriminant value is

(-2)^2 - 4(1)(-8), or 4 + 32  =  36.

Because the discriminant is real and positive, we know for certain that we have two real, unequal  roots

The percentage off of the coupon is 25%

From the question, we have the following parameters that can be used in our computation:

Normal price = $24

Amount saved = $6

The above parameters mean that

Percentage of the coupon = Amount saved/Normal price

Substitute the known values in the above equation, so, we have the following representation

Percentage of the coupon = 6/24

Evaluate

Percentage of the coupon = 25%

Hence, the percentage is 25%

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a) Yes, A ⊆ B. For any x in A, x^2 < 9, and since x^2 is always less than 9 for x < 3, A is a subset of B.

b) No, B ⊈ A. There exist elements in B (e.g., x = 2) that do not satisfy x^2 < 9, thus B is not a subset of A.

a) To determine if A ⊆ B, we need to verify if every element in set A is also an element of set B.

Set A is defined as A = {x ∈ ℝ | x^2 < 9}, which means A consists of all real numbers whose square is less than 9.

Set B is defined as B = {x ∈ ℝ | x < 3}, which means B consists of all real numbers that are less than 3.

To show that A ⊆ B, we need to prove that for any x in A, x must also be in B.

Let's consider an example. If we choose x = 2, it satisfies the condition x^2 < 9 (since 2^2 = 4 < 9), and it also satisfies the condition x < 3 (since 2 is less than 3).

Since x = 2 belongs to both sets A and B, we can conclude that A is a subset of B: A ⊆ B.

b) To determine if B ⊆ A, we need to verify if every element in set B is also an element of set A.

Using the definitions of sets A and B from the previous part:

Set A is defined as A = {x ∈ ℝ | x^2 < 9}, and set B is defined as B = {x ∈ ℝ | x < 3}.

To show that B ⊆ A, we need to prove that for any x in B, x must also be in A.

Let's consider an example. If we choose x = 2, it satisfies the condition x < 3 (since 2 is less than 3), but it does not satisfy the condition x^2 < 9 (since 2^2 = 4 is not less than 9).

Since x = 2 belongs to set B but not to set A, we have found a counterexample. Therefore, B is not a subset of A: B ⊈ A.

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