Find the number which when divided by 4 and increased by 12 is the same as when it is divided by 3 and decreased by 5

\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)

Answer:

(a) 5

Step-by-step explanation:

All negative numbers are less than 0, and 0 is less than 4, so all negative numbers are less than 4.

The calculation of the dot product of the vectors r1 and r2 results in a value of 58, which represents the magnitude of the projection of one vector onto the other.

The dot product (also known as the scalar product or inner product) of two vectors is a scalar value that represents the magnitude of the projection of one vector onto the other. In mathematical terms, it is defined as the product of the magnitudes of the two vectors and the cosine of the angle between them.

Given vectors r1 = 6i + 2j and r2 = 7i + j, the dot product r1•r2 can be calculated by multiplying the corresponding components of the vectors and summing them up.

In this case, the dot product r1•r2 is equal to:

r1•r2 = (6i + 2j)•(7i + j)

     = (6i•7i) + (6i•j) + (2j•7i) + (2j•j)

     = 42 + 0 + 14 + 2

     = 58

Note that the dot product of two vectors is commutative, meaning that r1•r2 = r2•r1. Also, the dot product of two orthogonal (perpendicular) vectors is zero, which represents the absence of a projection.

In this problem, the dot product r1•r2 is equal to 58, which means that the projection of r1 onto r2 has a magnitude of 58 units.

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Answer:

Step-by-step explanation:

23

Tyron receives a 30% discount on a hat. Calculations of discount percent are provided below.

The discount Percentage is calculated by = \(( Discount / Price )\) × \(100\)

What information do we have,

Usual cost = $28

Discount = $ 8.40

So,

Discount percentage \(= ( 8.40 / 28 )\) × 100

= 30%

Thus, 30% is the correct answer.

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a)

Values of the given angles  ∠A = 123°  , ∠B = 123° ,∠C = 57.

Given ,

One angle of the figure as 123°.

Now,

∠C and 123° form linear pair.

So,

∠C + 123° = 180°

∠C = 57°

Now,

∠C and ∠B are pairs of interior angles on same side of transversal, thus they are supplementary.

∠C + ∠B = 180°

Substitute the value of ∠C

53° + ∠B = 180°

∠B = 127°

Now,

∠B and ∠A are vertically opposite angles.

Thus,

∠B = ∠A

So,

∠A = 127° .

Hence,

∠A= 127°

∠B = 127°

∠C = 57°

b)

Values of ∠D = 98°, ∠E = 98°, ∠F = 98° .

Given one angle as 82°

Now,

∠F and 82° form linear pair.

So,

∠F + 82° = 180°

∠F = 98°

Now,

∠D and ∠F are corresponding angles. Thus,

∠D = ∠F

∠D = 98° .

Now,

∠D and ∠E are vertically opposite angles.

Thus,

∠D = ∠E

∠E = 98°.

Hence,

∠D = 98°

∠E = 98°

∠F = 98°

c)

Values of ∠G = 75° and ∠H = 75°

Given one angle as 75° .

∠H and 75° are corresponding angles. Thus,

∠H = 75°

Now,

∠H and ∠G are vertically opposite angles.

So,

∠G = 75° .

Hence,

∠G = 75°

∠H = 75°

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The fracture toughness, Kc, of the shaft with the given specifications can be computed by using the formula given below: Kc = ( σf (pi*a) ) / ( Y*sqrt(pi*c) )where:σf is the maximum stress value (N/m2) associated with fracture.a is the radius of curvature of the crack (m).Y is the form factor of the material.c is the length of the crack (m).

The form factor of the material can be computed using the following equation: Y = 1.99 - (3.02*(a/c)) + (3.92*(a/c)^2) - (1.29*(a/c)^3)In the given problem, the maximum load of 65,000 N during operation is not useful. We are given the radius of curvature of the crack, the diameter of the shaft, and the crack's length, and we have to find the fracture toughness of the shaft.

Therefore, the formula to be used here is as follows:Kc = σf (pi*d) / [ Y * sqrt(pi*a) ]Now let's solve for Kc using the given values of a, c, and d:Given values of a, c, and d:a = 0.16 x 10^-2 mc = 0.32 x 10^-3 md = 20 mm = 0.02 mHence,πd = π × 0.02 m = 0.0628 m.

Therefore, substituting the given values into the formula,Kc = σf × (pi*d) / [ Y * sqrt(pi*a) ]Kc = σf × (0.0628 m) / [ Y * sqrt(π × 0.16 × 10^-2 m) ]Note that Y is the form factor of the material and that it is not given. As a result, we can use Y = 1.12 (from the table of materials in Shigley's textbook, Table A-15).Y = 1.12The value of Y changes for different materials, so it is essential to select the correct one depending on the material utilized.

Finally, substituting the given values in the above equation, we get the answer as:Kc = ( 65,000 N/m^2 × 0.0628 m ) / [ 1.12 × sqrt(π × 0.16 × 10^-2 m) ]Kc = 225.37 MPa·m^1/2 .

In this problem, we are given the diameter of a shaft, a crack's radius of curvature, and its maximum load during operation. The fracture toughness of the shaft is what we need to find out. The formula for fracture toughness is Kc = ( σf (pi*a) ) / ( Y*sqrt(pi*c) ). We are given a, c, and d, and we need to find Kc. We can use the formula Kc = σf (pi*d) / [ Y * sqrt(pi*a) ] by replacing the appropriate values of the given parameters.The value of Y is different for different materials. It is provided in the table of materials in Shigley's textbook, Table A-15. In this example, we utilized Y = 1.12. We get the answer as Kc = 225.37 MPa·m^1/2.

The fracture toughness of the shaft is found to be 225.37 MPa·m^1/2.

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Answer:

the answer would be -4

Step-by-step explanation:

x + 5 =1

subtract the 5 from the 5 and 1, giving you...

x = -4

I hope this helps you out!

Answer: Each pen cost $0.75

Step-by-step explanation:

If A LaDawn buys a pack of 10 gel pens and the total cost is $7.50 then you divide 7.50 by 10.

A bicycle repair shop that offers two service packages: a tune-up and a complete overhaul.

The shop operates for 60 hours per week and receives an average of 180 bicycles each week. To analyze the capacity and utilization of the process, we need to consider the time taken at each stage and the demand for each service option. We'll break down the problem into multiple parts and provide a detailed explanation using mathematical terms.

a) Creating the Demand Matrix:

To create a demand matrix, we need to determine the number of bicycles going through each stage of the process. Let's denote the demand for tune-up as T and the demand for additional services as A.

Given that the average number of bicycles received per week is 180 and 25% of customers opt for additional services, we can calculate the demands as follows:

Demand for tune-up (T) = Total demand - Demand for additional services

T = 180 - (0.25 * 180)

T = 180 - 45

T = 135

Demand for additional services (A) = 0.25 * Total demand

A = 0.25 * 180

A = 45

Now, we can create a demand matrix based on the demand for each service option:

Demand Matrix:

Tune-up Additional Services Wheel Balancing

Tune-up  [135  0  0]

Additional [0  45  0]

Services

Total [ 135  45  0 ]

The demand matrix shows the number of bicycles flowing through each stage of the process.

b) Daily Capacity at Each Stage:

To calculate the daily capacity at each stage, we need to consider the time taken for each service option. Given that the shop operates for 60 hours per week, we can calculate the daily capacity at each stage:

Tune-up technician time per bicycle (\(T_{tuneup}\)) = 75 minutes

Additional services technician time per bicycle (\(T_{additional}\)) = 72 minutes

Wheel balancing specialist time per bicycle (\(T_{balancing}\)) = 20 minutes

Daily Capacity (C) = (60 hours * 60 minutes) / (\(T_{tuneup}\) + \(T_{additional}\) + \(T_{balancing}\))

Substituting the given values:

C = (60 * 60) / (75 + 72 + 20)

C = 21600 / 167

C ≈ 129.34 bicycles per day

Therefore, the daily capacity at each stage of the process is as follows:

Tune-up: 129 bicycles per day

Additional Services: 129 bicycles per day

Wheel Balancing: 129 bicycles per day

c) Implied Utilizations:

To find the implied utilizations, we need to compare the demand and the capacity at each stage of the process. Utilization can be calculated as the demand divided by the capacity.

Implied Utilization (U) = Demand / Daily Capacity

For the Tune-up stage:

\(U_{tuneup}\) = 135 / 129 ≈ 1.05

For the Additional Services stage:

\(U_{additional}\) = 45 / 129 ≈ 0.35

For the Wheel Balancing stage:

\(U_{balancing}\) = 0 / 129 = 0

The implied utilizations show how efficiently each stage of the process is being utilized. Utilization values greater than 1 indicate that the stage is operating beyond its capacity.

d) Weekly Capacity of the Process:

To calculate the weekly capacity of the process, we multiply the daily capacity by the number of days the shop is open per week:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Given that the shop is open for 60 hours per week, the number of days the shop is open per week can be calculated as follows:

Number of days shop is open per week = 60 hours / 24 hours per day = 2.5 days

Therefore, the weekly capacity of the process is:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Weekly Capacity = 129 bicycles per day * 2.5 days

Weekly Capacity = 322.5 bicycles per week

e) Flow Rate and Constraint Analysis:

To determine if the flow rate of the process is capacity-constrained or demand-constrained, we compare the weekly capacity to the demand for each service option.

Demand for Tune-up (\(T_{demand}\)) = 135 bicycles per week

Demand for Additional Services (\(A_{demand}\)) = 45 bicycles per week

Comparing the demands with the weekly capacity:

\(T_{demand}\) < Weekly Capacity (135 < 322.5)

\(A_{demand}\) < Weekly Capacity (45 < 322.5)

Since both the demands for tune-up and additional services are less than the weekly capacity, the flow rate of the process is demand-constrained. This means the shop has the capacity to handle the current demand without operating beyond its limits.

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Answer:

x= -1.8

Step-by-step explanation:

4x-22=9x+2(1-4x)

2(1 - 4x)

so you have to distribute

new equation

4x-22=9x+2-8x

you combine like terms on the right

9x + 2 -8

+8. +8

17x+2

new equation

4x-22=17x+2

-4x. -4x

-22=13x + 2

-2. -2

-24=13x

-24÷13= - 1.8

X= -1.8

Answer:

\(4x - 22 = 9x + 2 - 4x \\ - x = 24 \\ x = - 24\)

Answer:

B D F

Step-by-step explanation:

I dont really know how to explain it, and I need to reach 20 characters for an answer so pretend this is a good explanation

Answer:

=6-i+4+2i+2-i

=6+4+2+2i-i-i

=12+2i-2i

=12

In the context of mathematics, a series has a stagnant difference between terms. Therefore , we can find out the sum of the terms in arithmetic series by multiplying the number of times the average of the very last and first terms.

Thus we can observe that series and knowing the sum of the terms of series is a very crucial task in mathematics. In this head, we will talk about some very known series and series formulas with instances.

Actually, a series in math is very easy the sum of the different numbers or elements of the series. For instance, to make a series from the channel of the first five positive integers 1, 2, 3, 4, 5 we will simply sum   them up. Therefore 1 + 2 + 3 + 4 + 5 is a series.

So, the series of a sequence is the sum of the sequence to some given number of terms, or occasionally til infinity. It is frequently written as S_n.

If the series is 2, 4, 6, 8, 10, … , then the sum of the first 3 terms:

S

3

=2+4+6

S3=12.

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Answer:

Step-by-step explanation:

In the context of mathematics, a series has a stagnant difference between terms. Therefore , we can find out the sum of the terms in arithmetic series by multiplying the number of times the average of the very last and first terms.

Thus we can observe that series and knowing the sum of the terms of series is a very crucial task in mathematics. In this head, we will talk about some very known series and series formulas with instances.

Actually, a series in math is very easy the sum of the different numbers or elements of the series. For instance, to make a series from the channel of the first five positive integers 1, 2, 3, 4, 5 we will simply sum   them up. Therefore 1 + 2 + 3 + 4 + 5 is a series.

So, the series of a sequence is the sum of the sequence to some given number of terms, or occasionally til infinity. It is frequently written as S_n.

If the series is 2, 4, 6, 8, 10, … , then the sum of the first 3 terms:

S

3

=2+4+6

S3=12.

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Using Conditional probability,

The probability that after a fair coin is tossed 5 times that the result will contain 3 'heads' given that the first toss was a 'head' is 3/5.

A fair coin is tossed five times .

so, total possible outcomes = 2⁵ = 32

Let A: head observed on first toss

B: 3 heads observed.

Probability that the first toss was head (p) = 1/2

we have to find out probability that on 5 tosses result contain 3 heads given that first toss wss head .

Using Binomial Probability distribution

P (X= x) = ⁿCₓ (p)ˣ (q)⁽ⁿ⁻ˣ⁾

x = 3 , n = 5

we get , P(B) = P(X= 3 ) = ⁵C₃(1/2)³(1/2)²

=> P(B) = 10 ×(1/2)⁵= 5/16

since the first toss is fixed as a head.

P(A ∩ B) =P( X₁ = 1 and X₂+ X₃ + X₄ + X₅) = P(X₁= 1)P(X₂+X₃+X₄+X₅)

= 1/2 × ⁴C₂ (1/2)⁵ = 3 (1/2)⁴

The required probability is , Conditional probability P(B/A) = P(A ∩ B)/P(A)

= 3(1/2)⁴/ 5/16 = 3/5

Hence , the required probability is 3/5.

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Answer:

7.29 miles

Step-by-step explanation:

In 1 minute, Brian rides his bike for 0.27 of a mile.

in 27 mins the distance is going to be more than the other ( i.e 0.27 miles)

We use the proportion then get a solution

1 min = 0.27 miles

27 mins = (27 mins÷ 1 min) × 0.27

= 27 × 0.27 miles

= 7.29 miles

Step-by-step explanation:

Given parameters:

  Speed of the Brain's bike  = 0.27mile/min

Time = 27min

Unknown:

distance between Brain's house and where his friend lives =?

Solution:

Speed is a physical quantity.

   It is mathematically expressed as'

     Speed  = \(\frac{distance}{time}\)

   Distance  = speed x time

  Input the parameters;

    Distance  = 0.27mile/min x 27min  = 7.29miles

Answer:

D:(-8,-5)

Step-by-step explanation:

It is already negative and if plotted the coordinates then reflected, it will give this answer

Answer:

f(2) means what is the y value at x=2

so f(2) = -1

f(-2) is asking what the y value at x= -2 is

so f(-2) = -5

Answer:

Step-by-step explanation:

please brainleist please tysm☺️☺️☺️☺️☺️❤❤❤❤❤☻☻☻☻☻

Answers:

angle 1 = 125 degrees

angle 2 = 55 degrees

======================================================

Explanation:

Supplementary angles add to 180

(angle 1) + (angle 2) = 180

(2x+31) + (x+8) = 180

3x+39 = 180

3x = 180-39

3x = 141

x = 141/3

x = 47

Use this to find the angle measures

As a check, 125+55 = 180 to confirm the answer.

Answer:

125 , 55

Step-by-step explanation:

If sum of two angles is 180, then they are called supplementary angles

∠1 + ∠2 = 180

2x + 31 + x +8  = 180

2x + x + 31 + 8 = 180

Combine like terms

3x + 39 = 180

Subtract 29 from both sides

3x = 180 - 39

3x = 141

Divide both sides by 3

x= 141/3

x = 47

∠1 = 2x + 31

    = 2*47 + 31

    = 94 + 31

∠1 = 125

∠2 = x + 8

    = 47 + 8

∠2 = 55

Answer:

6,048

Step-by-step explanation:

l=3w

3w + 3w + w +w =96

8w =96

w=12

l= 36

12×36×14 = 6,048

Answer:

x=0,4/7

Step-by-step explanation:

Factor and set each factor equal to zero.

The standard equation of the circle whose diameter is the line segment with endpoints (-3, 4) and (3, -4) is x^2 + y^2 = 100.

To find the standard equation of a circle given its diameter, we need to find the center and the radius of the circle.

The center of the circle can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints of the diameter. In this case, the x-coordinate of the center is (-3 + 3)/2 = 0, and the y-coordinate of the center is (4 + (-4))/2 = 0. Therefore, the center of the circle is (0, 0).

The radius of the circle is half the length of the diameter. In this case, the distance between the endpoints (-3, 4) and (3, -4) is given by the distance formula: √[(x2 - x1)^2 + (y2 - y1)^2]. Plugging in the values, we get √[(3 - (-3))^2 + ((-4) - 4)^2] = √[6^2 + (-8)^2] = √(36 + 64) = √100 = 10. Therefore, the radius of the circle is 10.

The standard equation of a circle with center (h, k) and radius r is given by (x - h)^2 + (y - k)^2 = r^2. Plugging in the values, we get (x - 0)^2 + (y - 0)^2 = 10^2, which simplifies to x^2 + y^2 = 100.

Therefore, the standard equation of the circle whose diameter is the line segment with endpoints (-3, 4) and (3, -4) is x^2 + y^2 = 100.

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Step-by-step explanation:

To determine the number of candies inside the two boxes, we need to calculate the volume of each box and then convert the weight of the candy to a volume measurement. Let's break down the process step by step:

1. Calculate the volume of one box:

Volume = Length x Width x Height

Volume = 18 inches x 11 inches x 9 inches

Volume = 1782 cubic inches

2. Calculate the total volume of two boxes:

Total Volume = 2 x Volume

Total Volume = 2 x 1782 cubic inches

Total Volume = 3564 cubic inches

3. Convert the weight of the candy to a volume measurement:

Since we have 35 pounds of candy, we need to determine the density of the candy to convert it to volume. Without information about the candy's density, we cannot accurately convert the weight to volume.

Without knowing the density of the candy or its volume-to-weight ratio, it's not possible to determine the exact number of candies inside the two boxes based solely on the given information. The number of candies would depend on the density or the average volume of each candy.

The relative atomic mass of Interactium is 290.14 amu.


We can calculate the relative atomic mass of Interactium using the following equation:

Ar = (Ab × Mb) + (Ac × Mc) + (Ad × Md) where Ar is the relative atomic mass, Ab is the abundance of Interactium-284, Mb is the mass of Interactium-284, Ac is the abundance of Interactium-289, Mc is the mass of Interactium-289, Ad is the abundance of Interactium-294, and Md is the mass of Interactium-294.  

Substituting the given values in the equation, we get:

Ar = (0.16 × 284) + (0.27 × 289) + (0.57 × 294)
Ar = 45.44 + 77.97 + 167.43
Ar = 290.14 amu

Therefore, the relative atomic mass of Interactium is 290.14 amu.

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the optimal solution to maximize Z is x1 = 25 and x2 = 0, with Z = 3000.

To solve the given linear programming model graphically, we need to plot the feasible region and identify the corner points to find the optimal solution. Here's the step-by-step process:

1. Plot the constraints:

  - Plot the line x1 = 40 (vertical line at x1 = 40).

  - Plot the line x2 = 10 (horizontal line at x2 = 10).

  - Plot the line 20x1 + 10x2 = 500 (which can be rewritten as 2x1 + x2 = 50).

  - Shade the feasible region that satisfies all the constraints.

2. Identify the corner points:

  - Determine the coordinates of the corner points where the boundary lines intersect.

3. Evaluate the objective function:

  - Calculate the value of the objective function Z = 120x1 + 80x2 for each corner point.

4. Determine the optimal solution:

  - Select the corner point that maximizes the objective function Z.

Here's the graphical representation of the feasible region:

      |

 40   |           C

      |          /

      |         /

      |        /

      |       /

      |      /

      |     /    Feasible Region

 10   |_____/_________________

      0   10  20  30  40  50

            0`

The corner points of the feasible region are:

A: (0, 0)

B: (0, 10)

C: (25, 0)

D: (20, 5)

Now, we evaluate the objective function Z = 120x1 + 80x2 for each corner point:

Z(A) = 120(0) + 80(0) = 0

Z(B) = 120(0) + 80(10) = 800

Z(C) = 120(25) + 80(0) = 3000

Z(D) = 120(20) + 80(5) = 2400

From the above calculations, we can see that the maximum value of Z occurs at point C: (25, 0).

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Answer:

6

Step-by-step explanation: You can set up the equation: \(\sqrt{\frac{n}{3} }\) = \(\sqrt{n-4}\) You square both sides to cancel out the squares which leaves you with \(\frac{n}{3}\) = n - 4. Then you just solve as normal which ends you up with an answer of 6. You can check this by plugging 6 back into the equation and see that you end up with \(\sqrt{2}\) on both sides.

Borman famously quipped, "We're not very good at odds-making. But if I had to bet my life on it, I'd give the odds to us."

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.

During the Apollo 8 mission, which launched on December 21, 1968, the three-man crew consisting of Frank Borman, James Lovell, and William Anders became the first humans to orbit the Moon. Prior to the mission, Borman was asked about the chances of the crew's survival given that the Saturn V rocket had only been tested twice before and never with a crew. In response, Borman famously quipped, "We're not very good at odds-making. But if I had to bet my life on it, I'd give the odds to us."

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Lines l and m are parallel; line l will map onto line m with a 90° rotation; line l can map onto line m with a vertical line of reflection.

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