Vic works at a hardware store. He sells 144 bolts for $70. 56. What is the constant of proportionality

Answer:

6.98

Step-by-step explanation:

I think that you are looking for the diameter and you are given the area of a circle.

a =\(\pi r^{2}\)  You are given pi, so \(r^{2}\) = 72.

That means that r = \(\sqrt{72}\) or a rounded answer of 8.49 rounded to the hundreds place.  The diameter is equal to 2 radius, so the diameter rounded is 16.98

The system of equations that model the situation are:

8x + 3y = 73

4x + 3y = 53

(option b)

The duration of the singing act is 5 minutes.

The duration of the dance act is 11 minutes.

The form of the simultaneous equation is:

(number of singing acts at the first show x number of minutes they perform) + (number of dance acts at the first show x number of minutes they perform) = total number of minutes equation 1

(number of singing acts at the second show x number of minutes they perform) + (number of dance acts at the second show x number of minutes they perform) = total number of minutes equation 2

8x + 3y = 73 equation 1

4x + 3y = 53 equation 2

In order to determine the duration of each act, the elimination method would be used:

Multiply equation 2 by 2

8x + 6y = 106 equation 3

Subtract equation 1 from equation 3 :

3y = 33

Divide both sides of the equation by 3

y = 33 / 3

y = 11 minutes

Substitute for y in equation 1: 8x + 3(11) = 73

8x + 33 = 73

8x = 73 - 33

8x = 40

x = 40 / 8

x = 5 minutes

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The given function is  x(z) = 1/(z-2) with |z|>1. 1. Using partial fraction expansion: x(z) = 1/(z-2) => x(z) = A/(z-2) + B Now we write x(z) in terms of A and B. x(z) = A/(z-2) + B 2.

Multiply both sides by the common denominator (z-2): x(z)(z-2) = A + B(z-2) 3. Substituting z=2, we get: x(2)(2-2) = A 4. Since 2 is a pole of order 1, we can find A as follows:

lim_(z→2) ((z-2)x(z)) = A lim_(z→2) ((z-2)/((z-2)(z-2))) =

A lim_(z→2) (1/(z-2)) = A A = lim_(z→2) (1/(z-2)) = 1/0

(which is undefined) But since the denominator is a pole of order 1, we can find the limit as follows:

lim_(z→2) ((z-2)x(z)) = lim_(z→2) (1) = 1

Therefore, A=1. 5. Solving for B, we get:

x(z)(z-2) = A + B(z-2) x(z)(z-2) = 1 + B(z-2) x(z)z - 2x(z) = 1 + Bz - 2B x(z)z - 2x(z) - Bz + 1 = -2B

Rearranging:

-Bz - 2x(z)z + 1 - 2x(z) = -2B x(z)z + 2x(z) + Bz - 1 = 2B/(z-2) + B

Multiplying both sides by z-2: x(z)(z-2) = 2B + B(z-2) x(z)(z-2) = (2B-B) + Bz x(z)(z-2) = Bz x(z) = B(z-2)/z x(z) = (2B)/(z-2) + B

So we have: A = 1 and B = -1 x(z) = 1/(z-2) - 1/z Now we can find the inverse z-transform of x(z): \(x(n) = (1/2)^(n-1) - u(n-1)\)

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Raja is junk seller. He sells many things. Here is given the list of junk.

Check the Raja's rate list and solve the following questions.

\(\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \small\boxed{\begin{array}{c|c} \bf{Kind \: of\:junk} & \bf{Price \: of \: 1 \: kg } \\ \dfrac{\qquad\qquad\qquad}{ \sf News \: Paper} &\dfrac{\qquad \qquad\qquad}{ \sf Rs.5} & \\ \dfrac{\qquad\qquad\qquad}{ \sf Iron} &\dfrac{\qquad\qquad\qquad}{ \sf Rs.10} & \\ \dfrac{\qquad\qquad\qquad}{ \sf Brass} &\dfrac{\qquad\qquad\qquad}{ \sf Rs.50} & \\ \dfrac{\qquad\qquad\qquad}{ \sf Plastic} &\dfrac{\qquad\qquad\qquad}{ \sf Rs.8}&\end{array}} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\)

1. How much money will you pay to Raju for 20 kg of newspapers?

\(\quad{\longrightarrow{\sf{Cost \: of \: 1 \: kg \: newspaper = Rs.5}}}\)

\(\quad{\longrightarrow{\sf{Cost \: of \: 20 \: kg \: newspaper = Rs.20 \times 5}}}\)

\(\quad{\longrightarrow{\sf{Cost \: of \: 20 \: kg \: newspaper = Rs.100}}}\)

\(\quad{\longrightarrow{\underline{\boxed{\sf{\purple{Cost \: of \: 20 \: kg \: newspaper = Rs.100}}}}}}\)

∴ We need to pay Rs.100 for buy 20 kg of newspapers.

\(\rule{200}{1.5}\)

2. What is the cost of 5 kg Iron?

\(\quad{\longrightarrow{\sf{Cost\: of \: 1 \: kg \: iron = Rs.10}}}\)

\(\quad{\longrightarrow{\sf{Cost\: of \: 5 \: kg \: iron = Rs.10 \times 5}}}\)

\(\quad{\longrightarrow{\sf{Cost \: of \: 5 \: kg \: iron = Rs.50}}}\)

\(\quad{\longrightarrow\underline{\boxed{\sf{\purple{Cost \: of \: 5 \: kg \: iron = Rs.50}}}}}\)

∴ The cost of 5 kg iron is Rs.50.

\(\rule{200}{1.5}\)

3. What is the cost of 9 kg Plastic?

\(\quad{\longrightarrow{\sf{Cost \: of \: 1 \: kg \: plastic = Rs.8}}}\)

\(\quad{\longrightarrow{\sf{Cost \: of \: 9 \: kg \: plastic = Rs.8 \times 9}}}\)

\(\quad{\longrightarrow{\sf{Cost \: of \: 9 \: kg \: plastic = Rs.72}}}\)

\(\quad{\longrightarrow\underline{\boxed{\sf{\purple{Cost\: of \: 9 \: kg \: plastic = Rs.72}}}}}\)

∴ The cost of 9 kg plastic is Rs.72.

\(\rule{200}{1.5}\)

4. What is the cost of 7 kg Brass?

\(\quad{\longrightarrow{\sf{Cost \: of \: 1 \: kg \: brass = Rs.50}}}\)

\(\quad{\longrightarrow{\sf{Cost\: of \: 7 \: kg \: brass = Rs.50 \times 7}}}\)

\(\quad{\longrightarrow{\sf{Cost \: of \: 7 \: kg \: brass = Rs.350}}}\)

\(\quad{\longrightarrow\underline{\boxed{\sf{\purple{Cost \: of \: 5 \: kg \: brass = Rs.350}}}}}\)

∴ The cost of 7kg brass is Rs.350.

\(\underline{\rule{200pt}{2pt}}\)

Answer:A

Step-by-step explanation:

Answer:

Equation 1

hope this helps

Answer:

The answer is c

Step-by-step explanation:  

Theater 2 is less than the mean absolute deviation of the data for theater.  

I hope this helps

Answer: C

Step-by-step explanation: if im wrong let me know ill fix

Answer:

75.96 Degrees

Step-by-step explanation:

Use the trigonometric functions of Sine Cosine and Tangent

(SOH CAH TOA)

The unknown angle is near the adjacent side of 2 and the opposite side of 8

Therefore you use the Tangent function

However, since it's the angle that needs to be found, you need to use Arc Tangent (The inverse operation)

Unknown Angle = ArcTan (8 / 2)

Unknown Angle = 75.96 Degrees

Note: ArcTan is just Tan to the power of -1

On my calculator I have to click shift then click the tan function to access this it may be different on yours

Answer:

N = 3

Step-by-step explanation:

\( \frac{28}{4} = \frac{21}{N} \\ \\ 28N = 21 \times 4 \\ 28N = 84 \\ \\ N = \frac{84}{28} \\ \\ N = 3\)

I hope I helped you^_^

Answer:

Multiply by 2

Step-by-step explanation:

3×2=6

5×2=10

8×2=16

11×2=22

50×2=100

Answer:

Mean = 32.8

Step-by-step Explanation:

Mean is given as Mean = (Σfx)/Σf

First, find the mid-point, x, of each class, and multiply by the frequency (f) of the class to get fx:

Class ==> f ==> x ==> fx

0-10   =>  3   =>  5  => 15

10-20 =>  8  => 15 => 120

20-30 => 10 => 25 => 250

30-40 => 15 => 35 => 525

40-50 =>  7  => 45 => 315

50-60 =>  4  => 55 => 220

60-70 =>  3  => 65 => 195

Sum the fx of all classes together to get Σfx:

Σfx = 15 + 120 + 250 + 525 + 315 + 220 + 195 = 1,640

Σf = 3 + 8 + 10 + 15 + 7 + 4 + 3 = 50

(Σfx)/Σf = \( \frac{1,640}{50} \)

(Σfx)/Σf = \( 32.8 \)

Mean = 32.8

Answer:

19

Step-by-step explanation:

1 centimeter is 10 millimeters

190 / 10 = 19

Answer:

67667.7

Step-by-step explanation:

let the number= Y

the question simply means that 0.15 percent of Y which give 10.5

so, let find Y:

0.15% of Y 10.15

0.15/100×y = 10.15

0.0015y= 10.15

divide bothsides by 0.0015

0.0015y/0.0015= 10.15/0.0015

y=6766.66

y= 6766.7 approximately

Reserve Requirement

Took the test got 100

Answer:

Its D

Step-by-step explanation:

Reserve Requirement I got it right on my test

Given the function

First I'll rewrite it in terms of y

Next is to determine the values of y (range) for the given values of x

Now you can graph it:

When 6 fewer than s is no less than −78, the solution in interval notation is (84,∞)

Interval notation is a way of writing subsets of the real number line

Given,

6 fewer than s is no less than -78

6-s < -78

Move 6 to right hand side

-s < -78-6

-s < -84

s > 84

Then the interval notation is (84,∞)

Hence, when 6 fewer than s is no less than −78, the solution in interval notation is (84,∞)

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Answer: Approx 4.6

Step-by-step explanation:

5 necklaces, each 11/12 feet

(5*11)/12

55/12

Answer:

11/10°C

Step-by-step explanation:

7 x 3/10 = 21/10

Temperature at Midnight = -1°C

Temperature at 7.00am = 21/10 + (-1°C)

= 11/10°C

Answer:

A. 1/4

Step-by-step explanation:

The value of c that satisfies the conclusion of the mean value theorem is c≈7.69.

The mean value theorem states that if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), then there exists at least one point c in (a,b) where the value of the derivative of f(x) is equal to the slope of the line connecting the endpoints of the interval, i.e., \(f'(c)=(f(b)-f(a))/(b-a).\)

Here, the function \(f(x)=x^(3/4)\) is continuous on the closed interval [0,16] and differentiable on the open interval (0,16), as the derivative of f(x) is \(f'(x)=(3/4)x^(-1/4)\), which is defined for all x in (0,16).

Therefore, we can apply the mean value theorem to this function on the interval [0,16].

To find the value of c that satisfies the conclusion of the mean value theorem, we first calculate the slope of the line connecting the endpoints of the interval: \((f(b)-f(a))/(b-a)=[(16)^(3/4)-(0)^(3/4)]/(16-0)\)=\(2sqrt(2).\) Then, we set f'(c)=2sqrt(2) and solve for c:

\(f'(c)=(3/4)c^(-1/4)=2sqrt(2)c^(-1/4)=(8/3)sqrt(2)c=(3/2)^(4/3)≈7.69\)

Therefore, the value of c that satisfies the conclusion of the mean value theorem is c≈7.69.

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-14 is the value of the expression b - 3a at a =6 and b = 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression b - 3a

For this expression given,

a = 6 and b = 4

Thus the value of expression at given values

=> b - 3a

=> 4 - 3 * 6

=>4 - 18

=> -14

Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.

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Answer:

12:00 am midnight

Step-by-step explanation:

Given;

I can read a 336-page book in 6 hours.

My rate r1 = 336/6 pages per hour = 56 pages per hour

Jayne can read a 144-page book in 3 hours.

Jayne rate r2 = 144/3 = 48 pages per hour

If I start reading a 5000-page book at noon and Jayne starts reading the same book at 10 AM

Taking 10 am as the reference time.

Let x represent the time from 10 am at which they would both be on the same page.

For me;

Since i started by noon; 2 hours after 10 am

Time t1 = x-2

For Jayne;

She started by 10 am

Time t2 = x

For them to be on the same page they must have read the same number of pages;

Number of pages read = rate × time

r1(t1) = r2(t2)

Substituting the values;

56(x-2) = 48(x)

56x - 112 = 48x

x(56-48) = 112

x = 112/(56-48)

x = 14 hours

Since 10 am is the reference, the time would be;

=10 am + x = 10 am + 14 hours

= 24:00

= 12:00 am midnight

1. The average feet of cable used during the lead time is 11,430 feet, 2. The safety stock at a 70% service level is 2,063.7 feet, 3. The reorder point for a 90% service level is 1.28, 4. The reorder point for an 8% stockout probability is 16,848 feet, 5. The answer is d. 98.78%, 6. he answer is a. Left.

1. To calculate the average feet of cable used during the lead time, we can multiply the mean of 1270 feet by the lead time of 9 days.

Therefore, the detailed calculation is 1270 feet/day * 9 days = 11,430 feet.

So, the answer is e. 11,430 feet.

2. To calculate the safety stock at a 70% service level, we need to find the z-value corresponding to that service level. Using a standard normal distribution table, we find that the z-value is approximately 0.525.

Then, we multiply the z-value by the standard deviation of 380 feet to get the safety stock:

0.525 * 380 = 199.5 feet.

Therefore, the answer is e. 2,063.7 feet (rounded to the nearest tenth).

3. To calculate the reorder point for a 90% service level, we need to find the z-value corresponding to that service level. Using the standard normal distribution table, we find that the z-value is approximately 1.28. Then, we multiply the z-value by the standard deviation of 380 feet to get the reorder point: 1.28 * 380 = 486.4 feet. Therefore, the answer is c. 1.28.

4. To calculate the reorder point for an 8% stockout probability, we need to find the z-value corresponding to that probability. Using the standard normal distribution table, we find that the z-value is approximately -1.41.

Then, we multiply the z-value by the standard deviation of 380 feet and subtract it from the mean of 1270 feet to get the reorder point: 1270 - (-1.41 * 380) = 1684.8 feet.

Therefore, the answer is c. 16,848 feet (rounded to the nearest tenth).

5. To calculate the service level when the cable inventory reaches 14,000 feet, we need to find the z-value corresponding to that inventory level.

Using the formula (Inventory level - Mean) / Standard deviation, we get (14000 - 1270) / 380

= 34.789.

Using the standard normal distribution table, we find that the corresponding service level is approximately 0.9998. Therefore, the answer is d. 98.78% (rounded to the nearest hundredth).

6. To calculate the reorder point for an 18% service level, we need to find the z-value corresponding to that service level.

Using the standard normal distribution table, we find that the z-value is approximately -0.92.

Then, we multiply the z-value by the standard deviation of 380 feet and add it to the mean of 1270 feet to get the reorder point:

1270 + (-0.92 * 380) = 899.6 feet.

Therefore, the answer is a. Left.

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Answer:

$29.70

Step-by-step explanation:

The amount that his aunt earns more than him in a week is $24. and

the amount that his aunt earns per week is $196.

According to the statement

we have find that the How much more does the man's aunt earn than him per week.

So, For this purpose, we know that,

According to the information:

The amount A man earns $172 per week, while his aunt earns $784 per month.

His aunt earns per week = $784 /4

His aunt earns per week = $196.

And the man earns $172 per week and the His aunt earns per week is $196.

The amount that his aunt earns more than him in a week = 196-172

The amount that his aunt earns more than him in a week = 24.

So, The amount that his aunt earns more than him in a week is $24. and

The amount that his aunt earns per week is $196.

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For a prime p ≡ 1 (mod 4), the quadratic residue of -1 in the finite field \($\mathbb{F}_p$\) exists, i.e., -1 is a square in\($\mathbb{F}_p$\).

Let p be a prime such that p ≡ 1 (mod 4). We need to prove that -1 is a quadratic residue modulo p, i.e., there exists an integer a such that \($a^2 \equiv -1 \pmod p$.\)

We know that the Legendre symbol $\left(\frac{-1}{p}\right)$ is equal to 1 if p ≡ 1 (mod 4), and -1 if p ≡ 3 (mod 4). Since p ≡ 1 (mod 4), we have \($\left(\frac{-1}{p}\right) = 1$.\)

By Euler's criterion, we have

\($\left(\frac{-1}{p}\right) \equiv (-1)^{\frac{p-1}{2}} \pmod p$.\)

Since \($\left(\frac{-1}{p}\right) = 1$\),

we have \($(-1)^{\frac{p-1}{2}} \equiv 1 \pmod p$.\)

This implies that  \($\frac{p-1}{2}$ is even, i.e., $p \equiv 1 \pmod 8$.\)

Now, let's consider the field \($\mathbb{F}_p$,\)

which is a finite field of order p. Since p ≡ 1 (mod 4), we have\($p = 4k+1$\) for some integer k. Let's define a subgroup of order 4 in \($\mathbb{F}_p^{\times}$ as $H = {1,-1,i,-i}$, where $i^2 \equiv -1 \pmod p$.\)

Since H is a subgroup of \($\mathbb{F}_p^{\times}$\)  of order 4, any element of \($\mathbb{F}_p^{\times}$\) can be written as a power of i multiplied by a power of -1. That is, for any\($x \in \mathbb{F}_p^{\times}$\), there exist integers m and n such that \($x = i^m(-1)^n$.\)

Since $p \equiv 1 \pmod 8$, we have \($2^{(p-1)/2} \equiv 1 \pmod p$\)  by Euler's criterion. This implies that \($i^{p-1} = (i^2)^{(p-1)/2} \equiv 1 \pmod p$\). Thus, \($i^p \equiv i \pmod p$.\)

Now, consider the element \($(-i)^2 = i^2(-1)^2 = -1$\). This shows that -1 is a quadratic residue modulo p, i.e., there exists an integer a such that \($a^2 \equiv -1 \pmod p$\). Therefore, we have proved that −1 is a square in \($\mathbb{F}_p$.\)

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Given that 2y = x + 2

To graph the following equation, we need two solutions

To find x, put y = 0

To find y, put x = 0

The two solutions to be graph is (-2, 0) and (0, 1)