Two families visited an amusement park. The first family bought 4 hot dogs and 6 bottles of waters, which totaled $22. The second family bought 8 hot dogs and 3 bottles of waters, which totaled $35. How much did one hot dog cost?

$1
$2
$3
$4

Step-by-step explanation:

a. 17 + 6/10 = (17 x 10) / (1 x 10) + 6/10 = 170/10 + 6/10 = 176/10 = 17,6

b. 45 + 6/100 = (45 x 100) / (1 x 100) + 6/100 = 4 500/100 + 6/100 = 4 506/100 = 45,06

c. 3 + 5/10 + 2/100

= (3 x 100) / (1 x 100) + (5 x 10) / (10 x 10) + 2/100

= 300/100 + 50/100 + 2/100

= 352/100 = 3,52

d. 6 + 7/10 + 8/100 + 9/1 000

= (6 x 1 000) / (1 x 1 000) + (7 x 100) / (10 x 100) + (8 x 10) / (100 x 10) + 9/1 000

= 6 000/1 000 + 700/1 000 + 80/1 000 + 9/1 000

= 6 789/1 000 = 6,789

e. 11 + 6/10 + 8/1 000

= (11 x 1 000) / (1 x 1 000) + (6 x 100) / (10 x 100) + 8/1 000

= 11 000/1 000 + 600/1 000 + 8/1 000

= 11 608/1 000 = 11,608

f. 84 + 1/100 + 3/10

= (84 x 100) / (1 x 100) + 1/100 + (3 x 10) / (10 x 10)

= 8 400/100 + 1/100 + 30/100

= 8 431/100 = 84,31.

Hope this helps!!

The normal stress and shear stress acting on a plane perpendicular to direction inclined 30° counter clockwise to σ 11 are σn = 16−15√3 and τ = 2+15√3/4. The maximum shear stress is 17.5.

The stress tensor σ given in the problem is:

σ = 201504−400−1500−1010

The normal stress is given by

σn = σ11cos²θ+σ22sin²θ−2σ12sinθcosθ

where

θ = 30°

θ = 30° is the angle between the direction perpendicular to the plane and the direction of σ11

σ11 = 20

σ22 = −15

σ12 = −4

Here is a detailed calculation:
σn = 20cos²(30)+(-15)sin²(30)-2(-4)sin(30)cos(30)

σn = 20cos²(30)+(-15)sin²(30)+4sin(30)cos(30)

σn = 20(3/4)+(-15)(1/4)+4(1/2)(√3/2)

σn = 12−15√3+4√3

σn = 16−15√3

The normal stress is σn = 16−15√3

The shear stress acting on a plane perpendicular to direction inclined 30° counter clockwise to σ11

σ11 is given by:
τ = σ12(sin²θ−cos²θ)+0.5(σ11−σ22)sin2θ

where

θ = 30°

θ=30° is the angle between the direction perpendicular to the plane and the direction ofσ11.

σ11 = 20

σ22 = −15

σ12 = −4

Here is a detailed calculation:
τ = −4(sin²(30)−cos²(30))+0.5(20−(−15))sin(60)

τ = −4((1/4)−(3/4))+0.5(20+15)(√3/2)

τ = 4(1/2)+0.5(35)(√3/2)

τ = 2+15√3/4

The shear stress is τ = 2+15√3/4

Maximum shear stress
The maximum shear stress is given by

τmax = 0.5(σ1−σ2)

whereσ1σ1 andσ2σ2 are the first and second principal stresses.

The eigenvalues of the stress tensor σ are found by solving the characteristic equation:

det(σ−λI)=0

Here is a detailed calculation:
σ−λI = [20150−λ−400−1500−λ0−400−15−λ10−λ]

σ−λI = 0(20150−λ)[(−λ)(−λ−15)+0(−400)]−(−4)[0(−λ−15)+(−400)(−λ)]+0[0(−400)+(20150−λ)(−λ)]

σ−λI = 0λ³+35λ²−605λ−1875

σ−λI = 0

λ = −25,5,3

The maximum shear stress occurs on the plane of maximum shear stress which is at 45° 45° to the coordinate axes.

The maximum shear stress is found to be

τmax = 0.5(σ1−σ2)

τmax = 0.5(20−(−15))

τmax = 17.5.

Therefore, the maximum shear stress is τmax = 17.5.

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The solution cannot be written as a ratio of two integers, the solution is irrational

The formula calculating the area of a square is given as

A = L^2

Given the parameters

A = 150

Substitute

150 = L^2

l = √150
L= √25 * 6

L =5√6

Since the solution cannot be written as a ratio of two integers, the solution is irrational

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Answer:

10.997cm

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Circumference of a circle = 2πr

This is a 1/4 circle, therefore the length of the arc is:

1/4(2π7) = 10.996

Now add the 2 legs to get the total perimeter:

10.996 + 7 + 7 = 25

The initial value of the given problems are \(y = 3e^{(-2x)}, y = e^{(x^{2/2)}}, y(x) = ln|e^x - 1| and y(x) = (2/3)(x^{(3/2)} + 7)^{2/3}.\)
The given differential equation is dy/dx = -2y; y = 3 when x = 0.

Here,
dy/dx = -2y
dy/y = -2dx
Integrating both sides
ln|y| = -2x + C
here C is the constant of integration.

Now to solve for C,  the initial condition y = 3 when x = 0:
ln|3| = -2(0) + C
C = ln|3|

Then, the solution to the differential equation
ln|y| = -2x + ln|3|
ln|y/3| = -2x
\(y/3 = e^{(-2x)}\)
\(y = 3e^{(-2x)}\)
The given differential equation is dy/dx = xy; y = 1 when x = 0.

Similarly the other questions can be done by the same method,
dy/y = x dx
Integrating both sides
\(ln|y| = (x^2)/2 + C\)
here C is the constant of integration.
To solve for C,  the initial condition y = 1 when x = 0:
\(ln|1| = (0^2)/2 + C\)
C = 0

The n, the solution to the differential equation
\(ln|y| = (x^2)/2\)
\(|y| = e^(x^2/2)\)
\(y = ±e^{(x^2/2)}\)
Since y(0) = 1, we have:
\(y = e^{(x^{2/2})}\)
For the next question
\(dy/dx = e^{(x+y)}\); y = 0 when x = 0
\(dy/e^{y} = e^x dx\)
Integrating both sides
\(ln|e^y| + C_1= e^x + C_2\)
here C_1 and C_2 are constants of integration.
\(y(x) = ln|C_3e^x - 1|\)
Here C_3 is a constant of integration.
Utilizing the initial condition y(0) = 0:
\(y(x) = ln|e^x - 1|\)
Now,
\(dy/dx = \sqrt{(y/x')};\) y(1) = 1
\(sqrt{(y)} dy= sqrt{(x')} dxdxdxdx\)

Integrating both sides gives:

\((2/3)y^{(3/2)} + C_4= (2/3)x^{(3/2)} + C_5\)

here C_4 and C_5 are constants of integration.
\(y(x) = (2/3)(x^{(3/2)} + C_6)^{2/3}\)
here C_6 is a constant of integration.

Utilizing the initial condition y(1) = 1
\(y(x) = (2/3)(x^{(3/2)} + 7)^{2/3}\)

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Answer:

60 meters

Step-by-step explanation:

We are looking for the height when x = 0. When x is equal to zero, we get the y-int and height of 60.

Answer:

60

Step-by-step explanation:

Answer:

Step-by-step explanation:

    a) Diameter = 2.1 m

                      r = 2.1 ÷ 2 = 1.05 m

            Area   = πr²

                       = 3.14 * 1.05 * 1.05

                      = 3.46 = 3.5 m²

    b) To find the number of paint tins, divide the area of table top by 1.75 m²

     Number of tins =  3.5 ÷ 1.75

                               = 2 tins

c) Cost of 1 tin = $ 5.50

   Cost of 2 tin = 2 *5.50

                        = $ 11

\(\sf d) Cost\ of \ labour = \dfrac{2}{3} * 11\)

                         = $ 7.30

Answer:

a=3.46 (2dp)   b(ii)=2  

Step-by-step explanation:

a)

πr²=area

2.1/2 = 1.05 as the radius

1.05² x π= 3.46 (2dp)

b)

3.46/1.75= 1.98

1.98 can be changed into two

∴ 2 tins will be needed

Mark has to sell 20 marbles and Don has to sell 68 marbles at their garage sale.

Let's say Mark has "x" marbles. According to the problem, Don has 8 more than 3 times the number of marbles Mark has. Therefore, Don has 3x+8 marbles. The total number of marbles they have is 88, so we can set up an equation:
x + (3x+8) = 88

Simplifying this equation:
4x + 8 = 88
Subtracting 8 from both sides:
4x = 80
Dividing both sides by 4:
x = 20
So Mark has 20 marbles and Don has 3(20)+8=68 marbles.

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The center of the circle will be (2, -5) and the radius of the circle will be 1 unit.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x - h)² + (y - k)² = r²

The equation is given below.

x² - 4x + y² + 10y = -28​

Then the center and the radius of the circle will be

x² - 4x + 4 + y² + 10y + 25 = -28​ + 4 + 25

               (x - 2)² + (x + 5)² = 1²

Thus, the center and the radius of the circle will be (2, -5) and 1 unit respectively.

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Answer:

4 monetary units

Step-by-step explanation:

In a Poisson distribution, the expected value of the distribution is the same as the mean:

\(E(X)=\mu=4\ claims\)

The expected number of warranty claims is 4.

Since each claim results in a payment of 1, the expected value paid by the insurer is:

\(E(V)=E(X)*V(X)\\E(V)=4*1 = 4\)

The expected total payment on warranty claims is 4 monetary units.

The change in temperature for the day is 34.1°F.

In Mathematics and Statistics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.

In Mathematics and Statistics, the range of a data set can be calculated by using this mathematical expression;

Range = Highest number - Lowest number

From the given data set, we have:

By substituting the numerical values for the temperature, we have:

Range = 15.7 - (−18.4)

Range = 15.7 + 18.4

Range = 34.1°F.

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Answer:

The answer is C

Step-by-step explanation:

Using the associative property we will get the equivalent expression:

45*b

The associative property of the product tells us that we can solve the product in any order we want to.

So we can write:

A*(B*C) = (A*B)*C = (A*C)*B

etc...

Now, the given expression is:

8*(5*b)

Then we can take the product of the two first numbers first, so we write:

8*(5*b) = (8*5)*b = 45*b

Then the equivalent expression to the given one is 45*b

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Answer:

the slope of the graph is 3/2

Step-by-step explanation:

The measure of the mid - segment is 53 .

Given :

the measures of the bases of a trapezoid are 35 and 71.

What is trapezoid ?

A trapezoid is a four-sided shape which has one pair of sides as parallel. It is basically a two-dimensional shape or figure similar to a square etc .

Mid segment :

A mid segment of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides of a trapezoid.

A trapezoid mid segment is parallel to the set of parallel lines in a trapezoid and is equal to the average of the lengths of the bases.

Measure of mid segment = sum of two bases / 2

= 35 + 71 / 2

= 106 / 2

= 53

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Derek needs to make contributions of approximately $21,038.34 per year from his 26th birthday to his 65th birthday in order to accumulate $2,742,310.00 in his retirement account by the time he fully retires.

To determine the amount Derek needs in his retirement account on his 65th birthday, we can use the concept of present value. Since he plans to withdraw $184,036.00 per year, starting from his 66th birthday until his 90th, the cash flows can be treated as an annuity. The interest rate is 5.00%, and the time period is 25 years (from 66 to 90). Using the formula for the present value of an annuity, we can calculate the required amount. The formula is:

PV = PMT * (1 - \((1 + r)^(-n)\)) / r

where PV is the present value, PMT is the annual withdrawal amount, r is the interest rate per period, and n is the number of periods.

Plugging in the values, we get:

PV = $184,036.00 * (1 - \((1 + 0.05)^(-25)\)) / 0.05 ≈ $2,744,607.73

Therefore, Derek needs approximately $2,744,607.73 in his retirement account on his 65th birthday to cover his desired annual withdrawals.

Moving on to the second part, Derek plans to make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal of having $2,742,310.00 in his retirement account after fully retiring, we can calculate the necessary contributions using the formula for the future value of an ordinary annuity:

FV = PMT * \(((1 + r)^n\) - 1) / r

Rearranging the formula, we can solve for the required contributions (PMT):

PMT = FV * (r / (\(((1 + r)^n\) - 1))

Plugging in the values, we get:

PMT = $2,742,310.00 * (\(\frac{0.05} {((1+0.05)^{39}-1 )}\))≈ $21,038.34

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Answer:

1,057.

524,000.

300,000,000

Step-by-step explanation:

A is not proportional

Use the graph to record the value of y axis when x is 1, 2, 3, 4, 5, 6

And record the values of x when y is 1, 2, 3, 4, 5, 6 till the end

Using the graph Value of y

(1, 0.9) (2,1.5) (3,2.2) (4,2.5) (5, 3) (6,4) (7, 5) (10,6)

Using the graph, find the value of x when y is 1 - 10)

1.2, 2.5, 5,.....

The slope of the graph also shows that it is not proportional

B is proportional

X is 0 and y is 0

When x is 5, y is 10

Ratio x: y = 5:10 = 1:2

When x is 10, y is 20

Ratio x:y is 10: 20 = 1:2 same as above

C is not proportional

When Moyra is 32, daughter is 8

When her daughter is 22, Moyra will also be 4years older, which is 36

32: 8 = 4:1

36: 12 =3:1

Step-by-step explanation:

\(( {x}^{2})(x + 3) - (x + 3)\)

\((x + 3)( {x}^{2} - 1) \)

\((x - 1)(x + 1)\)

\((x - 1)(x + 1)(x + 3)\)

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

(x+1) (x-1) (x+3)

Step-by-step explanation:

. .....................

Answer:

12,-2

Step-by-step explanation:

After the Nuremberg trials and the Geneva Conventions, the responsibility to prosecute crimes against humanity or genocide was entrusted by the organization to the United Nations. (option b)

The Geneva Conventions, a series of international treaties, were first adopted in 1864 and have since been expanded and updated. These conventions set out the legal framework for the protection of victims of armed conflicts, including civilians and prisoners of war. They aim to ensure that humane treatment is provided to individuals affected by armed conflicts and that certain acts are considered war crimes.

While the Nuremberg trials and the Geneva Conventions were significant milestones in the development of international law and the protection of human rights, they did not establish a permanent court to prosecute crimes against humanity. Instead, the United Nations took on this responsibility.

In 2002, the UN established the International Criminal Court (ICC), a permanent international tribunal located in The Hague, Netherlands. The ICC has the authority to investigate and prosecute individuals accused of committing crimes against humanity, genocide, war crimes, and the crime of aggression.

Hence the correct option is (b).

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None of the provided answer choices accurately represents the value of T⁴ when T is 10 K. The correct value is 10⁸ K².

The value of T⁴ can be calculated by multiplying the temperature (T) by itself four times. In this case, the given temperature is 10 K. Let's perform the calculation step by step.

T⁴ = T × T × T × T

T⁴ = 10 K × 10 K × 10 K × 10 K

Now, let's calculate the value of T⁴.

T⁴ = 10,000 K × 10,000 K

T⁴ = 100,000,000 K²

To simplify further, we can rewrite 100,000,000 K² as 10⁸ K².

Therefore, the value of T⁴ is 10⁸ K².

Now let's consider the answer choices provided:

a. 1: The value of T⁴ is not equal to 1; it is much larger.

b. 10,000: The value of T⁴ is not equal to 10,000; it is much larger.

c. 4,000: The value of T⁴ is not equal to 4,000; it is much larger.

d. -1,000: The value of T⁴ is not equal to -1,000; it is a positive value.

In conclusion, the value of T⁴ when T is 10 K is 10⁸ K².

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Answer:

x = 10

Step-by-step explanation:

\(\frac{1}{5}\) x - \(\frac{2}{3}\) = \(\frac{4}{3}\)

multiply through by 15 ( the LCM of 5 and 3 ) to clear the fractions

3x - 10 = 20 ( add 10 to both sides )

3x = 30 ( divide both sides by 3 )

x = 10

Answer:

I can't comment, but we can't see what we are supposwd to bw doing

Answer:

09165574045I want 2 use dis medium 2 thk y’all 4 being part of my 2022.

As a frnd I say a Big Thk u

As a customer I say a Big Thk u

As a partner I say a Big Thk u

As a family member I say a Big Thk u

As my god ordained helper I say a Big Thk u!

God bless u n see y’all in 2023 in Grand Style. Amending of your 7

In a case whereby sheri’s cab fare was $32, with a 20% gratuity and no taxes. sheri's write a check to the cab driver for $40, this can be considered as being reasonable amount because it is  $1.60 more to the cab driver.

A gratuity is a sum of money that customers typically give to specific service sector employees, including those in the hotel industry, in addition to the service's base charge for the work they have completed.

Given ; Sheri’s cab fare was $32 and the percentage of gratuity is 20%

amount of gratuity = 20% 0f 32 = 6.40

The fare of the cab  + gratuity = 32 + 6.40 = 38.40

Check to the cab driver for $40 ,  implies ($40 - $38.40)= $1.60 more to the cab driver.

Hence, it is reasonable.

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The other number if the average of two numbers is 41 and one is 27 is 55

Average of number is also known as the mean.

Let the unknown number be "x" such that:

x +27/2 = 41

Determine the value of x

x + 27 = 2(41)
x + 27 = 82
x = 82 - 27

x = 55

Hence the other number if the average of two numbers is 41 and one is 27 is 55

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Five professional development models are selected for comparison. A graphic organizer is created to describe and compare these models. The organizer provides a visual representation of the key features, components, and differences among the models.

The graphic organizer presents the selected professional development models side by side, highlighting their distinct characteristics. Each model is described with its name, key features, and components. The organizer may include information such as the focus of the model, target audience, delivery methods, duration, and expected outcomes.

By comparing these models in a structured manner, educators and professionals can easily identify similarities, differences, and unique aspects of each model. This comparison facilitates informed decision-making when selecting a professional development approach that aligns with specific goals, learning objectives, and organizational requirements.

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