Find the 5 number summary for both boys and girls .

The probability that Omar randomly selects a sugar cookie from the bag eats it, then randomly selects an oatmeal cookie is 0.06.

Omar buys a bag of cookies that contains,

5 chocolate chip cookies,9 peanut butter cookies, 6 sugar cookies, and 7 oatmeal cookies,

We have to find the probability that Omar randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie

Total number of cookies in bag = 27

the probability that Omar randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie

\(=\frac{6}{27}.\frac{7}{26}\\\\=0.0598 =0.06\)

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Answer:

Step-by-step explanation:

-2x^-1-7

True. The coefficient of determination, also known as R-squared (R²), is a statistical measure used in regression analysis to determine how well a regression model fits the data.

It measures the proportion of the variability in the dependent variable that is explained by the regression equation. A higher R² value indicates a better fit of the model, as it shows that more of the variability in the dependent variable can be explained by the independent variable(s) used in the model. Therefore, it is true that the coefficient of determination gives the proportion of the variability in the dependent variable that is explained by the regression equation.

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We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer: Area of path = 1492 m^2 Area of "no path" = 123508 m^2

Step-by-step explanation:

Probably wrong

Maclaurin series of `f(x)` is given by:f(x) = `f(0)` + `f'(0)x` + `(f''(0)/2!) x²` + `(f'''(0)/3!) x³` + `(f⁴(0)/4!) x⁴` + `(f⁵(0)/5!) x⁵` + `(f⁶(0)/6!) x⁶` = `0 + 0x + 0x² + 0x³ + 0x⁴ + 0x⁵ + (7200/6!)x⁶` = `10x⁶`

Answer: `10x⁶`.

The given function is `f(x) = x⁶ sin(10x⁵)`. We need to find the Taylor series of `f` centered at `0` (Maclaurin series of `f`).

Formula used: The Maclaurin series for `f(x)` is given by `f(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3 + ...... + (f^n(0)/n!)x^n`.

Here, `f(0) = 0` because `sin(0) = 0`.

Differentiating `f(x)` and its derivatives at `x = 0`:`f(x) = x⁶ sin(10x⁵)`

First derivative: `f'(x) = 6x⁵ sin(10x⁵) + 50x¹⁰ cos(10x⁵)`

Differentiate `f'(x)`

Second derivative: `f''(x) = 30x⁴ sin(10x⁵) + 200x⁹ cos(10x⁵) - 250x¹⁰ sin(10x⁵)`

Differentiate `f''(x)`

Third derivative: `f'''(x) = 120x³ sin(10x⁵) + 1800x⁸ cos(10x⁵) - 2500x⁹ sin(10x⁵) - 5000x²⁰ cos(10x⁵)`

Differentiate `f'''(x)`

Fourth derivative: `f⁴(x) = 360x² sin(10x⁵) + 7200x⁷ cos(10x⁵) - 22500x⁸ sin(10x⁵) - 100000x¹⁹ cos(10x⁵) + 100000x²⁰ sin(10x⁵)`

Differentiate `f⁴(x)`

Fifth derivative: `f⁵(x) = 720x sin(10x⁵) + 36000x⁶ cos(10x⁵) - 112500x⁷ sin(10x⁵) - 1900000x¹⁸ cos(10x⁵) + 2000000x¹⁹ sin(10x⁵)`

Differentiate `f⁵(x)`

Sixth derivative: `f⁶(x) = 7200 cos(10x⁵) - 562500x⁶ cos(10x⁵) + 13300000x¹⁷ sin(10x⁵)`

Evaluate at `x = 0`:

The derivatives of `f(x)` evaluated at `x = 0` are:f(0) = 0f'(0) = 0f''(0) = 0f'''(0) = 0f⁴(0) = 0f⁵(0) = 0f⁶(0) = 7200

Maclaurin series of `f(x)` is given by:f(x) = `f(0)` + `f'(0)x` + `(f''(0)/2!) x²` + `(f'''(0)/3!) x³` + `(f⁴(0)/4!) x⁴` + `(f⁵(0)/5!) x⁵` + `(f⁶(0)/6!) x⁶` = `0 + 0x + 0x² + 0x³ + 0x⁴ + 0x⁵ + (7200/6!)x⁶` = `10x⁶`

Answer: `10x⁶`.

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Answer:

18972

Step-by-step explanation:

With an area model, the model will have dimensions of 576 and 36. The product of the units will be within the model.

The value of the equation is A = 18,972

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be p = 527

Let the second number be q = 36

Now , the equation will be

A = p x q

Substituting the values in the equation , we get

A = 527 x 36

On simplifying the equation , we get

A = 18,972

Hence , the equation is A = 18,972

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Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. We may be aware of the result of an occurrence or not. When this is the case, we refer to the likelihood that the event will occur or not.

Here,

X υ N (22,1)

Probability that  basketball  will weigh between 20.5 and 23.5

is:

=> P(20.5 < x < 23.5)= P[ 20.5-22/1 < z < 23.5-22/ 1   ]

=>   P(20.5 < x < 23.5) = P(-1.5 < z < 1.5)

=>  P(20.5 < x < 23.5) = 0.866

Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

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Answer:

the secound one

Step-by-step explanation:

hope it helped:3

Step-by-step explanation:

|6| = 6 means the absolute value of 6 is 6.

Answer:

Its 6.

Step-by-step explanation:

the absolute value of a positive number is that number and the absolute value of a negative number is the same number just positive.

Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

Answer:

none of the

Step-by-step explanation: none of them

Answer:

yes

Step-by-step explanation:

Answer + Step-by-step explanation:

Example: =================

3D figure = rectangular prism

………………………………………………………………………………

Formula : =================

Volume of Rectangular Prism: V = lwh.

Surface Area of Rectangular Prism: S = 2(lw + lh + wh)

the shell momentum balance is performed by assuming steady, laminar, and fully developed flow between parallel plates. The velocity profile between the plates can be obtained by solving the Hagen-Poiseuille equation using MATLAB, considering the given dimensions and boundary conditions.

a) The shell momentum balance is a method used to analyze fluid flow between parallel plates. It involves dividing the fluid into concentric shells and applying the principle of conservation of momentum to each shell. In this case, the assumptions include steady-state flow, incompressibility, and the absence of a pressure gradient. By considering the forces acting on the fluid element between the plates, the velocity profile can be determined. b) To solve the momentum balance and obtain the velocity profile between the parallel plates, MATLAB can be used. MATLAB offers various numerical methods and tools for solving differential equations, including the Navier-Stokes equations for fluid flow. By setting up the appropriate equations based on the shell momentum balance and implementing them in MATLAB, the velocity distribution within the fluid can be calculated.

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Let's assume the number of boys in Stephen's class is B. According to the given information, the number of girls in the class exceeds the number of boys by 8. Therefore, the number of girls would be B + 8.

The total number of pupils in the class is given as 36. We can write this as an equation:

B + (B + 8) = 36

Simplifying the equation, we have:

2B + 8 = 36

2B = 36 - 8

2B = 28

B = 28/2

B = 14

So, there are 14 boys in Stephen's class. Since the number of girls exceeds the number of boys by 8, the number of girls would be 14 + 8, which is equal to 22.

Therefore, there are 14 boys and 22 girls in Stephen's class.

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\(4x+22~ > ~-2(14+3x)\implies 4x+22~ > ~-28-6x\implies 10x+22 > -28 \\\\\\ 10x > -50\implies x > \cfrac{-50}{10}\implies x > -5\)

Check the picture below.

The 40th term of the arithmetic sequence (a) will be -183 and the 60th term of the arithmetic sequence (b) will be 242

An arithmetic sequence in algebra is a sequence of numbers where the difference between every two consecutive terms is the same.

a) Given that, an arithmetic sequence has a 2nd term equal to 7 and 8th term equal to -23, we need to find the term of the sequence that has value -183.

We know that,

aₙ = a+(n-1)d

Where, aₙ = nth term, d = common difference, a = first term and n = number of terms.

Therefore,

7 = a+(2-1)d

7 = a+d

a = 7-d....(i)

Similarly,

-23 = a+(8-1)d

-23 = a+7d

a = -7d-23....(ii)

Equating the RHS of the equations,

7-d = -7d-23

30 = -6d

d = -5

Put d = -6 in eq(i)

a = 7-(-5) = 12

Now,

-183 = 12+(n-1)(-5)

-183 = 12-5n+5

-183-17 = -5n

n = 40

Therefore, 40th term will be -183

b) Given that, an arithmetic sequence has a 6th term equal to 26 and 9th term equal to 38, we need to find the 60th term

We know that,

aₙ = a+(n-1)d

Where, aₙ = nth term, d = common difference, a = first term and n = number of terms.

26 = a+5d

a = 26-5d...(i)

38 = a+8d

a = 38-8d....(ii)

Equating the RHS of the equations,

26-5d = 38-8d

3d = 12

d = 4

Put d = 4 in eq(i)

a = 26-5(4)

a = 6

Therefore,

a₆₀ = 6+(60-1)(4)

= 242

Hence, the 40th term of the arithmetic sequence (a) will be -183 and the 60th term of the arithmetic sequence (b) will be 242

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Answer:

can you please provide a graph

Step-by-step explanation:

I'm baked as hell

The systems of inequalities given is,

Since he can't sell more than 8 items per day, then from the graph given the best region that should be shaded is region 4.

Given:x = 5cos 3ty = 4sin 3tWe need to find the first two derivatives dy/dx and d²y/dx² for the given function using the chain rule.

Now, we know thatcosec²θ = cot²θ + 1Therefore, we can write the above expression asd(dy/dx)/dt = 12(cot²(π/27) + 1) cot (π/27)= 12(1+cot²(π/27)) cot (π/27)Now, substituting the value of cot (π/27) from the given function, we getcot (π/27) = cot (3×1/3) = 1Therefore,d(dy/dx)/dt = 12(1+1²)×1= 24To find d²y/dx²,Therefore,d²y/dx² = [(-36sin 3t)/(225sin² 3t)] - [12cos 3t×24] / (-15sin 3t)³= (-4/25) csc² 3t - 64cot 3t csc³ 3t= -4cosec² 3t/25 - 64cot 3t/125The value of t at which we need to evaluate the second derivative is t = 1/9.Therefore,d²y/dx² = -4cosec²(π/27)/25 - 64cot(π/27)/125= -4/(5+5√3) - 64/(25√3 + 125) = (-20-20√3)/425. Hence, the value of d²y/dx² is (-20-20√3)/425 when t = 1/9.

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Answer:

4

Step-by-step explanation:

Multiplication Property of equality.

multiply 5 on both side to have x alone on One side.

The amount that Nancy can save each month and put in the savings account is $10.

Savings are funds that are not used right away but are instead set aside for unforeseen expenses or future needs. It is the gap between one's earnings (income) and their outlays (expenditures) (the amount of money spent). Regular income, investment profits, tax refunds, and gifts are just a few of the several ways that people might support their savings. You may save money in a variety of ways, such as by creating a budget and eliminating wasteful spending, opening a savings account, buying stocks or bonds, and making contributions to retirement plans like 401(k)s or IRAs.

The total income earned by Nancy is:

30 + 50 + 25 + 35 = $140

The total expenses are:

40 + 60 + 30 = $130

The amount remaining after expenses is:

Savings = 140 - 130 = $10

Hence, the amount that Nancy can save each month and put in the savings account is $10.

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The price  for  the mean of all seven of the car prices is  mathematically given as

NP=$=19400

This is further explained below.

Generally,  From the question, we have that

Average prices= $18,500

The total number of pricing estimates= 7

This mean is produced by the expected sum, which is.

= 7*18,500

=$129,500

Therefore, The resulting Sum of quoted prices=

SQP= $(15,500+ 18,800+ 16,900+ 19,900+18,000+21,000)

SQP=$110100

And, The following price that will be quoted is:

NP= $129,500-$110,100

NP=$=19400

In conclusion, The required price is given as

NP=$=19400

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CQ

Nick and Liz have decided to move from the city to the suburbs. This means that they will have to make the essential purchase of a car in order to get to work. They researched used 2-year-old cars of the same make, model, condition, and equipped with the same options. They found a website stating that the average price should be $18,500. These are the prices they were quoted: $15,500, $18,800, $16,900, $19,900, $18,000, $21,000 If they continued their search for one more price quote, what would that price have to be so that the mean of all seven of the car prices would be the same as the mean quoted on the website?

Answer:

7.5

Step-by-step explanation:

750 is the volume, so divided by then is 75, then divided by 10 again is 7.5

Hope this helps!

Answer:

7.5

Step-by-step explanation:

10x10x7.5=750

Using the divergence theorem we can compute that the outward flux of the vector field is 16π .

The outward flux of F over the solid cylinder and z = 0 is

∫∫F·ds  = ∫∫∫ DivF dv

F = 2xy² i   +  2x²y j + 2xy k

Div F  =  D/dx (2xy²)  +   D/dy (2x²y )

Div F  =  2y²  +  2x²

In cylindrical coordinates   dV = rdrdθdz and as z = 0 the region is a surface ds = r·dr·dθ

Using the parametric form of the surface equation

x = rcosθ        y =  r sinθ      and z = z

Div F  = 2r² sin²θ  + 2r²cos²θ

∫∫∫ DivF dv  =  ∫∫ [2r²sin²θ  + 2r²cos²θ] × rdrdθ

∫∫ 2r² [sin²θ  + cos²θ] × rdrdθdz   ⇒  ∫∫ 2r³ drdθ

Integration limits

0 < r < 2          0 < θ < 2π

2∫₀² r³ ∫dθ

(2/4) × (2)⁴ × 2π

The divergence theorem, commonly known as Gauss' theorem or Ostrogradsky's theorem, is a theorem that connects the flow of a vector field across a closed surface to the field's divergence in the volume enclosed.

In more detail, the divergence theorem states that the surface integral of a vector field across a closed surface, sometimes referred to as the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface.

Therefore the flux is 16π .

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