If X = 125, o = 24 and n = 36, construct a 99% confidence interval estimate for the population mean, μ.

Answer:

1/2

Step-by-step explanation:

The fraction that is equivalent to 15/30 will be 1/2.

Since fraction represents a part of a number or any number of equal parts then;

To determine the fraction that is equivalent to 15/30, we need to simplify the given fraction by dividing both the numerator and denominator by their greatest common factor.

The greatest common factor of 15 and 30 is 15.

Therefore, dividing both the numerator and denominator by 15, we get:

\(\[\frac{15}{30} = \frac{15\div 15}{30\div 15} = \frac{1}{2}\]\)

Therefore, the fraction that is equivalent to 15/30 = 1/2.

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The second derivative of v with respect to t, denoted as d²v/dt², is equal to 4

The second derivative of v with respect to t, we will differentiate v twice.

v = 2t² + 7t + 11

First, let's find the first derivative of v with respect to t (dv/dt):

dv/dt = d/dt (2t² + 7t + 11)

Using the power rule of differentiation, we differentiate each term separately:

dv/dt = 2(2t) + 7(1) + 0

dv/dt = 4t + 7

Now, let's find the second derivative of v with respect to t (d²v/dt²):

d²v/dt² = d/dt (4t + 7)

Again, using the power rule of differentiation, we differentiate each term separately:

d²v/dt² = 4(1) + 0

d²v/dt² = 4

Therefore, the second derivative of v with respect to t, denoted as d²v/dt², is equal to 4.

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Answer:

d=5/3x

Step-by-step explanation:

Let's solve for d.

(2/3x)(d)=10/9

Step 1: Divide both sides by (2x)/3.

2/3dx / 2x/3=10/9 / 2x/3

d=5/3x

Given vector field, F(x, y, z) = y cos (xy) i + x cos (xy) j – sin z k To calculate the curl of F, we need to take the curl of each component and subtract as follows,∇ × F = ( ∂Q/∂y - ∂P/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂R/∂x - ∂Q/∂y ) k...where P = y cos(xy), Q = x cos(xy), R = -sin(z)

Now we calculate the partial derivatives as follows,

∂P/∂z = 0, ∂Q/∂y = cos(xy) - xy sin(xy), ∂R/∂x = 0...

and,

∂P/∂y = cos(xy) - xy sin(xy), ∂Q/∂z = 0, ∂R/∂y = 0

Therefore,

∇ × F = (cos(xy) - xy sin(xy)) i - sin(z)j

The curl of F is given by:

(cos(xy) - xy sin(xy)) i - sin(z)j.

To state whether F is conservative, we need to determine if it is a conservative field or not. This means that the curl of F should be zero for it to be conservative. The curl of F is not equal to zero. Hence, the vector field F is not conservative. Let C be the curve joining the origin (0,1,-1) to the point with coordinates (1, 2V2,2) defined by the following parametric curve:

r(t) = n* i + t}j + tcos atk, 15t52.

The curve C is defined as follows,r(t) = ni + tj + tk cos(at), 0 ≤ t ≤ 1Given vector field, F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk Using the curve parameterization, we get the line integral as follows,∫CF.dr = ∫10 F(r(t)).r'(t)dt...where r'(t) is the derivative of r(t) with respect to t

= ∫10 [(t cos(at))(cos(n t)) i + (n cos(nt))(cos(nt)) j + (-sin(tk cos(at)))(a sin(at)) k] . [i + j + a tk sin(at)] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) + (-a t sin(at) cos(tk))(a sin(at))] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) - a^2 (t/2) (sin(2at))] dt

= [sin(at) sin(nt) - (a/2) t^2 cos(2at)]0^1

= sin(a) sin(n) - (a/2) cos(2a)

The vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is given. Firstly, we need to calculate the curl of F. This involves taking the curl of each component of F and subtracting. After calculating the partial derivatives of each component, we get the curl of F as (cos(xy) - xy sin(xy)) i - sin(z)j. Next, we need to determine whether F is conservative. A conservative field has a curl equal to zero. As the curl of F is not equal to zero, it is not a conservative field. In the second part of the problem, we have to calculate the scalar line integral of the vector field F. dr along the curve C joining the origin to the point with coordinates (1, 2V2, 2). We use the curve parameterization to calculate the line integral. After simplifying the expression, we get the answer as sin(a) sin(n) - (a/2) cos(2a).

The curl of the given vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is (cos(xy) - xy sin(xy)) i - sin(z)j. F is not conservative as its curl is not zero. The scalar line integral of the vector field F along the curve C joining the origin to the point with coordinates (1, 2V2,2) is sin(a) sin(n) - (a/2) cos(2a).

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Answer:

8

Step-by-step explanation:

Step 1:

0.5x - 3 = 2 - 0.75x  Equation

Step 2:

1.25x - 3 = 2     Add 0.75x on both sides

Step 3:

1.25x = 5     Add 3 on both sides

Step 4:

5 ÷ 1.25  Divide

Step 5:

x = 4  Solution to x

Step 6:

2 × 4    Multiply to find answer of 2x

Answer:

2x = 8

Hope This Helps :)

Applying the Pythagorean theorem, the length of the altitude is: 7.79 units.

The Pythagorean Theorem is given as: c² = b² + a², where c is the hypotenuse.

An altitude of an equilateral triangle bisects the base of the triangle forming equal segments. Therefore, we would have the following:

c = 9

b = 4.5

Length of altitude = a = ?

Thus:

a = √(c² - b²)

a = √(9² - 4.5²)

a = 7.79 units.

Thus, applying the Pythagorean theorem, the length of the altitude is: 7.79 units.

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Answer:

A)

Step-by-step explanation:

first one

Answer:

A

Because 2×6.5= 13

And 4×6.5= 26

And 8×6.5=52

The probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.

The given data is

x 1 2 3 4 5 6 7 8

p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01

(a) calculate mean value of x:

μ = E(x)

  = ∑(xi.P(xi))

 = 4.13

(b)  calculate variance of x:

σ² = ∑(xi - E(x))².P(xi)

   = 1.81331

(c)  calculate standard deviation of x:

σ = √σ²

σ = √1.831

σ = 1.3539

The likelihood that the quantity of systems sold will be within one standard deviation of the its mean:

P(μ  - σ < x < μ  + σ ) = P(4.13 - 13539 < x < 4.13 + 1.3539)

                                = P(2.7761 < x < 5.4839)

                                = P(x = 3) + P(x = 4) + P(x = 5)

                                = 0.13 + 0.30 + 0.31

                                = 0.74

Thus, the probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.

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The complete question is-

Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in one month is given by the following table.

x 1 2 3 4 5 6 7 8

p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01

What is the probability that the number of systems sold is within 1 standard deviation of its mean value?

1000000 times larger

Step-by-step explanation:

2x10^2 is 200.

2x10^8 is 200000000

2x10^8  is 1000000 times larger that 2x10^2

The equivalent expressions are is  √75, √25 • √3, √15 • √5

When two expressions can be reduced to a single third expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.

Because both expressions have the same value for any value of x, 3(x + 2) and 3x + 6 are identical expressions. 3x + 6 = 3 × 4 + 6 = 18.

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The positive square root of 0.1445 by division method is approximately 0.38 (correct to two decimal places).

To find the positive square root of 0.1445 by division method, we can follow these steps:

Step 1: Add a decimal point after the first digit to make it 0.14. Step 2: Pair the digits from the decimal point in pairs starting from the decimal point and moving left. If there is an odd number of digits, pair the leftmost digit with a zero. So, we have: 0. 14 45 Step 3: Find the largest number whose square is less than or equal to 14. Write this number on top of the paired digits and subtract its square from 14. The largest number whose square is less than or equal to 14 is 3. 3 | 0.14 45 9

5 14 4 89

255

Step 4: Bring down the next pair of digits (45) and double the quotient (3) to get the dividend for the next step. So, we have: 3 | 0.14 45 9

5 14 4 89

255

249

---

  66

Step 5: Find the largest digit d such that 6d multiplied by d is less than or equal to 66. Write this digit on top of the remainder (66) to get the next digit of the square root.

The largest digit d such that 6d multiplied by d is less than or equal to 66 is 7.

So, we have:

3 | 0.14 45

9  4

5 14 66 4 89

255

249

---

  66

  63

  --

   3

Step 6: Repeat steps 4 and 5 until you have found the desired number of decimal places. In this case, we stop here since we only need to find the square root correct to two decimal places.

Therefore, the positive square root of 0.1445 by division method is approximately 0.38 (correct to two decimal places).

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20,000 pounds equals to 10 US ton.

Value conversion from Pound to US Ton

Add the value and the conversion ratio together.

1 pound = 0.0005 US ton

20,000 pounds worth

20,000 pounds × value of one US ton

20,000 × 0.0005

10 tons

Therefore, 20,000 pounds equals to 10 US ton.

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Answer:

50 in ^3

Step-by-step explanation:

V = 1/3 pi r^2 h

We know that pi = 3  

the diameter is 5 so the radius is 1/2 the diameter of 5/2 = 2.5

The height is 8

V = 1/3 ( 3) ( 2.5)^2 ( 8)

V = 50 in ^3

Area of rectangle - area of semicircle

L×B - πr square /2

Area = 124/7...

create your own scale, it could be 2cm=40mm, so 3cm=60mm and 2.5cm=50mm.

then draw your trapezium in the given space using your scale

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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Assuming everything else stays the same, an increase in the price of smartphones will decrease the quantity supplied of smartphones. Option c is the correct answer.

This is because the quantity supplied is the number of smartphones that suppliers are willing and able to sell at a given price, while supply refers to the entire range of quantities that suppliers are willing and able to sell at different prices.

When the price of smartphones increases, the cost of production and supply also increases. This leads to a decrease in the profitability of supplying smartphones at the current market price, and hence suppliers reduce the quantity supplied.

As a result, the quantity supplied of smartphones decreases, causing a leftward shift in the supply curve.

However, it is important to note that a decrease in the quantity supplied does not mean that there is a decrease in demand for smartphones. The demand for smartphones could remain the same, or even increase, leading to a shortage of smartphones in the market.

Therefore, the correct option is c.

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Maria must cut an additional $70 from her expenses each month in order to save enough money to buy a new TV that costs $420 in 6 months. By allocating this additional amount towards her savings goal, she will be able to reach her target within the desired timeframe. It's important for Maria to review her budget and identify areas where she can reduce expenses in order to make room for the additional savings. This could involve cutting back on discretionary spending, finding ways to save on daily expenses, or exploring opportunities to increase her income.

Maria must cut an additional $70 from her expenses each month.

To determine how much additional money Maria must cut from her expenses each month to afford a new TV that costs $420 in 6 months, we divide the total cost by the number of months.

Additional money per month = Total cost / Number of months

Additional money per month = $420 / 6

Additional money per month = $70

With careful planning and commitment to her budget, Maria can achieve her goal of purchasing a new TV without compromising her financial stability.

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In a 2 x 3 between subjects ANOVA, there are a total of 6 groups. The first factor, with 2 levels, divides the participants into two distinct groups. The second factor, with 3 levels, further divides each of the two groups into three subgroups. This results in a total of 6 groups.

In this design, each group consists of a unique combination of the two factors, ensuring that each participant is assigned to only one group.

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Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 1, - 4) and (x₂, y₂ ) = (2, 2) ← 2 points on the line

m = \(\frac{2-(-4)}{2-(-1)}\) = \(\frac{2+4}{2+1}\) = \(\frac{6}{3}\) = 2

None of the answer choices match the derived equation. Therefore, the correct answer is: D. No solution. To solve the given differential equation, we can use separation of variables.

Starting with the differential equation:

(1/x) dy/dx = ye^(x^2) + 2√y e^(x^2)

We can rearrange the equation by multiplying both sides by x:

dy = x(ye^(x^2) + 2√y e^(x^2)) dx

Next, we separate the variables by dividing both sides by (ye^(x^2) + 2√y e^(x^2)):

(1/y) dy / (√y + 2) = x e^(x^2) dx

Now, we integrate both sides with respect to their respective variables. On the left side, we can use the substitution u = √y + 2, which gives du = (1/2)(1/√y) dy. The integral becomes:

∫(1/y) dy / (√y + 2) = ∫(1/2) du

Integrating, we get:

ln|√y + 2| = (1/2)x e^(x^2) + C

Applying the logarithmic property ln(ab) = ln(a) + ln(b), the equation can be written as:

ln(√y + 2) = (1/2)x e^(x^2) + C

To eliminate the square root, we can square both sides:

[ln(√y + 2)]^2 = [(1/2)x e^(x^2) + C]^2

Expanding and simplifying, we have:

ln^2(√y + 2) = (1/4)(x^2)(e^(2x^2)) + Cx e^(x^2) + C^2

Now, we can rewrite the equation in a more convenient form:

4 ln^2(√y + 2) = 2x^2 e^(2x^2) + 4Cx e^(x^2) + 4C^2

Comparing this with the answer choices provided:

A. 4 ln(√y + 2) = 2 e^(x^2) + C

B. ln(√y + 2) = e^(x^2) + C

C. 4 ln(√y + 2) = e^(x^2) + C

None of the answer choices match the derived equation. Therefore, the correct answer is:

D. No solution

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Answer:

2.5h=20

Step-by-step explanation:

:D

1.) 10x-5=y

2.) $85

3.) 5.25 yards of fabric.

1.) To write an equation for this problem, we need to figure out what every value means:

the variable x, represents the amount of yards of fabric you can buy

the variable y, represents the total amount of money after you found out (x) or the amount of yards of fabric.

1 yard of fabric equals $10, and we have a $5 coupon (-5)

Our equation is:

10x-5=y

This equation represents the relationship between the total cost of fabric, and the amount that you can buy.

2. In order to solve this problem we need to use our equation, one value is given which is 9.

9 represents x, the amount of yards of fabric.

Substitute 9 into x:

10(9)-5=y

90-5=y

85=y

85 represents the cost of 9 yards of fabric, including the $5 coupon.

3.) This problem is similar to #2, although it's flipped.

The value given is $47.50, which represents (y), the total amount of money after (x) was found out.

But, we need to figure out (x).

Substitute $47.50 into (y):

10(x)-5=$47.50

Next, we need to figure out x by solving the opposite.

Adding the coupon to our answer can represent 10(x).

$47.50+5=52.50

10(x)=52.50

Lastly, divide both sides of the equation by 10.

10(x) / 10=52.50 /10

x=5.25

5.25 represents the amount of yards of fabric purchased if you paid $47.50.

Answer:

the volume is 5 to the next power which is 3 u end up with multiplication which mean u multiply 5 with 3 to get ur units

Answer:

Its (1.0, 1.4)

Step-by-step explanation:

Cuz i said soo :3

Answer:

b

Step-by-step explanation:

just took the test : )

Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

For I did this by trial and error.

= (4.6x10^5) / (7.5 x 10^4)

= 460,000 / 75,000

= 6.13333333333

= 6.13 times hotter than the Thai Pepper

Take the square root of each side.

\(\sf \sqrt{x^{2} } =\sqrt{25} \\\\\\ x=\± 5\)

The area of the actual flower bed include the following: D. 96 square meters.

In Mathematics and Geometry, the area of a triangle can be calculated by using this formula:

Where:

Scale:

0.5 cm = 2 m

0.5/2 = New length of flower bed/Actual length of flower bed

Actual length of flower bed = (2 × 3)/0.5 = 12 meters

0.5/2 = New height of flower bed/Actual height of flower bed

Actual height of flower bed = (2 × 4)/0.5 = 16 meters

By substituting the given parameters into the formula, we have;

Area of triangle = 1/2 × base area × height

Area of actual flower bed = 1/2 × 12 × 16

Area of actual flower bed = 96 m².

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.