Birth weights in the United States have a distribution that is approximately normal with a mean of 3369 g and a standard deviation of 567 g.
a) One definition of a premature baby is that the birth weight is below 2500 g. Draw the normal distribution (with appropriate labels) and shade in the area that represents birth weights below 2500 g. Convert 2500 g into a standard score. If a baby is randomly selected, find the probability of a birth weight below 2500 g.
b) Another definition of a premature baby is that the birth weight is in the bottom 10%. Find the 10th percentile of birth weights.
c) If 40 babies are randomly selected, find the probability that their mean weight is greater than 3400 g.
A Gallup survey indicated that 72% of 18- to 29-year-olds, if given a choice, would prefer to start their own business rather than work for someone else. A random sample of 400 18- to 29-year-olds is obtained today.
a) Describe the sampling distribution of p, the sample proportion of 18- to 29-year-olds who would prefer to start their own business.
b) In a random sample of 400 18- to 29-year-olds, what is the probability that no more than 70% would prefer to start their own business?
c) Would it be unusual if a random sample of 400 18- to 29-year-olds resulted in 300 or more who would prefer to start their own business? Why?

The values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

To find ∂z/∂r and ∂z/∂s, we need to differentiate z = F(u, v, w) with respect to r and s.
Given that u = r^2, v = -2s^2, and w = ln(r) + ln(s), we can substitute these values into z = F(u, v, w).
So, z = F(r^2, -2s^2, ln(r) + ln(s)).
To find ∂z/∂r, we differentiate z with respect to r while treating s as a constant. This gives us:
∂z/∂r = ∂F/∂u * ∂u/∂r + ∂F/∂w * ∂w/∂r.
Similarly, to find ∂z/∂s, we differentiate z with respect to s while treating r as a constant. This gives us:
∂z/∂s = ∂F/∂v * ∂v/∂s + ∂F/∂w * ∂w/∂s.
Since we don't have the specific function F(u, v, w) mentioned in the question, we cannot determine the values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

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Answer:

24 = x

Step-by-step explanation:

You use Pythagorean theorem. Since the normal equation is \(a^{2} + b^{2} =c^{2}\), you already have the \(c^{2}\) and another side which can be \(a^{2}\) or \(b^{2}\).

Because you have the hypotenuse and a side , your equation looks like this now: \(7^{2} +b^{2} = 25^{2}\)

and when you solve for be you just subtract \(25^{2} -7^{2}\) to get 24.

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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Answer:

3.14 inches squared

Step-by-step explanation:

A = π r²

A = π (1)²

A = π 1

A = 3.12

Answer:

the answer is 67.44 hope it helps smile

Answer: y = −(4/3)x  +   3.

Step-by-step explanation: 4x+3y=9  is the standard form for a linear equation. To convert the standard form to slope-intercept form, solve the standard form for y

4x+3y=9

Subtract 4x from both sides.

3y=−4x+9

Divide both sides by 3.

Answer: y = −(4/3)x  +   3.

Answer:

y = − 4/3x+3  

Step-by-step explanation:

4 x + 3 y = 9

Subtract  

4 x  from both sides.

3 y = − 4 x + 9

Divide both sides by 3

y=-4/3x+9/3

Simplify and you get y=-4/3x+3

Answer:

D 2.10+0.80m=11.70, 12 miles

Step-by-step explanation:

11.70-2.10=9.6

9.6/0.80=12

so there is 12 miles and only d has 12 miles

hope this helps have a blessed day

Step-by-step explanation:

set that width is x

and length become 2X

P = 2×( X+ 2X )

200 = 6 X

X=33. 3

width = 33.3 inch

length = 66. 6 inch

Answer:

A is not a right triangle

B is a right triangle

Step-by-step explanation:

A.

6^2 = 36
12^2 = 144.

36 + 144 = 180

15^2 = 225

180 ≠ 225, so it is not a right triangle

----------------------------------------------------------------------------

B.

5^2 = 25

12^2 = 144

25 + 144 = 169

13^2 = 169

169 = 169, so it is a right triangle

Answer:

No solution

Step-by-step explanation:

If two lines are parallel, they'll never intersect each other. Therefore, there's no solution.

Answer:

3,-2

Step-by-step explanation:

the solution set is the point where the two lines intercept. in this case it's 3,-2

Answer:

No, Yes, No, No

Step-by-step explanation:

Input the x and y values in the coordinates into the equation

(-3,-11):

-11 =  -5(-3) - 4

-11 =  15 - 4

-11 ≠ 11

The equation is not correct, so it is not a solution

(-7,31):

31 = -5(-7) - 4

31 = 35 - 4

31 = 31

The equation is correct, so it is a solution

(4,17):

17 = -5(4) - 4

17 = -20 - 4

17 ≠ -24

The equation is not correct, so it is not a solution

(6,-25):

-25 = -5(6) - 4

-25 = -30 - 4

-25 ≠ -34

The equation is not correct, so it is not a solution

-Chetan K

Answer:

2 1/3

Step-by-step explanation:

7/3 = 2 1/3

Hope it helps :D

Answer:

9 / 13

Step-by-step explanation:

From the question :

Let :

Hostel students = h

Day students = d

Students with A grade = a

P(h) = 60% = 0.6

P(d) = 40% = 0.4

P(hostel with A grade) ; P(A / H) = 0.3

P(day with A grade) ; P(A / D) = 0.2

The probability that a student picked at random withbA grade is an hostel student is given as :

Probability of being an hostel student gun he has A :

P(H | A) = (P(A/H) * P(H)) ÷ P(A/H) * P(H) + P(A/D) * P(D))

P(H | A) = (0.3 * 0.6) ÷ ((0.3*0.6) + (0.2*0.4))

P(H | A) = 0.18 ÷ (0.18 + 0.08)

P(H | A) = 0.18 ÷ 0.26

P(H | A) = 9 / 13

Answer:

work is shown and pictured

Answer:

Infinite

Step-by-step explanation:

Hope that this helps!

Answer:

Step-by-step explanation:

2 or 3 im not v sure tho

Answer:

Option F: $71.43 is the correct answer.

Step-by-step explanation:

By the question we can observe that 35% of regular price is $25 so this information will be used to calculate the original price of the shoes.

Let

P be the price of shoes

and d be the discount

So

\(d = \$25\\P=?\)

The discount is 35% of P so

\(d = 35\%\ of\ P\\25 = 0.35 * P\\P = \frac{25}{0.35}\\P = 71.42857...\)

Rounding off to the nearest hundredth

The regular price is: $17.43

Hence, option F: $71.43 is the correct answer.

Answer:

If the REGULAR price of the t-shirt is $18, the SALE price with a 20% discount is $14.40.

18.00 * .20 = 3.60

18.00 - 3.60 = 14.40 14.40 is answer

Answer:

g = 1/2

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define equation

9 + 3.5g = 11 - 0.5g

Step 2: Solve for g

Step 3: Check

Plug in g into the original equation to verify it's a solution.

Here we see that 10.75 does indeed equal 10.75.

∴ g = 1/2 is a solution of the equation.

Answer: g= 0.5

Step-by-step explanation:

Add

3.5g and 0.5g. to get

9+4g=11

then subtract 9 from the 11 and you should get 4g=2.

then divide 4 from 2 and you should get the answer of 2/4.

simplify it and you should get the answer g=0.5

Answer: 49m^12-36

Step-by-step explanation:

You'd multiply them :)

To answer the questions about group G with order 77: (1) Show that there are normal subgroups H and K of the group with order 7 and 11, respectively.

Since the order of G is 77, by the Sylow theorems, there exist Sylow 7-subgroups and Sylow 11-subgroups in G.

Let H be a Sylow 7-subgroup of G and K be a Sylow 11-subgroup of G. Since Sylow subgroups are conjugate to each other, H and K are both normal subgroups of G.

(2) Show that HK={hk|h∈H, k∈K} is an Abelian subgroup of group G.

Since H and K are normal subgroups of G, we have that HK is a subgroup of G. To show that HK is an Abelian subgroup, we need to prove that for any elements hk and h'k' in HK, their product is commutative.

Let hk and h'k' be arbitrary elements in HK. Since H and K are normal subgroups, we have that h'khk' = kh'h. Thus, the product hk h'k' is equal to kh'h, which implies that HK is an Abelian subgroup.

(3) Show that HK=G.

To show that HK=G, we need to prove that every element g in G can be expressed as a product hk, where h∈H and k∈K.

Since H and K are normal subgroups of G, their intersection H∩K is also a normal subgroup of G. By Lagrange's theorem, the order of H∩K divides both the order of H (which is 7) and the order of K (which is 11). Since 7 and 11 are coprime, the only possible order for the intersection is 1.

Thus, H∩K={e}, where e is the identity element of G. This implies that every element g in G can be uniquely expressed as g = hk, where h∈H and k∈K. Therefore, HK=G.

(4) Show that G is a cyclic group.

Since HK=G, and HK is an Abelian subgroup, we have that G is an Abelian group. Every Abelian group of prime order is cyclic. Since the order of G is 77, which is not prime, G cannot be cyclic.

Therefore, G is not a cyclic group.

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To answer the questions about group G with order 77: (1) Show that there are normal subgroups H and K of the group with order 7 and 11, respectively.

Since the order of G is 77, by the Sylow theorems, there exist Sylow 7-subgroups and Sylow 11-subgroups in G.

Let H be a Sylow 7-subgroup of G and K be a Sylow 11-subgroup of G. Since Sylow subgroups are conjugate to each other, H and K are both normal subgroups of G.

(2) Show that HK={hk|h∈H, k∈K} is an Abelian subgroup of group G.

Since H and K are normal subgroups of G, we have that HK is a subgroup of G. To show that HK is an Abelian subgroup, we need to prove that for any elements hk and h'k' in HK, their product is commutative.

Let hk and h'k' be arbitrary elements in HK. Since H and K are normal subgroups, we have that h'khk' = kh'h. Thus, the product hk h'k' is equal to kh'h, which implies that HK is an Abelian subgroup.

(3) Show that HK=G.

To show that HK=G, we need to prove that every element g in G can be expressed as a product hk, where h∈H and k∈K.

Since H and K are normal subgroups of G, their intersection H∩K is also a normal subgroup of G. By Lagrange's theorem, the order of H∩K divides both the order of H (which is 7) and the order of K (which is 11). Since 7 and 11 are coprime, the only possible order for the intersection is 1.

Thus, H∩K={e}, where e is the identity element of G. This implies that every element g in G can be uniquely expressed as g = hk, where h∈H and k∈K. Therefore, HK=G.

(4) Show that G is a cyclic group.

Since HK=G, and HK is an Abelian subgroup, we have that G is an Abelian group. Every Abelian group of prime order is cyclic. Since the order of G is 77, which is not prime, G cannot be cyclic.

Therefore, G is not a cyclic group.

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x = \(\sqrt{2+\sqrt{2+\sqrt{2+...} } }\) = 2

We have to find the value of x = \(\sqrt{2+\sqrt{2+\sqrt{2+...} } }\)

First take squares on both sides, then,

⇒ x² = 2 + \(\sqrt{2+\sqrt{2+\sqrt{2+...} } }\)

As the terms inside the square roots are non terminating, we can substitute x = \(\sqrt{2+\sqrt{2+\sqrt{2+...} } }\) into the above equation.

i.e.,  x² = 2 + x

⇒ x² - x -2 = 0

This is a quadratic equation which can be solved using factorization.

⇒  x²+(-2+1)x +(-2.1) = 0

⇒ (x-2)(x+1) = 0

So x = 2 or -1

But here the value of √2 is positive and square root of sum of positive numbers will always be positive.

So we can conclude that

x = \(\sqrt{2+\sqrt{2+\sqrt{2+...} } }\) = 2

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The values of determinant ,

\(\left|\begin{array}{ccc}3a&3b&3c\\-d&-e&-f\\4g&4h&4i\end{array}\right| = 72\)

\(\left|\begin{array}{ccc}a&b&c\\2d&2e&2f\\g+3a&h+3b&+3ci\end{array}\right| = - 12\)

The given determinant is,

\(\left|\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right| = -6\)

This is possible when we take,

a = -1 , e = 1, i = 6, b = c = 1

And d = g = h = 0

The the determinant becomes,

\(\left|\begin{array}{ccc}-1&1&1\\0&1&1\\0&0&6\end{array}\right|\)

Since this is an upper triangular matrix,

Therefore,

Determinant be the product of diagonal element,

Thus,

⇒  -1x1x6 = -6

Now using these values we can calculate the further given determinants,

Q4: Given that,

\(\left|\begin{array}{ccc}3a&3b&3c\\-d&-e&-f\\4g&4h&4i\end{array}\right|\)

Therefore put the values of a, b, c, d, e, f, g, h, and i defined above,

\(\left|\begin{array}{ccc}3(-1)&3(1)&3(1)\\0&-1&-1\\0&0&4(6)\end{array}\right|\)

Therefore, Determinant be,

⇒ -3 x  (-1) x 24 = 72

Hence,

\(\left|\begin{array}{ccc}3a&3b&3c\\-d&-e&-f\\4g&4h&4i\end{array}\right| = 72\)

Q5 : Given determinant is,

\(\left|\begin{array}{ccc}a&b&c\\2d&2e&2f\\g+3a&h+3b&+3ci\end{array}\right|\)

put the values of a, b, c, d, e, f, g, h, and i defined above,

we get,

\(\left|\begin{array}{ccc}-1&1&1\\0&2&2\\-3&3&9\end{array}\right|\)

= -1(12) -1(6) + 1(6)

= -12

Hence, The determinant be

\(\left|\begin{array}{ccc}a&b&c\\2d&2e&2f\\g+3a&h+3b&+3ci\end{array}\right| = - 12\)

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The complete question is attached below:

Answer:

the answer is |−70 − 15| = |−85| = 85 units [ C ]

hope this helps :)

Step-by-step explanation:

Answer: 75 u²

Step-by-step explanation:

1/2(5)((14)+(16))

Add in parenthesis

1/2(5)(30)

Multiply

1/2(150)

Multiply

75

Hope it helps <3

The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

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Answer: 30

Step-by-step explanation:

Given

Polyhedron has (E)58 edges

It has same number of faces and vertices

Using Euler's formula

\(\Rightarrow V-E+F=2\)

where

V=no of vertices

E=no of edges

F=no of edges

Suppose there are x faces

Insert the values

\(\Rightarrow x-58+x=2\\\Rightarrow 2x=60\\\Rightarrow x=30\)

Thus, polyhedron has 30 faces.

Answer:

30

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since we are given all of the necessary information we simply need to divide the total number of crayons by the total number of students that are getting crayons. This will give use the number of crayons that each student will get which will be represented by the variable x. Therefore, the equation would look like the following...

x = 48 / 6