a hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. a sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. what is the sample variance? multiple choice 1.177 6.6 1.386 7.6

The number of students studying abroad in 2001 is 150.38 thousand

The number of students studying abroad in 2018 is 467.53 thousand

The given equation is known as an exponential equation. An exponential equation is a non-linear equation.

The given equation is 123.1(1.069)^x

Where:

Number of students studying abroad in 2001 = 123.1(1.069)^3= 150.38 thousand

Number of students studying abroad in 2018 = 123.1(1.069)^20 = 467.53 thousand

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The different combinations of reggaeton and hip-hop songs that Jae could use for his playlist include:

In this scenario, Jae makes a playlist of 24 songs for a party and he prefers reggaeton and hip-hop music and then builds the playlist from the two music types.

In this case, the combination will be gotten by the addition of two values that can give 24.

The combination can include:

10 reggaeton + 14 hip hop music = 24 songs

18 reggaeton + 6 hip hop music = 24 songs.

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If Tina's score is in the 50th percentile and the grades were normally distributed, Tina's score on the exam is 78.

A percentile refers to the comparison score between a particular score and the scores of the rest of a group. It represents the percentage of scores that a specific score surpassed. For example, if the score of 75 points on a test is ranked in the 85th percentile, it implies that the score 75 is higher than 85% of the scores. The 50th percentile, which is also the median score implies that 50% of the score is below or above the average score in a normally distributed data. In the given situation, if the grades are normally distributed with a mean of 78, that implies that 50% of the scores are above 78 and 50% of the scores are below 78. The standard deviation in this case is irrelevant. As Tina’s score is at the 50th percentile, her score on the exam would be 78.

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Emmanuel paid $50 for each watch.

Profit describes the financial benefit realized when revenue generated from a business activity exceeds the expenses, costs, and taxes involved in sustaining the activity in question.

Given that, Emmanuel started a business selling watches. He sells each watch for 30% more than he pays for them. Last week, he sold 7 watches for a total of $455.

Let the original price of each watch be x

According to question,

x*130% = 455/7

x = 65*100/130

x = 50

Hence, Emmanuel paid $50 for each watch.

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This rubber band's work in stretching from x = 0 to x = l is:

[tex]W=(\frac{aL^2}{2}+\frac{bL^3}{3}})[/tex]

Work is a measure of energy transfer that occurs when an object is moved over a distance by an external force that is applied in the direction of Work is a measure of energy transfer that occurs when an object is moved over a distance by an external force that is applied in the direction of displacement .

We say that work has been done whenever a force moves an object. When a ball rolls down a hill due to gravity, when you pick up your backpack from the ground, or when your car's internal engine applies a force to move your wheels, all of these events involve a force moving an object over a distance and thus involve some work. No work is done when a force is applied to an object but it does not move.

Given,

force , [tex]f=ax+bx^2[/tex]

work done can be determined by formula,

[tex]W=\int\limits^a_b F\, dx \\\\W=\int\limits^L_0(ax+bx^2)dx\\\\W=(\frac{ax^2}{2}+\frac{bx^3}{3}})|\limits^L_0\\\\W=(\frac{aL^2}{2}+\frac{bL^3}{3}})-0\\\\W=(\frac{aL^2}{2}+\frac{bL^3}{3}})[/tex]

Thus, the work done is [tex]W=(\frac{aL^2}{2}+\frac{bL^3}{3}})[/tex].

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Answer:

7/66

Step-by-step explanation:

Given problem,

→ (7/10) × (1/3) × (5/11)

Let's solve the given problem,

→ (7/10) × (1/3) × (5/11)

→ (7 × 1 × 5)/(10 × 3 × 11)

→ 35/330

→ 7/66

Hence, the answer is 7/66.

Answer:

a(647)

b(25)

Step-by-step explanation:

A permutation is an arrangement of objects in a specific order

i.e. AB ≠ BA

In Permutation order is important.

Here there are 12 Letters and symbols

Out of which E is repeated.

here we are given that duplicates from the list of 12 are not allowed, and We see that letter E is repeated.

So There are 12 letters in all, out of which we need 7 letters and symbol, where order is important.

So formula for permutation is nPr = [tex]\frac{n!}{(n-r)!}[/tex] where ! is called fractional symbol n! = n*(n-1)*(n-2)

*3*2*1x! = reputation of any word.

So Permutation with reputation of any letter or object is [tex]\frac{nPr}{x!}[/tex]

for example 4! = 4*3*2*1 = 24

So the answer is,

12P7 = [tex]\frac{12!}{2!*(12-7)!} = \frac{12!}{5!*2!} = \frac{12*11*10*9*8*7*6*5!}{5!*2!}[/tex] If we cancel 5! from both numerator and denominator.

12P7 = 12*11*10*9*8*7*3 = 1995840

So the answer is 1995840.

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The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

[tex]\pi[/tex](R +3)^2

Area of the pool is:

[tex]\pi R^2[/tex]

Now, Our equation is:;

[tex]\pi[/tex](R +3)^2 - [tex]\pi R^2[/tex] = 198

[tex]\pi[/tex]((R+3)^2 - [tex]R^2[/tex]) = 198

Open the inner bracket :

[tex]\pi[/tex]([tex]R^2+6R+9-R^2[/tex]) = 198

[tex]\pi[/tex](6R +9) = 198

6R+9 = 198/[tex]\pi[/tex]

6R = 198/[tex]\pi[/tex] - 9

R = (198/[tex]\pi[/tex] - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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Answer:

lmfa you answer my questions i recently posted ill answer yours...

Step-by-step explanation:

okay?

The probability that the student is a boy with glass is 3/20

Number of boys in the class = 6 boys

Number of girls in the class = 14 girls

Half of the boys wear glass

The number of boys that wear glass = 6 / 2

= 3 boys

Total number of students in the class = 6 + 14

= 20 students

Probability = Number of favorable outcomes / Total outcomes

= The number of students that wear glass / Total number of students

Substitute the values in the equation

= 3/20

Hence, the probability that the student is a boy with glass is 3/20

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Answer:

Step-by-step explanation:

4x - 3y = 8

5x - 2y = -11

8x - 6y = 16

-15x + 6y = 33

-7x = 49

x = -7

4(-7) - 3y = 8

-28 - 3y = 8

-3y = 36

y = -12

Answer:

2.375 inches

Step-by-step explanation:

Main Steps

1. Identifying important parts of the question

2. Solving the problem

Step 1. - Identifying important parts of the question

In the question, there is some extraneous information.  For instance, the question introduces the terms "diameter" and "loaded in shear" and "with a safety factor of 1.5".  However, given the information in the problem, and the question asked, it isn't necessary to know that it is "loaded in shear" means, or to know what a diameter is (since everything stays with diameters, and doesn't involve another dimension), and the problem gives the result that will satisfy "a safety factor of 1.5".

Sifting through the problem/question, these are the important parts:

- "to the nearest 1/8 inch" (meaning round to the nearest 1/8th of a unit)

- with "units of inches to 3 decimal places"

- The number to round is "2.4183 inches

Step 2. - Solving the Problem

To round to the nearest 1/8 inch, we can divide the number 2.4183 by 1/8.  

[tex]2.4183 \div(1/8)[/tex]

Recall that dividing by a fraction is the same as multiplying by the reciprocal

[tex]2.4183 * 8[/tex]

19.3464

So, there are approximately 19, one-eighth-inches in the measurement.  (Note that 19.3464 is closer to 19 than it is to 20).  To find the final rounded measurement, multiply 19 by 1/8

[tex]19 * (1/8)[/tex]

2.375 inches

So, the diameter of the bolt that should be used (if rounded to the nearest 1/8 inch, to allow for a factor of safety of 1.5) is 2.375 inches

Answer:11.4

Step-by-step explanation: Set up a proportion: [tex]\frac{15}{x}[/tex]=[tex]\frac{5}{3.8}[/tex]

To solve a proportion, multiply the numbers diagonal from each other, then divide by the last number. In this problem, we would multiply 15 and 3.8, which equals 57, then we would divide by 5. That is why the answer is 11.4.

hope this helps!

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The number of chocolate cookies that were sold is 22100.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Since the ratio of chocolate : vanilla is 2:1 and the charity sells 2210 boxes of cookies, the number of chocolate will be:

= 2/(2+1) × 2210 × 15

= 2/3 × 2210 × 15

= 22100

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Answer:

Factor 49x^2-4 49x2 − 4 49 x 2 - 4 Rewrite 49x2 49 x 2 as (7x)2 (7 x) 2. (7x)2 − 4 (7 x) 2 - 4 Rewrite 4 4 as 22 2 2.

Step-by-step explanation:

Hoped it helped

Answer:

(7x-2)(7x+2)

Step-by-step explanation:

This was the easiest thing I had in Analytic Geometry!!

The value of d i s 1 .

ie. d=1

Define linear equation .

An equation between two variables that gives a straight line when plotted on a graph.

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables .

Given:

d - 10 - 2d + 7 = 8 + d - 10 - 3d

On rearranging the given equation ,we get

In other words on taking the like terms to on one side ,so

⇒(d-2d-d+3d)=(8-10+10-7)

⇒d=1

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The value of x is -40.

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

One fifth times quantity x plus 15=(1/5)(x+15)

So, one fifth times quantity x plus 15 end quantity equals negative 5 shows"

(1/5)(x+15)= -5

0.2(x+15)= -5

0.2x+3= -5

0.2x=-5-3

0.2x=-8

x=-8/0.2 = -40

So, the value of x is -40.

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Answer:

  A. 1/2

  D. -1/3

Step-by-step explanation:

You want to know the solutions to 6x² -x -1 = 0.

We can factor the equation as ...

  6x² -3x +2x -1 = 0

  3x(2x -1) +1(2x -1) = 0

  (3x +1)(2x -1) = 0

The solutions will make the factors zero:

  3x +1 = 0   ⇒   x = -1/3

  2x -1 = 0   ⇒   x = 1/2

The solutions are 1/2 and -1/3.

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The angle in radians and the sector area are 2/9 π and 804.248 m² respectively

A sector of a circle is the part of a circle made of the arc along with its two radii

Given:  angle = 40° and distance(r) = 48m

To convert the angle to radians, multiply the angle by π/180:

Angle in radian(α) = 40 x π/180  = 2/9 π radian         (Note: π = 180°)

The formula for sector area = (α×r²)/2

Thus, sector area = (2/9π × 48²)/2 = 804.248 m²

Therefore, the angle in radians is 2/9 π and the sector area is 804.248 m²

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The dimensions of the box of height 36in and the side of the square is 18in.

A topological measure of the size of an object's covering properties is its dimension. It is roughly the number of coordinates required to specify a point on the object.

Given that the u.s.post office will accept a box for shipment only if the sum of height and girth(the distance around of bottom) is at most 108 in.

We must first determine the box's dimensions.

Let s be the side of the square base and h be the height of the box

So , h + 4s = 108

H = 108 – 4s -----(1)

Volume = s^2 h

V = s^2(108-4s)

= 108s2 – 4s3

V’ = 216s – 12s2

Let v’ = 0

S[216-12s] = 0

216 – 12s = 0

12s = 216

S = 216/12

S = 18

V” = 216 – 24s for s =18

V” = 216 – 432

= -216(-ve)

Volume is maximum when s =18

So h= 108-72

=36 in

Therefore the dimensions of the box of height 36in and the side of the square is 18in.

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The Proportion of exam results between 82 and 89.2 points is 0.3330.

What is standard deviation?

A measurement of a data set's deviation from the mean is referred to as "standard deviation" (or ""). A low standard deviation means that the data are grouped around the mean, whereas a large standard deviation says that the data are more spread out..

For instance, the mean of the two integers 2, 7, 14, 22, 30 and 15, 15, 15, 14, 16 is the same. But the second is clearly more diffused.

Given:

Mean is 83.2 points, and

8 points is the standard deviation.

Consequently, the proportion is

P(82 ≤ x ≤ 89.2)

=P( 82- 83.2 / 8 ≤ z ≤ 89.2 - 83.2/8)

=P (0.75) - P(-0.15)

=0.7734 -(0.4404)

= 0.3330

So, the Proportion of exam results between 82 and 89.2 points is 0.3330.

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Answer: 30,000

Step-by-step explanation: 50,000 - 20,000 = 30,000

Answer:

4 (x+4)

Step-by-step explanation:

4x+16      =     4 * x   +   4*4    =   4 (x+4)

Answer:

6

Step-by-step explanation:

24/6 = 4

36/6 = 6

6 bags, 4 lollipops and 6 pieces of gum in each bag.

Answer:

12 bags

Step-by-step explanation:

You would need to find the GCF of both numbers: 12

24*12 = 2

38*12 = 4

12 bags with 2 lollipops and 4 pieces of gum in each

The length of RT is 12 units.

What is length?

Distance is measured by length. Length is a quantity having the dimension distance in the International System of Quantities. Most measuring systems use a base unit for length from which all other units are derived. The metre is the basic unit of length in the International System of Units (SI). The greatest extended dimension of a stationary item is typically believed to be its length. This is not always the case, as it may depend on the location of the item. When there is a basis from which vertical measurements may be made, height is employed. When length is the greatest dimension, width or breadth generally relate to a lesser dimension.

given, RS+ST=RT

or, 9 + x - 1 = 3x

or, 8 + x = 3x

or, 3x - x = 8

or, 2x = 8

or, x = 8/2

or, x=4

Then, the length of RT = 3x = 3.4 = 12 units

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Answer:

[tex]\huge\boxed{\sf Area = 454.4\ mm\²}[/tex]

Step-by-step explanation:

Given that,

Radius = r = 12 mm

We know that,

So,

Area = (3.14)(12)²

Area = (3.14)(144)

Area = 454.4 mm²

[tex]\rule[225]{225}{2}[/tex]