Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the mean of the sample means?.

Swimmer is 47 dm away from the sailboat.

The mentioned problem will use cosine trigonometric functions to find the distance between swimmer and sailboat. Assuming the distance between lifeguard and swimmer be x and the distance between lifeguard and sailboat be y.

Taking the triangle between swimmer and lifeguard -

cos theta = base/hypotenuse

cos 32 = x/36.5

x = 0.8×36.5

x = 29.2 dm

Taking the triangle between lifeguard and sailboat -

cos 13 = y/84.7

y = 0.9×84.7

y = 76.23 dm

Therefore, the distance between sailboat and swimmer is y - x

Distance = 76.23 - 29.2

Performing subtraction

Distance = 47.03 dm

Round to nearest tenth

Distance = 47 dm

Thus, the sailboat and swimmer are 47 dm apart.

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The expression that will give a value of 74 is C. (75 - 5) × 1 + 4.

It should be noted that an expression is used to how the relationship between the variables that are expressed in the data or information given.

In this case, we want to find the expression that will give a value of 74. This will be :

= (75 - 5) × 1 + 4

= 70 × 1 + 4

= 70 + 4

= 74

The correct option is C.

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Answer: yes then no

Step-by-step explanation:

Creative Section - B

7. a) The average of daily income of a plumber from Sunday to Friday is Rs 1,300

in the last week. If he earned Rs 2,000 on Saturday, find

income of the week.

The fraction of the reading assignment done by Tuesday night is 1/2.

Given:

Let the total reading assignment be x.

Fraction of the reading assignment finished by Tori on Monday afternoon = (1/6)x

Fraction of the reading assignment finished by Tori on Tuesday afternoon = (1/3)x

The fraction of the reading assignment done by Tuesday night is,

Total - Fraction of the reading assignment completed by Tori

= [tex]x -(\frac{x}{6} + \frac{x}{3} )[/tex]

= [tex]x -(\frac{x+ 2x}{6} )[/tex]

= [tex]x - \frac{3x}{6}[/tex]

= [tex]x -\frac{x}{2}[/tex]

= [tex]\frac{2x-x}{2}[/tex]

= [tex]\frac{x}{2}[/tex]

So, 1/2 of the reading assignment(x) was done by Tuesday night.

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Answer:

Step-by-step explanation:

Answer: 9.77 m

Step-by-step explanation:

xyz

When two amounts are proportionate, they fluctuate at the same rate, maintaining the constancy of their relationship.

Here x be the proportionality constant  its value 5.5.

Matthew bought 2 movie tickets for $11,

Rosa bought 7 movie tickets for $38.50.

let the value of per ticket is x

2x = 11 and 7x = 38.5

7x- 2x = 38.5 -11

x = 5.5

here x be the proportionality constant  its value 5.5.

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Answer:

The measure of the largest angle is 145°

Step-by-step explanation:

Since the angles form a linear pair taking two angles that add to 180 and solving for x will give you the answer. the sentence "One angle is 5 more than four times the size of the other angle." your equation should look like this:

5 + 4x. the other angle uses the variable x. So the equation 5 + 4x + x = 180 should result in x = 35. That saying, the smaller angle is 35 and to find the larger angle either plug in x or subtract 180-35. both shoukd result in 145° which is the larger angle.

Given: x = -2; y = -3; z = 5

It is clear that a numerical term can only be evaluated from an expression filled with numbers (no variables). In the expression provided, we have two variables, where y is being subtracted from x.

The expression can't be simplified because there is no like terms in the expression. However, since there are specific numerical values for each variable, we can substitute the numerical values for the variables in the expression and simplify the expression.

As planned, let's substitute the variables into the expression

Here, we know that x = -2 and y = -3.

If -2 is being subtracted by a negative integer, the negative integer will become positive, and the "minus sign" will be converted to a "plus sign".

We can conclude that 1 is the solution to the expression.

Answer:

y = 5

Step-by-step explanation:

2(40 - 5y) : 80 - 10y

10y + 5(1 + y) : 5y + 5

80 - 10y = 5y +5

-10y = 5y -75

-10y - 5y = 5y - 75 - 5y

-15y/-15 = -75/-15

-15y/-15 : y

-75/-15 : 5

Hence, The answer should be 5

The monetary value of gold, silver and bronze is $0.5, $0.35 and $0.25 respectively.

The given conditions in the question are-

Let the monetary value of gold be 'a'.

Let the monetary value of silver be 'b'.

Let the monetary value of bronze be 'c'.

The total monetary value is $20.

The equation will be;

14 gold, 20 silver, and 24 bronze

14a + 20b + 24c = 20      .......eq1

20 gold, 15 silver, and 19 bronze

20a + 15b + 19c = 20   .......eq 2

30 gold, 5 silver, and 13 bronze.

30a + 5b + 13c = 20       .....eq 3.

Solving equation 1,2 and 3 by elimination method.

a = 1/2

b = 7/20 and

c = 1/4

Thus, the monetary value of gold, silver and bronze is $0.5, $0.35 and $0.25 respectively.

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answer:

I hope the solution is helpful.

The answer is x = 1, assuming that the space is meant to be an equal sign.

Answer:

275-234 = 41

41/275 times 100

4100/275

=14.90909

=15%

Step-by-step explanation:

Answer:

80%

Step-by-step explanation:

you're occupying 800 out of 1000

the way to write this mathematically is to write: 800/1000,

which equals 0.8

then to make this a percentage you x100

and your answer is 80%

The sales in 2012 is estimated to be $40546.5 million if we use the midpoint formula assuming that the sales followed a linear pattern.

Midpoint is a term used in geometry and can be described as the center or middle point of a line segment. It enables you to take two endpoints, and then by using these endpoints you can find the point that is midway between them in the line segment.

Considering,

[tex]P_{1} = (x_{1},y_{1})[/tex]

[tex]P_{2} = (x_{2},y_{2})[/tex]

Here;

[tex]x_{1}[/tex] = 2010

[tex]x_{2}[/tex] = 2014

[tex]y_{1}[/tex] = $35,109 million

[tex]y_{2}[/tex] = $45,984 million

The formula for the midpoint is given as;

[tex]P_{m}[/tex] = {( [tex]x_{1} + x_{2}/2[/tex] ), ( [tex]y_{1} + y_{2} / 2[/tex] )}

[tex]P_{m}[/tex] = {(2010 + 2014 / 2), (35109 million + 45984 million / 2)}

[tex]P_{m}[/tex] = {(4024 / 2), (81,093 million / 2)}

[tex]P_{m}[/tex] = {2012 , 40546.5 million}

Therefore, the sales in 2012 are calculated to be $40546.5 million by using the midpoint formula.

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Using the law of indices, [tex]1024^{\frac{2}{5} } = 16[/tex]

The expression can be solved using the law of indices as follows:

[tex]1024^{\frac{2}{5} }[/tex]

using law of indices, involving bracket.

Brackets with indices are where we have a term inside a bracket with an index (or power) outside of the bracket.

To do this we can raise everything inside the bracket to the power.

[tex](a^{b} )^{x} = a^{bx}[/tex]

Therefore,

1024 = 2¹⁰

Hence,

[tex]2^{\frac{2}{5} (10)} = 2^{\frac{20}{5} } = 2^{4} = 16[/tex]

Therefore,

[tex]1024^{\frac{2}{5} } = 16[/tex]

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A rock climber throws a first aid kit to the another climber who is higher up the mountain, the initial velocity of the kit is 12 m/s at an angle of 71 above the horizontal, at the instant when the kit is caught, it is traveling horizontally, so its vertical speed is zero, height difference between climbers is 0.85 m.

Velocity is the direction at which an object is moving and serves as a measure of the rate at which its position is changing as seen from a specific point of view and as measured by specific unit of time (for example, 60 km/h northbound). In kinematics, area of classical mechanics that deals with the motion of bodies, velocity is a fundamental idea.

Vertical motion of the first aid kit:

The Initial vertical velocity, u = 5.70 sin 45.7 = 4.08 m/s

Acceleration, g = -9.81 m/s²

When climber who is higher up the mountain catches the kit it's vertical speed is zero.

Final vertical velocity, v = 0 m/s

We have the equation of motion, v² = u² + 2as

Substituting

0² = 4.08² + 2 x -9.81 x s      

s = 0.85 m

So kit travels 0.85 m vertically.

Height difference between the climbers = 0.85 m.

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Answer:

Below in bold.

Step-by-step explanation:

3/20

We divide 3 by 20:-

3 / 20 = 0 so we divide 30 by 20 and proceed as below:

20)3.00 ( 0.15

     20

      100

      100

       ......

The answer is 0.15 which is terminating.

5/11

If we divide as above we get 0.45454545....

The 45 keeps repeating

2/15

Dividing gives 0.133.........

Repeating

7/8 = 0.875

terminating.

9/16

= 0.5625

terminating.

Answer:

3/20 = 0.15 (Terminating)

5/11 = 0.45454 (Repeating)

2/15 = 0.13333 (Repeating)

7/8 = 0.875 (Terminating)

9/16 = 0.5625 (Terminating)

Explanation:

The definition of Terminate means to bring to an end. This would also apply to the decimals. To find whether a fraction is terminating or not, is to simply divide and you will get a decimal, unless it is mixed fraction. Terminating will bring an end, Ex: 1/2 ( 1 ÷ 2 ) which would equal = 0.5 This is an example of a terminating decimal. A repeating decimal is a decimal that never ends of its repetition, Ex: 0.13333333 (Continuous).

I hope this helps my grammar might bit a bad sorry.

Hope you get an A ^^

Have a great day

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:\pm b + 9 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The given expression is :

[tex]\qquad \tt \rightarrow \: |b + 1| + 8[/tex]

[tex]\qquad \tt \rightarrow \: |b| + 1 + 8[/tex]

[ as 1 is a positive number, it can come out of modulus function as it is ]

[tex]\qquad \tt \rightarrow \: |b| + 9[/tex]

Now, there are two cases possible.

Case 1 :

[tex]\qquad \tt \rightarrow \: b + 9[/tex]

[ if b is a positive number, it will come out of modulus as it is ]

Case 2 :

[tex]\qquad \tt \rightarrow \: - b + 9[/tex]

[ if b is a negative number, it will come out of modulus with a negative sign, to make the overall term out of modulus positive ]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Employee's gross pay is their salary before any payroll deductions such as taxes, benefits, and other expenses are made.

Her goss weekly pay is $409.13.

Before taxes, benefits, and other payroll deductions are deducted, an employee's gross pay is what they are paid.

Net pay, often known as take-home pay, is the sum that is left over after all deductions have been taken into consideration.

Federal income tax:

306.36+ 43 = 349.36

Medical insurance:

349.36 + 22.35 = 371.71

Credit union:

371.71 + 25 = 396.71

State tax:

396.71 increased by 1.5% is 396.71 * (1.015) = 402.66

Local tax:

402.66 increased by 1.5% is 402.66 * (1.015)= 409.13

Her goss weekly pay is $409.13.

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Answer:

x = 7.2 , y = 57 , z = 10.8

Step-by-step explanation:

the sum of the 3 angles in the outer triangle = 180° , that is

y + 88 + 35 = 180

y + 123 = 180 ( subtract 123 from both sides )

y = 57

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

the outer and inner triangles are similar ( AA postulate ) then the ratios of corresponding sides are in proportion, that is

[tex]\frac{x}{12}[/tex] = [tex]\frac{9}{9+6}[/tex] = [tex]\frac{9}{15}[/tex] ( cross- multiply )

15x = 108 ( divide both sides by 15 )

x = 7.2

and

[tex]\frac{z}{18}[/tex] = [tex]\frac{9}{15}[/tex] ( cross- multiply )

15z = 162 ( divide both sides by 15 )

z = 10.8

Answer:

y=-5x+6

Step-by-step explanation:

the two lines are parallel so they have the same slope and if you put the like in y=mx+b it would be y=-5x+1 so the slope is -5

Then you need to put it into point slope for to figure it out y-y1=m(x-x1)

y-1=-5(x-1) (simplify)

y-1=-5x+5 (add 1 to both sides)

y=-5x+6

Amount of water produced in 6 days is 15.6×10⁶.

We will simply perform multiplication to find the amount of water produced in 6 days.

Amount of water produced in 6 days = amount of water produced in one day × 6

Amount of water produced in 6 days = 2.6×10⁶×6

Performing multiplication to find the amount of water produced in 6 days

Amount of water produced in 6 days = 15.6×10⁶

The answer is in scientific notation as 15.6 is coefficient, 10 is base and 6 is exponent. Therefore, amount of water produced by plant in 6 days is 15.6×10⁶.

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As a result, angle M's supplement is 167 degrees, while angle M's complement is 77 degrees.

Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. The sum of complimentary angles is 90 degrees. If the two additional angles are combined, they create a straight line and an angle.

Complementary angles are those whose combined angle is 90 degrees or less. To put it another way, two angles are said to be complimentary if they combine to make a right angle. In this case, we say that the two angles work well together.

So as per the given information:

we know that

a).  180-angle M=supplement of angle M

180-13=167 degree

b).  90-angle M=compliment of angle M

    =77 degree

Therefore, the supplement of the angle M is 167 degree and the complement of angle m is 77 degree.

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Ai) 5575 Swedish kronor      500*11.15

Aii) 312.50 swiss frans      250*1.25

B) £345     407.10/1.18

Hope this helps, have a great day!!