30 POINTS PLEASEEEEEEEEEEEE HELP

Answer:

1. Most professional athletes are from the ages 25-30.

2. Do people over 40 years of age participate in professional sports?

Hope this helps!

~PumpkinSpice1

Answer:

1. Most professional athletes are from the ages 25-30.

2. Do people over 40 years of age participate in professional sports?

Step-by-step explanation:

1. Most professional athletes are from the ages 25-30.

2. Do people over 40 years of age participate in professional sports?

1. Most professional athletes are from the ages 25-30.

2. Do people over 40 years of age participate in professional sports?

1. Most professional athletes are from the ages 25-30.

2. Do people over 40 years of age participate in professional sports?

1. Most professional athletes are from the ages 25-30.

2. Do people over 40 years of age participate in professional sports?

1. Most professional athletes are from the ages 25-30.

2. Do people over 40 years of age participate in professional sports?

1. Most professional athletes are from the ages 25-30.

2. Do people over 40 years of age participate in professional sports?

Considering the equations of a circle and of a parabola, we have that:

a) Tunnel A is a circle, with it's radius meaning that both the width and the height are of 12.

b) Tunnel B is a parabola, with it's vertex and it's roots meaning that it has a width of 32 feet and a height of 16 feet.

c) The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.

The equation of a circle of center \((x_0, y_0)\) and radius r is given by:

\((x - x_0)^2 + (y - y_0)^2 = r^2\)

For Tunnel A, the equation is given by:

x² + y² + 28x + 52 = 0

Completing the squares:

(x + 14)² + y² = -52 + 14²

(x + 14)² + y² = 144.

Hence:

Tunnel A is a circle, with it's radius meaning that both the width and the height are of 12.

A parabolic(quadratic) equation is modeled by:

y = ax^2 + bx + c

The vertex is given by:

\((x_v, y_v)\)

In which:

For Tunnel B, the equation is given as follows:

x² - 36x + 16y + 68 = 0.

16y = -x² + 36x - 68.

Simplifying by 16:

y = -0.0625x² + 2.25x - 4.25.

Hence the coefficients are a = -0.0625, b = 2.25, c = -4.25, and the maximum height is:

\(y_v = -\frac{(2.25)^2 - 4(-0.0625)(-4.25)}{(-0.0625)} = 16\)

The width is the difference between the roots, which, using a calculator, are:

2 and 34, hence the width is of 32 feet, as 34 - 2 = 32.

Hence:

Tunnel B is a parabola, with it's vertex and it's roots meaning that it has a width of 32 feet and a height of 16 feet.

For item c, considering the previous items, we have that:

The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.

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The first step in evaluating the expression 3x{9-(4+2)/2 is to simplify the innermost parentheses. By performing operations within parentheses first, we can simplify the expression and make it easier to evaluate.

To begin, we evaluate the expression within the parentheses (4+2), which equals 6. Thus, the original expression becomes 3x{9-6/2}.

The next step is to simplify the division operation. We divide 6 by 2, resulting in 3. Now the expression becomes 3x{9-3}.

The subsequent step is to simplify the subtraction operation. We subtract 3 from 9, giving us 6. The expression now becomes 3x6.

Finally, we multiply 3 by 6, yielding a final result of 18. Therefore, the evaluation of the expression 3x{9-(4+2)/2 is equal to 18.

By simplifying the parentheses, performing the division, and evaluating the subtraction, we systematically reduce the expression to its simplest form. Following the order of operations (also known as PEMDAS or BODMAS), which prioritizes parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right), ensures an accurate evaluation of the expression.

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Answer:

Yes, it is a polynomial identity (work below).

Step-by-step explanation:

Let's start by expanding the left side of the equation.

\((2x^2+y^2)^2=\\4x^4+y^4+4x^2y^2\)

Now, let's expand the second side.

\((2x^2-y^2)^2+(2xy\sqrt{2} )^2=\\4x^4+y^4-4x^2y^2+4x^2y^2(2)=\\4x^4+y^4-4x^2y^2+8x^2y^2\)

There are no like terms on the left side, so let's combine the like terms on the right side.

\(4x^4+y^4-4x^2y^2+8x^2y^2=\\4x^4+y^4+4x^2y^2\)

Now, let's check if the left and right sides are equal:

\(4x^4+y^4+4x^2y^2= 4x^2+y^4+4x^2y^2\)

Both sides are the same. Thus, the equation is a polynomial identity.

The amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

Recall the compounding formula:

A = P * \(e^{rt}\)

Where:

A = Final amount in the account

P = Initial principal (deposit)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (as a decimal)

t = Time in years

Given:

Initial principal (P) = $16,000

Annual interest rate (r) = 2%  = 0.02

time (t) = 4 years.

Substitute these values into the formula, we get:

A = $16,000 * \(e^{0.02 * 4}\)

Using a calculator, we can calculate:

A = $16,000 * \(e^{0.08}\)

A = $16,000 * 1.0833

A = $17,332.8

Therefore, the amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

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It will take 3.5 hours for the two cars to be 280 miles apart.

To determine the time it takes for the two cars to be 280 miles apart, we can use the concept of relative velocity.

Since the cars are traveling in opposite directions, their velocities can be added together to find their relative velocity:

Relative velocity = Velocity of car traveling east + Velocity of car traveling west

Relative velocity = 60 mph + 20 mph

Relative velocity = 80 mph

The relative velocity of the cars is 80 mph, which means that they are moving away from each other at a combined speed of 80 mph.

To find the time it takes for them to be 280 miles apart, we can use the formula:

Time = Distance / Speed

Plugging in the values, we have:

Time = 280 miles / 80 mph

Time = 3.5 hours

Therefore, it will take 3.5 hours for the two cars to be 280 miles apart.

During this time, the car traveling east would have covered a distance of 60 mph × 3.5 hours = 210 miles, while the car traveling west would have covered a distance of 20 mph × 3.5 hours = 70 miles.

The sum of these distances is indeed 280 miles, confirming the result.

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The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).

It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.

In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.

Let the capacity of the mug be x.

Given,

Mug is 5/8 full and contains 3/4 of water

So, 5/8 of the mug is filled with water

Therefore,

5/8 of x = 3/4

(5/8 )x = (3/4)

x = (3/4) × (8/5)

x = (24/20)

x = 1.2

Therefore, the capacity of the mug is 1.2.

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The measure of the length EF of the triangle is; 21

We are given the the triangle BCD and we are told that;

E is the midpoint of BD.

F is the midpoint of CD

Now, since we have those midpoints, it means that by the concept of similar triangles, that;

DF/DC = EF/BC

Since F is the midpoint of DC, then it means that;

2DF = DC

We are given;

EF = 43 - 4x, and BC = 32 - 2x

Thus, we now have;

DF/(2DF) = (43 - 4x)/(32 - 2x)

1/2 = (43 - 4x)/(32 - 2x)

Cross multiply to get;

32 - 2x = 43 - 4x

4x - 2x = 43 - 32

2x = 11

x = 11/2

x = 5.5

Thus;

EF = 43 - 4(5.5)

EF = 43 - 22

EF = 21

Thus, we conclude that the side length EF is 21.

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Answer:

The formula that is used to calculate the surface area of a triangular prism is, Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh; where 'b' is the bottom edge of the base triangle, 'h' is the height of the base triangle, L is the length of the prism and S1, S2 and S3 ...

We see that in both options the expression we are analyzing is

and we see that the procedure they are trying to apply is to write an equivalent expression that has positive exponents. To do that, we will use the property of exponentiation. Given a non zero number a and any number b, then we have that

So, applying this property to our expression, we have that

Checking our options, we see that the incorrect one is option A. It is wrong because the only expression that should be changed is the one related to the negative exponent

Answer:

4,330

Step-by-step explanation:

Multiply 21.35 times 200 and you get 4,270, then multiply 200 times 43 and you will get 8,600. then subtract and you will get 4,330

The answers are :

a) The total purchase price for the 200 shares was $4270.

b) The total selling price for the 200 shares was $8600.

c) The capital gain for the 200 shares was $4330.

What is the unitary method ?

The unitary method is a method in which you find the value of one unit and then the value of a required no. of units.

It is given that 20 years ago Zach bought 200 shares.

Price of 1 share = $21.35

a)

The total purchase price for the 200 shares was :

= 200 × $21.35

= $4270

b)

It is given that Zach sold 200 shares today.

Price of 1 share = $43

The total selling price for the 200 shares was :

= 200 × $43

= $8600

c)

The capital gain for the 200 shares was :

= $8600 - $4270

= $4330

Therefore , the answers are :

a) The total purchase price for the 200 shares was $4270.

b) The total selling price for the 200 shares was $8600.

c) The capital gain for the 200 shares was $4330.

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The correct responses found using trigonometric ratios are as follows;

1. The depth of the water = 15 × tan(4°) = 1.049 m

The height of Brooke's boot = 1 m

Therefore;

2. The angle of elevation of the plan = arccos(99/100) ≈ 8.110°

Given that the angle of elevation the plan, 8.110°, is more than 8° limit, we find;

3. Height reached by the plane = 9 × tan(21°) = 3.455

Therefore;

4. Height of the chimney at the factory = 50 × tan(51°) = 61.745

The minimum chimney height = 65 m.

Therefore;

6. Length of the bridge = 72 × tan(55°) ≈ 102.83

Therefore;

7. Height reached by the ladder = 26 × sin(43°) ≈ 17.7

Therefore;

8. Height reached by the ski lift = 1000 × sin(29°) ≈ 484.8

Therefore;

9. Height reached by plane = 26 × tan(9°) ≈ 4.12

The plane flies under the cloud therefore;

10. Length required for the metal brace = 21/(cos(73°)) ≈ 71.83

Therefore;

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Given data:

The given expression y=50+20x.

Here, x is the number of weeks.

Substitute 3 for x in the above expression.

y=50+20(3)

=50+60

=110

Thus, the coordinate pair is (3,110).

Answer:  \(\$162\)

Step-by-step explanation:

Given

There are 210 units of hotel

Each room charge $90 when fully occupied

occupied room charges is $24 per day

Suppose x rooms are vacant, so, there 210-x occupied

Daily expense on maintenance\(=(210-x)\times 24\)

Earning from 210-x rooms\(=(210-x)(90+x)\)

Profit(P)=Earning - Expense

\(\Rightarrow P=(210-x)(90+x)-(210-x)24\\\Rightarrow P=21,600+210x-90x-x^2-5040+24x\\\Rightarrow P=-x^2+144x+16,560\\\)

To get the maximum profit, determine the derivative of P w.r.t. x and equate it to zero

\(\Rightarrow \dfrac{dP}{dx}=-2x+144\\\\\Rightarrow -2x+144=0\\\\\Rightarrow x=72\)

Charges for maximum profit is \(90+72=\$162\)

Number of occupied rooms are \(210-72=138\)

The hotel charge per day will be $162  in order to maximize daily profit.

Given that,  Hotel has 210 units

Let us consider that x rooms are vacant.

Total occupied rooms = \((210-x)\)

Since, Each occupied room costs $24 per day to service and maintain

So, Total expense = \(24*(210-x)=5040-24x\)

Since, For  all rooms are occupied when the hotel charges $90 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant.

So, Total earing = \((210-x)*(90+x)=-x^{2} +120x+21600\)

Profit = Total earning - Total expense

\(P=-x^{2} +120x+21600-5040+24x\\\\P=-x^{2} +144x+16560\)

In order to maximize profit, Differentiate profit expression with respect to x.

    \(\frac{dP}{dx}=\frac{d}{dx}(-x^{2} +144x+16560) \\\\\frac{dP}{dx}=-2x+144=0\\\\\\x=\frac{144}{2}=72\)

Thus, Hotel charges per day for maximum profit = \(90+x=90+72=162\)

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Answer:

5

Step-by-step explanation:

Because when you walk in there is now 35 people 35 - 30 = 5

There are 34 people in the garden.

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Complete Question

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is 1.25? The standard deviation in a pre-selected sample is  7.5

Answer:

The minimum sample size is  \(n =97\)

Step-by-step explanation:

From the question  we are told that

 The margin of error is  \(E = 1.25\)

   The  standard deviation is  \(s = 7.5\)

Given that the confidence level is  90% then the level of significance is mathematically represented as

             \(\alpha = 100 - 90\)  

             \(\alpha =10\%\)  

             \(\alpha =0.10\)

Next we obtain the critical value of \(\frac{\alpha }{2}\) from the normal distribution table  

    The value is  \(Z_{\frac{ \alpha }{2} } = 1.645\)

   The  minimum sample size is mathematically evaluated as

         \(n = \frac{Z_{\frac{\alpha }{2} * s^2 }}{E^2 }\)

=>        \(n = \frac{1.645^2 * 7.5^2 }{1.25^2 }\)

=>        \(n =97\)

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Answer:

5/3

Step-by-step explanation:

use the rise/run tactic

It will take Adrian 16 full months to save enough money for the electric keyboard.

- Price of the keyboard (with tax) at Macelli's: $2,400
- Adrian's monthly savings: $150
We need to find how long it will take Adrian to save for the keyboard. To do this, we'll divide the total cost of the keyboard by his monthly savings and round up to the nearest full month.
Step 1: Divide the total cost by monthly savings.
Time (in months) = (Total Cost) / (Monthly Savings) = ($2,400) / ($150)
Step 2: Calculate the result.
Time (in months) = 16
So, it will take Adrian 16 full months to save enough money for the electric keyboard.

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Answer:

Option D,four is correct

Step-by-step explanation:

The tax withholding from the gross income of $951 is the gross income itself minus the income after tax withholding i.e $189  ($951-$762)

The percentage of the withholding =189/951=20% approximately

Going by the multiple  choices provided,option with 4,189 dollars seems to the correct option as that is the exact of the tax withholding on Robert's gross income and his earnings fall in between $950 and $960

The number of allowances that Robert has claimed is four. Option d is correct.

A withholding tax is a tax that an employer deducts from an employee's paycheck and delivers it straight to the government (federal income tax).

From the given information:

The tax allowance = Gross income - savings amount

The tax allowance = $951 - $762

The tax allowance = $189

From the weekly income between 950 and 960 data, we can see that the number of allowances claimed related to the withholding allowances are:

0  → $259

1   →  $242

2   → $224

3   → $207

4  → $189

5   → $173

6  →  $162

7   → $151

8  →  $140

Therefore, we can conclude that the number of allowances that Robert has claimed is four.

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

tulog na po 2:23 na po bye good night

Answer:

D

Step-by-step explanation:

From the given information:

At the confidence interval of 0.98 for the slope of the regression; the expectancy of life for men and women appears to be positive. This clearly implies that there are sufficient evidence and information that the two variables is positively correlated. As a result, if the expectancy of life for men increases, the same will also increase for women.

The values of interval are positive thus it can be said that there is an increase on average life expectancy. Thus the option D is correct.

The life expectancy is the statically measure of the average organism expected to live. The life expectancy is based on the birth rate.

As the C.I is of 0.98 the slope of the regression that is expectancy of the life for the men and the women appears positive.

Thus its clearly that the two variables is positively correlated. Hence, the expectancy for for men increases the same will be for women.

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Answer

Explanation

The amount of water in each container shall be calculated using

the volume of a cylinder formula

Note The volume of a cylinder is given by the formula

where r = radius of the cylinder and h = height of the cylinder

For the first cylinder,

diameter d =6 feet,this implies that

radius r = 6/2 = 3 feet

h = 6 feet.

Therefore the volume of the Container A is calculated as thus

And the volume of the container B as thus

r =4/2 = 2 feet, h = 10 feet

After the pumping is complete, the volume of the empty space inside

Container A will be

Answer:

yes

to determine if she would have enough space, divide 20.4 by 3.4. this gives 6

Katrin has 6 letters

so it would be enough

Step-by-step explanation:

Number of spaces created = length of the line / distance between each space

20.4 / 3.4 = 6

Katrina is made up of 6 letters.

the space would fit

The requried, there are 240 possible ways the race can finish with a mouse placing first, second, and third.

To find the number of ways the race can finish with a mouse placing first, second, and third, we can use the concept of permutations.

Since the mouse is guaranteed to finish first, there are 5 mice to choose from for the first position.

Once the first place is determined, there are 4 mice left for the second position.

After the first two positions are filled, there are 3 mice left for the third position.

Now, we need to determine the order of the cats. There are 4 cats to choose from for the fourth position.

The total number of ways the race can finish with a mouse placing first, second, and third is given by the product of these choices:

Number of ways = 5 (for first place) * 4 (for second place) * 3 (for third place) * 4 (for fourth place)

Number of ways = 5 * 4 * 3 * 4

Number of ways = 240

There are 240 possible ways the race can finish with a mouse placing first, second, and third.

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Answer:

Step-by-step explanation:

Given function:

This is a quadratic function with positive leading coefficient, therefore it is an increasing function with its minimum at vertex. It has no maximum value.

The vertex is at x = -b/2a:

The minimum value is:

The range of the function is:

f(x)=x^2+8x+8

\(\\ \sf\longmapsto \dfrac{-b}{2a}\)

\(\\ \sf\longmapsto \dfrac{-8}{2(1)}\)

\(\\ \sf\longmapsto \dfrac{-8}{2}\)

\(\\ \sf\longmapsto -4\)

\(\\ \sf\longmapsto f(-4)\)

\(\\ \sf\longmapsto (-4)^2+8(-4)+8\)

\(\\ \sf\longmapsto 16-32+8\)

\(\\ \sf\longmapsto -16+8\)

\(\\ \sf\longmapsto -8\)

The range is

\(\\ \sf\longmapsto (8,\infty)\)