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A scientist records the motion of a dolphin as it jumps from the water. The function`h\left(t\right)=-8t^{2}+32t` models the dolphin’s height in feet above the water after t seconds. Show all work and explain your answers clearly. Use complete sentences.


What is the dolphin's maximum height?

5 students took part in both individual and team events.

Data is information that has been translated into a form that is efficient for movement or processing. Relative to today's computers and transmission media, data is information converted into binary digital form. It is acceptable for data to be used as a singular subject or a plural subject.

Given:

Total students participated = 27

20 students participated in individual events

12 students took part in team events.

We have N(All students) = 27

N(individual) = 20

N(Team)= 12

So,

[tex]N_{\text{individual \; and \; team}} & = N_{\text{individual}} + N_{\text{team}} - N_{\text{All students}}[/tex]

=20+12-27

=32-27

=5

Hence, 5 students took part in both individual and team events.

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Using sampling concepts, one sample of 5 high schools in the city of Chicago is given by:

Englewood Stem, Hyde Park, Lake View, Marshall, Noble - UIC.

The problem is incomplete, but researching it on a search engine, it gives us a list of 15 high schools in Chicago, and asks us to take a sample of 5.

Hence, from the concepts of sample and populations, the sample of 5 means that we have to select 5 schools from the 15 listed, hence they are:

Englewood Stem, Hyde Park, Lake View, Marshall, Noble - UIC.

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Answer:

[tex] \sf \large \: - 10[/tex]

Step-by-step explanation:

−7+a

Evaluate for a=−3

−7+−3

=−10

Answer:

-10 given a = -3

Step-by-step explanation:

-7 + -3 = -10

Hope this helps! :)

Step-by-step explanation:

do 1.50 times 10 and the multiple by 30 to get the answer

The ratio of the lengths of the model to the actual distance is approximately 2 x 10⁻¹³.

To find the ratio of the lengths of the model to the actual distance, we need to compare the lengths in the same unit. Let's convert the actual distance between the Sun and Earth from meters to centimeters, so both values are in centimeters.

1 meter = 100 centimeters

Actual distance from the Sun to Earth = 1.50 x 10¹¹ meters

Actual distance from the Sun to Earth in centimeters = 1.50 x 10¹¹ meters * 100 centimeters/meter

Actual distance from the Sun to Earth in centimeters = 1.50 x 10¹¹ meters * 100 centimeters/meter = 1.50 x 10¹³ centimeters

Now, we can compare the lengths:

Length on the model = 30 centimeters

Actual distance from the Sun to Earth = 1.50 x 10¹³ centimeters

The ratio of the lengths of the model to the actual distance is:

Ratio = Length on the model / Actual distance from the Sun to Earth

Ratio = 30 centimeters / (1.50 x 10¹³ centimeters)

To simplify this ratio, let's express the actual distance in scientific notation:

1.50 x 10¹³ = 15 x 10¹² = 1.5 x 10¹³

Now, the ratio becomes:

Ratio = 30 centimeters / (1.5 x 10¹³ centimeters)

Now, notice that both values are in the same unit (centimeters). We can proceed with the division:

Ratio ≈ 0.0000000000002

Therefore, the ratio of the lengths of the model to the actual distance is approximately 2 x 10⁻¹³. This means that every 1 centimeter on the model represents approximately 2 x 10⁻¹³ centimeters in actual distance between the Sun and Earth.

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The tree was 210 cm tall.

Let 'h(t) ' models the height of the tree in centimeters and 't' denotes the number of years since Renata moved in.

Given, h(t) = 210 + 33t

This is a linear function in 't'.

This function says that in each year the tree grows 33 cm tall.

We need to find the height of the tree when Renata moved in.

When Renata moved in, the number of years, t = 0

Applying this into h(t) , we get,

h(t) = 210 + 33 x 0 = 210 cm

Therefore the tree was 210 cm tall when Renata moved in.

The question was incomplete. Find the complete question here:

Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window. h(t) models the height of the tree (in centimeters), t years since Renata moved in. h(t)=210+33t

How tall was the tree when Renata moved in?

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Answer:

little tricky question but i managed to do it..

Answer:

51

Step-by-step explanation:

Answer:

the answer is a because if you calculate it correctly that the answer I got

Answer:7lb

Step-by-step explanation:

7x180=1260lb

1260+235=1495lb

Answer:

3.35

Step-by-step explanation:

5,000,000*6.7 * 10^-7

= 5 * 10^6 * 6.7*10^-7

= 33.5 * 10^-1

= 3.35

The weight of 5 million grains of sand is 3.35 kg.

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Weight of each grain of sand = 6.7 x [tex]10^{-7}[/tex] kg

Weight of 5 million grains of sand.

= 5,000,000 x  6.7 x [tex]10^{-7}[/tex] kg

= 5 x [tex]10^6[/tex] x 6.7 x [tex]10^{-7}[/tex]

= 33.5 x [tex]10^{-1}[/tex] kg

= = 3.35 kg

Thus,

The weight of the total grain of sand is 3.35 kg.

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The LCM of the set of numbers are:

1. {12,15} = 60

2. {16,24} = 48

3. {18,27} = 54

4. {20,28} = 140

5. {36,54} = 108

6. {9,12,24} = 72

7. {15, 20, 45} = 180

8. {6,8,12} = 24

9. {4,6,9} = 36

10. {8,9,12} = 72

The least common multiple of two or more numbers is the least multiple that is common to two or more numbers. A multiple of a number is the product of an integer and that number. For example, the multiples of 6 are 12 and 18.

Prime factors of 12 = 2 x 2 x 3

Prime factors of 15 = 3 x 5

LCM = 2 x 2  x 3 x 5 = 60

Prime factors of 16 = 2 x 2 x 2 x 2

Prime factors of 24 = 2 x 2 x 2 x 3

LCM = 2 x 2 x 2 x 2 x 3 = 48

Prime factors of 18  = 2 x 3 x 3

Prime factors of  27  = 3 x 3 x 3

LCM = 2 x 3 x 3 x 3 = 54

Prime factors of 20  = 2 x 2 x 5

Prime factors of 28  = 2 x 2 x 7

LCM = 2 x 2 x 5 x 7 = 140

Prime factors of 36  =2 x  2 x 3 x 3

Prime factors of 54  = 2 x 3 x 3 x 3

LCM = 2 x 2 x3 x 3 x3 = 108

Prime factors of 9  = 3 x 3

Prime factors of 12 = 2 x 2 x 3

Prime factors of 24 = 2 x 2 x 2 x 3

LCM = 2 x 2 x 2 x 3 x 3 = 72

Prime factors of 15 = 3 x 5

Prime factors of 20 = 2 x 2 x 5

Prime factors of  45 = 3 x 3 x 5

LCM = 2 x 2 x 3 x 3 x 5 = 180

Prime factors of 6  = 2 x 3

Prime factors of 8= 2 x 2 x 2

Prime factors of  12= 2 x 2 x 3

LCM = 2 x 2 x 2 x 3 = 24

Prime factors of 4  = 2 x 2

Prime factors of 6= 2 x 3

Prime factors of  9= 3 x 3

LCM = 2 x 2 x 3 x 3 = 36

Prime factors of 8 = 2 x 2 x 2

Prime factors of 9= 3 x 3

Prime factors of 12 = 2 x 2 x 3

LCM = 2 x 2 x 2 x 3 x 3 = 72

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Answer:

Step-by-step explanation:

x=2

Hence , the price of the system $295 .

Let the price of the system be "x" .

It is given that in the first week her savings were $8 less than 2/5 the price of the system which can be represented by equation

First week savings =  (2/5)x -8

It is also given that in the second week, she saved 50 cents more than 1/2 the price of the system which can be represented by equation

Second week savings = (1/2)x +0.5

savings + short = price of system

(2/5)x -8 + (1/2)x +0.5 + 37 = x

 (2/5)x +  (1/2)x + 29.5 = x

   4x + 5x/ 10 + 29.5 = x

     9x/10+ 29.5 = x

       0.9x + 29.5 = x

          29.5 = x - 0.9x

           29.5 = 0.1x

           $ 295 = x

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Answer:

b. No

Step-by-step explanation:

7/6 can be changed to an equivalent ratio(fraction) by multiplying by the same number on top and on the bottom.

example:

7/6 = 7×3 / 6×3

= 21/18

21/18 is equivalent to 7/6.

7 doesn't even go into 52 for one thing. But 6×8 is 48 so try 8.

7/6 = 7×8 / 6×8

= 56/48

56/48 is equivalent to 7/6, not 52/48

The number of visits that Alang makes to earn a free movie ticket will be 8.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Alang has a rewards card at a cinema.

The mere act of joining up earns him 55 reward points.

Every time he enters a movie theater, he receives 3.5 points.

To receive a free movie ticket, he needs 83 points.

Let x be the number of visits. Then the equation is given as,

3.5x + 55 = 83

Simplify the equation, then the value of x will be

3.5x = 83 - 55

3.5x = 28

x = 28 / 3.5

x = 8

The number of visits that Alang makes to earn a free movie ticket will be 8.

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Answer:

Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.

Step-by-step explanation:

"Shawn stated that 5x+2 is equal 7x" its is an incorrect statement, because we can only add like terms.

Given,

The statement

5x+2 is equal to 7x

Here 5x and 2 are not like terms. So we can't add them together.

So the given statement is incorrect

5x+2 is not equal to 7x

Hence, "Shawn stated that 5x+2 is equal 7x" it is an incorrect statement, because we can only add like terms.

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The volleyball team ended up practicing for 1.2 hours on Friday.

The total number of hours the volleyball team practiced on Monday, Tuesday, Wednesday, and Thursday can be determined by adding the values given in the statement.

Therefore,

the total number of hours the team practiced on Monday, Tuesday, Wednesday, and Thursday=0.5 hours+1.3hours+2.2hours+0.8hours= 4.8 hours

Total number of hours the team practiced last week = 6 hours

The number of hours they practiced on Friday can be calculated by subtraction of the total number of hours of the week from the total number of hours on Monday, Tuesday, Wednesday, and Thursday.

Hence, the number of hours the team practiced on Friday = 6 - 4.8= 1.2 hours.

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Seeing that substituting the value x ≤ -2, did not yield a result that is correct with the equation x5 +7 > x3 we can say that Sam's conjecture is incorrect

Given data

x ≤ -2

x5 +7 > x3

Sam's conjecture is tested by substituting the value x ≤ -2 into the equation x5 +7 > x3.  If the result is in accordance with the equation then Sam's conjecture is correct, however if the result is not in accordance with the equation the Sam's conjecture is incorrect.

The substitution will give

( -2 )^5 + 7 > ( -2 )^3

-32 + 7 > -8

-25 > -8  (since -25 is less than -8, Sam's conjecture is incorrect )

Seeing that substituting the value x ≤ -2, did not yield a result that is correct we can say that Sam's conjecture is incorrect

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Answer:

Step-by-step explanation:

Write each statement as a conditional.

a. A triangle with all angles congruent is equilateral.

b. Alberto can go to the movies if he washes the car.

a. If all angles of a triangle are congruent then the triangle is an equilateral triangle

b. If Alberto washes the car he can go to the movies

The independent variable: lengths of the sides

The dependent variable: the perimeter of a square,

K(5) = 20.

The dependent variable of a function is the output of a function that changes as a result of any change in the independent variable, which is the input of the function.

The input (independent variable) determines the output (dependent variable) of a function.

Therefore, we can make the following deductions:

The independent variable, x, represents lengths of the sides, and the dependent variable is the perimeter of a square, because the perimeter of the square depends on the length of the side of the square.

The function that relates to the variables is: K(x) = 4x

So, K(5) = 4(5) = 20.

This means, if 5 is the length of one of the sides of the square, then 20 is the perimeter of the square.

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Answer:

20 %

Step-by-step explanation:

There was a change from 25 m to 30 m. When we find percentage change of something, we first calculate the difference of final and initial value. Then divide it by initial value × 100.

Change:

= 30 m - 25 m

= 5 m

% change:

= 5 m / 25 m × 100

= 100 / 5

= 20 % (ans)

2.3,3.3% and 2/3 in order of greatest to least is 3.3% > 2/3 > 2.3.

Arrangement in a series that begins with the greatest or largest and ends with the least or smallest.

Now the given numbers are,

2.3,3.3% and 2/3

Converting them into decimals we get,

2.3 = 2.300

3.3% = 0.033

2/3 = 0.667

Arranging them from greatest to least we obtain,

0.033  > 0.667 > 2.3

Thus, the given numbers from greatest to least are,

3.3% > 2/3 > 2.3

Hence, 2.3,3.3% and 2/3 in order of greatest to least is 3.3% > 2/3 > 2.3.

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The right answer is that there are four electrons.

The charge number of an atomic nucleus is the chemical element's atomic number, also known as the nuclear charge number.

For conventional nuclei, this is comparable to the proton number, or the number of protons found in the nucleus of each atom of that element.

Equal numbers of protons and electrons make up a neutral atom. This figure establishes the atom's atomic number.

The fourth element on the periodic table is beryllium.

Number of protons in Be-atom = 4

Number of electrons in Be-atom = 4

Therefore, it is true that there are four electrons.

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