Vera is an ecologist who studies the change in the bear population of Siberia over time. The relationship between the elapsed time, t, in years, since Vera began studying the population, and the total number of bears, N(t), is modeled by the function:

Answer:

3

Step-by-step explanation:

YS = DI = 6

A = YS * AI = 24

height = A/b = 24 / 8 = 3

Answer: a

first you solve the top one find it for x

solve the bottom one  combine the numbers

Answer:

4 as a trapezoid, a rectangle, and two squares

Step-by-step explanation:

The diagram below is a composite figure .To determine it area the composite figure can be decomposed into various shapes.

The shapes it can be decomposed are a trapezoid , a rectangle and 2 squares.

The top side of the composite figure forms a trapezoid . A trapezoid is a quadrilateral with one pair of parallel sides. It is also known as trapezium.

The shape below the trapezoid can be cut into a rectangle .A rectangle is a quadrilateral with opposite sides equal in length and are also parallel.

The two shapes formed below the rectangle are squares. Squares are quadrilaterals with all sides equal in length and opposite sides are parallel.  

Answer:

D

Step-by-step explanation:

Answer:

The volume of a cone that fits perfectly inside the soda can is 7.

Volume of a can:

21 = r² π h

21 = 3² π h

21 = 9 π h

h = 21/ 9π = 7/ 3π 

Volume of a cone that fits perfectly inside a can:

V = 1/3 r² π h = 1/3 · 9 π · 7 / 3π = 7

Or you can use: V cone = 1/3 V cylinder ( with the same basis )

V cone = 1/3 * 21 = 7

Step-by-step explanation:

Since we have given that

Volume of soda can = 21

Diameter of can = 6

As we know the formula for "Volume of cylinder:"

Now, we have to find the volume of a cone that fits perfectly inside the soda can.

so, its radius will be 3 cm and height will be

As we know the formula for "Volume of cone":

Hence, the volume of a cone that fits perfectly inside the soda can is 7.

Answer:

6x+12

Step-by-step explanation:

Answer:

2 gallons of orange juice

Step-by-step explanation:

Final answer:

The Nelson family drank a total of 11/12 of a gallon of orange juice.

Explanation:

To find the total amount of orange juice the Nelson family drank, we need to add the amount they drank on Saturday morning and Sunday morning. They drank 1/4 of a gallon on Saturday and 2/3 of a gallon on Sunday. To add these fractions, we need to find a common denominator. The least common denominator (LCD) for 4 and 3 is 12.

Converting 1/4 to twelfth, we get 3/12. Converting 2/3 to twelfths, we get 8/12. Now we can add 3/12 + 8/12 to get a total of 11/12. Therefore, the Nelson family drank 11/12 of a gallon in total.

The y values are y₁ = 0.04, y₂ = 0.2, y₃ = 1, y₄ = 5

A graphing calculator is an electronic device capable of performing various mathematical calculations and plotting graphs of various functions. It is commonly used in education and engineering for tasks such as solving equations, graphing functions, and statistical analysis. Graphing calculators typically have a screen for displaying graphs, a keypad for entering equations and commands, and various built-in functions and tools.

Desmos is a free online graphing calculator that allows users to plot graphs, create animations, and perform various mathematical calculations. It has an easy-to-use interface and supports a wide range of mathematical functions and operations.

Given y = 0.2 ([tex]5^{x}[/tex]) and [tex]x_{1}[/tex] = -1, x₂ = 0, x₃ = 1, x₄ = 2

Putting x values x₁, x₂, x₃, x₄ in the equation of y we get y₁ = 0.04, y₂ = 0.2, y₃ = 1, y₄ = 5 are the corresponding y values

Hence the y values are y₁ = 0.04, y₂ = 0.2, y₃ = 1, y₄ = 5

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Answer:

The equation of the line is y = 3 x - 5.

Step-by-step explanation:

The slope intercept form of the equation of a straight line is:

[tex]y=mx + b[/tex]

Here,

m = slope

b = intercept.

The two points are:

A = (2, 1)

B = (3, 4)

Use two-point form method to determine the equation of straight line.

[tex](y-y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\ (x-x_{1})[/tex]

 [tex](y-1)=\frac{4-1}{3-2}\ (x-2)[/tex]

    [tex]y-1=3(x-2)\\y-1=3x-6[/tex]

          [tex]y=3x-5[/tex]

Thus, the equation of the line is y = 3 x - 5.

The equation of the line in slope-intercept form is y = 3x - 5.

To find the equation of the line containing the points (2, 1) and (3, 4) in slope-intercept form (y = mx + b), you first need to determine the slope (m) and then use one of the points to solve for the y-intercept (b).

The slope (m) can be found using the formula:

m = (y2 - y1) / (x2 - x1)

Let's plug in the coordinates of the two points:

Point 1: (x1, y1) = (2, 1)

Point 2: (x2, y2) = (3, 4)

Now, calculate the slope (m):

m = (4 - 1) / (3 - 2)

m = 3 / 1

m = 3

Now that you have the slope (m), you can use one of the points, for example, (2, 1), and the slope to find the y-intercept (b). You can use the point-slope form of the equation:

y - y1 = m(x - x1)

Using the point (2, 1):

y - 1 = 3(x - 2)

Now, distribute the 3 on the right side:

y - 1 = 3x - 6

Next, add 1 to both sides to isolate y:

y = 3x - 6 + 1

Simplify:

y = 3x - 5

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Answer:

20% or 1/5

Step-by-step explanation:

20% is equal to 1/5. That means that out of 5 marbles, there is only 1 red one.

Answer:$253

Step-by-step explanation: A=220(1+(0.05*3))=253

Answer: You are not comparing two things, and you're asking a question that can only be answered one way.

Step-by-step explanation: Statistical questions are comparing two things, or one alone. Therefore, Asking someone what grade are they in is not statistical  because of how it is one student being compared, not anyone else.

Answer:

1/3

Step-by-step explanation:

Answer:

you would multiple length base and height together and since they're all 6 centimeters you would multiply 6 by 6 by 6 and you get216 cubic centimeters

Hope this helps!

Step-by-step explanation:

The volume of a cube with a side length of 6 cm is 216 cm³. Since we know that volume of a cube is obtained by multiplying its side length three times.

The volume of  a cube is given as:

Volume = [tex]s^3[/tex]

Where 's' is the length of its side

Since all the side lengths of a cube are the same, the volume of a cube can be found by multiplying the edge length three times.

Given that the length of the side of a cube is s=6 cm

Then, the volume of the cube is:

Volume = s³

             = 6³

             = 6 × 6 × 6

             = 216 cm³

Therefore, the volume of the cube is 216 cubic centimeters.

So, option D is correct.

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In order to solve using substitution, we'll need to first isolate one variable in one equation. I will be using 7x - 2y = 3 and solving for y to begin.

7x - 2y = 3

-2y = -7x + 3

2y = 7x - 3

y = 3.5x - 1.5

Next, we'll plug in our value of y (found above) into the equation 3x + 4y = 11 and solve for x.

3x + 4(3.5x - 1.5) = 11

3x + 14x - 6 = 11

17x = 17

x = 1

Finally, we'll plug our value of x in to the first equation (7x - 2y = 3) and solve for y.

7(1) - 2y = 3

7 - 2y = 3

-2y = -4

y = 2

The solution to these equations is (1, 2).

Hope this helps! :)

Answer:

A

Step-by-step explanation:

Those two lines are the same. If you divide the second equation by 2, you will end up with the first equation. A system of linear equations cannot have two of the same line.

Answer:

D

Step-by-step explanation:

You have to find a slope but when you apply the slope to the intercept the intercept can not be equal to the neaver mind i suck at explaining.

There are 45 oranges and 90 apples in the beginning.

Step-by-step explanation:

Let the no. of orange be 'b'

Let the no. of apples be 'a'

Given that,

2b = a

3(b-15) = a

3b - 45 = a

3b - 45 = 2b

3b - 2b = 45

b = 45

2b = a

2(45) = a

a = 90

There are 45 oranges and 90 apples in the beginning.

Answer:

Number of hits of Paulo favorite baseball player is 26.

Step-by-step explanation:

Given:

Average of favorite baseball player = 0.47272727

Number of bats = 55

We need to find the number of hits.

Solution:

Let the number of hits be 'x'.

Now we know that.

Batting average can be calculated by dividing Number of hits from number of bats.

framing in equation form we get;

[tex]\frac{x}{55}=0.47272727[/tex]

Multiplying both side by 55 we get;

[tex]\frac{x}{55}\times 55=0.47272727\times 55\\\\x=26[/tex]

Hence Number of hits of Paulo favorite baseball player is 26.

Using the formula Number of hits = Batting average * Number of bats, Paul's favorite baseball player had approximately 26 hits from 55 bats, given a batting average of 0.4727272.

To calculate the number of hits of the baseball player, if we know their batting average, we can use the formula:

Number of hits = Batting average * Number of bats

In this case, the batting average is 0.4727272. The number of bats is 55. By substituting these values into the formula, we get:

Number of hits = 0.4727272 * 55 = 26

So, the baseball player had 26 hits. Please note that in practical situation, number of hits should be a whole number, so we might round the result to the closest whole number.

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Final answer:

The experimental probability that the next student will be a boy with brown eyes cannot be determined without specific observational data. You would need the number of boys with brown eyes and the total number of students Theo observed to calculate it.

Explanation:

To find the experimental probability that the next student Theo sees will be a boy with brown eyes based on his observations, we need to count the number of boys with brown eyes that were observed and then divide by the total number of students observed. However, the data provided does not include specific information on the number of boys with brown eyes seen by Theo. To calculate the experimental probability, you would need that information, as it is defined by the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.

For example, if Theo observed 10 boys and 4 of them had brown eyes, and the total number of students observed was 30, then the experimental probability of the next student being a boy with brown eyes would be 4 out of 30, or 4/30. To express this as a percentage, divide 4 by 30 and then multiply by 100 to get 13.33%.

Answer: the first number is 11 38/41

The second number is 10 4/41

Step-by-step explanation:

Let x represent the first number.

Let y represent the second number.

4 times one number plus 3 times the other is 78. It means that

4x + 3y = 78- - - - - - - - - -1

3 times the first number minus 8 times the other is -45. It means that

3x - 8y = - 45- - - - - - - - - 2

We would eliminate x by multiplying equation 1 by 3 and equation 2 by 4. It becomes

12x + 9y = 234

12x - 32y = - 180

Subtracting, it becomes

41y = 414

y = 414/41

y = 10 4/41

Substituting y = 414/41 into equation 1, it becomes

4x + 3 × 414/41 = 78

4x + 1242/41 = 78

4x = 78 - 1242/41

4x = 1956/41

x = 1956/41 × 1/4

x = 1956/164

x = 11 38/41

Answer:

7x7x7x7x7

    7x7

Step-by-step explanation:

7 to the fifth power is equal to 7x7x7x7x7

7 to the second power is equal to 7x7

Answer:

D, (7 x 7 x 7 x 7 x 7) / (7 x 7)

Step-by-step explanation:

Look at the numerator of the fraction. You will see 7^5, or 7 to the 5th power. This means you must multiply 7 by itself 4 times, to get yourself the numerator of 7 x 7 x 7 x 7 x 7. This means your choices are B (or the second option from the top) or D (or the last option from the top).

However, take note that your original equation is a fraction, meaning you would divide, and not multiply. This means B, or the second option, is incorrect, because they are multiplying in that expression, when a fraction means to divide.

Your only other option is D, where they have portrayed both 7 to the fifth correctly in the numerator, and then 7 squared in the denominator.

Answer:

B) 65°

Step-by-step explanation:

The formula for this would be x = 1/2 (a -b)

X being the angle you're trying to find

a being the larger arc and b being the smaller arc

Since a circle has 360°, and 245 is the larger arc, the smaller arc would be 115°

Now, just plug that into the equation; x = 1/2 (245-115)

This gives you x = 1/2 (130)

x = 65°

Answer:

x = 3- 3y/2

Step-by-step explanation:

Answer:

x= 3/2 (3 over 2)

Step-by-step explanation:

2x + 3y= 6

(2x + 3) + (- 3) = 6+ (- 3)

2x + 3 - 3 + 6 - 3

2x = 3

2x/2 = 3/2

x = 3/2

Answer:

T is 13.9 years to the nearest 10th of a year

Step-by-step explanation:

In this question, we are to calculate the number of years at which someone who invests a particular amount will have a particular amount based on compound interest.

To calculate the number of years, what we do is to use the compound interest formula.

Mathematically,

A = P(1+ r/n) ^nt

Where A is the final amount after compounding all interests which is $19,200 according to the question

P is the initial amount invested which is $10,000 according to the question

r is the rate which is 4.75% according to the question = 4.75/100 = 0.0475

n is the number of times per year in which interest is compounded. This is 2 as interest is compounded semi-annually

t= ?

we plug these values;

19200 = 10,000(1+0.0475/2)^2t

divide through by 10,000

1.92 = (1+0.02375)^2t

1.92 = (1.02375)^2t

We find the log of both sides

log 1.92 = log [(1.02375)^2t)

log 1.92 = 2tlog 1.02375

2t = log 1.92/log 1.02375

2t = 27.79

t = 27.79/2

t = 13.89 years

The question asks to give answer to the nearest tenth of a year and thus t = 13.9 years

Answer:

Large - 24

Small - 15

Step-by-step explanation:

The graph clearly shows that the ball has a height of 35 feet at t = 0.947 s and 2.178 s.

A rugby player kicks a rugby ball 2 feet above the ground at a 50-foot-per-second starting vertical velocity. After t seconds, the height h of the rugby ball is given by:

h = -16t² + 50t +2 ......(1)

Here,

h is the height in feet, and t is the time in seconds

We must determine the time when the ball's height reaches 35 feet. (1) will be transformed into

h = -16t² + 50t +2 - 35

h = -16t² + 50t - 33.

Using the Desmos calculator, we can plot the graph of the preceding equation. The linked graph depicts the period when the rugby ball's height is 35 feet.

The graph clearly shows that the ball has a height of 35 feet at t = 0.947 s and 2.178 s.

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Answer:

154 millimeters

Step-by-step explanation:

Answer:

154

Step-by-step explanation:

Plato test said i was right

The expected value of Eva flipping a coin is $0.5. If she flips a fair coin, she can expect to gain half a dollar on average with each flip over a long period of time.

The question asks to find the expected value of a coin flip for Eva's case. The expected value is a statistical concept used to predict the outcome of a random event, calculated by multiplying each possible outcome by their respective probability, and then adding these values together.

In Eva's case, a coin has 2 outcomes, heads or tails, and both have an equal chance of occurring i.e., 0.5 probability each in a fair coin flip. If Eva gets heads, she wins $4; if tails, she loses $3. So, we need to calculate the expected gain or loss for each flip.

Her expected value of a coin flip would be calculated as follows:

So, in the long term, Eva's expected value per flip of the coin is $0.5. This implies that on average, Eva can expect to gain $0.5 for each coin flip over the long haul.

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The student asked about the expected value in a coin flip game. Eva's expected value per coin flip is $0.50, calculated by multiplying the probability of each outcome by its respective win or loss and summing these products.

The student has asked about the expected value of a game involving a coin flip. Expected value is a concept from probability theory used to determine the average outcome of a random event over a long period of time. In the described scenario, to calculate the expected value, Eva must consider the amount she wins or loses on a head or tail and the probability of each event.

The formula for expected value (EV) is EV = (probability of heads × winnings on heads) + (probability of tails × loss on tails). Since a fair coin has an equal chance for heads and tails, the probability for each is 0.5. Thus, the expected value for Eva's game is calculated as follows:

EV = (0.5 × $4) + (0.5 × -$3) = ($2) + (-$1.5) = $0.5.

So the expected value for a single flip of the coin in Eva's game is $0.50. This means that on average, Eva will earn 50 cents per flip over a large number of flips.

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Answer:

[tex]=81[/tex]

Step-by-step explanation:

[tex]\left(-3\right)^4[/tex]

Use exponent rule [tex]\left(-a\right)^n=a^n[/tex]:

[tex]=3^4[/tex]

[tex]=81[/tex]

The complete question is:

Elizabeth has a lot of jewelry. She has four times as many earrings as watches but half the number of necklaces as earrings. Elizabeth has the same number of necklaces as bracelets. If Elizabeth has 117 pieces of jewelry, has many earrings does she have?

Answer:

Elizabeth has 52 pieces of earrings.

Step-by-step explanation:

- Let the number of Elizabeth's watches = p

- Earrings = 4p (Because she has 4 times as many earrings as watches)

- necklaces = (1/2)4p = 2p (half the number of necklaces as earrings)

=> necklaces = 2p

- bracelets = 2p (same number of necklaces as bracelets.)

Since the total number of pieces of jewelry = 117, the addition of all the jewelry will be 117

That is, watches + earrings + necklaces + bracelets = 117

p + 4p + 2p + 2p = 117

9p = 117

p = 117/9 = 13

Therefore,

p = 13 (watches)

4p = 4×13 = 52 (earrings)

2p = 2×13 = 26 (necklaces)

and 26 bracelets.

Elizabeth has 52 pieces of earrings.