The bears in Alaska are limited to a certain area to live due to the resources available for
food and shelter. After years, the number of bears living in the area is modeled by the function below. Using the function, find the number of bears after 17 years.

Answer: volume of box must be 90 \(cm^{3}\)

Step-by-step explanation:

Given that:

total no. of candies = 18

width of candy = 2cm

length of candy = 2cm

height of candy = 2cm

solution:

volume of a candy = l×b×h

                               = 2×2×1

                               = 5 \(cm^{3}\)

volume of box = total no. of candies × volume of a candy

                        = 18 × 5

                        = 90 \(cm^{3}\)

Answer:

N = 6

Step-by-step explanation:

7 + N = 13

subtract 7 from both sides

N = 6

hope this helps

Hi!

Your answer will be: N=6

Reason being: 7+6=13

Therefore, the answer is 6.

Hope this helps!

Let me know if you need anymore help, I'd be delighted to!

Yours truly,

The value of x is 11.

m∠ACD is 65 degrees and m∠BDC is 115 degrees.

To find the value of x, we need to establish a relationship between these two angles.

Given that m∠ACD = (7x - 12) and m∠BDC = (10x + 5), we can analyze the figure to determine how these angles are related. Since there is no additional information about the angles, let's assume that they are supplementary angles, meaning that their sum is equal to 180 degrees. This is a common situation when dealing with adjacent angles that form a straight line.

So, we can write an equation expressing that the sum of m∠ACD and m∠BDC equals 180°:

(7x - 12) + (10x + 5) = 180

Now, we'll solve this equation to find the value of x:

7x - 12 + 10x + 5 = 180
17x - 7 = 180

Next, isolate x by adding 7 to both sides of the equation:

17x = 187

Finally, divide by 17 to obtain the value of x:

x = 187 ÷ 17
x = 11

So, the value of x is 11. With this information, you can now find the measures of m∠ACD and m∠BDC by plugging the value of x back into their respective expressions:

m∠ACD = 7(11) - 12 = 77 - 12 = 65°
m∠BDC = 10(11) + 5 = 110 + 5 = 115°

Therefore, m∠ACD is 65 degrees and m∠BDC is 115 degrees.

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Answer:

f(x)=1.25x

Step-by-step explanation:

It goes up at a constant rate of 1.25, meaning it's a linear equation. The formula for a linear equation is:

f(x)=mx+b

M = The average rate of change

B = The initial value

And since the initial value of this data starts at 0 on the x intercept, if you subtract 1.25 from 1.25 you get 0. The average rate of change is 1.25 so you would format the equation as:

f(x)=1.25x

And there is no need to add +0, which means instead of the equation being f(x)=1.25x+0, it is much simpler as f(x)=1.25x.

I hope this was helpful!

The required function to model this data is,

f(x)=1.25x.

A mathematical expression, rule, or law that specifies the relation between an independent variable and a dependent variable (the dependent variable).

The property that every input is related to exactly one output defines a function as a relation between a set of inputs and a set of permissible outputs.

It goes up at a constant rate of 1.25, meaning it's a linear equation. A linear equation is written as:

f(x)=mx+b

M = The average rate of change

B = The initial value

And since the initial value of this data starts at 0 on the x intercept, if you subtract 1.25 from 1.25 you get 0. The average rate of change is 1.25 so you would format the equation as:

f(x)=1.25x

Additionally, there is no need to include 0,

which means instead of the equation being f(x)=1.25x+0,

it is much simpler as f(x)=1.25x.

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Answer:

2 g/cm3

Step-by-step explanation:

D=m/V

D=12g/6 cm3

D=2 g/cm3

Answer:

2g/cm3

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

1 hour = 60 minutes

1200 riders = 60 minutes: divide by sixty to set equal to 1

20 riders = 1 minute

Just divide 1,200 by 60 because there are 60 minutes in 1 hour.

Just think about it this way: If you eat 1 banana a minute, you eat 60 bananas an hour. The amusement park ride goes around once a minute. In one hour it goes around 60 times. Each time it carries the same amount of people.

1,200 divided by 60 is...

20!

The ride can carry 20 riders each ride, and each ride lasts a minute.

Answer:

y-intercept and slope

Step-by-step explanation:

When we graph a line using slope and y-intercept, the first point that you graph is  y-intercept.

What is Mathematical equation ?

By definition, an equation is a mathematical statement made up of two expressions linked by an equal sign. In other words the equation represents the graph between x and y that is for each value of x there exist one value of y.

So, When we graph a line using slope and y-intercept, the first point that you graph is  y-intercept.

Let, consider the equation of y = mx+c, where, m is the slope of line and c is the y - intercepts. So to draw the graph firstly we find the two points to connect the line in which first is y-intercepts by putting x=0 in the given equation.

Therefore, When we graph a line using slope and y-intercept, the first point that you graph is y-intercept.

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The linear regression to analyze is log(T) vs log(a) or, in other words, (D) log T vs log a. Linear regression is a statistical technique used to model the relationship between a dependent variable and one or more independent variables.

To determine the power-law relation between the semi-major axes (a) and orbital periods (T) of the solar planets, we need to analyze the linear regression between the logarithm of T and the logarithm of a. Therefore, the correct choice is (D) logT vs loga.

In the power-law relation, if we assume T = bxa^m, we can take the logarithm of both sides to linearize the equation:

log(T) = log(b) + m * log(a)

By doing this transformation, we obtain a linear equation of the form y = mx + h, where y represents log(T), x represents log(a), m represents the slope of the line (related to the exponent of a in the power-law relation), and h represents the y-intercept (related to the constant term in the power-law relation).

By performing linear regression on the logarithmic values of T and a, we can estimate the values of m and h, which will help us determine the power-law relation between T and a.

So, the linear regression to analyze is log(T) vs log(a) or, in other words, (D) logT vs loga.

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Step-by-step explanation:

Quadratic Zeros: One Only

Priya Ravindran

What are the zeros of f(x) = x² - 10x+25?

OA. x= -5 and x = 5

O B. x = 5 only

OC. x = -5 and x = 10

O D. x = -5 only

We can find the zeros of the quadratic function f(x) = x² - 10x + 25 by setting f(x) equal to zero and solving for x:

x² - 10x + 25 = 0

This quadratic equation can be factored as:

(x - 5)² = 0

Using the zero product property, we can see that this equation is true when:

x - 5 = 0

So the only zero of f(x) is x = 5.

Therefore, the correct answer is option B: x = 5 only.

Priya Ravindran

In a newspaper, it was reported that the number of yearly robberies in Springfield in 2013 was 100, and then went down by 11% in 2014. How many robberies were there in Springfield in 2014?

If there were 100 robberies in Springfield in 2013 and the number of robberies went down by 11% in 2014, we can calculate the number of robberies in 2014 as follows:

Number of robberies in 2014 = Number of robberies in 2013 - 11% of Number of robberies in 2013

Using this formula, we get:

Number of robberies in 2014 = 100 - 0.11(100)

Number of robberies in 2014 = 100 - 11

Number of robberies in 2014 = 89

Therefore, there were 89 robberies in Springfield in 2014.

Tim was initially given 81 carrots. He ate one-third of the carrots each day until he had only 8 carrots left.

Let's assume that Tim was given x carrots in the beginning. After eating one-third of the carrots, he has (2/3)x carrots remaining. The next day, he eats one-third of the remaining carrots, leaving him with (2/3)(2/3)x = (4/9)x carrots. On the following day, he eats one-third of the remaining carrots, leaving him with (2/3)(4/9)x = (8/27)x carrots.

According to the given information, Tim has 8 carrots left, which means (8/27)x = 8. Solving for x, we have x = 27.

Therefore, Tim was initially given 27 carrots.

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Answer:

g(- 4) = 12

Step-by-step explanation:

To evaluate g(- 4), substitute x = - 4 into g(x), that is

g(- 4) = (- 4)² - 4 = 16 - 4 = 12

By decomposing the figure into a rectangle and a triangle, we will see that the total area is 100 square units.

For a rectangle of width W and length L, the area is:

A = L*W

And for a triangle of base B and height H, the area is:

A = B*H/2

Here the composite figure can be decomposed into a triangle and a rectangle, such that the rectangle has:

L = 11

W =  7

Then the area is A = 7*11 = 77

And for the triangle (the base is the top side in this case):

B = 6

H = 11

A = 6*11/2 = 33

Then the total area of the figure is:

area = 77 + 33 = 100

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Answer:

7r + 2

Step-by-step explanation:

I hope this helps have a great day

To prove the identity sinh(2x) = 2 sinh(x) cosh(x), we can use the definitions of sinh(x) and cosh(x) and apply trigonometric identities for exponential functions.

We start with the left-hand side of the identity, sinh(2x). Using the definition of the hyperbolic sine function, sinh(x) = (e^x - e^(-x))/2, we can substitute 2x for x in this expression, giving us sinh(2x) = (e^(2x) - e^(-2x))/2.

Next, we focus on the right-hand side of the identity, 2 sinh(x) cosh(x). Again using the definitions of sinh(x) and cosh(x), we have 2 sinh(x) cosh(x) = 2((e^x - e^(-x))/2)((e^x + e^(-x))/2).

Expanding this expression, we get 2 sinh(x) cosh(x) = (e^x - e^(-x))(e^x + e^(-x))/2.

By simplifying the right-hand side, we have (e^x * e^x - e^x * e^(-x) - e^(-x) * e^x + e^(-x) * e^(-x))/2.

This simplifies further to (e^(2x) - 1 + e^(-2x))/2, which is equal to the expression we derived for the left-hand side.

Hence, we have proved the identity sinh(2x) = 2 sinh(x) cosh(x) by showing that the left-hand side is equal to the right-hand side through the manipulation of the exponential functions.

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The lower and upper values of the confidence interval of the population mean for the minutes spent getting to work is (31.74,38.4)

What is Standard Deviation?

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance. The bigger the deviation within the data collection, the more the data points deviate from the mean; Hence, the higher the standard deviation, the more dispersed the data.

We know that:

\(\text { Standard Deviation }=\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n-1}}\)

where \(x_{i}\)  is the mean and n is the number of observations.

\(\text { Standard Deviation }=\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n-1}}\)

98% Confidence interval:  

\(\bar{x} \pm t_{\text {critical }} \frac{s}{\sqrt{n}}\)

Putting the values, we get,  

\(t_{\text {critical }} \alpha_{0.02}\\=\pm 2.14535.07 \pm 2.145\left(\frac{6.02}{\sqrt{15}}\right)\\=35.07 \pm 3.33\\=(31.74,38.4)\)

Hence, The lower and upper values of the confidence interval of the population mean for the minutes spent getting to work is (31.74,38.4)

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The point (-1, 1, 1) in rectangular coordinates can be expressed in cylindrical coordinates as (r, θ, z) = (√2, 3π/4, 1).

To convert a point from rectangular coordinates (x, y, z) to cylindrical coordinates (r, θ, z), we can use the following relationships:

r = √(x² + y²)

θ = atan2(y, x)

z = z

In this case, we have the point (-1, 1, 1) in rectangular coordinates.

First, we calculate r:

r = √((-1)² + 1²) = √2

Next, we determine θ:

θ = atan2(1, -1) = 3π/4

Finally, we have z as it is already given as 1.

Therefore, the point (-1, 1, 1) in rectangular coordinates can be expressed in cylindrical coordinates as (r, θ, z) = (√2, 3π/4, 1).

In cylindrical coordinates, r represents the distance from the origin to the point projected onto the xy-plane, θ is the angle in the xy-plane measured counterclockwise from the positive x-axis, and z is the same as the z-coordinate in rectangular coordinates.

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Answer:

the quotient of 4 and n

Step-by-step explanation:

or 4 divided by n

Answer:

square root 162

Step-by-step explanation:

Answer:

\(9 \sqrt{2 } \)

The solution of the quadratic equation is x = 2. Therefore, \(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)  or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

The quadratic formula can be use to solve the quadratic equation as follows:

x² - 4x + 4 = 0

Modelling it to quadratic equation, ax² + bx + c

Hence,

using quadratic formula,

\(\frac{-b+\sqrt{b^{2}-4ac } }{2a}\) or \(\frac{-b-\sqrt{b^{2}-4ac } }{2a}\)

where

Hence,

a = 1

b = -4

c = 4

Therefore,

\(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\) or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

Finally

x = 2

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Answer:

36

Step-by-step explanation:

There are several ways to find area of triangle from vertex coordinates, the easiest is: (x₁*(y₂-y₃) + x₂*(y₃-y₁) + x₃*(y₁-y₂)) / 2

Area = ((-1)*(-6 - -6) + (-6)*(-6 - 2) + (3)*(2 - -6)) / 2

        = (0 + 48 + 24) / 2

        = 72/2

        = 36

The blue team at Will's job made a collective decision to vote on whether to contribute money to buy their boss a gift for Boss' Day.

In other words, the team made a democratic choice or a democratic decision. They likely took a vote, where each team member had the opportunity to express their opinion and cast their vote.

By voting, the team members had a chance to voice their thoughts and preferences, and ultimately come to a consensus on whether to contribute towards buying the boss a gift. This process allowed for fairness and inclusion, ensuring that everyone's opinion was taken into consideration before making the final decision.

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The blue team at Will's job took a vote to decide whether to pitch in to buy the boss a gift for Boss' Day. In other words, the team made a(n) decision.

When a group of people gathers together to make a choice or come to an agreement, they are making a decision. In this case, the blue team at Will's job had to decide whether or not to contribute money to buy a gift for their boss on Boss' Day.

Making a decision involves considering different options and weighing the pros and cons of each. The team members likely discussed the idea of buying a gift, talked about the cost and what they could contribute, and then took a vote to determine the final decision. The vote could have been a show of hands or a secret ballot, depending on how they decided to conduct it.

After considering everyone's opinions and preferences, the team reached a decision through the vote. They may have concluded that it was a good idea to pitch in and show appreciation for their boss, or they might have decided not to buy a gift for various reasons. Either way, the decision-making process involved the team coming together and reaching a consensus through the vote.

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The kinetic energy of the Mars Climate Orbiter spacecraft is approx    3.31 x 10^7 joules.

To determine the kinetic energy of the Mars Climate Orbiter spacecraft, we can use the formula:

Kinetic energy = (1/2) * mass * velocity^2

Given:

Mass of the spacecraft (m) = 629 kg

Velocity of the spacecraft (v) = 1.20 x 10^4 km/h

First, we need to convert the velocity from km/h to m/s:

1 km = 1000 m

1 h = 3600 s

Velocity in m/s = (1.20 x 10^4 km/h) * (1000 m/km) / (3600 s/h) ≈ 333.33 m/s

Now, we can calculate the kinetic energy:

Kinetic energy = (1/2) * (629 kg) * (333.33 m/s)^2

Kinetic energy ≈ 3.31 x 10^7 joules

Therefore, the kinetic energy of the Mars Climate Orbiter spacecraft is approximately 3.31 x 10^7 joules.

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Answer:

Step-by-step explanation:

Answer: A line segment

Explanation:

Since the line is straight, line segment for me. Hope it helps!

Answer:

A line

Step-by-step explanation:

Roughly, we can say that a line is an infinitely thin, infinitely long collection of points extending in two opposite directions. When we draw lines in geometry, we use an arrow at each end to show that it extends infinitely.

since there are 12 more females that means that, since the ratio is defferenced by 2, 1 is equal to 6. Threfor, there are 5*6+3*6 people at the party -> 30+18= 48 people

Answer:

the answer is A, B’(-1,2)

Step-by-step explanation:

for problem two it is a 90 degree rotation

Answer:

60000

Step-by-step explanation:

Answer:

Step-by-step explanation:

6 × \(10^{4}\) =

6 × 10000 =

60000