an equation for measuring height of a balloon versus time is h=2t+10, using the variables h and t write the equation in function notation

It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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The system of equation that can be used to represent the price of each pound of raspberries and grapes is as follows:

44x + 43y = 217

45x + 18y = 144

Brayden runs a farm stand that sells raspberries and grapes. Yesterday, Brayden sold 44 pounds of  raspberries and 43 pounds of grapes for a total revenue of 217 dollars.

Today, he sold  45 pounds of  raspberries and 18 pounds of grapes for a total revenue of 144 dollars.

Therefore, the system of equation that can be used to describe the price of each pound of raspberries and grapes can be represented as follows:

let

x = price of each pounds of raspberries

y = price of each pound of grapes

Therefore, the system of equation is as follows

44x + 43y = 217

45x + 18y = 144

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Answer:

x = 9.6 meters

y = 20.98 meters

Shadow length = 11.38 meters

Step-by-step explanation:

By applying tangent rule in right triangle ABD,

tan(21)° = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

tan(21) = \(\frac{x}{25}\)

x = 25(tan 21)

x = 9.5966

x ≈ 9.60 meters

Similarly, by applying tangent rule in ΔABC,

tan(40)° = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

tan(40)° = \(\frac{BC}{AB}\)

tan(40)° = \(\frac{y}{25}\)

y = 25(tan 40°)

y = 20.98 meters

Length of the shadow of the man = y - x

                                                        = 20.98 - 9.60

                                                        = 11.38 meters

Answer:20

Step-by-step explanation:

because why not you know

Few nutrients

I just took the test and this is the correct answer

The one quality of the entire open-ocean zone is few nutrients

The open-ocean zone is the part of the sear where over half of the ocean is filled with water.

Because of the presence of water, there are only few nutrients that can be found on the entire open-ocean zone

Hence, the one quality of the entire open-ocean zone is few nutrients

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Answer:

540 is the answer

Step-by-step explanation:

Move the decimal point 2 places to the right.

I hope my answer was helpful!:)

The figures below are similar.  By using this, the perimeter of the smaller rectangle P₂ = 3 cm.

When applying a scale factor, similar shapes are enlarged versions of one another. All of the corresponding angles and lengths in related shapes are equal and in the same ratio.

We divide the length of the enlarged shape by the length of the original shape to calculate the length scale factor.

The ratio of perimeter of both shapes is same as the ratio their corresponding side.

Given that one side of shape 1 is 4 cm and its perimeter P₁ is 12 cm.

and the corresponding side of shape 2 is 1 cm.

comparing the sides and perimeter of both shapes we get

4cm/1cm = 12cm/P₂

by cross multiplication we get,

4 * P₂ = 12cm * 1

P₂ = 12cm/4

P₂ = 3cm

So the perimeter of the smaller rectangle P₂ = 3 cm.

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The trigonometric functions sin θ = - 2 / 3 and csc θ = - 3 / 2 are related to each other in accordance with the trigonometric formula: sin θ · csc θ = 1. (Correct choices: 1, 4)

In this question we must look for two trigonometric functions that are associated to one and same angle. This can be done by relations between fundamental and derivate trigonometric functions. There are two fundamental trigonometric functions (sine, cosine) and four derivate trigonometric functions (tangent, cotangent, secant, cosecant).

After a quick inspection, sin θ = - 2 / 3 is related to csc θ = - 3 / 2 as it fulfill the following trigonometric formula: sin θ · csc θ = 1

The graph is missing and cannot be found, so we decided to change the intend of the question to find two trigonometric functions associated with the same angle.

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The cost for making one phone is 125 dollars.

A linear equation is a equation that has degree as one.

To find the solution of n unknown quantities n number of equations with n number of variables are required.

The given table shows the cost of producing different number of phones.

Suppose the cost of making each phone be x.

And, the fixed cost be y.

Then, as per the given table following equations can be made:

For making one phone,

1 × x + y = 1125

=> x + y = 1125             (1)

For making five phones,

5 × x + y = 1625

=> 5x + y = 1625          (2)

In order to find the cost per phone solve equation (1) and (2) as below,

Multiply equation (1) by 5 then subtract equation (2) from it.

5(x + y) - (5x + y) = 5 × 1125 - 1625

=> 4y = 4000

=> y = 1000

Substitute y = 1000 in equation (2) to get,

5x + 1000 = 1625

=> x = 125

Hence, the cost for making each phone is 125 dollars.

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Answer:

22 m/s

Step-by-step explanation:

Take the distance and divide by the time

1210 m/55s

22 m/s

Answer:

Step-by-step explanation:

\(speed = \frac{distantce}{time} \\ = \frac{1210m}{55s} \\ = 22m {s}^{ - 1} \)

The amount of money that will be in the account at the end of the four years to use as the down payment on the property is $26,102.47.

In the above question, we need to use the formula for compound interest and it is:

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

Note that:

A = the amount of money at the end of the investment

P = the principal amount

r = the annual interest rate

n = the number of times the interest is compounded per year

t = the number of years of the investment

Since:

P = $20,000

r = 6.5% = 0.065

n = 365 (note the interest is compounded everyday)

t = 4

We shall put the values into the formula:

A = $20,000(1 + 0.065/365)^(365*4)

A = $20,000(1.0178)¹⁴⁶⁰

A = $20,000  x  1.305124

A = $26,102.47

Therefore, at the end of the four years, there will be $26,102.47.

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Answer:

B

Step-by-step explanation:

since a²+b²=c²

this is proven correct in answer B

As;

(8^0.5)² +(3)²=(17^0.5)²

Answer:

2&3

Step-by-step explanation:

They have the same absoulte value

You have to go 18 numbers to get from each other.

They are opposite numbers.

One is negative and one is positive.

Hope it Helps

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

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

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

Shaquana's age will be equal to 5 years for the given data.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Given that Shaquana is younger than Alonso. Their ages are consecutive odd integers. Shaquana's age if the sum of the square of Shaquana's age and 2 times Alonso's age is 39.

Let Shaquana's age will be x. The equation can be written as:-

x² + 2 ( x + 2 ) = 39

x² + 2x + 4 = 39

x² +2x -35 = 0

Solve the quadratic equation,

x² +2x -35 = 0

x² + 7x - 2x - 35 = 0

x ( x + 7 ) - 2 ( x + 7 ) = 0

( x + 7 ) ( x - 5 ) = 0

x = 5

Therefore, for the given data, Shaquana's age will be 5 years.

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Answer:

C

Step-by-step explanation:

Please refer to the picture above.

Assuming a =

\( \sqrt[5]{x}^{2}y } \)

You can visualise the solution easily.

Answer:

Step-by-step explanation:

Area of circle:

Area of α degree sector:

The shaded area is:

The value of her investment at compound interest after 4 years will be £8934.34.

What is compound interest?

Compound interest is the adding of interest to the principle sum of a loan or deposit, or interest on interest plus interest. It is the outcome of making an investment interest, or adding it to the lent assets, rather than repaying it out or requesting return from the borrower, so that interest is received on the principle sum plus previously accrued interest in the next month. In finance and economics, compound interest is the norm. Compound interest differs from simple interest in that previously accrued interest is not added to the main amount of the current month, resulting in no compounding. The simple annual interest rate is calculated by multiplying the interest amount per period by the number of periods per year.

Given,

Principal (P) = £8000

Rate of interest (r) = 2.8% compound interest p.a.

Time (n) = 4 years

Then, according to compound interest compounded annually,

Amount = P(1+r/100)ⁿ

             = 8000(1+2.8/100)⁴

             = 8000(102.8/100)⁴

             = 8934.34

Hence, the value of her investment at compound interest after 4 years will be £8934.34.

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Answer:

if its answer for x its

Step-by-step explanation:

=4

=8

In each scenario, we are given a bag containing various colored marbles and asked to determine the number of sets that meet specific conditions.

A. To find the number of sets including all the red marbles, we can treat the three red marbles as a single entity and combine them with any three marbles from the remaining colors. The number of such sets can be calculated using combinations.

B. To find the number of sets including none of the red marbles, we can choose four marbles from the remaining colors, excluding the red marbles.

C. To find the number of sets including one of each color other than lavender, we can choose one marble from each of the color categories, excluding lavender.

D. To find the number of sets including at least two red marbles, we can consider two cases: selecting exactly two red marbles and selecting three red marbles. The combinations for each case can be calculated, and their sum will give the desired number of sets.

E. To find the number of sets including at most one of the yellow marbles, we can consider three cases: selecting no yellow marble, selecting one yellow marble, and selecting two yellow marbles. The combinations for each case can be calculated, and their sum will give the desired number of sets.

F. To find the number of sets including either the lavender marble or exactly one yellow marble but not both, we can consider two cases: selecting the lavender marble and selecting exactly one yellow marble. The combinations for each case can be calculated, and their sum will give the desired number of sets.

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The Malthusian law for population growth states that the rate of population growth is proportional to the current population size.

Mathematically, we can express this as:

dP/dt = rP

where P is the population size, t is time, and r is the growth rate.

Assuming a constant growth rate, we can integrate this equation to get:

ln(P) = rt + C

where C is an integration constant. We can solve for C using the initial population estimate:

ln(1200) = r(1980) + C

C = ln(1200) - r(1980)

Substituting the values of C and P from the second estimate (P=7500 in 2008), we get:

ln(7500) = r(2008) + ln(1200) - r(1980)

Solving for r, we get:

r = [ln(7500) - ln(1200)] / (2008 - 1980) = 0.0496

Using this value of r, we can predict the alligator population in 2020, which is 12 years after the second estimate (2008). We have:

ln(P) = rt + ln(7500)

ln(P) = 0.0496(12) + ln(7500) = 9.058

P = e^9.058 = 8656

Therefore, the estimated alligator population in the region in the year 2020 is 8656.

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answer:

the answers are undefined and zero ( and in that order )

step-by-step explanation:

for question 12,

x = 10

since that equation is just a vertical line, the slope is undefined!

but for question 13

y = -5

the equation is just a horizontal line rather then a vertical line, the slope is zero ( since it is not moving )

i hope this helps you and if you need anymore help then please feel free to ask me! :)

Using the volume of the rectangular prism and the cube we know that it is (D) impossible that cubes will fit the rectangular prism as its volume is greater.

The space occupied within an object's borders in three dimensions is referred to as its volume.

It is sometimes referred to as the object's capacity.

The capacity of an object is measured by its volume.

For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.

The quantity of space occupied by a three-dimensional object can also be used to describe volume.

Rectangular prism volume:
V = whl

V = 2*212*4

V = 1,696 in³

Cube's Volume:

V = a³

V = 12³

V = 1728

Then, cubes are needed to fill the rectangular prism:
1696/1728 = 0.98

Hence, not possible.

Therefore, using the volume of the rectangular prism and the cube we know that it is (D) impossible that cubes will fit the rectangular prism as its volume is greater.

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Correct question:

A rectangular prism has a length of 4 in., a width of 2 in., and a height of 212 in.

The prism is filled with cubes that have edge lengths of 12 in.

How many cubes are needed to fill the rectangular prism?

A. 2

B. 4
C. 6

D. Not possible

Answer:

distance = 7.07 units

Step-by-step explanation:

x difference = 7

y difference = -1

using the Pythagorean theorem:

7² + -1² = d²

d² = 49 + 1 = 50

d = 7.07

Answer:

7.1

Step-by-step explanation:

distance between the x is 7 and y is 1

And to find the hypotenuse, you use the quadratic formula, 7^2 + 1^2 = c^2

c=50

and take the square root, which is 7.071, rounds to 7.1

a. The probability that the system will operate as shown is approximately 0.6141.

b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141

The probability that the system will operate as shown is approximately 0.6141.

b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:

Probability = 0.85 × 0.90 × 0.85

Probability ≈ 0.6485

The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

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When x^3+2x^2+x+1 is divided by (x+1) then remainder is 1.

In the given question, we have to find what is remainder when x^3+2x^2+x+1 is divided by (x+1).

To find the remainder there are two ways. First we divide the x^3+2x^2+x+1 by (x+1). Second we find the value of from (x+1) by equating (x+1) equal to zero. The put the value of x in the expression x^3+2x^2+x+1.

In this we ca easily find the remainder.

Now we firstly find the value of x;

(x+1) = 0

Subtract 1 on both side we get;

x= −1

Now put x= -1 in the expression x^3+2x^2+x+1.

x^3+2x^2+x+1 = (−1)^3+2(−1)^2+(−1)+1

x^3+2x^2+x+1 = −1+2−1+1

x^3+2x^2+x+1 = 1

Hence, when x^3+2x^2+x+1 is divided by (x+1) then remainder is 1.

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The right question is:

What is remainder when x^3+2x^2+x+1 is divided by (x+1)?

The probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is 0.2461.

Option C is correct

The probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is given by the binomial probability formula:

P(X = k) = (n choose k) \(* p^k * (1-p)^(n-k)\)

where X is the random variable representing the number of heads, n is the total number of coin flips, k is the number of heads obtained, and p is the probability of getting a head on any individual flip.

Since we are assuming that the coin is fair, p = 0.5. Let's say you flipped the coin n times and obtained k heads. Then the probability of obtaining exactly k heads with a fair coin is:

P(X = k) = (n choose k \(* 0.5^k * ()1-0.5)^(n-k)\)

We don't know what n or k are, so we can't compute the exact probability. However, we can use the fact that the coin is fair to get an estimate. If we assume that the number of heads obtained is roughly half of the total number of flips, then k = n/2. Plugging this into the formula, we get:

\(P(X = n/2) = (n choose n/2) * 0.5^(n/2) * (1-0.5)^(n/2)\)

Simplifying this expression, we get:

\(P(X = n/2) = (n choose n/2) * 0.5^n\)

Now, we want to find the probability of obtaining exactly as many heads as we just obtained. Let's say we flipped the coin 10 times and obtained 5 heads. Then we want to find P(X = 5), which is:

P(X = 5) = (10 choose 5) \(* 0.5^5 * (1-0.5)^(10-5)\) = 0.2461

Therefore, the probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is 0.2461.

Option C is correct

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The correct interpretation of the 90% confidence interval is: c) 90% of the time, Kat can be certain that the calculated interval (22.96, 26.64) accurately represents the real average number of eggs that chickens on this farm lay.

What is confidence interval?

An predicted range of values for the true population parameter is known as a confidence interval.

The calculation for the 90% confidence interval can be done using the formula:

Confidence Interval = Sample Mean ± (Critical Value * Standard Deviation / √(Sample Size))

Given:

Sample Mean (x) = 24.8 eggs

Standard Deviation (σ) = 6.9 eggs

Sample Size (n) = 40

Confidence Level = 90%

For a 90% confidence level, the critical value is approximately 1.645.

Now, plug in the values into the formula:

Confidence Interval = 24.8 ± (1.645 * 6.9 / √(40))

Calculate the standard error (SE) by dividing the standard deviation by the square root of the sample size:

SE = 6.9 / √(40)

Calculate the margin of error by multiplying the critical value with the standard error:

Margin of Error = 1.645 * SE

Finally, calculate the confidence interval:

Confidence Interval = 24.8 ± Margin of Error

Perform the calculations to find the lower and upper bounds of the confidence interval:

Lower Bound = 24.8 - Margin of Error

Upper Bound = 24.8 + Margin of Error

The resulting confidence interval is (22.96, 26.64).In this case, the confidence interval (22.96, 26.64) is constructed based on the sample mean of 24.8 and the standard deviation of 6.9.

Option c correctly states that Kat can be 90% confident that the true mean number of eggs chickens from this farm lay falls within the interval (22.96, 26.64). This means that if we were to repeat the sampling process multiple times and construct confidence intervals, about 90% of those intervals would contain the true mean.

Options a and b are incorrect because they do not accurately describe the interpretation of a confidence interval. Option d is also incorrect as it mentions "repeated sampling" but does not accurately convey the meaning of the confidence interval capturing the true mean.

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Answer:

x=6

alternative exterior angles

Step-by-step explanation:

to prove y and z parallel then the two angles must be equal:

11x-3=4x+39

11x-4x=39+3

7x=42

x=42/7

x=6