Verify the following identity. To transform the left side into the right side, should be changed to and the left side simplified.

The function that models the population t years after 2000 is P(t) = 14400 * (1.04)^t

The population growth function is of the form:

P(t) = P₀ * (1 + r)^t

Where:

P(t) is the current population after t years

P₀ is the starting population

r is the annual growth rate in percent

Thus, P₀ = 14400 and 4% = 0.04

P(t) = P₀ * (1 + r)^t

P(t) = 14400 * (1 + 0.04)^t

P(t) = 14400 * (1.04)^t

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Complete Question

The fox population in a certain region has an annual growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 14400.

a) Find a function that models the population t years after 2000 (t=0 for 2000).

Your answer is P(t) =

Answer:

4. n + 24

5. b - 11

6. d/5

The missing sides of each geometric system are summarized below:

Case 9: (x, y) = (9, 12)

Case 12: (x, y) = (√51, 7)

Case 15: (x, y) = (8, 15)

In this question we find three cases of geometric systems formed by two right triangles, all missing sides can be found by means of Pythagorean theorem:

r = √(x² + y²)

Where:

Now we proceed to determine all missing sides:

Case 9

y = √(15² - 9²)

y = 12

x = 9

Case 12

x = √(10² - 7²)

x = √51

y = 7

Case 15

y = √(17² - 15²)

y = 8

x = 15

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In a case whereby  stack of two hundred eighty cards is placed next to a ruler, and the height of stack is measured to be 7/ 8 inches the thickness  of one card is 1/320 inches

Based on  the provided information, two hundred eighty cards is placed next to a ruler ten we can set up the expression as

( 7/ 8) / 280

7/ 8 * 1/280

1/320

Therefore, based on the given information, this implies that Each card is 1/320 inches

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Answer:

Using the logarithmic identity log(a) + log(b) = log(ab), we can simplify the left-hand side of the equation:

log2(x-1) + log2(x+5) = log2((x-1)(x+5))

So the equation becomes:

log2((x-1)(x+5)) = 4

Using the exponential form of logarithms, we can rewrite the equation as:

2^4 = (x-1)(x+5)

Simplifying:

16 = x^2 + 4x - 5

Rearranging:

x^2 + 4x - 21 = 0

Using the quadratic formula:

x = (-4 ± sqrt(4^2 - 4(1)(-21))) / (2(1))

x = (-4 ± sqrt(100)) / 2

x = (-4 ± 10) / 2

So x = -7 or x = 3.

However, we need to check whether these solutions satisfy the original equation. We can see that x = -7 does not work, because both terms inside the logarithms would be negative. Therefore, the only solution is x = 3.

Answer:

Using the properties of logarithms, we can simplify the left-hand side of the equation:

log2(x-1) + log2(x+5) = log2((x-1)(x+5))

Therefore, the equation becomes:

log2((x-1)(x+5)) = 4

Using the definition of logarithms, we can rewrite this equation as:

2^4 = (x-1)(x+5)

16 = x^2 + 4x - 5

Simplifying further:

x^2 + 4x - 21 = 0

We can now use the quadratic formula to solve for x:

x = (-4 ± sqrt(4^2 - 4(1)(-21))) / (2*1)

x = (-4 ± sqrt(100)) / 2

x = (-4 ± 10) / 2

x = -7 or x = 3

However, we need to check if these solutions satisfy the original equation.

When x = -7:

log2(x-1) + log2(x+5) = log2((-7-1)(-7+5)) = log2(16) = 4

So x = -7 is a valid solution.

When x = 3:

log2(x-1) + log2(x+5) = log2((3-1)(3+5)) = log2(16) = 4

So x = 3 is also a valid solution.

Therefore, the solutions to the equation log2(x-1) + log2(x+5) = 4 are x = -7 and x = 3.

Step-by-step explanation:

The probability that exactly 19 men and 7 women are chosen is 0.053107%.

Probability:

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

[tex]C_n_,_x[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_n_,_x=\frac{n!}{x!(n-x)!}[/tex]

Desired outcomes:

19 men, from a set of 21

7 women, from a set of 11

[tex]D= C_2_1_,_1_9[/tex]  × [tex]C_1_1_,_7[/tex] [tex]=\frac{21!}{19!2!}[/tex] ×  [tex]\frac{11!}{7!4!}[/tex][tex]=69,300[/tex]

Total outcomes:

26 people from a set of 21 + 11 = 32.

[tex]T=C_3_2_,_2_6=\frac{32!}{26!6!}[/tex][tex]=13,049,164,800[/tex]

The probability is :

P = [tex]\frac{D}{T}= \frac{69,300}{13,049,164,800} = 5.3107[/tex]

0.053107% probability that exactly 19 men and 7 women are chosen.

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Answer: 4m-24n+3

Step-by-step explanation:

Expand and collect like terms!

[tex](17m-12n-1) + (4-13m-12n)\\= 17m - 12n - 1 + 4 - 13m - 12n\\=4m-24n+3[/tex]

Hope this helps <3

The equations solved for the variables T₁ and P₁ are:

We start with the equation:

(P₁*V₁)/T₁ = (P₂*V₂)/T₂

And we want to solve this for T₁, we can multiply both sides by T₁ and divide both sides by the expression in the right side.

(P₁*V₁) = T₁*[ (P₂*V₂)/T₂]

(P₁*V₁)*[T₂/(P₂*V₂)] = T₁

That is the equation solved for T₁.

34: Now we have the same equation but we want to solve it for P₁, to do so, just multiply both sides by T₁/V₁

We will get:

(T₁/V₁)*(P₁*V₁)/T₁= (T₁/V₁)*(P₂*V₂)/T₂

P₁ = (T₁/V₁)*(P₂*V₂)/T₂

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Answer:

The domain in interval notation is (-infinity, infinity), or all real numbers.

Answer:

The correct equation to find the total number of bags of glass and plastic Silas will take to the recycling center is C. x - 18 = 6.

In this equation, x represents the total number of bags of glass and plastic Silas will take to the recycling center. The left side of the equation represents the number of bags of glass Silas will take to the recycling center (x - 18), and the right side represents the number of bags of plastic he still needs to take to the recycling center (6).

By setting the two expressions equal to each other (x - 18 = 6), we can solve for x and determine the total number of bags Silas will take to the recycling center. Adding 18 to both sides of the equation gives us x = 24, which means Silas will take a total of 24 bags (18 bags of glass and 6 bags of plastic) to the recycling center.

Step-by-step explanation:

(a) The lower limit of the 90% confidence interval can be calculated using the formula:

lower limit = sample mean - margin of error

Plugging in the given values, we have:

lower limit = 7.43 - 1.32

lower limit = 6.11 (rounded to 2 decimal places)

Therefore, the lower limit of the 90% confidence interval is approximately 6.11 hours per night.

(b) If 500 random samples like this were selected, and a 90% confidence interval was constructed using each sample, the expected number of intervals that would contain the population mean can be approximated using the margin of error as a guide.

Since the margin of error is 1.32 hours, we can expect roughly 90% of the confidence intervals to contain the true population mean. Therefore, out of 500 samples, we would expect approximately:

500 * 0.9 = 450

So, approximately 450 of these confidence intervals would contain the population mean.

The probability of rolling a number less than 9 is 1

The probability of rolling a number less than 9 is 1, since all the possible outcomes are 1, 2, 3, 4, 5, 6 and all of them are less than 9.

The set of equally likely outcomes when rolling a 6-sided die is {1, 2, 3, 4, 5, 6}.

There are no outcomes greater than 6 since that is the maximum number on the die.

Therefore, the probability of rolling a number less than 9 is equal to the probability of rolling any number on the die, which is 1, since all outcomes in the sample space are equally likely.

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true

Step-by-step explanation:

all square have the same features and properties like

all side are equal

Area of the two right triangles:

A = 1/2(b)(h)

A = 1/2(10)(24)

A = 120

Total area = 240

Area of the left-most rectangle:

A = (b)(h)

A = (24)(25)

A = 600

Area of the right-most rectangle:

A = (b)(h)

A = (25)(26)

A = 650

Area of the base rectangle:

A = (b)(h)

A = (10)(25)

A = 250

Surface Area:

240 + 600 + 650 + 250

1740

Answer: 1740 cm^2

Hope this helps!

[tex]\sf SA=\boxed{\sf 1740cm^{2} }.[/tex]

Check attached 1 to see what parts we're referring to in this step.

This part forms a right triangle. Therefore, the formula to use to find it's area is the following:

[tex]\sf A=\dfrac{bh}{2}[/tex]; where "b" is the length of the base of the triangle, and "h" is its height.

Since we have another section identical to this part at the back, we multiply this area by 2 and calculate:

[tex]\sf A=2\dfrac{bh}{2}=(10cm)(24cm)=240cm^{2}[/tex]

Check image 2 to see this part highlighted.

This shape forms a rectangle. Therefore, use the following formula to calculate:

[tex]\sf A=lw[/tex]; where "l" is length, and "w" is width.

[tex]\sf A=(25cm)(10cm)=250cm^{2}[/tex]

Check image 3.

This shape also forms a rectangle, therefore its area is calculated like this:

[tex]\sf A=(24cm)(25cm)=600cm^{2}[/tex]

Check image 4.

This shape also forms a rectangle, therefore its area is calculated like this:

[tex]\sf A=(26cm)(25cm)=650cm^{2}[/tex]

The total surface area of this prism is given by the addition of all of its individual areas that we just calculated.

[tex]\sf SA=240cm^{2} +250cm^{2} +600cm^{2} +650cm^{2} =\boxed{\sf 1740cm^{2} }.[/tex]

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(a)The arrow will reach a maximum height of 130 feet.

(b) After around 5 seconds, the arrow will strike the ground.

(c) At 1 second and 4 seconds after launch, the arrow will be 114 feet high.

a) The maximum height of the arrow occurs at the vertex of the parabolic pathway. The x-coordinate of the vertex is given by -b/2a, where a=-16 and b=80. So, t= -b/2a = -80/(2x(-16)) = 2.5 seconds. To find the maximum height, plug in t=2.5 into the equation: h(2.5) = -16(2.5)² + 80(2.5) + 50 = 130 feet.

Therefore, the maximum height of the arrow is 130 feet.

b) To find the time it takes for the arrow to reach the ground, find the value of t when h(t)=0 (since the arrow hits the ground when h=0). We can use the quadratic formula to solve for t:

t = (-V₀ ± √(V₀² - 4ah₀)) / 2a

where a=-16, V₀=80, and h₀=50.

t = (-80 ± √(80² - 4x(-16)50)) / 2(-16) = 5 seconds or -1.5625 seconds

Since time can't be negative, the arrow will hit the ground after about 5 seconds.

c) To find the time it takes for the arrow to be 114 feet high, solve for t when h(t) = 114.

-16t² + 80t + 50 = 114

-16t² + 80t - 64 = 0

Dividing both sides by -16 gives:

t² - 5t + 4 = 0

Factoring gives:

(t-4)(t-1) = 0

So t=4 seconds or t=1 second.

Therefore, the arrow will be 114 feet high at 1 second and 4 seconds after launch.

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The answer choice that matches the calculated confidence interval is 62.9 to 83.1

In statistics, the mean is a measure of central tendency that represents the average value of a set of numerical data. It is also known as the arithmetic mean, and it is calculated by adding up all the values in the dataset and dividing the sum by the number of values.

The mean is a useful measure of central tendency because it is easy to calculate, and it provides a single value that represents the center of the dataset. It is affected by outliers, which are extreme values that are far from the other values in the dataset, so it may not accurately represent the typical value of the data if there are outliers present.

To construct a 95.44% confidence interval for the mean score, u, of all students taking the test, we can use the formula:

CI = x ± t(alpha/2, n-1) * (s / √(n))

where CI is the confidence interval, x is the sample mean (73), t(alpha/2, n-1) is the t-value for the given alpha level (0.0278) and degrees of freedom (n-1=4) from the t-distribution table, s is the sample standard deviation, and n is the sample size.

The sample standard deviation is not given, so we will assume that it is the same as the population standard deviation, which is 15. Thus, s = 15.

Using the t-distribution table with 4 degrees of freedom and an alpha level of 0.0278, we find that the t-value is approximately 3.747.

Plugging in the values into the formula, we get:

CI = 73 ± 3.747 * (15 / √(5))

Simplifying, we get:

CI = 73 ± 16.27

Therefore, the 95.44% confidence interval for the mean score, u, of all students taking the test is:

CI = (73 - 16.27, 73 + 16.27)

CI = (56.73, 89.27)

Rounding to one decimal place, we get:

CI = (56.7, 89.3)

Therefore, the answer choice that matches the calculated confidence interval is:

62.9 to 83.1

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The complete question is:

The mean score, x on an aptitude test for a random sample of 5 students was 73, assuming that 0 = 15, construct a 95.44% confidence interval for the mean score, u of all students taking the test. answer choices, 43 to 103, 59.6 to 86.4, 62.9 to 83.1, and 67.0 to 79.0.

Answer:

9. 40 = 2πr

r = 20/π inches = 6.4 inches

d = 40/π inches = 12.7 inches

10. 256 = 2πr

r = 128/π feet = 40.7 feet

d = 256/π feet = 81.5 feet

Answer: ∠DGB or ∠EGA

Step-by-step explanation:

Supplementary: Either of two angles whose sum is 180°.

Starting Angle: ∠DGE

Possible Supplements: ∠DGB or ∠EGA

I hope this helps ^^

The probability of selecting an R or an E without replacement, and then selecting an S is 5/36

Because the word SEPTEMBER has 9 letters, there are 9 different alternatives for the initial letter.

The probability of selecting a R or an E without replacing is 2+3=5.

The odds of picking a R or an E on the initial draw are 5/9.

After the first letter is drawn, the bag contains eight letters, including one S. If the first letter is not replaced, there are only four letters that fit the requirement.

Given that a R or an E was selected without replacement on the first draw, the probability of selecting a S on the second draw is 4/8.

When we multiply these probability together, we get:

P(R or E, not replacing) * P(S after R or E, not replacing) = (5/9) * (4/8) = 10/72 = 5/36

Hence, the probability of selecting an R or an E without replacement, and then selecting an S is 5/36

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The Amplitude is 1/2 and period is π/2.

We have the function as

y= 1/2 cos π/4 x

As, The general equation of a Cosine function is

y=A cos (B(x−D))+C

where A is Amplitude , D is the shift.

So, the amplitude is 1/2

Period = 2π / 4= π/2

and, the phase shift is not possible to determine.

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The equation which represents the rule for the variable values is given by option c. y = 2x + 2

The values in the table are,

x  -2   -1    0   1   2

y   -2    0   2   4  6

let us consider two coordinates of the given values in the table .

( x₁ , y₁ ) = ( -2 , -2 )

( x₂ , y₂ ) = ( 0 , 2 )

Using the formula for the slope intercept form of the line we get the equation,

( y - y₁ ) / ( x - x₁ ) = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substitute the values to get the equation of the line we have,

⇒ ( y - ( - 2 ) ) / ( x -  ( -2 ) ) = ( 2 - ( - 2 ) ) / ( 0 - ( - 2 ) )

⇒  ( y + 2 ) / ( x + 2 ) = ( 2 + 2 ) / ( 0 + 2)

⇒  ( y + 2 ) / ( x + 2 ) = 4  / 2

⇒  ( y + 2 ) / ( x + 2 ) = 2

⇒ y + 2 = 2 ( x + 2)

⇒ y + 2 = 2x + 4

⇒ y = 2x + 4 - 2

⇒ y = 2x + 2

Therefore, the equation which represents the rule for the given values of the variable is equal to option c. y = 2x + 2

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The value of x, based on the Alternate Interior Angles Theorem, is calculated as: x = 5.

The Alternate Interior Angles Theorem states that if two parallel lines are intersected by a transversal, then the pairs of alternate interior angles formed are congruent. In other words, if two lines are parallel and a third line intersects them, then the angles that are inside (or "interior" to) the two parallel lines and on opposite sides of the transversal are congruent.

Therefore, we have:

3x - 8 = x + 2 [based on the Alternate Interior Angles Theorem]

Combine like terms:

3x - x = 8 + 2

2x = 10

2x/2 = 10/2

x = 5

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The limit of the trigonometric function f(x) = (1 - cos x) / x is equal to 0.

In this problem we need to determine the limit of a trigonometric function for x → 0. This can be done by simplifying the expression by trigonometric formulas. First, write the trigonometric function:

f(x) = (1 - cos x) / x

Second, modify the expression by means of algebra properties and trigonometric formulas:

f(x) = (2 / x) · (1 - cos x) / 2

f(x) = sin² (x / 2) / (x / 2)

f(x) = sin (x / 2) · [sin (x / 2) / (x / 2)]

For u = x / 2:

f(u) = sin u · (sin u / u)

Third, use limits to evaluate the trigonometric function:

f(u) = 0 · 1

f(u) = 0

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Answer:

D

Step-by-step explanation:

All the numbers that have fraction are irrational therefore the numbers are real

Answer:

Step-by-step explanation:

First, we need to find the z-scores for q1 and q3.

Q1:

Using the formula for z-score, we get:

z = (x - μ) / σ

where x is the IQ score we want to find the z-score for, μ is the mean IQ of the population, and σ is the standard deviation of the population.

For the first quartile (q1), we want to find the z-score such that 25% of the population has an IQ score below that value. From the standard normal distribution table, we find that the z-score corresponding to a cumulative area of 0.25 is -0.674.

So we have:

-0.674 = (x - 110) / 16

Solving for x, we get:

x = 99.8

Therefore, q1 is approximately 99.8.

Q3:

Similarly, for the third quartile (q3), we want to find the z-score such that 75% of the population has an IQ score below that value. From the standard normal distribution table, we find that the z-score corresponding to a cumulative area of 0.75 is 0.674.

So we have:

0.674 = (x - 110) / 16

Solving for x, we get:

x = 120.8

Therefore, q3 is approximately 120.8.

A) (2x+1)⁰ = 96⁰

=> 2x = 96⁰ - 1⁰ = 95⁰

=> x = 95⁰/2 = 47⁰30' (= 47.5⁰)

B) x⁰ = (2x-7)⁰

=> x - 2x = -7

=> -x = -7

=> x = 7⁰

C) mIJ = 45⁰ ; mJK = 57⁰

m✓ IJK = 180⁰- 45⁰ - 57⁰ = 78⁰

=> mIK = 78⁰

Ans: a) 47.5⁰ b) 7⁰ c) mIJ = 45⁰ ; mJK = 57⁰ ; mIK = 78⁰

Ok done. Thank to me >:333