José encontró un álbum de fotos del abuelo cuando tenía nueve años si el álbum tenía 108 páginas cuantas veces se habría es que se habría escrito la cifra nueve para enumerar todo el libro

Vinay buys "two thousand seven" fruits.

To find the number of fruits that Vinay buys, we need to determine the place value of 2 in the number 37,523 and add 7 to it.

In the number 37,523, the digit 2 is in the thousands place.

The place value of 2 in the thousands place is 2,000.

Adding 7 to the place value of 2, we get:

2,000 + 7 = 2,007.

Therefore, Vinay buys 2,007 fruits.

In number names, we can write 2,007 as "two thousand seven."

So, Vinay buys "two thousand seven" fruits.

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The values in the expression is as follows:

a = 2

b = 0

c = -1

The expression can be solve using the exponential law. Therefore,

g = 2³ × 3 × 7²

h = 2 × 3 × 7³

Therefore, let's solve the following:

g/h = 2ᵃ × 3ᵇ × 7ⁿ

Therefore,

g = 2³ × 3 × 7² = 2 × 2 × 2 × 3 × 7 × 7

h = 2 × 3 × 7 × 7 × 7

Hence,

g / h =  2 × 2 × 2 × 3 × 7 × 7 / 2 × 3 × 7 × 7 × 7

Hence,

g / h = 2 × 2 / 7

g . h = 2² × 3° × 7⁻¹

Hence,

a = 2

b = 0

c = -1

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The estimated population of the state in the year 2022 is 19,280,700 people.

The given equation represents the population of a certain state as a function of time, where p is the population in thousands of people and t is the number of years since 2010.

The equation is given as p = 80.7t + 18,312.3.

To estimate the population of the state, we substitute the value of t into the equation. For example, if we want to estimate the population in the year 2022 (12 years since 2010), we substitute t = 12 into the equation:

p = 80.7(12) + 18,312.3

= 968.4 + 18,312.3

= 19,280.7.

The estimated population of the state in the year 2022 is 19,280,700 people.

We can estimate the population for any given year by substituting the corresponding value of t into the equation.

It's important to note that the population is given in thousands of people, so we multiply the final result by 1,000 to obtain the population in actual numbers.

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Brianna will owe $23,249.33 on her new vehicle after applying the down payment and taking advantage of the 33% off sale.

We need to follow these steps:

Calculate the discount on the Silverado:

Discount = 33% of $57,999

Discount = 0.33 * $57,999

Discount = $19,079.67

Subtract the discount from the original price of the Silverado:

Price after discount = $57,999 - $19,079.67

Price after discount = $38,919.33

Subtract Brianna's down payment from the price after discount:

Amount owed = Price after discount - Down payment

Amount owed = $38,919.33 - $15,670

Amount owed = $23,249.33

So, Brianna will owe $23,249.33 on her new vehicle after applying the down payment and taking advantage of the 33% off sale.

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Answer:

BC = 24 units

Step-by-step explanation:

This is an isosceles triangle which always has:

In this triangle, the legs CA and BA are congruent so CA = BA and the angles C and B are congruent to each other so angle C = angle B.

Thus, we can find x by setting CA and BA equal to each other:

(3x - 15 = x + 33) + 15

(3x = x + 48) - x

(2x = 48) / x

x = 24

Thus, x = 24

Since the length of BC is x and x = 24, BC is 24 units long.

Answer:

In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg. So AC = 80√3.

In a 45°-45°-90° triangle, both legs are congruent. So BC = 80.

AB = AC - BC = (80√3 - 80) meters

= 80(√3 - 1) meters

= about 58.56 meters

The distance between points A and B is approximately 138.6 meters.

To find the distance between points A and B, we can use the concept of trigonometry and the given information.

Let's denote the distance between points A and B as x.

From point A, the angle of elevation to the top of the cliff at point D is 30°. This means that in the right triangle formed by points A, D, and the top of the cliff, the opposite side is the height of the cliff (80.0 m) and the adjacent side is x. We can use the tangent function to calculate the length of the adjacent side:

tan(30°) = opposite/adjacent

tan(30°) = 80.0/x

Simplifying the equation, we have:

x = 80.0 / tan(30°)

Using a calculator, we can find the value of tan(30°) ≈ 0.5774.

Substituting the value, we get:

x = 80.0 / 0.5774

Calculating the value, we find:

x ≈ 138.6 meters

In light of this, the separation between positions A and B is roughly 138.6 metres.

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The equivalent ratio of the corresponding sides and the triangle proportionality theorem indicates that the similar triangles are;

1. ΔAJK ~ ΔSWY according to the SAS similarity postulate

2. ΔLMN ~ ΔLPQ according to the AA similarity postulate

3. ΔPQN ~ ΔLMN

LM = 12, QP = 8

4. ΔLMK~ΔLNJ

NL = 21, ML = 14

Similar triangles are triangles that have the same shape but may have different sizes.

1. The ratio of corresponding sides between the two triangles circumscribing the congruent included angle are;

24/16 = 3/2

18/12 = 3/2

The ratio of each of the two sides in the triangle ΔAJK to the corresponding sides in the triangle ΔSWY are equivalent and the included angle, therefore, the triangles ΔAJK and ΔSWY are similar according to the SAS similarity rule.

2. The ratio of the corresponding sides in each of the triangles are;

MN/LN = 8/10 = 4/5

PQ/LQ = 12/(10 + 5) = 12/15 = 4/5

The triangle proportionality theorem indicates that the side MN and PQ are parallel, therefore, the angles ∠LMN ≅ ∠LPQ and ∠LNM ≅ ∠LQP, which indicates that the triangles ΔLMN and ΔLPQ are similar according to the Angle-Angle AA similarity rule

3. The alternate interior angles theorem indicates;

Angles ∠PQN ≅ ∠LMN and ∠MLN ≅ ∠NPQ, therefore;

ΔPQN ~ ΔLMN by the AA similarity postulate

LM/QP = (x + 3)/(x - 1) = 18/12

12·x + 36 = 18·x - 18

18·x - 12·x = 36 + 18 = 54

6·x = 54

x = 54/6 = 9

LM = 9 + 3 = 12

QP = x - 1

QP = 9 - 1 = 8

4. The similar triangles are; ΔLMK and ΔLNJ

ΔLMK ~ ΔLNJ by AA similarity postulate

ML/NL = (6·x + 2)/(6·x + 2 + (x + 5)) = (6·x + 2)/((7·x + 7)

ML/NL = LK/LJ = (24 - 8)/24

(24 - 8)/24 = (6·x + 2)/((7·x + 7)

16/24 = (6·x + 2)/(7·x + 7)

16 × (7·x + 7) = 24 × (6·x + 2)

112·x + 112 = 144·x + 48

144·x - 112·x = 32·x = 112 - 48 = 64

x = 64/32 = 2

ML = 6 × 2 + 2 = 14

NL = 7 × 2 + 7 = 21

MN = 2 + 5 = 7

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To find the area of a rectangle, we need to know its length and width. Let's solve the problem step by step:

Let's assume that the width of the rectangle is represented by "w" (in feet).

According to the given information, the length of the rectangle is 4 feet longer than its width, which means the length can be represented as "w + 4" (in feet).

The perimeter of a rectangle is calculated by adding up all the sides. In this case, the perimeter is given as 32 feet.

Since a rectangle has two pairs of equal sides (length and width), we can express the perimeter equation as the following:

2(length + width) = perimeter

Substituting the values into the equation, we get:

2(w + (w + 4)) = 32

Simplifying the equation, we have:

2(2w + 4) = 32

4w + 8 = 32

4w = 24

w = 6

Now we know that the width of the rectangle is 6 feet. To find the length, we can substitute this value back into the equation for the length:

Length = w + 4 = 6 + 4 = 10 feet

The width is 6 feet, and the length is 10 feet. Now we can calculate the area of the rectangle:

Area = Length × Width = 10 × 6 = 60 square feet

Answer: The area of the rectangle is 60 square feet.

Answer:

Step-by-step explanation:

I cannot see the graphs.

Answer:

Step-by-step explanation:

a) To solve the equation tan θ = 1/√3, we can find the angle whose tangent is 1/√3 by taking the inverse tangent (arctan) of 1/√3.

θ = arctan(1/√3)

θ ≈ 30.0°

Therefore, the angle in standard position that satisfies tan θ = 1/√3 is approximately 30.0°.

b) To solve the equation 2cos θ = √3, we can isolate the cosine term by dividing both sides of the equation by 2.

cos θ = √3 / 2

Now, we can find the angle whose cosine is √3/2 by taking the inverse cosine (arccos) of √3/2.

θ = arccos(√3/2)

θ ≈ 30.0°

Therefore, the angle in standard position that satisfies 2cos θ = √3 is approximately 30.0°.

Step-by-step explanation:

Let Peter's present age be "p" and his father's age be "x"

So, p = x-24 ;

5 years from now,

Peter's age will be (x-24) + 5 = x-19

His father's age will be x+5.

It is given that 3(x-19)= x+5.

3x - 57 = x + 5 => 2x = 62.

On solving, his father's present age (x) is 31.

So Peter's present age is (p) is x - 24 = 31 - 24 = 7.

Now going in the reverse oder to check the answer.

Peter's present is 7.

5 years from now, it will be 12.

His father's age is 31.

5 years from now, his age will be 36 (which is 3x12).

Hence , the answer to the given problem is 7

Answer:

all real numbers

Step-by-step explanation:

Try a negative number, a positive number and zero for x.

All of them work.

Answer: all real numbers

The graph of the function and its inverse is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x) = 3 + 2ln(x)

Express as an equation

So, we have

y = 3 + 2ln(x)

Swap x and  y in the above equation

x = 3 + 2ln(y)

Next, we have

2ln(y) = x - 3

Divide by 2

ln(y) = (x - 3)/2

Take the exponent of both sides

[tex]y = e^{\frac{x - 3}{2}}[/tex]

Next, we plot the graphs

The graph of the functions is added as an attachment

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Answer:

  B.  linear

Step-by-step explanation:

You want to know the type of function represented by the table of values ...

When the differences in x-values are 1 (or some other constant), the differences in y-values will tell you the kind of function you have.

Here, the "first differences" are ...

They are constant with a value of 4.

The fact that first differences are constant means the function is a first-degree (linear) function.

The table represents a linear function.

__

Additional comment

The function is y = 4x. That is, y is proportional to x with a constant of proportionality of 4.

The level at which differences are constant is the degree of the polynomial function. The differences of first differences are called "second differences," and so on. A cubic function will have third differences constant.

If differences are not constant, but have a constant ratio, the function is exponential.

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The limit of the trigonometric expression is equal to 0.

In this problem we find the case of a trigonometric expression, whose limit must be found. This can be done by means of algebra properties, trigonometric formula and known limits. First, write the entire expression below:

[tex]\lim_{\Delta x \to 0} \frac{\cos (\pi + \Delta x) + 1}{\Delta x}[/tex]

Second, use the trigonometric formula cos (π + Δx) = - cos Δx to simplify the resulting formula:

[tex]\lim_{\Delta x \to 0} \frac{1 - \cos \Delta x}{\Delta x}[/tex]

Third, use known limits to determine the result:

0

The limit of the trigonometric function [cos (π + Δx) + 1] / Δx evaluated at Δx → 0 is equal to 0.

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Answer:

the radius of the cylinder is approximately 2.26 feet.

Step-by-step explanation:

To find the radius of the cylinder, we can use the formula for the volume of a cylinder:

Volume = π * radius^2 * height

Given that the volume is 400 feet, the height is 25 feet, and using π ≈ 3.14, we can rearrange the formula to solve for the radius:

400 = 3.14 * radius^2 * 25

Divide both sides of the equation by (3.14 * 25):

400 / (3.14 * 25) = radius^2

Simplifying:

400 / 78.5 ≈ radius^2

5.09 ≈ radius^2

To find the radius, we take the square root of both sides:

√5.09 ≈ √(radius^2)

2.26 ≈ radius

Rounding to the nearest hundredth, the radius of the cylinder is approximately 2.26 feet.

Answer:

Step-by-step explanation:

Volume Formula for a cylinder is  V=πr²h

Substitute the following:    400 = 3.14(r²)(25)

r=[tex]\sqrt{\frac{V}{\pi h} }[/tex]

r=[tex]\sqrt{\frac{400}{\pi 25} }[/tex]

r≈2.25676ft

Answer:

$6.84

Step-by-step explanation:

This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.

Answer:

x=50

Step-by-step explanation:

Make this equal to 180.

x+3x-35+x-35 = 180

5x = 180 + 70

5x=250

x=50

The completed sequence would then be: 2, 4, 7, 9, 16, 19, 29.

To complete the given number sequence, let's analyze the pattern and identify the missing terms.

Looking at the given sequence 2, 4, 7, __, 16, __, 29, __, we can observe the following pattern:

The difference between consecutive terms in the sequence is increasing by 1. In other words, the sequence is formed by adding 2 to the previous term, then adding 3, then adding 4, and so on.

Using this pattern, we can determine the missing terms as follows:

To obtain the third term, we add 2 to the second term:

7 + 2 = 9

To find the fifth term, we add 3 to the fourth term:

16 + 3 = 19

To determine the seventh term, we add 4 to the sixth term:

__ + 4 = 23

Therefore, the missing terms in the sequence are 9, 19, and 23.

By identifying the pattern of increasing differences, we can extend the sequence and fill in the missing terms accordingly.

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Answer:

(a) To find the average cost in 2011, substitute 11 for x in the function.

g(11) = -1,736.7 + 1,661.6 ln 11 = $2,247.64

The average cost in 2011 was $2,247.64.

(b) Using the graphing calculator, graph the function in the viewing window

[6, 15] by [1,000, 3,000].

The correct graph is B.

(c) A. The average cost increases at a slower rate as time goes on.

Answer:

52% used.

Step-by-step explanation:

13/25=52/100=52%

Ki Tae used 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides are each 15 meters long, while the remaining four sides are each 6 meters long.

Let's solve the problem step by step. We know that Ki Tae used a total of 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides have a length of 15 meters each.

Let's denote the length of the remaining four sides as "x."

Since the dog pen has six sides, we can set up an equation based on the total length of the fencing:

15 + 15 + x + x + x + x = 54

Simplifying the equation, we have:

30 + 4x = 54

Subtracting 30 from both sides, we get:

4x = 24

Dividing both sides by 4, we find:

x = 6

Therefore, each of the remaining four sides has a length of 6 meters.

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Answer:

It's 7.81

Step-by-step explanation:

The measure of the indicated arc angle is 134 degrees.

The angle subtended by the arc at the centre of the circle is the angle of the arc.

Therefore, the central angle of an arc is the angle at the centre of the circle between the two radii subtended by the arc.

Hence, the central angle is also known as the arc's angular distance.

Therefore, the measure of an arc is the measure of its central angle.

Hence, the measure of the indicated arc is 134 degrees.

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The cafeteria can conclude that a majority of the senior high school students like the newly served snack.

To determine if more than 50% of the students like the newly served snack, we need to analyze the responses of the 60 randomly selected students.

Analyzing the responses:

Out of the 60 students surveyed, we have:

- Number of students who responded with "1" (liking the snack): 32 students.

- Number of students who responded with "0" (not liking the snack): 28 students.

To determine the percentage of students who liked the snack, we divide the number of students who liked it by the total number of students surveyed and multiply by 100: (32/60) * 100 = 53.33%.

Since the percentage of students who liked the newly served snack is 53.33%, which is greater than 50%, we can conclude that more than 50% of the students like the snack based on the given survey results.

Therefore, the cafeteria can conclude that a majority of the senior high school students like the newly served snack.

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