4. *
This pattern of squares continues. Which equation below relates the number of squares, n, in a picture to the size number, s ?
Size 1
Size 2
a) n=s+4
b) n=4 s
c) n=4 s+1
d) s=4 n
A
B
c
D

Answer:

1464 Students

Step-by-step explanation:

10% increase of 1000 = 1100 year 1

10% increase of 1100 = 1210 year 2

10% increase of 1210 = 1331 year 3

10% increase of 1331 = 1464 year 4

Answer:

C

Step-by-step explanation:

All others can be proved false.

Answer and Step-by-step explanation:

Part A: Exponential equation is the "opposite" of logarithmic equation, so:

\(y=log_{b}m\)

\(b^{y}=m\)

Part B: Using log with base c:

\(log_{c}b^{y}=log_{c}m\)

Power property of logarithm states that if the anti-logarithm is elevated at a power, the elevated number can be pulled in front of the logarithm:

\(ylog_{c}b=log_{c}m\)

Solving for y:

\(y=\frac{log_{c}m}{log_{c}b}\)

Part C: To facilitate the use of calculators, which only have values for the base-10 log and natural log, we use change of base formula, i.e., transform

\(y=log_{b}m\)

into

\(y=\frac{log_{c}m}{log_{c}b}\)

Part D: \((log_{3}z)(log_{z}27)\)

Change of base will be:

\(log_{3}z=\frac{log_{10}z}{log_{10}3}\)

\(log_{z}27=\frac{log_{10}27}{log_{10}z}\)

Solving:

\((log_{3}z)(log_{z}27)\) = \((\frac{log_{10}z}{log_{10}3})(\frac{log_{10}27}{log_{10}z} )\)

\((log_{3}z)(log_{z}27)\) = \(\frac{log_{10}27}{log_{10}3}\)

\((log_{3}z)(log_{z}27)\) = \(\frac{log_{10}3^{3}}{log_{10}3}\)

\((log_{3}z)(log_{z}27)\) = \(\frac{3log_{10}3}{log_{10}3}\)

\((log_{3}z)(log_{z}27)\) = 3

Part E: \(log_{7}300\)

Using change of base:

\(log_{7}300=\frac{log300}{log7}\)

\(log_{7}300=\frac{2.48}{0.85}\)

\(log_{7}300\) ≈ 3

Answer:

B: alternate exterior angle

hope it helps.

Answer:

the relationship between t and y is B:Alternate exterior angles

The percentage that can be filled with $3 in 1990 is: 29.41%

To calculate percentage growth rate:

Beginning:

Calculate the difference (increase) between the two numbers you are comparing. after that:

Divide the increment by the original number and multiply the result by 100. Growth rate = increment / original number * 100.  

We are told that it cost $3 to fill a gas tank as at 1970.

Now, there was a percentage price increase of (78.8 - 23.1)% = 55.2% from 1970 to 1990. Thus:

Cost of a gallon in 1970 = $0.36

Thus, number of gallons bought with $3 = 3/0.36 = 8.33 gallons at full tank

Now, in 1990, the cost is $1.23 and as such:

Quantity that can be bought = 3/1.23 = 2.45 gallons

Percentage of tank filled = 2.45/8.33 * 100% = 29.41%

Read more about Percentage increase at: https://brainly.com/question/11360390

#SPJ1

Answer:

y= 11x

Step-by-step explanation:

find the slope: 22-11/2-1= 11/1 or 11

To find the y-intercept you can use the slope by subtracting 11 (inverse operation) from the y value of (1,11). So the y- intercept is (0,0). To write the equation plug in 11 for m and 0 for b. Since 0 has no value the equation would be y= 11x

Answer:

\(\huge\boxed{\bf\:19}\)

Step-by-step explanation:

Given,

Now, the expression is: \(20 - (3y - 4x)\).

To solve this question we just need to substitute the values of x & y in the given expression. Then,

\(20 - (3y - 4x)\\= 20 - (3(7) - 4(5))\\= 20 - (21 - 20)\\= 20 - 1\\= \boxed{\bf\:19}\)

\(\rule{150pt}{2pt}\)

Mary has left with a 1 kilometer  i.e. \(\frac{2}{7}\) of the journey is incomplete

Given that Mary is going for a 3.5 km walk. So far she’s walked 1.55 km through the park, 0.6 km across the bridge, and 0.35 km up the hill and asked to find the  fraction of the walk she has left

Total journey distance = 3.5 kilometers

Distance walked by mary on the bridge=0.6 kilometers

Distance walked by mary through the park=1.55 kilometers

Distance walked by mary up the hill=0.35 kilometers

Total distance traveled by mary=(0.6+1.55+0.35)kilometers

Total distance traveled by mary=2.5 kilometers

The distance left=3.5 kilometers-2.5 kilometers

The distance left=1 kilometer

1 kilometer is  \(\frac{2}{7}\) of the journey by assuming 3.5 kilometer will complete the jouney

Therefore, Mary has left with a 1 kilometer  i.e. \(\frac{2}{7}\) of the journey is incomplete

Learn  more about kilometer here:

https://brainly.com/question/13987481

#SPJ9

The equation for the proportion, p, of consumers who shop with coupons is: p = C/N where C is the number of consumers who use coupons and N is the total number of consumers asked.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

This equation represents the ratio of the number of consumers who use coupons to the total number of consumers. It is commonly used in statistics and market research to measure the prevalence of a certain behavior or preference among a population. By calculating the proportion of consumers who use coupons, businesses can make informed decisions about their pricing strategies, promotions, and advertising campaigns.

To know more about equation,

https://brainly.com/question/2228446

#SPJ9

An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

Read more on rotation here: brainly.com/question/28854313

#SPJ1

\(\stackrel{\textit{one added to the }\sqrt{\qquad }}{1+\sqrt{\quad }}~~,~~ \stackrel{\sqrt{~~}\textit{ of a number and one}}{\sqrt{x+1}}\implies 1+\sqrt{x+1}\stackrel{\textit{equals}}{=}4 \\\\\\ \sqrt{x+1}=3\implies \left( \sqrt{x+1} \right)^2=3^2\implies x+1=9\implies \boxed{x=8}\)

Answer:

  4 minutes

Step-by-step explanation:

You want to know how long it takes to drain a cylindrical tank 1.8 ft in diameter and 3 ft long at the rate of 1.7 ft³/minute. (π = 3.14)

The volume of a cylinder can be found using the formula ...

  V = (π/4)d²h . . . . . . . diameter d, height h

Then the volume of the oil tank is ...

  V = 3.14/4(1.8 ft)²(3 fft) = 7.6302 ft³

The time it takes to empty the tank is found by dividing the volume by the rate:

  (7.6302 ft³)/(1.7 ft³/min) ≈ 4.49 min ≈ 4 min

It will take about 4 minutes to empty the tank.

<95141404393>

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

learn more about word problem from

https://brainly.com/question/21405634

#SPJ1

The strongest correlation is represented by -0.97. It can be find out using knowledge of correlation coefficients.

What is the correlation coefficient between 1 and -1?

The formula returns a value between 1 and -1 :

where 1 indicates a strong positive relationship and -1 indicates a strong negative relationship.

According to the rule of correlation coefficients , the strongest correlation is considered when the value is closet to either (+1) or (-1).

So, in given options -0.97 is closet to (-1).

Learn more about correlation coefficients using given link :
https://brainly.com/question/3560028

#SPJ1

Answer:

3.Yes, because triangle ABC has a 90 degree angle.

4.No, because triangle XYZ doesn’t have a 90 degree angle.

a. The areas of the square is 81m² and for rectangle is 72m²

b. The perimeter of the square is 40m

a. To determine the area of the shapes in which we have that have a perimeter of 36m, we can consider rectangle and square.

For a square;

Perimeter of square = 4L

36 = 4L

L = 9m

The area of the square will be L² = 9² = 81m²

For a rectangle;

The perimeter of rectangle is;

P = 2(L + W)

We can assume that two numbers which will represent the length and width are;

L = 12m, W = 6m or L = 6m, W = 12m

A = 12 * 6 = 72m²

b.

The area of the wire is 100m², the perimeter for this can be calculated when we consider square and rectangle;

Perimeter of square = 4L

Area of square = L² = 100m²

L = 10m

The perimeter of the wire is 4(10) = 40m

Learn more on perimeter and area of rectangle and square here;

https://brainly.com/question/25292087

#SPJ1

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

Learn more about integrations here:

https://brainly.com/question/30217024

#SPJ1

Complete question is;

In a class of 40 students, 17 have ridden an airplane, 28 have ridden boat, 10 have ridden a train, 12 have ridden an airplane and a boat, 3 have ridden a train only, and 4 have ridden airplane only. Some students in the class have not ridden any of the three modes of transportation and an equal number have taken all three. How many students have used all three modes of transportation?

Answer:

4 students

Step-by-step explanation:

Let the number of students who used airplane be A

Let the number of students who used boat be B

Let the number of students who used train be C

Now, we are told that 17 rode plane.

Thus; A = 17

28 rode boat; B = 28

10 rode train; C = 10

12 rode airplane and boat; A ∩ B = 12

4 rode plane only; A' = 4

3 rode boat only; C' = 3

Total number of students; T = 40

Now, total number of students is represented by;

T = A - B - C - (A ∩ B) - (B ∩ C) - (C ∩ A) + (A ∩ B ∩ C)

We don't have (B ∩ C) and (C ∩ A).

Now, the can be derived from the expression of C' which is;

C' = C - (B ∩ C) - (C ∩ A)

C' = C - [(B ∩ C) + (C ∩ A)]

We are given C' = 3 and C = 10

Thus;

3 = 10 - [(B ∩ C) + (C ∩ A)]

10 - 3 = [(B ∩ C) + (C ∩ A)]

7 = [(B ∩ C) + (C ∩ A)]

Rearranging the total number of students equation, we now have;

T = A - B - C - (A ∩ B) - [(B ∩ C) + (C ∩ A)] + (A ∩ B ∩ C)

Where;

(A ∩ B ∩ C) is the number of students that used all three modes of transportation.

Thus, plugging in the relevant values;

40 = 17 + 28 + 10 - 12 - 7 + (A ∩ B ∩ C)

40 = 36 + (A ∩ B ∩ C)

(A ∩ B ∩ C) = 40 - 36

(A ∩ B ∩ C) = 4

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

for more search question point  

https://brainly.com/question/28162977

#SPJ8

Entry ticket = $7

Gift shop money = $g

Maximum to spend = $30

Inequality => 7+g ≤ 30

Hope it helps!

The required graph of the given equation y=x+2, y=-x+2, and y=|x|+2 has been shown.

The first equation, y = x + 2, represents a straight line with slope 1 and y-intercept 2. The graph passes through the point (0, 2) and has a positive slope, which means it slants upwards from left to right.

The second equation, y = -x + 2, also represents a straight line, but with slope -1 and y-intercept 2. The graph passes through the point (0, 2) and has a negative slope, which means it slants downwards from left to right.

The third equation, y = |x| + 2, represents the absolute value function of x translated up 2 units. The graph of y = |x| is a V-shape with its vertex at the origin, and when we add 2 to every y-coordinate, the graph is shifted upwards by 2 units. The resulting graph has a V-shape with its vertex at (0, 2).

Learn more about the graph of the equation here:

https://brainly.com/question/16905822

#SPJ1

let

the smaller number = x

the larger number = y

x + y = 30

4y + 6x = 128

The numbers are 4 and 26.

Answer:

3+(x*2)=amount of tulips planted

Answer:

24

Step-by-step explanation:

i dont know if its correct

The correct answer is C. It is the graph of f(x) translated 11 units to the left.

The correct answer is:

C. It is the graph of f(x) translated 11 units to the left.

When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.

In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.

The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.

Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.

for more such question on graph visit

https://brainly.com/question/19040584

#SPJ8

The logarithmic function f(x) = a·log₃(x - 4), passing through the points (13, 7), has the values;

5 a. The value of a is 3.5

b. Please find attached the graph of the function, f(x) = 3.5·log₃(x - 4), created with MS Excel

A logarithmic function is a function that contain and involves logarithm operation and it is the inverse of an exponential  function

The function is f(x) = a·log₃(x - 4),

x > 4 and a > 0

The coordinates of a point on the graph of the function, f is A(13, 7)

5 a. The value of a can be found by plugging in the value of (13, 7) = (x, f(x)), as follows

f(13) = 7 = a·log₃(13 - 4) = a·log₃9 = a·log₃3²

7 = a·log₃3²

7 = 2·a·log₃3 = 2·a·1 = 2·a

2·a = 7

a = 7 ÷ 2 = 3.5

a = 3.5

5 b. The coordinates of the x-intercept of the graph = (5, 0)

The equation of the function is;

f(x) = 3.5·log₃(x - 4)

A third point on the graph is given when f(x) = 14 as follows;

f(x) = 14 = 3.5·log₃(x - 4)

log₃(x - 4) = 14 ÷ 3.5 = 4

3⁴ = x - 4

x = 3⁴ + 4 = 85

Which gives the point, (85, 14)

Similarly, we have the point (31, 10.5), (7, 3.5)

Please find attached the graph of f(x) created with MS Excel

Learn more about logarithmic functions here:

https://brainly.com/question/28033379

#SPJ1