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What is the constant rate of change of the graph below?


20
10
3
2

You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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Answer:

I'de say about 5.40$ would be a good 15% tip

Step-by-step explanation:

Answer:

5.40

Step-by-step explanation

Assuming the number of people who listen to the video increases by 45% each day, there would be approximately 24 new people who listen to the video on the 7th day after the initial 8 people.

According to the problem, the number of people listening to the video increases by 45% each day. Therefore, we can use the formula for compound interest to calculate the number of new people who listen to the video on the 7th day.

Let P be the initial number of people who listened to the video, which is 8.

Let r be the daily increase rate, which is 45% or 0.45 as a decimal.

Let n be the number of days, which is 7.

Then, the formula for compound interest is:

A = P(1 + r)^n

where A is the final number of people who listen to the video.

Plugging in the values, we get:

A = 8(1 + 0.45)^7

A ≈ 32

Therefore, the number of new people who listen to the video on the 7th day is approximately 32 - 8 = 24 people.

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The surface area of the triangular prism is 2016 \(feet ^2\), we get to the answer by adding area of all faces in this prism.

What is surface area ?

Surface area is the sum of the areas of all the faces or surfaces of a 3D object, measured in square units.

To find the surface area of the triangular prism, we need to calculate the area of each of its faces and then add them up.

First, let's find the area of the triangular base.

Area of triangle = (1/2) x base x height

Area of triangle = (1/2) x 18 x 24

Area of triangle = 216 \(feet ^2\)

Next, let's find the area of each rectangular face.

Area of rectangle = length x width

Area of rectangle 1 = 24 x 22 = 528 \(feet ^2\)

Area of rectangle 2 = 18 x 22 = 396 \(feet ^2\)

Area of rectangle 3 =  22 x 30 = 660 \(feet ^2\)

Now, we can add up the areas of all three faces to get the total surface area of the prism:

Surface area = area of rectangle (1+2+3) + 2 x area of triangle

Surface area = 528 + 396 + 660 + 2(216)

Surface area = 2016 \(feet ^2\)

Therefore, the surface area of the triangular prism is 2016 \(feet ^2\).

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The scale οf the drawing in the given question is 9.

A scale is the ratiο οf distance that is used tο represent large distance οn a single sheet οf map οr graph.

An equatiοn is a fοrmula in mathematics that expresses the equality οf twο expressiοns by cοnnecting them with the equals sign (=). The wοrd equatiοn and its cοgnates in οther languages may have subtly different meanings; fοr example, in French, an équatiοn is defined as cοntaining οne οr mοre variables, whereas in English, an equatiοn is any well-fοrmed fοrmula cοnsisting οf twο expressiοns linked by an equals sign.

The parking lοt is 54 meters wide in the real life but in the drawing it is οnly 6 centimeters.

The scale οf the the drawing is \(\frac{54}{6}=9\).

It means that for every 9 meters a 1 cm space is required in the drawing and this thing is applicable in the whole drawing.

Hence, the scale of the drawing is 9.

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To calculate the magnetic fields at points A to C in the figure, we need to consider the magnetic field generated by the long wires carrying a current of 10 A.

The magnetic field can be calculated using the Biot-Savart law or Ampere's law, depending on the configuration of the wires. Additional information or details about the orientation and arrangement of the wires are needed to provide a specific calculation of the magnetic fields at points A to C.

To calculate the magnetic fields at points A to C, we need more information about the orientation and arrangement of the wires in the figure. The magnetic field generated by a long wire carrying a current can be determined using the Biot-Savart law or Ampere's law.

However, without knowing the specific configuration of the wires, such as their lengths, positions, and orientations, it is not possible to provide a direct calculation of the magnetic fields at points A to C in unit vector notation. To obtain a precise calculation, additional details about the geometry of the wires and their relative positions with respect to points A to C are necessary.

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Answer: (-9, -3, -2, 6, 8)

Step-by-step explanation:

The relative frequency of the class interval 65-75 is .20.

The word 'relative' is used to indicate that an event is being considered in relation or in proportion to something else.

Frequency is a way to measure how often a particular event occurs. Relative frequency, on the other hand, is a way to measure how often a particular event occurs against total occurrences.

Given that: 50 participants scored between 65 and 75 on a test.

Hence,

The relative frequency of the class interval 65-75 = 75 - 65 = 20

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Answer:

\( \boxed{d = \frac{5}{3}}\)

Step-by-step explanation:

\(given \: points \: (2,1) \: and \: (1, - \frac{1}{3}): \\ d \: = \sqrt{ (x _{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} } \\ d \: = \sqrt{ (1 - 2)^{2} +( - \frac{1}{3} - 1)^{2} } \\ d \: = \sqrt{ ( - 1)^{2} +( - \frac{4}{3})^{2} } \\d \: = \sqrt{ (1) +( \frac{16}{9}) } \\d \: = \sqrt{ 1 + \frac{16}{9} } \\d \: = \sqrt{ \frac{9}{9} + \frac{16}{9} } \\d \: = \sqrt{ \frac{25}{9} }\\d \: = \frac{\sqrt{ 25 }}{\sqrt{ 9 }} \\d \: = \frac{ 5}{3} \)

Answer:

a > 12

Solutions can be anything over 12

Step-by-step explanation:

Well this one is pretty simple we just add 1 to both sides so the inequality turns into,

a > 12

Answer:

\(a>12\)

Step-by-step explanation:

\(a-1>11\)

Add \(1\) on both sides.

The \(a\) variable must be isolated on one side.

\(a-1+1>11+1\)

\(a>12\)

Answer: The friends who shared 2 chocolate chip cookies.

Step-by-step explanation: 3/2= 1.5  and 4/3= 1.3

1.5>1.3

hello

the probability of having a 2 on ine dice = 1/6

the probability of having a 6 on the other dice = 1/6

the probability of having a 2 on one dice and a 6 on the other dice = x

the probability of having a one dice of 2 and the other dice of 6 is equal to 1/36

Answer:

Line 3

Step-by-step explanation:

Proper solution step-by-step:

1. 3(x-2)=18

2. 3x - 6 = 18

3. 3x = 18 + 6

4. 3x = 24

5. x = 8

Answer:?

Step-by-step explanation:

The area of the sprinkled lawn is approximately 19.625 square meters.

The formula for the area of a circle is:

A = πr²

Where A is the area and r is the radius and π is constant pi ( 3.14 ).

If the sprinkler as a circle with a radius of 2.5 meters. The area that the sprinkler can cover is the area of this circle.

Here, the radius is 2.5 meters, so we can substitute that into the formula:

A = πr²

A = 3.14 × 2.5²

Area = 3.14 × 6.25

Area = 19.625 m²

Therefore, the area is 19.625 m²

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Answer:

x < -3

  _

explanation:

_ is under <

so its b

Answer:

\(x \leq - 3\)

Step-by-step explanation:

The dot on the line represents that the line is including the number on the dot. If dot in hollow, it would just be greater than or less than. Since the line if facing to the right towards the positive side, the numbers are greater than or equal to -3.

The area of the region enclosed by the curve y² = x²(1 − x²) is 1/6.

To find the area, we can integrate the square root of the expression inside the curve from x=0 to x=1. This gives us the definite integral ∫(0 to 1) √(x²(1 − x²)) dx = 1/6.


The equation y² = x²(1 − x²) represents a curve that is symmetric about both the x-axis and the y-axis. To find the area enclosed by this curve, we need to integrate the square root of the expression inside the curve from x=0 to x=1.

We can simplify the expression inside the square root as follows: x²(1 − x²) = x² - x⁴. So, the area of the region can be found by evaluating the definite integral ∫(0 to 1) √(x² - x⁴) dx.

We can use substitution to evaluate this integral. Let u = x² - x⁴, then du/dx = 2x - 4x³. Rearranging, we get x(2 - 4x²) dx = 1/2 du. So, the integral becomes 1/2 ∫(0 to 1) √u du.

Integrating this gives us (1/2) * (2/3) * u³/² evaluated from 0 to 1, which simplifies to 1/3. However, since we used the substitution u = x² - x⁴, we need to multiply the result by 2 to account for the other half of the curve, giving us a final answer of 1/6.

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\(y \: \alpha \: x\)

Let c be the constant

\(y = cx \\ 16 = c4 \\ c = \frac{16}{4} \\ c = 4\)

\(y = cx \\ y = 4 \times ( - 2) \\ y = ( - 8)\)

Answer:

y = 4x

Step-by-step explanation:

Given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 16 when x = 4 , then

16 = 4k ( divide both sides by 4 )

4 = k

y = 4x ← equation of variation

When x = - 2 , then

y = 4 × - 2 = - 8

A stratified sample size is a method of sampling where the population is divided into homogeneous subsets and a sample is taken from each subset.

A stratified sample is a method of sampling where the population is divided into distinct subgroups, or strata, based on specific characteristics. This method of sampling ensures that each stratum is represented in the sample in the same proportion as it is in the population. This ensures that the sample is representative of the population. Stratified sampling is useful when the population is heterogeneous, which means that it is composed of subgroups that vary significantly in size or composition. By stratifying the population, it is possible to ensure that each subgroup is adequately represented in the sample. This method also helps to reduce sampling errors, which can occur if the sample is not representative of the population. Stratified sampling is a useful tool for researchers who want to accurately represent the population in their sample.

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Answer:

1320 feet

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

Hi there!

1) Prove similarity

The two triangles are similar due to angle-angle similarity. They both have an angle measured 90 degrees and the angles of the two corners that touch are equal, because opposite angles are equal.

2) Solve for x

Now, we can set up a proportion to solve for x:

\(\frac{x}{4} =\frac{4.5}{6} \\x=\frac{4.5}{6} *4\\x=3\)

Therefore, x is 3 units long.

I hope this helps!

Answer:

-28

Step-by-step explanation:

We have the equation \(5x-3y\) and are given that \(x=-2, y=6\).  To solve this equation, we simply replace the variables with their real value.  In action, this would be \(5(-2)-3(6)=-10-18=-28\).

The correct statement is: Both expressions are equivalent to 264 when t = 9.

To determine whether the two expressions are equivalent, we can substitute the given values of t and compare the results.

Let's evaluate the expressions for t = 5 and t = 9.

Expression 1: 8(4t - 3)

Substituting t = 5:

8(4(5) - 3) = 8(20 - 3) = 8(17) = 136

Substituting t = 9:

8(4(9) - 3) = 8(36 - 3) = 8(33) = 264

Expression 2: 32t - 24

Substituting t = 5:

32(5) - 24 = 160 - 24 = 136

Substituting t = 9:

32(9) - 24 = 288 - 24 = 264

Comparing the results, we find that:

When t = 5, both expressions evaluate to 136.

When t = 9, both expressions evaluate to 264.

Therefore, the correct statement is: Both expressions are equivalent to 264 when t = 9.

It's important to note that neither of the other statements (Both expressions are equivalent to 157 when t = 5 or Both expressions are equivalent to 46 when t = 5) is true based on the calculations above.

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Using the relation between velocity, distance and time, it is found that the equation that describes a speed greater than Bolt's record-breaking speed in 2009 is:

\(v = \frac{d}{t}\)

In this problem:

Hence, his velocity is:

\(v = \frac{d}{t} = \frac{100}{9.58}\)

A velocity greater than his velocity is:

\(v > \frac{100}{9.58}\)

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Step-by-step explanation:

please give me brainlest

Answer: \(x= 187.5p\)

Step-by-step explanation:

Given : An equation relating packets to bytes of information : \(b = 1,500p\) where p represents the number of packets and b represents the number of bytes of information.

1 byte = 8 bits

Let x= Number of bits such that 1 b = 8x

Put b = 8x in given equation , we get

\(8x=1500p\)

Divide both sides by 8 , we get

\(x= 187.5p\)

Hence, the equation represent the relationship between the number of packets and the number of bits : \(x= 187.5p\)

Answer:

x=12000p

Step-by-step explanation:

It is Right

I Fink

Scientists found an animal skull during an excavation and tested the amount of carbon -14 left in it. They found that 55 percent of the carbon-14 in the skull remained.

55% of the Carbon is left in the skull.

If A₀ was the original amount of Carbon, the amount of Carbon that is remaining will be 55% of A₀  which equals 0.55A₀

Using the given equation:

\(A = A_{o}e^{-0.000124t}\\\\ 0.55A_{o} = A_{o}e^{-0.000124t}\\ \\0.55 = e^{-0.000124t}\\\\In(0.55) = In(e^{-0.000124t})\\\\In(0.55) = -0.000124t*In(e)\\\\In(0.55) = -0.000124t\\\\\)

\(t = \frac{In(0.55)}{-0.000124} \\\\t = 4821\)

Rounding of to nearest year, we can conclude that the animal was buried 4821 years ago.

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Answer:

Second Option

2x^10 y^12

Hope it helps....!

Answer:

\(\sf A) \quad \begin{cases}\sf y > -5x+5\\\sf y < -5x+12\end{cases}\)

B)  see below

C)  points C, E and F

Step-by-step explanation:

Given points:

A system of inequalities is a set of two or more inequalities in one or more variables.

To create a system of inequalities that only contains C and F in the overlapping shaded region, create a linear equation where points C, F and E are to the right of the line and a linear equation where points C, F, A, B and D are to the left of the line.

The easiest way to do this is to find the slope of the line that passes through points C and F, then add values to move the lines either side of the points.

\(\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{y_F-y_C}{x_F-x_C}=\dfrac{-4-1}{3-2}=-5\)

Therefore:

\(\sf y = -5x + 5\)  →  points C, F and E are to the right of the line.

\(\sf y=-5x+12\)  →  points C, F, A, B and D are the left of the line.

Therefore, the system of inequalities that only contains points C and F in the overlapping shaded regions is:

\(\begin{cases}\sf y > -5x+5\\\sf y < -5x+12\end{cases}\)

To graph the system of inequalities:

To verify that the points C and F are solutions to the system of inequalities created in Part A, substitute the x-values of both points into the system of inequalities.  If the y-values satisfy both inequalities, then the points are solutions to the system.

Point C (2, 1)

\(\implies \sf x=2 \implies 1 > -5(2)+5 \implies 1 > -5\quad verified\)

\(\implies \sf x=2 \implies 1 < -5(2)+12\implies 1 < 2 \quad verified\)

Point F (3, -4)

\(\implies \sf x=3 \implies -4 > -5(3)+5 \implies -4 > -10\quad verified\)

\(\implies \sf x=3 \implies -4 < -5(3)+12\implies -4 < -3 \quad verified\)

Method 1

Graph the line y = 7x - 4 (making the line dashed since it is y < 7x - 4).

Shade below the dashed line.

Points that are contained in the shaded region are the houses in which Erica is interested in living:  points C, E and F.

Method 2

Substitute the x-value of each point into the given inequality y < 7x - 4.

Any point where the y-value satisfies the inequality is a house that Erica is interested in living.

\(\sf Point\: A: \quad x=-5 \implies 5 < 7(-5)-4 \implies -5 < -39 \implies no\)

\(\sf Point\: B: \quad x=-4 \implies -2 < 7(-4)-4 \implies -2 < -32 \implies no\)

\(\sf Point\: C: \quad x=2 \implies 1 < 7(2)-4 \implies 1 < 10 \implies yes\)

\(\sf Point\: D: \quad x=-2 \implies 4 < 7(-2)-4 \implies 4 < -18 \implies no\)

\(\sf Point\: E: \quad x=2 \implies 4 < 7(2)-4 \implies 4 < 10 \implies yes\)

\(\sf Point\: F: \quad x=3 \implies -4 < 7(3)-4 \implies -4 < 17 \implies yes\)

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Answer: Scale factor is 4

Explanation:

56 / 14 = 4

I hope this helped!

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Answer:

The scale factor from Figure A to Figure B is 4

Step-by-step explanation:

As the sides of these triangles do not have angles for use to calculate the exact areas, allowing us to divide the larger triangle by the smaller to find the scale factor, we must look at the lengths of the sides within these two triangles. After inspection, we can see that corresponding sides may instead be divided into one another. For example,

56/14

64/16

28/7

These pairs of corresponding sides may be divided as so and all reach the conclusion of a value of 4. This means that the larger triangle has sides that are a multiple of 4 to the smaller triangle.

Thus the scale factor from Figure A to Figure B is 4!