$1,000 is deposited into a savings account. Interest is compounded annually. After 1 year, the value of the account is $1,020. After 2 years, the value of the account is $1,040. 40. This scenario can be represented by an exponential function of the form fx=1000bx, where fxis the amount in the savings account, and x is time in years. What is the value of b?

Answer:

U HAD IT RIHH THERE..........GO ON b AND D

Step-by-step explanation:

After answering the prοvided questiοn, we can cοnclude that As a result, equatiοn the range οf the relatiοnship 3x + y = 3 is 9, -3, -9.

An equatiοn is a statement in mathematics that states the equality οf twο expressiοns. An equatiοn has twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The gοal οf equatiοn sοlving is tο determine which variable(s) must be changed in οrder fοr the equatiοn tο be true.

Simple οr cοmplicated equatiοns, regular οr nοnlinear equatiοns, and equatiοns with οne οr mοre factοrs are all feasible. In the equatiοn "x² + 2x - 3 = 0," fοr example, the variable x is raised tο the secοnd pοwer. Lines are used in a variety οf mathematical disciplines, including algebra, calculus, and geοmetry.

Tο determine the range οf the relatiοnship 3x + y = 3, we must first sοlve fοr y in terms οf x:

3x + y = 3

y = 3 - 3x

We can nοw use the given x values in the equatiοn tο find the cοrrespοnding y values:

When x = -2:

y = 3 - 3(-2) = 9

When x = 2:

y = 3 - 3(2) = -3

When x = 4:

y = 3 - 3(4) = -9

As a result, the range οf the relatiοnship 3x + y = 3 is 9, -3, -9.

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Answer:

The slope of the line passing through the points (1, -1) and (4, 8) is 3.

Step-by-step explanation:

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the following formula:

\(slope = (y2 - y1) / (x2 - x1)\)

Here, the given points are (1, -1) and (4, 8). So,

\(slope = (8 - (-1)) / (4 - 1) = 9 / 3 = 3\)

Therefore, the slope of the line passing through the points (1, -1) and (4, 8) is 3.

The mean, standard deviation and variance, respectively, for the 10 day vacation are given by:

a) The mean is of $2,470.

b) The standard deviation is of $189.74.

c) The variance is of $²36,000.

The mean is the sum of the observations divided by the number of observations in the data-set.

By the Central Limit Theorem, when n instances of a data-set with mean M are formed, the mean becomes n x m, hence:

247 x 10 = $2,470.

The standard deviation is the square root of the sum of the differences squared between each observation and the mean, divided by the number of observations of the data-set.

By the Central Limit Theorem, when n instances of a data-set with standard deviation \(\sigma\) are formed, the standard deviation is given by:

s = \(\sigma\sqrt{n}\)

For this problem, we have that the measures are:

\(\sigma = 60, n = 10\)

Hence:

s = 60 x sqrt(10) = $189.74.

The variance is the square of the standard deviation, hence:

s² = ($189.74)² = $²36,000.

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Answer:

option b a circle with a radius of 21.0 CM

The frequency distribution of the commute time in minutes is:

Commute time   Frequency

1 - 15                        10

16 - 30                      18

31 - 45                        11

46 - 60                        5

61 - 75                        0

76 - 90                        1

The distribution of the commute time in minutes is given as

Commute time​ (minutes) frequency

60 15 35 30 15 45 10 15 15 30 30 30 45 30 20 20 15 45 60 15 30 30 60 30 45 30 12 45 20 10 45 45 35 60 20 20 30 4 80 45 30 60 45 25 30

From the question, we have:

Frequency = 45

Minimum lower class limit = 1

Class width = 15 minutes

This means that the class intervals are

1 - 15, 16 - 30, 31 - 45, 46 - 50.......

When the distribution of the commute time in minutes is sorted into the class intervals, we have:

1 - 15: 15 15 10 15 15 15 15 12 10 4

16 - 30: 30 30 30 30 30 20 20 30 30 30 30 20 20 20 30 30 25 30

31 - 45: 45 35 45 45 45 45 45 45 45 35  45

46 - 60: 60 60 60 60 60

61 - 75:

76 - 90: 80

Determine the frequencies

1 - 15:    10

16 - 30: 18

31 - 45: 11

46 - 60: 5

61 - 75: 0

76 - 90: 1

Hence, the frequency distribution of the commute time in minutes is:

Commute time   Frequency

1 - 15                        10

16 - 30                      18

31 - 45                        11

46 - 60                        5

61 - 75                        0

76 - 90                        1

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The cost of constructing the path at the rate of Rs. 25 per m2 would be Rs. 38,465.

To find the cost of constructing the path, we need to determine the area of the path and then multiply it by the cost per square meter.

The total diameter of the pond and the path is 21m + 3.5m + 3.5m = 28m.

So the radius of the pond is half of the diameter, which is 21m/2 = 10.5m.

The radius of the pond with the path is (21m+3.5m)/2 = 12.25m.

Area of the path = Area of the outer circle - Area of the pond

\(= π(12.25)^2 - π(10.5)^2\)

\(= π[(12.25)^2 - (10.5)^2]\)

= 3.14 x (24.5 + 10.5) x (24.5 - 10.5)

= 3.14 x 35 x 14

= 1538.6 m2 (rounded to one decimal place)

Therefore, the cost of constructing the path at the rate of Rs. 25 per m2 would be:

Cost = Area x Rate per m2

= 1538.6 x 25

= Rs. 38,465.

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Answer:

168cm

Step-by-step explanation:

Length: 8cm

Width: 3cm

Height: 7cm

I divided 8 and 7 first and got 56.

Next I multiplied 56 and 3 and got 168.

So the length is 168cm

(Hope this helped! <3)

(sorrry if its wrong I feel stupid today)

From the figure, the maximum is (5, 11) and the minimum is (20, 2).

Maxima and minima are the peaks and valleys in the curve of a function. There can be any number of maxima and minima for a function. In calculus, we can find the maximum and minimum value of any function without even looking at the graph of the function. Maxima will be the highest point on the curve within the given range and minima would be the lowest point on the curve.

7) In the figure 7,

The maximum is (5, 11) and the minimum is (20, 2)

Domain = {0, 5, 12, 20}

Range = {2, 11, 9, 2}

8) In the figure 8,

The maximum is (0, 8) and the minimum is (16, 0)

Domain = {0, 3, 6, 8, 12, 16}

Range = {8, 1, 4, 2, 6, 0}

Therefore, from the figure, the maximum is (5, 11) and the minimum is (20, 2).

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The volume of the cylinder  V = πr²h. Therefore, we need to have more information about the cylinder's height in order to solve this problem.

To find the volume of the cylinder, we first need to know the height of the cylinder. However, the height is not given in the question. Therefore, we cannot determine the volume of the cylinder with the given information.

We can use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height.

Since r = 11 units and x = 15 units, we can find the diameter of the base of the cylinder by multiplying r by 2, which gives us 22 units. However, we still do not know the height of the cylinder.
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Step-by-step explanation:

x = ??

y = 72 + 40 = 112

x =112 - 180

x = 180-112

x = 68

or = 180 - 72 = 108

180 - 40 = 140

140 - 108 = 32

Answer:

The green box would be \(\frac{1}{8}\).

Step-by-step explanation:

\(\frac{1}{2^{3}} = \frac{1}{8}\)

Answer:

Step-by-step explanation:

R.A. = 50(1 - .5)^3

your question askes for the decay factor "green box"

that number is 1/2 (.5)

Answer:

b=34

Step-by-step explanation:

<a(340 corresponds to <b

Answer:

4x - 8 + 5x + 26 = 180

9x + 18 = 180

9x = 162

x = 18

angle FGD = angle CGE = 4(18) - 8 = 64°

angle EGD = angle CGF = 5(18) + 26 = 116°

Answer:

\(\huge\boxed{\sf d < 7}\)

Step-by-step explanation:

Given inequality is:

d + 6 < 13

Subtract 6 to both sides

d < 13 - 6

d < 7

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

8 moles.

Moles is the amount of oxygen and not pressure, volume or mass.

Step-by-step explanation:

9514 1404 393

Answer:

  16 moles

Step-by-step explanation:

At the same pressure and temperature, double the volume will hold double the quantity of gas. There will be 16 moles of oxygen if the volume is doubled at the same temperature and pressure.

Answer:

he read 11

Step-by-step explanation:

Answer:

there are 225 total coins in her collection

Answer:

there isn't a slope, because this line isn't even a function, because it is a vertical line... so it doesn't pass the vertical line test...

Step-by-step explanation:

Answer:

undefined

Step-by-step explanation:

the equation for the slope of the line is (y2-y1)/(x2-x1)

here are the given points: (-6,-8) and (-6,12)

label the points:

x1=-6

y1=-8

x2=-6

y2=12

now substitute into the equation (m is slope)

m=(12--8)/(-6--6)

m=(12+8)/(-6+6)

m=20/0

m=undefined

the slope is undefined because you cannot divide by 0

Hope this helps!

Given:

Consider the number as x.

The objective is to represent algebraic expression for, 2 is subtracted from the square of a number.

Explanation:

Since the number is given as x, the square of the number can be represented as,

Now, subtract 2 from the above expression,

Hence, the required expression is x²-2.

Answer:

r = -6 cos(θ)

Step-by-step explanation:

got it right on edge

The equation (x + 3)² + y² = 9 into polar form is r = -6 cos(θ). The correct answer would be option (A).

The polar form of a complex number is given by r(cos(θ) + i sin(θ)), where r is the distance from the origin and θ is the angle formed by the point and the positive x-axis.

To convert the equation (x + 3)² + y² = 9 into polar form, we can complete the square on the x and y terms:

(x + 3)² + y² = (x² + 6x + 9) + y² = 9

Then we can express x and y in terms of r and θ:

x = r cos(θ) , y = r sin(θ)

Substituting these values into the equation and simplifying:

r² cos²(θ) + 6r cos(θ) + r² sin²(θ) = 9

r²(cos²(θ) + sin²(θ)) + 6r cos(θ) = 0

r² + 6r cos(θ) = 0

r(r + 6cos(θ)) = 0

Since r ≠ 0

So, the polar form of the equation is:

r = -6cos(θ)

Thus, the correct answer would be an option (A).

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In the total amount of $261,000 received from contributors, a majority of $240,000 came from four contributors, with each contributing $60,000. The remaining $21,000 was obtained from smaller individual contributions.

This statement describes the breakdown of contributions received from different sources. Out of the total amount of $261,000, the majority, which is $240,000, came from four specific contributors. Each of these contributors donated $60,000, resulting in a combined contribution of $240,000. The remaining $21,000 represents the sum of smaller individual contributions from various sources.

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A real-world example of an enlargement transformation can be observed in the field of architecture and construction.

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Answer:

Picture please

Step-by-step explanation:

I cannot identify the 3-D shapes unless if there is a picture.

The total volume of the solid is 2,160 unit³.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies.

The unit of volume is in cubic units such as m3, cm3, in3 etc.

First, Base area

= 1/2 x b x h

= 1/2 x 15 x 12

= 15 x 6

= 90 unit²

Now, Volume of Figure

= Base area x h

= 90 x 24

= 2,160 unit³

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The exact numerical value of this expression depends on the precision of the decimal approximations of e.

To find the area A of the region bounded between the curve f(x) = 4 - e²x - 1 and the line g(x) = 2x + 1 over the interval [-2, 2], we need to calculate the definite integral of the absolute difference between the two functions over that interval.

Let's denote the absolute difference between f(x) and g(x) as h(x):

h(x) = |f(x) - g(x)| = |(4 - e²x - 1) - (2x + 1)| = |3 - e²x - 2x|

To find the area A, we integrate h(x) over the interval [-2, 2]:

A = ∫[-2,2] |3 - e²x - 2x| dx

Since the integrand is not continuous on the interval, we need to break it down into two separate integrals based on the intervals where the function changes sign. In this case, it happens at x = -1.

Therefore, the area A is given by:

A = ∫[-2,-1] (e²x + 2x - 3) dx + ∫[-1,2] (-e²x - 2x + 3) dx

Evaluating the integrals, we get:

A = [e²x + x²2 - 3x] [-2,-1] + [-e²x - x²2 + 3x] [-1,2]

Substituting the limits of integration, we have:

A = [(e²-1 + 1 - 3) - (e²-2 + 4 - 6)] + [(-e²2 - 4 + 6) - (-e²-1 - 1 + 3)]

Simplifying, we get:

A = [-e²-2 + e²-1 - 1] + [-e²2 + e²-1 + 3]

Therefore, the exact area A of the region bounded between the given curve and line over the interval [-2, 2] is:

A = -e²-2 + e²-1 - 1 - e²2 + e²-1 + 3

Note: The exact numerical value of this expression depends on the precision of the decimal approximations of e.

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Answer:m∠1 = 145°

m∠2 = 35°

m∠3 = 35°

m∠4 = 145°

m∠5 = 145°

m∠6 = 35°

m∠7 = 35°

m∠8 = 145°

Step-by-step explanation:

The required value of a is 20°.

In geometry, complementary angles are defined as two angles whose sum is 90 degrees. In other words, two angles that add up to 90 degrees are known as complementary angles.

Now it is given that,

m22 = (a + 15)° and m23 = (a + 35)°

Let m22 and m33 be the angle between HL and HJ.

And since HL is perpendicular to HJ therefore they are complement ot each other.

Thus,

m22 + m23 = 90°

⇒ (a + 15)° +  (a + 35)° = 90°

⇒ a° + 15° +  a° + 35° = 90°

⇒ 2a° +50° = 90°

⇒ 2a° = 90° - 50°

⇒ 2a° = 40°

⇒ a° = 40°/2

⇒ a° = 20°

Thus, the required value of a is 20°.

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The skeletons are 1056.474145 years old in 1989

Given:

Exponential decay model for carbon-14, A = A₀ e^(-0.000121 t)

The skeletons contained 88% of the expected amount of carbon-14 found in a living person

To determine how old the skeletons were, you will need to solve for t  in the exponential decay model:

A = A₀ e^(-0.000121 t)

A/A₀ = e^(-0.000121 t)          (Given: A/A₀ = 88%  = 0.88 )

0.88 = e^(-0.000121 t)

e^(-0.000121 t)  = 0.88

-0.000121 t = ln (0.88)

t = ln (0.88) / -0.000121

t = 1056.474145 years

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Examining the driving information between Roger and Rita we can say that

Since the Roger and Rita drive at constant speed we check their speed at 1 hour

Roger = in 1 hour covers a distance of 65 miles

Rita = in 1 hour covers a distance of 93 miles

Hence we can say that Rita has a head start,

solving for the head start

= 93 miles - 65 miles

= 22 miles

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