Write the equation function, in the form y = ab^x, whose graph passes through the coordinate points (2,12) and (3,24)

The areas of the composite figures are:

Case 1: 21 m²

Case 2: 217.5 m²

Case 3: 42 m²

Case 4: 168 cm²

Case 5: 252 m²

Case 6: 27 in²

Case 7: 39 cm²

Case 8: 44 cm²

Case 9: 558

Case 10: 70

Case 11: 78 cm²

Case 12: 21 ft²

In this problem we need to determine the areas of triangles, rectangles and composite figures formed by adding triangles and rectangles. The area formulas are introduced below:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Where:

The areas are now determined below:

Case 1:

A = 0.5 · (7 m) · (6 m)

A = 21 m²

Case 2:

A = (9 m) · (15 m) + 0.5 · (11 m) · (15 m)

A = 217.5 m²

Case 3:

A = 0.5 · (7 m) · (12 m)

A = 42 m²

Case 4:

A = 2 · 0.5 · (6 cm) · (8 cm) + 2 · 0.5 · (15 cm) · (8 cm)

A = 168 cm²

Case 5:

A = 2 · 0.5 · (7 m) · (9 m) + 2 · 0.5 · (21 m) · (9 m)

A = 252 m²

Case 6:

A = (9 in) · (2 in) + (3 in)²

A = 27 in²

Case 7:

A = (9 cm) · (3 cm) + (6 cm) · (2 cm)

A = 39 cm²

Case 8:

A = (4 cm) · (5 cm) + (2 cm) · (3 cm) + (3 cm) · (6 cm)

A = 44 cm²

Case 9:

A = 2 · 0.5 · 10 · 18 + 18 · 21

A = 558

Case 10:

A = 14 · 5

A = 70

Case 11:

A = (12 cm) · (6.5 cm)

A = 78 cm²

Case 12:

A = (3 ft) · (5 ft) + (3 ft) · (2 ft)

A = 21 ft²

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Answer: 23.9

Step-by-step explanation:

It's asking: after how many years will there be half of the sample remaining?

555e^-0.029t=555/2

Solving this gives you 23.9

The associated p-value for this left-tailed t-test is 0.0359 or 3.59%.

Now, The p-value for a one-tailed t-test with a sample size of 18 and a test statistic of 1.9,

Hence, we need to look up the t-distribution table.

So, Using a one-tailed test with,

df = n - 1

= 18 - 1 = 17 degrees of freedom

We find that the area to the left of 1.9 under the curve is 0.0359.

This means that there is a 3.59% probability of observing a t-statistic less than or equal to 1.9 if the null hypothesis is true.

Therefore, the associated p-value for this left-tailed t-test is 0.0359 or 3.59%.

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The expression in the form (x +a)² + b is shown below.

We have to expression given expression in the form (x +a)² + b.

1. x² + 12x

x² + 12x + 36 - 36

= (x +6)² - 36

2. x² + 3x - 2

x² + 2 . 3x /2 - 9/4 + 9/4 -2

(x+ 3/2)² - 17/4

3. x²+ 1/2 x

x² + 2 . 1/4 x + (1/2)² - (1/2)²

= (x+ 1/2)² - 1/4

4. x² - 2/9 x

=  x² + 2 . 2/20 x + 4/400 - 4/400

= (x+ 2/200)² - 1/100

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Answer:

To find the explicit equation for the nth term of an arithmetic sequence, we use the formula:

an = a1 + (n-1)d

where:

an represents the nth term of the sequence

a1 represents the first term of the sequence

d represents the common difference between consecutive terms in the sequence

In this case, we can see that the first term of the sequence is 7.2, and the common difference between consecutive terms is -3.4 (we subtract 3.4 from each term to get to the next term). Therefore, we have:

an = 7.2 + (n-1)(-3.4)

Simplifying this expression gives:

an = 7.2 - 3.4n + 3.4

which can be further simplified to:

an = 10.6 - 3.4n

So the explicit equation for the nth term of the arithmetic sequence 7.2, 3.8, 0.4, −3, −6.4, ... is an = 10.6 - 3.4n.

Step-by-step explanation:

The first circle have the values of x = 89° and y = 8.49. The second circle have values of x = 132° and y = 15.72. And the third circle have the value of a = 8.67.

Circle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.

For the first circle:

28° = x - 61° {secant tangent angle}

x = 28° + 61°

x = 89°

y² = 4 × 18

y = √72

y = 8.4853

For the second circle:

triangles formed by intersecting tangents are congruent so;

x = 2 × [180 - (24 + 90)]

x = 2 × 66°

x = 132°

tan 24 = 7/y {opposite/adjacent}

y = 7/tan 24

y = 15. 7223

For the third circle:

9(9 + a) = 21 × 8 {secant secant}

81 + 9a = 168

9a = 168 - 81

9a = 87

a = 87/9

a = 9.6667.

Therefore, the first circle have the values of x = 89° and y = 8.49. The second circle have values of x = 132° and y = 15.72. And the third circle have the value of a = 8.67.

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You would have $1.75 left before tax after purchasing all the vitamins.

Let's calculate the total cost of the vitamins first.

From the question, we can deduce the following:1 bottle of multivitamins = $3.751 bottle of vitamin D = $4.851 bottle of vitamin C = $2.95

Now, let's calculate the cost of what you got:2 bottles of multivitamins = 2 x $3.75 = $7.501 bottle of vitamin D = 1 x $4.85 = $4.852 bottles of vitamin C = 2 x $2.95 = $5.90

Total cost of the vitamins is = $7.50 + $4.85 + $5.90 = $18.25

If you have $20 (total amount) to spend on this purchase, after spending, you would have: balance = total amount - total cost balance = $20 - $18.25 balance = $1.75

So you would have $1.75 left before tax after purchasing all the vitamins.

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Using both hoses will take 10 minutes to fill up the kiddie pool. Mary can fill up 1/3 of the pool using the front yard hose in 10 minutes and 1/6 of the pool using the backyard hose in 10 minutes.

To solve this problem, we need to use the concept of rates. Let's assume the rate of the hose in the backyard is x, so the rate of the hose in the front yard is 2x (because it is twice as fast as the other hose).

The combined rate of the two hoses is x + 2x = 3x, which means they can fill the pool in 30/3x = 10/x minutes.

We know that the area of the pool is 600 square feet and each small rock covers 20 square feet, so we need a total of 600/20 = 30 small rocks to cover the pool.

Since the mass of each rock is 20 grams, the total mass of all 30 rocks is 30 x 20 = 600 grams.

To find the density, we divide the total mass (600 grams) by the total volume of the rocks (30 x 20 cubic feet = 600 cubic feet)

Density = 600g / 600 cubic feet = 1g/cubic foot

Therefore, the answer is B. 10 minutes for the pool to fill up, and the density of the rocks is 1 gram per cubic foot.

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Answer:

This is the formula:

1 degree = π/180 radians

To convert 70 degrees to radians, we can multiply by the conversion factor:

70 degrees × π/180 = 7π/18 radians

So 70 degrees is equal to 7π/18 radians.:)

The measure of the arc angle DE is derived to be 46.5055° using the arc length of the sector.

The arc measure DE and the angle it subtends at the center of the circle are directly proportional.

so arc DE = m∠DQE {central angle}

Arc length of the sector = (central angle / 360) x (2 x π x radius)

8.73 in = (m∠DQE / 360) x (2 x 22/7 x 10 in)

m∠DQE = (8.13 in × 360 × 7)/(2 × 22 × 10) {cross multiplication}

m∠DQE = 46.5055° = arc DE

Therefore, the measure of the arc angle DE is derived to be 46.5055° using the arc length of the sector.

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Housekeeping and cleaning are considered a service in the U.S. economy.

Option B is the correct answer.

We have,

A service is an economic activity where an immaterial exchange of value occurs between a producer and a consumer.

It is intangible and does not result in ownership or possession.

Examples of services include housekeeping and cleaning, healthcare, education, transportation, and entertainment. In contrast, goods are physical objects that can be owned or possessed, such as diesel fuel for trucks, milk, and bulk health foods.

Services play a significant role in the U.S. economy, accounting for a substantial portion of the country's gross domestic product (GDP)

Thus,

Housekeeping and cleaning are considered a service in the U.S. economy.

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The Area of Patio is 65.12 ft².

We have,

Bases of Trapezoid = 12 feet and 8 feet

Height of Trapezoid= 4 feet

So, the Area of Trapezoid

= 1/2 (Sum of base) x height

= 1/2 (12+8 ) x 4

= 1/2 x 20 x 4

= 10x 4

= 40 square feet

Now, Radius of semi circle = 8/2 = 4 feet

So, Area of semicircle

=  (1/2)πr²

= 1/2 (3.14)(16)

= 25.12 square feet

Thus, Area of patio

= 40 +  25.12

= 65.12 ft²

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Answer:

slope = - 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 5 ) and (x₂, y₂ ) = (3, - 5 )

m = [tex]\frac{-5-5}{3-(-2)}[/tex] = [tex]\frac{-10}{3+2}[/tex] = [tex]\frac{-10}{5}[/tex] = - 2

The 30th percentile of the data is 9 and the 75th percentile is 21.

The given data is 1, 3, 5, 6, 9, 10, 11, 13, 14, 15, 16, 18, 18, 24, 27, 31 and 32.

Here, consider 1, 3, 5, 6, 9, 10, 11, 13, 14

30th percentiles is 9.

Consider 15, 16, 18, 18, 24, 27, 31, 32

75th percentiles = (18+24)/2

= 42/2

= 21

Therefore, the 30th percentile of the data is 9 and the 75th percentile is 21.

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Answer:

The area of a trapezoid can be calculated as:

Area = (1/2) × (sum of bases) × (height)

In this case, the sum of the bases is 4m + 3m = 7m, and the height is 4m. Therefore:

Area = (1/2) × 7m × 4m = 14m²

So the area of the trapezoid is 14 m². The answer is O 14 m².

The compound amount after 3 years is $2275.22.

In this case, you are given:

Principle = $2,000

rate = 0.0353

time = 3

You need to find A, the compound amount after 3 years.

To do this, you need to plug in the values of P, r and t into the formula and use a calculator:

A=P×e^rt

A=2000×(e)^0.0353×3

A≈2275.22

Therefore, by the compound interest the answer will be $2275.22.

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Answer:

The correct answer is the second option: (-1,-2).

Step-by-step explanation:

To solve the system of equations:

2x - 4y = 6

2x + 4y = -10

We can use the method of elimination to eliminate one of the variables. Adding the two equations, we get:

4x = -4

Solving for x, we get:

x = -1

Substituting x = -1 in the first equation, we get:

2(-1) - 4y = 6

Simplifying, we get:

-2 - 4y = 6

Subtracting 2 from both sides, we get:

-4y = 8

Dividing by -4 on both sides, we get:

y = -2

Therefore, the solution to the system of equations is (-1, -2). So, the correct answer is (2nd option): (-1, -2).

[tex]\dfrac{x}{19.48} =0.189[/tex]

[tex]x=0189\times19.48[/tex]

[tex]\boxed{\bold{x=3.68172}}[/tex]

An equation of the linear function represented by the table below in slope-intercept form is y = -x + 4.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (2 - 5)/(2 + 1)

Slope (m) = -3/3

Slope (m) = -1

At data point (2, 2) and a slope of -1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = -1(x - 2)  

y = -x + 2 + 2

y = -x + 4

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The length of time that each workout plan lasts, given the total time that Greg took to train is :

Assuming the time taken for Plan A is x and the time taken for Plan B is y, the system of equations to represent the time taken per workout is:

3x + 5y = 10

6x + 2y = 10

Using elimination, we can solve for x:

(30 x + 10 y) - ( 6x + 10y ) = 50 - 20

24 x = 30

x = 30 / 24

x = 1.25

Then we can find y to be :

3x + 5y = 10

3 (1. 25 ) + 5 y = 10

y = 6. 25 / 5 = 1.25

In conclusion, both Plan A and Plan B lasts for 1.25 hours.

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Answer:

(x, y) = (-10, 0) and (x, y) = (-2, 0)

Step-by-step explanation:

To find the points on the x-axis that are a distance 5 from P(-6,3), we can use the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Since we want to find the points that are a distance of 5 from P(-6,3) on the x-axis, we know that y = 0 for these points. So we can simplify the distance formula to:

d = √((x - (-6))^2 + (0 - 3)^2)

d = √((x + 6)^2 + 9)

We want to find the values of x that make d = 5. So we can set up the equation:

5 = √((x + 6)^2 + 9)

Squaring both sides, we get:

25 = (x + 6)^2 + 9

Subtracting 9 from both sides, we get:

16 = (x + 6)^2

Taking the square root of both sides (remembering to include both the positive and negative square root), we get:

x + 6 = ±4

Subtracting 6 from both sides, we get:

x = -10 or x = -2

So the two points on the x-axis that are a distance of 5 from P(-6,3) are (-10, 0) and (-2, 0).

Therefore, the two answers are:

(x, y) = (-10, 0) and (x, y) = (-2, 0)

Answer:

(x, y) = (-10, 0)   (smaller x-value)

(x, y) = (-2, 0)     (larger x-value)

Step-by-step explanation:

To find the all the points on the x-axis that are a distance of 5 from P(-6, 3), we can use the distance formula.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where:\\ \phantom{ww}$\bullet$ $d$ is the distance between two points. \\\phantom{ww}$\bullet$ $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

As the distance is 5,  d = 5.

Let (x₁, y₁) = (-6, 3).

As the points to be found are on the x-axis, their y-coordinates are zero.

Therefore, let (x₂, y₂) = (a, 0).

Substitute these values into the distance formula:

[tex]\implies \sqrt{(a-(-6))^2+(0-3)^2}=5[/tex]

Simplify and solve for a:

[tex]\implies \left(\sqrt{(a+6)^2+(-3)^2}\right)^2=5^2[/tex]

[tex]\implies (a+6)^2+9=25[/tex]

[tex]\implies (a+6)^2+9-9=25-9[/tex]

[tex]\implies (a+6)^2=16[/tex]

[tex]\implies \sqrt{(a+6)^2}=\sqrt{16}[/tex]

[tex]\implies a+6=\pm 4[/tex]

[tex]\implies a+6-6=-6\pm 4[/tex]

[tex]\implies a=-10, -2[/tex]

Therefore, the points on the x-axis that are a distance of 5 units from P(-6, 3) are:

The probability that both officers will be seniors is 0.29 or 29%.

There are a total of 22 council members.

To find the probability that both officers are seniors, we need to find the probability of selecting a senior for the first officer and then a senior for the second officer.

The probability of selecting a senior for the first officer is 12/22 since there are 12 seniors out of 22 total members.

After one senior has been selected, there are only 11 seniors left out of a total of 21 remaining members.

Therefore, the probability of selecting another senior for the second officer is 11/21.

To find the probability of both events occurring together, we multiply the probabilities:

P(selecting 2 senior officers) = (12/22) x (11/21) = 0.287 or 0.29 (rounded to two decimal places).

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Answer:

Step-by-step explanation:

Hello! 12+60 does not need to be factored because it is not division. 12 + 60 = 72.

If you meant 12/60, then I can help you.

The factors of 12 are: 1, 2, 3, 4, 6, 12.
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

From this, we can see the greatest common factor they share is 12.

12/12 is 1, and 60/12 = 5. So, 12/60 = 1/5.

Answer:

17

Step-by-step explanation:

We can split the expression:

3² + 2³

into two terms:

3²   and   2³

We can evaluate each term individually, then add them at the end.

First, we can evaluate 3²:

3² = 3 × 3 = 9

Remember that an exponent specifies how many times a number should be multiplied by itself.

Next, we can evaluate 2³.

2³ = 2 × 2 × 2 = 8

Finally, we can add these two terms.

9 + 8 = 17

Answer:

Step-by-step explanation:

If the train was travelling nonstop for 5.5 hours, it would travel approximately 90 km. This can be estimated by observing the graph and finding the corresponding distance for 5.5 hours on the y-axis.

What is graph?

Graph is a data structure composed of nodes (vertices) and edges. It is a non-linear data structure that is used to represent relationships between objects, events, or ideas. Graphs are widely used in computer science, mathematics, engineering, and other fields for representing various types of data. Graphs can be used to represent a wide variety of data sets, including networks, social relationships, and even biological systems. Graphs can also be used to identify patterns, trends, and correlations in data.

The graph below shows the relation between time (hours) and distance (km) for a train trip that lasted from 0 to 7 hours.

The line of best fit is a linear line with a positive slope, indicating that the distance travelled increases as the time spent travelling increases. Therefore, it can be estimated that if the train was travelling nonstop for 5.5 hours, it would travel approximately 90 km. This can be calculated by observing the graph and finding the corresponding distance for 5.5 hours on the y-axis, which is approximately 90 km.

In conclusion, if the train was travelling nonstop for 5.5 hours, it would travel approximately 90 km. This can be estimated by observing the graph and finding the corresponding distance for 5.5 hours on the y-axis.

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Complete questions as follows-

On the grid below, draw a graph of the relationship between and for a trip that lasted from 0to 7 hours. 8Time (hours) If the train was traveling nonstop, how many would it travel in 5.5 hours?

Train A weighs 174.5 tons and Train B weighs 39.5 tons.

To solve the following problem we use Algebraic equations. An algebraic equation is a mathematical statement that uses algebraic symbols (such as variables, constants, and mathematical operations) to express a relationship between two or more quantities.

Since we don't know the weights of each train represent them with two different variables and form two algebraic equations as per the given condition. Solve both equations for the weights of two trains.

Here we have

Train A and Train B weigh a total of 241 tons train A is heavier than Train B the difference in their weight is 135 tons.

Let x be the weight of Train A and y be the weight of Train B in tons.

According to the given data,

=> x + y = 214 tons ---- (1)

=> x - y = 135 tons ---- (2)

Add (1) and (2)

=> x + y + x - y = 214 + 135

=> 2x = 349

=> x = 174.5 tons

From (1)

=> 174.5 - y = 135  

=> y = 174.5 - 135

=> y = 39.5

Therefore,

Train A weighs 174.5 tons and Train B weighs 39.5 tons.

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The equation of the linear relationship is y = 232x

We know that the general equation of the linear function is y = mx + c.

m is the slope of the line

x₁ = 2, y₁ = 464

x₂ = 15, y₂ = 3,480

The formula for Slope of the line = (y₂ - y₁)/(x₂ - x₁)

= (3480 - 464)/(15 - 2)

= 3016/13

= 232

The equation of a line

(y - y₁) = m(x - x₁)

(y - 464) = 232(x - 2)

y - 464 = 232x - 464

y = 232x

Therefore, the equation of the linear relationship is y = 232x

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The calculated value of the cost of the printer ink per ounce is $1.99

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

2300 ounces of printer ink costs $4,577

This means that

Ounces = 2300

Total costs = $4,577

using the above as a guide, we have the following:

Unit rate = Total costs / Ounces

substitute the known values in the above equation, so, we have the following representation

Unit rate = 4577 / 2300

Evaluate

Unit rate = 1.99

Hence, the printer ink costs $1.99 per ounce

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Answer:

the slope is 3,-6. this may not be correct wait for someone else whos really smart

Let's say the cost price of the box of noodles is x.

The grocer fixed the selling price at 25% above the cost price, which means he sold it for 1.25x.

But he allowed a 5% discount, so the selling price becomes 0.95(1.25x) = 1.1875x.

Now, the profit is the difference between the selling price and the cost price: 1.1875x - x = 0.1875x.

The profit percent is calculated as (profit/cost price) x 100.

So, the profit percent is (0.1875x/x) x 100 = 18.75%.

Therefore, the grocer's profit percent is 18.75%.