In art class, Jake is copying a detail from a painting. He pants slowly for the first few days, but
manages to increase his rate after that. The graph shows his
progress after he increased his rate.

The value of the sum of the series is are 234 and 10200

In an arithmetic series, the sum of the first "n" terms (Sn) is given by the formula:

Sn = n/2 * (a1 + an)

Where "a1" is the first term and "an" is the nth term.

For the first series, we have

In this series, a1=3 , an=36 , n=12

Plugging these values into the formula, we get:

Sn = 12/2 * (3 + 36)

Sn = 234

For the second series, we have

In this series, a1=3 , d = 2 , n=100

So, we have

an = a + (n - 1)d = 3 + 99 * 2 = 201

Plugging these values into the formula, we get:

Sn = 100/2 * (3 + 201)

Sn = 10200

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A cuboid has 6 faces and the formula for its total surface area is:

2lw + 2lh + 2wh, where l is the length, w is the breadth, and h is the height.

Given the total surface area of 1168 cm² and the length and breadth being 16 cm and 14 cm, respectively:

2(16)(14) + 2(16)h + 2(14)h = 1168

Expanding the expression:

448 + 32h + 28h = 1168

Combining like terms:

60h = 720

Dividing both sides by 60:

h = 12 cm

So the height of the cuboid is 12 cm.

Answer:

1

Step-by-step explanation:

Y intercept is 1

Y intercept is the point where the line crosses the y axis (point where x=0, you see the line crosses y axis at 1). Thus even if you put 0 in equation 9^x you will get 9^0 and anything power of 0 is 1.

The amount invested at 10% by $568.65 and investment rate is -

amount invested at 13%. is $5275

amount invested at 10%.  is $1171

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

here, we have,

Let x represent the amount invested at 13%.

Let y represent the amount invested at 10%.

$6,446 is invested, part at 13 % and the rest at 11%.

This means that

x + y = 6,446

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

Considering the amount invested at 13%,

P = x

R = 13%

T =1 year

I = (x × 13 × 1)/100 = 0.13x

Considering the amount invested at 10%,

P = y

R =10%

T = 1 year

I = (x × 10 × 1)/100 = 0.10y

If the interest earned from the amount invested at

13% exceeds the interest earned from the amount invested at

10% 10 % by $568.65, it means that

0.13x - 0.10y = 568.65,- - -- - - - - -1

Substituting x = 6,446 - y into equation 1, it becomes

0.13(6,446- y) - 0.10y =568.65

i.e. y= 1171

solving, we get,

x=5275

y= 1171

amount invested at 13%. is $5275

amount invested at 11%.  is $1171

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Assuming you meant 3/12, 1/3 and 1/2. The answer would be 5[tex]\frac{1}{4\\}[/tex].

Answer:

[tex]288\frac{0}{13}[/tex]

We can use the proportional method in this question

This case is a direct proportion

Direct proportion is a type of proportionality relationship. For direct proportion, as one value increases, so does the other value and conversely, as one value decreases, so does the other value. The symbol ∝ represents a proportional relationship.

We put the variable as x that represents the hour

We put it into a fractional form

[tex]\frac{312}{13} = \frac{x}{12}[/tex]

Cross Multiplying

[tex]312X12 = 13x[/tex]

[tex]3744 = 13x[/tex]

[tex]\frac{3744}{13} = x[/tex]

[tex]288\frac{0}{13} = x[/tex]

For a dozen cookies, 0.75 cups of sugar are needed in total.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

given, A cookie recipe calls for 1.5 cups of sugar for two dozen cookies.

Since,

For two dozen of cookies, there are a total of 1.5 cups of sugar required.

In 2 dozen cookies, required sugar = 1.5 cups

In 1 dozen cookies, required sugar = 1.5/2 cups

In 1 dozen cookies, required sugar = 0.75 cups

Therefore, The total number of cups of sugar required for one dozen cookies is 0.75.

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Answer:

Step-by-step explanation

y≥  2x + 3 is -6,2

The variance for waiting times for patients who are discharged after receiving treatment is more, so waiting times for patients who are discharged after receiving treatment is more variable.

In probability and statistics, variance is the actual value of the squared variation of a stochastic process from its mean value. Informally, variance calculates the degree to which a random group of numbers deviates from the mean value.

Another essential tool, the measurement of variance is equal to the square of the standard deviation.

Since the variance for waiting times for patients who are discharged after receiving treatment is more, so waiting times for patients who are discharged after receiving treatment is more variable.

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Factor Trees are diagrams that show the prime factorization of a number by breaking it down into smaller factors until only prime numbers are left.

Here are the factor trees for the numbers you provided:

8:

8

/

2 4

/

2 2

20:

20

/

2 10

/

2 5

27:

27

/

3 9

/

3 3

36:

36

/

2 18

/

2 9

/

3 3

72:

72

/

2 36

/

2 18

/

2 9

/

3 3.

To solve this, I used the process of prime factorization. Prime factorization is the process of finding the prime numbers that multiply together to form a given number.

The steps I followed to solve this problem are:

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Step-by-step explanation:

The average speed is 42 km/hr.

To calculate the average speed, you divide the total distance by the time it took to travel that distance:

189 km / 4.5 hours = 42 km/hr

[tex]\texttt{speed}=\dfrac{d}{t}[/tex]

distance = 189 km

time = 4.5 hours

[tex]\texttt{speed}=\dfrac{189}{4.5}[/tex]

[tex]\fbox{speed = 42 km/hr}[/tex]

The only table that represents both a linear and proportional relationship is table 4

A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal.

In the first table, we see that the proportion of y to x are;

-4/-2 = 2

-3/0 = undefined

-2/2 = -1

Second table shows that;

0/-1 = 0

2/0 = undefined

4/1 = 4

Third table shows that;

-4/-1 = 4

-1/0 = undefined

2/1 = 2

Fourth table shows that;

-1/-3 = 1/3

0/0 = 0

1/3 = 1/3

Looking at the tables. the only one that is a proportional relationship is table 4

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Answer:

The only table that represents both a linear and proportional relationship is table 4

How to identify a proportional relationship?

A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal.

In the first table, we see that the proportion of y to x are;

-4/-2 = 2

-3/0 = undefined

-2/2 = -1

Second table shows that;

0/-1 = 0

2/0 = undefined

4/1 = 4

Third table shows that;

-4/-1 = 4

-1/0 = undefined

2/1 = 2

Fourth table shows that;

-1/-3 = 1/3

0/0 = 0

1/3 = 1/3

Looking at the tables. the only one that is a proportional relationship is table 4

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Step-by-step explanation:

The exponential equation is y = 2700 ( 1 + 0.17 )ⁿ , where n = t , the number of hours since the start of the study

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the exponential equation be represented as y

Now , the number of bacteria cells = y

The number of hours since the start of the study = n = t

The initial number of bacteria = 2,700 cells

The percentage of increase in the cells = 17 %

So , The exponential growth formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

Substituting the values in the equation , we get

y = 2700 ( 1 + 0.17 )ⁿ

On simplifying the equation , we get

y = 2700 ( 1.17 )ⁿ

where n = t , the number of hours since the start of the study

Hence , the equation is y = 2700 ( 1.17 )ⁿ

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The total number of hours for Jim to drive 900 miles is given by the proportion A = 25 hours

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the number of hours for Jim to drive 900 miles be A

Now , the number of hours = 5 hours

The total distance traveled by Jim in 5 hours = 180 miles

Now , the distance traveled by Jim = 900 miles

And , the proportion will be

A / 900 = 5 / 180

Multiply both sides of the equation by 900 , we get

A = ( 5 x 900 ) / 180

On simplifying the equation , we get

A = 5 x 5

A = 25 hours

Hence , the number of hours is 25 hours

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The required decimal that is greater than the decimals shown in the diagram are 0.5, 0.32, and 0.4. Options B, C, and D are correct.

Decimal value is defined as showing the place value of the digits in a decimal number. If any proportion of the digit is lower than 1 it would be represented after the dot right to the absolute value,

here,
The decimal value is shown in the image,
= 31 / 100

= 0.31

From the options,
0.31 > 0.1
0.31 < 0.5
0.31 < 0.32
0.31 < 0.4

Thus, the required decimal that is greater than the decimals shown in the diagram are 0.5, 0.32, and 0.4. Options B, C, and D are correct.

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Answer:

3 and 20 are NOT factors of 50.

15, 2, 5, 50, 25, and 10 are factors of 50.

Step-by-step explanation:

Hope it helps! =D

Answer:

Below

Step-by-step explanation:

Solve the given equation for y

3x+9y = 18

9y = -3x + 18       divide by 9

y = - 1/3 x + 2     done

Answer:

I also believe it is -4.9 but I may be mistaken

Step-by-step explanation:

Answer:

Mixed number: 1  3/8

Improper fraction: 11/8

Step-by-step explanation:

The first circle is 1 whole  1 = 8/8

The second circle is 3/8 *

8/8 + 3/8 = 11/8

----------------------

If you want to write a mixed number as improper fraction just multiply the whole number by the denominator and add the numerator's fraction.

1  3/8 Mixed number

1x8=8

8+3=11

11/8 Improper fraction

-----------------------

* the second circle is not divided into 4 parts. It is divided into 8 equal parts. Each part is 1/8. There are three shaded parts which means 3/8.

----------------------

I hope this helps!

The equation of the line that is parallel to this line and passes through the point (-4,-6) is y = 7x + 22

The equation of the line that is perpendicular to this line and passes through the point (-4,-6) is y = -(1/7)x - 46/7

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

The slope intercept form of a line is:

y = mx + b

where m is the slope and b is the y intercept

Two lines are parallel if they have the same slope and are perpendicular if the product of their slope is -1.

Given the line:

y = 7x - 3

The slope is 7. The line parallel to this line would also have a slope of 7, while the line perpendicular have a slope of -1/7

The equation of the line that is parallel to this line and passes through the point (-4,-6) is:

y - (-6) = 7(x - (-4))

y = 7x + 22

The equation of the line that is perpendicular to this line and passes through the point (-4,-6) is:

y - (-6) = (-1/7)(x - (-4))

y = -(1/7)x - 46/7

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Answer:

13 since the second power (-3) is doubled.

Answer: The area of the base of the triangular pyramid is given as 15.6 in² and each side of the base is 6 in, so we can use the formula for the area of an equilateral triangle to find the height of the base:

A = (s^2 * sqrt(3)) / 4

where s is the side length of the triangle. Plugging in the values, we get:

15.6 = (6^2 * sqrt(3)) / 4

Solving for the height of the base, h:

h = (4 * 15.6) / (6^2 * sqrt(3)) = 4 / sqrt(3)

Next, we can use the Pythagorean theorem to find the height of the pyramid, since the slant height is given:

h^2 + (base/2)^2 = slant height^2

where base is the length of one side of the base of the pyramid. Plugging in the values, we get:

h^2 + (6/2)^2 = 8^2

Solving for h:

h = sqrt(64 - 9) = sqrt(55)

Finally, the surface area of the pyramid can be found using the formula:

SA = base area + (perimeter * slant height) / 2

where perimeter is the total length of the sides of the base. Plugging in the values, we get:

SA = 15.6 + (3 * 6 * 8) / 2 = 15.6 + 36 = 51.6 in²

So, the surface area of the triangular pyramid is 51.6 in².

Step-by-step explanation:

The graph of function g(x) is given by the following option:

First graph.

(right below the text).

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The definition of function g(x) for this problem is given as follows:

g(x) = f(x) + 2.

Meaning that it underwent a translation of 2 units up, hence the first graph is correct, as the values of x remain constant, just the values of y are increased by two for each point on the graph.

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Answer:

Sunrise: 95x5+25 = 500

Bright Eyes: 110x5= 550

Sunrise Will be 50$ Cheaper

oops sorry did my math wrong

Answer: Sunrise Hotel is cheaper by $50

Step-by-step explanation:

First, you do $95 x 5 nights = $475, and then add $25 and get $500 per night (Sunrise).

Then multiply $110 and 5 nights and get $550 per night (Bright Eyes).

Lastly, subtract $550 and $500 and get $50.

The total cost for a given number of notebooks is 30 + 3x

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

Headset = $30.00

Notebook = $3.00

The total cost for x number of notebooks can be calculated as follows:

$30.00 + (3.00 * x)

So, we have

Total Cost = 30 + 3x

The response in two decimal places is Total cost = 30.00 + x * 3.00

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The radius is the center of circle to its edge or half of a diameter so half of 4/5 is 0.4 since 0.8 / 2 = 0.4.

To find the volume we need to do the equation π r² h.

So, π x 0.4^2 x 10 = 5.02654825.

Round 5.02654825 to the nearest hundredth and it is 5.03.

Volume is 5.03.

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The area of the figure in this problem is given as follows:

A. 30 in².

The area of a triangle is given by half the multiplication of the base length by the height of the triangle.

Applying the Pythagorean Theorem, we can obtain the missing side length, as follows:

4² + x² = 6²

x² = 36 - 16

x² = 20

x = square root of 20

x = 4.47.

For a right triangle, one side is considered the height of the other, hence the sides are:

Hence the area of the triangle is then obtained as follows:

Area = 0.5 x 4 x 12.47

Area = 25 in².

Which is closest to 30 in².

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