1.5 x 10^9 and 1.1 x 10^8 as scientific notation

According to the given statement the first 13 words in this sequence add up to 260.

In mathematics, a sequence is an itemized group of elements where repeats are tolerated and order is significant. It has members, just like a set (also called elements, or terms). The length of the series is the number of items (potentially infinite). In contrast to a set, the same items might occur more than once in a sequence at various points, and unlike a set, the order is important. A sequence can be described formally as a function from natural numbers (the locations of the sequence's members) to the items at each of those positions. An indexed family, which is a function from an index set that may not be integers to another set of elements, can be thought of as a more extended version of a sequence.

We are informed that the order is2,5, 8, 11, ..... ..............(1)

The total of the first 13 terms must always be established.

Sum of n terms formula is

Sn (2a + (n − 1)d)

First term = a = 2 from

(1)The average difference is 3 (5-2=8-5=11-8=3).

via formula

S13 13 (2a +(13 – 1)d) 2S13 13

(2 x 2 + (13 - 1) 3) 213

(4+36)13 (40)

= 260

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Carl had 1920 dollars at first.

Given that Carl had $840 more than Daisy.

Let Daisy money = M

Carl Money = 840 + M

If Carl spent 3/4 and Daisy spent 3/5 of their money respectively. That is,

for Carl: 3/4 × (840 + M) = 630 + 3M/4

The remaining amount = (840 + M) - (630 + 3M/4)

Amount = 210 + M/4

for Daisy: 3/5 × M = 3M/5

The remaining amount = M - 3M/5

Amount = 2M/5

Daisy was then left with $60 more than Carl. Then,

2M/5 = 60 + 210 + M/4

2M/4 = 270 + M/4

Collect the like terms

2M/4 - M/4 = 270

M/4 = 270

M = 4 × 270

M = 1080 dollars

Since Carl had $840 more than Daisy, Carl amount = 840 + 1080

Carl amount = 1920 dollars

Therefore, Carl had 1920 dollars at first.

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The quadratic function h(x) = x^2 - 12x + 36 is a quadratic function in standard form

The quadratic function is given as:

h(x) = x^2 - 12x + 36

Quadratic functions in standard form are represented as

h(x) = ax^2 + bx + c

Where the value of a is not 0

This means that we can conclude that h(x) = x^2 - 12x + 36 is a quadratic function in standard form

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Factors estimate 5,897 times 67

The estimate product of the factors 5897 times 67 is 383500.

We have to use strategies to estimate the products.

We can round each factor to the greatest place value which is the place value farthest to the left.

we can use compatible numbers.

compatible numbers are friendly numbers they are easy to compute numbers.

Given 5897[tex]\times[/tex]67=395099

This is the actual factor

But the estimation product is

We use mental math and compatible numbers here.

step1: 5900[tex]\times\\[/tex]70=413000

step2:5900[tex]\times[/tex]65=383500

Both the step1 and step2 are reasonable because the factor are close to the actual factor.

But 5900[tex]\times[/tex]65=383500 is better because it is very close to the actual factor compared to 5900[tex]\times\\[/tex]70=413000.

Therefore, The estimate product of the factors 5897 times 67 is 383500.

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Using linear functions, we have that:

a. Sara will have driven 2.25 hours when Pedro catches up with her.

b. They are 146.25 miles from home when Pedro catches up with Sara.

A linear function is modeled by:

y = mx + b

In which:

We have to consider the starting time as when Pedro leaves, when Sara will be at position 45 miles. Considering the velocities as the slope, the functions are:

Pedro will catch up with Sara when:

P(t) = S(t)

Hence:

65t = 45t + 45

20t = 45

t = 45/20

t = 2.25 hours.

Sara will have driven 2.25 hours when Pedro catches up with her.

The distance from home will be given by:

P(2.25) = S(2.25) = 65(2.25) = 45(2.25) + 45 = 146.25.

They are 146.25 miles from home when Pedro catches up with Sara.

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The pounds of green beans in the vegetable medley is 2.78 pounds

Pounds of green beans in the vegetable medley = Fraction of green beans in vegetable medley × Total pounds of vegetable medley

= 5/9 × 5

= (5 × 5) / 9

= 25 / 9

= 2.777777777777777 pounds

Approximately,.

Pounds of green beans in the vegetable medley = 2.78 pounds

Therefore, the pounds of green beans in the vegetable medley is 2.78 pounds

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Answer:

option 3

Step-by-step explanation:

4x² - 100 = 0 ( add 100 to both sides )

4x² = 100 ( divide both sides by 4 )

x² = 25 ( take square root of both sides )

x = ± [tex]\sqrt{25}[/tex] = ± 5

then

x = - 5 , x = 5

Answer:

D has the coordinate 17

Step-by-step explanation:

Given

DE  has as the mid point H at 5

D > E

DE = 24

Find the coordinate of D

5 + (24/2) = 5+12 = 17

Answer:

c.143

Step-by-step explanation:

No estoy seguro de que esté Mal o mal

The proportion of the measurements lie in the interval is 0.9.

According to the given question.

Weigths of 10 young dogs.

W : 7, 5, 11, 8, 14, 19, 16, 15, 13, 27

As we know that mean si calculated by the formula

Mean = ΣW / n

Thereofre, the mean of the weights of 10 young dogs

= 7 + 5 + 11 + 8 + 14 + 19 + 16 + 15 + 13 + 27/ 10

= 13.5

And, Standard deviation (s) = 6.433

Proportion that lies in mean ± 2s

Lower = Mean - 2s

⇒ 13.5 - 2(6.433) = 0. 632

Also, Upper = Mean + 2s

⇒ 13.5 + 2(6.433) = 26.376

Mean ± 2(sd) = (0.632, 26.276)

The only digit from the data which falls outside the defined range = 27

Proportion within interval = 9 / n

Proportion which falls within interval = 9/10 = 0.9

Hence, the proportion of the measurements lie in the interval is 0.9.

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When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

Given,

The cost of Carpet per square foot = $4

Total cost of the carpet = $616

We know

Area of the rectangle = Length × Width

Length = 14 feet

Consider the width of the rectangular room as x

Then the area of the room = 14x

Total cost of carpet = Area of the rectangular room× Cost of carpet per foot

Substitute the values

14x×4=616

14x=154

x=11 feet

Hence, When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

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Answer:

Step-by-step explanation:

The left option

(4,3), (1,3), (0,5), (1,8)

The factored expression of 21x^7y^7z^4 + 31x^4y^4 is  x^4y^4(21x^3y^3z^4 + 31)

The expression is given as

21x^7y^7z^4 + 31x^4y^4

Express the above expression as a product

So, we have

21x^7y^7z^4 + 31x^4y^4 = 21x^3y^3z^4 * x^4y^4 + 31 * x^4y^4

Factor out x^4y^4

So, we have

21x^7y^7z^4 + 31x^4y^4 =  x^4y^4(21x^3y^3z^4 + 31)

Hence, the factored expression of 21x^7y^7z^4 + 31x^4y^4 is  x^4y^4(21x^3y^3z^4 + 31)

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The total commission of Jorge was $2459.173.

So,

Now,

3.5% of $16,583

5.4% of $34,792

Total commission: $580.405 + $1,878.768 = $2459.173

Therefore, total commission of Jorge was $2459.173.

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Using proportions, we have that:

A. 0.05x + 0.4(10 - x) = 0.2(10).

B. You need 5.7 liters of the 5% solution and 4.3% liters of the 40% solution.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

In item A, we have that the total amount that she has is 20% acid of 10 liters, hence:

0.2(10).

She wants to split it into a 5% solution and a 40% solution, a total of 10 liters, hence the amounts to each solution are x and 10 - x, as follows:

0.05x + 0.4(10 - x).

Hence the equation is:

0.05x + 0.4(10 - x) = 0.2(10).

The solution for x is found as follows:

0.05x + 4 - 0.4x = 2.

0.35x = 2

x = 2/0.35

x = 5.7.

Hence, for item b:

You need 5.7 liters of the 5% solution and 4.3% liters of the 40% solution.

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Answer:

ans) 4G and 6/x+y

Step-by-step explanation:

10) it says the product of both so when both multiply each other , we get the product

Answer:

45mph

Step-by-step explanation:

Answer:

so if add everything and subtract them for d you get 7

Answer:

[tex]y = \frac{ac}{a - b - c} [/tex]

The counterweight lifted in each rotation of the drum is 18.85m.

The diameter of the drum is : d=6m

hlift=C=πd

C=[tex]\frac{22}{7}[/tex]×6

C=18.85 m

Any straight line segment that cuts through the center of a circle and has ends that are on the circle is considered a circle's diameter in geometry. It is also known as the circle's longest chord.

Diameter also refers to the length d of a diameter. As opposed to a diameter, which refers to the line segment itself, one uses the term "diameter" in this context since all diameters of a circle or sphere have the same length, which is equal to twice the radius r. The longest distance that may be generated between the tangents of two opposite parallel lines is referred to as the diameter for a convex shape in the plane.

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The distance between the two points ( − 2 , 5 ) and ( − 8 , − 3 ) is 10 units.

We are given the two points:

( − 2 , 5 ) and ( − 8 , − 3 )

We need to find the distance between the two points.

The formula for distance is given as:

Distance = √ (x₂ - x₁)² + (y₂ - y₁)²

Substituting the values, we get that:

Distance = √ ( - 8  + 2 )² + (- 3 - 5)²

Distance = √ ( - 6 )² + ( - 8 )²

Distance = √ 36 + 64

Distance = √ 100 .

Distance = 10 units.

Therefore, we get that, the distance between the two points ( − 2 , 5 ) and ( − 8 , − 3 ) is 10 units.

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Take the difference in y coordinates and divide that by the difference in the x coordinates. That's the slope, sometimes called the "rise over run"  For a straight line or a linear function the slope is a constant

(6-10)(7,10) = 2/3 = slope

the line is

y-h = m(x-k) where m=2/3 and (k,h) = (10,10) or either point

to get y-10 = (2/3)(x-10)

3y -30 = 2x-20

2x-3y = -10

or use (k,h) as (7,8)

y-8 = (2/3)(x-7)

3y-24 = 2x-14

2x-3y = -10

or if you write it in y=mx + b form

it's y=(2/3)x + 10/3  where 10/3 is the y-intercept and 2/3 = slope

In this form, take the derivative of (2/3)x + 10/3

to get y' = 2/3,  the derivative is the slope

Answer:

9.22 units (3 s.f.)

Step-by-step explanation:

The distance between a pair of points can be found using the distance formula shown below, where [tex](x_1, y_1)[/tex] is the 1st coordinate and [tex](x_2,y_2)[/tex] is the 2nd coordinate.

[tex]\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}[/tex]

Substituting the coordinates into the formula:

Distance between (21, 5) and (28, -1)

= [tex]\sqrt{(-1-5)^{2} + (28-21)^{2} } }}[/tex]

= [tex]\sqrt{(-6)^2+7^2}[/tex]

= [tex]\sqrt{85}[/tex]

= 9.22 units (3 s.f.)

Additional:

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The answers are as follows -

(a) f(x) = 0.15 + 0.89x

(b) $ 10.83.

(c) 7 donuts

(a) Firstly, forming the function using given information. Let x be the number of donuts. Adding the one-time fee and cost per donut.

f(x) = 0.15 + 0.89x

(b) As per the known fact, 1 dozen = 12 quantities. Hence, there will be 12 donuts. Keeping the values in formula to find the price of box.

f(12) = 0.15 + 0.89 × 12

f(12) = 0.15 + 10.68

f(12) = 10.83

Thus, the price of box containing one dozen donuts is 10.83.

(c) Now, finding the value of x as per given cost.

6.38 = 0.15 + 0.89x

0.89x = 6.38 - 0.15

0.89x = 6.23

x = 6.23 ÷ 0.89

x = 7

Thus, a box costing $6.38 will contain 7 donuts.

Hence, (a) f(x) = 0.15 + 0.89x, (b) $ 10.83 and (c) 7 donuts.

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Answer:

Domain { -3,-1,6,9}

Step-by-step explanation:

The domain is the input values

Domain { -3,-1,6,9}

Finding the numeric value of the function, it is found that the car is worth $24,780 after 4 years.

This problem is incomplete, but researching it on a search engine, we have that:

The straight line depreciation equation for a car is y = -3680x + 39500.

It asks the value of the car after 4 years.

The numeric value of a function is found replacing each instance of x by the value that we want to find.

For this problem, means that the value of the car after x years is given by:

y = -3680x + 39500.

Hence, after 4 years, the value is:

y = -3680(4) + 39500 = $24,780.

The car is worth $24,780 after 4 years.

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