Express the following in scientific notation: 0.0000079

Answer:

The sum of the series is Sₙ = n/2 [2·a + (n - 1)·d] where a = 8 and d = 8, therefore 8 + 16 + 24 + ... + 8·n = 4·n·(n + 1)

Step-by-step explanation:

The parameters given are;

8 + 16 + 24 + ... + 8·n = 4·n·(n + 1)

The given series of numbers can be checked to find;

16 - 8 = 24 - 16 = 8

Therefore, the series of numbers is an arithmetic progression with first term = 8, and common difference = 8, we have;

The sum of n terms of an arithmetic progression, Sₙ, is given as follows;

Sₙ = n/2 [2·a + (n - 1)·d]

Where;

a = The first term of the series of numbers = 8

d = The common difference = 8

∴ Sₙ = n/2 × [2×8 + (n - 1)×8] = n [2×8/2 + (n - 1)×8/2]  =  n × [8 + (n - 1)×4]

Sₙ =  n × [8 + (n - 1)×4] =  n × [8 + 4·n - 4] = n × [8  - 4 + 4·n] = n × [4 + 4·n]

Sₙ =n × [4 + 4·n] = 4 × n×(n + 1) = 4·n·(n + 1).

Answer:

1/4

Step-by-step explanation:

25 people took a vitamin and still got the flu and the total number is 100 so the fraction is 25/100 which can be reduce to 1/4

The P(took a vitamin | got the flu) will be 1/4.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Here, the table below shows one doctor's patients who got the flu and whether or not they took a vitamin each day.

We need to find the P(took a vitamin | got the flu).

Now, 25 people took a vitamin and still got the flu.

The total number is 100.

So, the fraction is 25/100 which can be reduce to 1/4.

P(took a vitamin | got the flu) = 25/100

P(took a vitamin | got the flu) = 1/4

Therefore, the P(took a vitamin | got the flu) will be 1/4.

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Answer:

(a) Candy's initial sum as a terms of x is $6x

(b) x = $60

(c) $350

Step-by-step explanation:

The given parameters are;

The ratio in which Aliyah, Brenda and Candy share the sum of money = 3:5:6

The amount Candy later gives Aliyah = $100

The amount Candy later gives Brenda = $50

The new ratio of the sum of the shared money between Aliyah, Brenda and Candy = 2:3:3

(a) Whereby Aliyah has $3x at the start, we have;

Total sum of mony = Y

Amount of Aliyah's initial share = Y × 3/(3 + 5 + 6) = Y×3/14

Therefore, Y×3/14 = $3x

x = Y×3/14 ÷ 3 = Y/14

Amount of Candy's initial share = Y × 6/14

Therefore Candy's initial sum as a terms of x = $6x

(b) Given that Aliyah's and Candy's initial sum as a function of x are   $3x and $6x, therefore, in the ratio 3:5:6, Brenda's  initial sum as a function of x = $5x

Which gives;

Total amount of money = $14x

With

6x - 150, 3x + 100, and 5x + 50, the ratio =is 2:3:3

Therefore, we have;

14·x × 2/(2 + 3 + 3) = (6·x - 150)

14·x × 2/(8) = (6·x - 150)

14·x × 1/4 = (6·x - 150)

7·x/2 = (6·x - 150)

12·x - 300 = 7·x

12·x - 7·x = 300

5·x = 300

x = $60

(b) The final amount of money with Brenda = 5x + 50 = 5 × 60 + 50 = $350

The final amount of money with Brenda = $350.

Answer:

The number of seedlings the three boys planted together is 560 seedlings

Step-by-step explanation:

The possible information in the question are;

Percentage of the seedlings planted by Ali = 40%

Percentage of the seedling planted by Ben = 45%

The percentage of the seedling planted by Cliff = The rest of the seedling

The number of seedling planted by Cliff = 84 siblings

Therefore, the percentage of the seedling planted by Cliff = 100% - 45% - 40% = 15%

Given that Cliff planted 15% of the seedlings, we have;

15% of seedlings Cliff planted = 84

Let X = the total number of seedlings

15/100 × X = 0.15×X = 84

X = 84/0.15 = 560

The total number of seedlings = The number of seedlings the three boys planted together = 560 seedlings.

Answer:

Step-by-step explanation:

So we know that there are 213 oranges and Theresa fills each bag with 3 oranges, so we can represent each bag as 3x. She keeps filling until she reaches 51 oranges.

First. let's write this as an equation, She is starting with 213 oranges and filling x bags with 3 oranges to the point she has less than 51 oranges.

213 - 3x < 51

Now add 3x to both sides,

213 - 3x + 3x < 51 + 3x

213 < 51 + 3x

Now we subtract 51 from both sides,

213 - 51 < 51 - 51 + 3x

162 < 3x

Now we divide both sides by 3,

162/3 < 3x/3

We find the answer,

54 < x

x > 54 bags

Answer:

1109.12

Step-by-step explanation:

Answer:

y = 2x + 1

Step-by-step explanation:

first find slops

(9-5)/(6-4) = 4/2 = 2 = m

y = mx + b

5 = 2(2) + b

1 = b

y = 2x + 1

Answer:

y = 2x - 3

Step-by-step explanation:

gradient of the line is

[tex] \frac{9 - 5}{6 - 4 } = 2[/tex]

equation will be:

[tex] \frac{y - 5}{ x - 4} = 2[/tex]

y - 5 = 2x - 8

y = 2x - 3

Answer:

Hey There!! The Correct answer C: ) is the average number of days a house stays on the market before being sold for price p in $1,000s

A little more clearer explanation:

p is the price in $1000s, and

f(p) is the number of days before its sold for p

Hence, f(250) would be the number of days before its sold for 250,000 (since p is in $1000s)

Answer choice C is the correct one.

Hope It Helped!~ ♡

ItsNobody~ ☆

Answer: C

Step-by-step explanation:  This is the average number of days the house stayed on the market before being sold for $250,000

Answer:

[tex]\large\boxed{x=-\frac{5}{6}}[/tex]

Step-by-step explanation:

f(x) is the same value as y. Therefore, y = 17. We can place this into slope intercept form (except with a defined value for y) and solve for x.

Start by subtracting 7 from both sides. Then, divide by -12 to solve for x. Finally, simplify the fraction.

17 = -12x + 7

10 = -12x

-10/12 = x

-5/6 = x

[tex]\large\boxed{x=-\frac{5}{6}}[/tex]

Answer:

The apartment with the number 207 is in the second floor of the building that comes before the building with apartments numbered 109, 110, 111, and 112

Step-by-step explanation:

The given information of the naming of the apartments are;

The four apartments on the first floor of the building were numbered, 109, 110, 111, and 112

Therefore;

The first digit number, 1, which is consistent, represent the floor number (first floor)

The buildings in the complex are 9-story buildings, with 9 × 4 = 36 Apartments each

Therefore, for the numbers of the apartment to be from 9 to 12, on the floor, the numbering of the apartments is sideways such that the numbers of the apartment in the given building will be X09, X10, X11, and X12, where X is the floor number

The previous building apartment will be numbered X05, X06, X07, X08

Therefore, the apartment with the number 207 is in the second floor of the previous building to the one given.

Answer:

Apartment 207 is in 7th floor of the building number 6 .

Step-by-step explanation:

Given:

There are 9 floors in the building

The number of building and floor of apartment 207 .

Each floor in the building has four apartments

The number of apartment in a building = 4 * 9 = 36

Numbers on each floors are 01 to 36 after floor number

first floor of one of the buildings, we have four apartments numbered 109, 110, 111, and 112.

From the numbers, 1 is representing the floor number

9 , 10 , 11 & 12 are representing four apartments number

Recall,

Each floor has 4 apartments

207 = 36 * 5 + 4 * 6 + 3

36 * 5 = 5 buildings

4 * 6 = 6 floor of 6th building

180+24=204

205 - 208 =6th building 7th floor

Apartment 207 is in 7th floor of the building number 6 .

Answer:

The correct option is;

y < x - 2, and y > x + 1

Step-by-step explanation:

The given graph of inequalities is made up of parallel lines. Therefore, the slope of the inequalities are equal

By examination of the graph, the common slope = (Increase in y-value)/(Corresponding increase in x-value) = (0 - 1)/(-1 - 0) = 1

Therefore, the slope = 1

We note that the there are three different colored regions, therefore, the different colored regions opposite to each inequalities should be the areas of interest

The y-intercept for the upper bounding linear inequality, (y >) is 1

The y-intercept for the lower bounding linear inequality, (y <) is -2

The two inequalities are y > x + 1 and y < x - 2

The correct option is y < x - 2, and y > x + 1.

The system of linear inequalities is represented by  the graph is y> x-2 and y < x + 1

Inequalities is an expression that shows the non equal comparison of two or more variables and numbers.

Given that:

The system of linear inequalities is represented by  the graph is y> x-2 and y < x + 1

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Answer:

Purchasing rate = ₹45 per kg

Profit percent = 33.33%

Step-by-step explanation:

Selling price of 1 kg fruit = ₹60

Therefore, S. P. of 40 kg fruits = 40*60 = ₹2400

Gain = ₹ 600 (given)

Cost price (C. P.) = S. P. - Gain

= ₹2400 - ₹600

= ₹ 1800

Rate of purchasing

= C. P. /quantity of fruits

= 1800/40

= ₹45 per kg

Profit percent

= (Gain* 100)/C.P.

= (600*100)/1800

= 60000/1800

=33.33%

Answer:

12

Step-by-step explanation:

There are 4 points, so there are C(4,2) = 4C2 = 6 pairs of  

points and since two equilateral triangles can be drawn having

that pair of points as vertices, there are 12 equilateral  

triangles that can be drawn having two vertices in the set  

{(0,0), (0,1), (1,0), (1,1)}.

The number of the equilateral triangles in the plane have two vertices in the set {(0, 0), (0, 1), (1, 0), (1, 1)} will be 12.

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

There are 4 points, so there are C(4,2) = 4C2 = 6 pairs of points and since two equilateral triangles can be drawn having that pair of points as vertices, there are 12 equilateral triangles that can be drawn having two vertices in the set {(0,0), (0,1), (1,0), (1,1)}.

Therefore, the number of the equilateral triangles in the plane that have two vertices in the set {(0, 0), (0, 1), (1, 0), (1, 1)} will be 12.

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Answer:

[tex]AC=20[/tex]

Step-by-step explanation:

The line segment AC is the entire length of the line. Within this segment, point  B is found.

Point B, in a way, splits the segment into two, creating the segments AB and BC.

To find the length of AC, add the lengths of the lines AB and BC together:

[tex]AB=11\\BC=9\\AB+BC=AC\\11+9=AC\\20=AC[/tex]

The length of AC is 20.

:Done

Answer:

20 units.

Step-by-step explanation:

Segment AC is broken into two parts by point B. That means that the length of segment AB plus the length of segment BC equals the length of segment AC.

If BC = 9, and AB = 11, AC = 9 + 11 = 20 units.

Hope this helps!

Answer: Amount of pinto beaks [tex]=30\dfrac{3}{5}\text{ pounds}[/tex]

Step-by-step explanation:

Given: Amount of beans a farmer has = [tex]40\dfrac{4}{5}\text{ pounds}=\dfrac{40\times5+4}{5}\text{ pounds}[/tex]

[tex]=\dfrac{204}{5}\text{ pounds}[/tex]

Also, [tex]\dfrac{3}{4}[/tex] of the beans are pinto beans .

Amount of pinto beaks = [tex]\dfrac 34\times[/tex] (Amount of beans a farmer has)

= [tex]\dfrac34\times\dfrac{204}{5}=\dfrac{153}{5}\text{ pounds}[/tex]

[tex]=30\dfrac{3}{5}\text{ pounds}[/tex]

Amount of pinto beaks [tex]=30\dfrac{3}{5}\text{ pounds}[/tex]

Answer:

The pepper plant has 15 fruits on it.

Step-by-step explanation:

Let the tomato plant have x plants. Let the pepper plant have y plants. Since the pepper plant has 2/3 more fruits on it than the tomato plant, we have that y - x = 2x/3

collecting like terms,

y = 2x/3 + x

The above is the number of plants the pepper plant has.

y = 2x/3 + x

y = (2x + 3x)/3

y = 5x/3

Since x = number of fruits on tomato plant = 9, then

y = 5x/3

y = 5(9)/3

y = 5 × 3

y = 15

Since y = number of fruits on pepper plant = 15

So, the pepper plant has 15 fruits on it.

Answer:

To determine if Y=-8 is a function, you must do the vertical line test. If you were to plot Y=-8 on a coordinate plane, you would see that at the point of (0,-8)[which is what Y=-8 is also] is on the Y axis and makes a horizontal linet hat passes through (o,-8).

Step-by-step explanation:

Answer:

graph

Step-by-step explanation:

did you mean in graph

Answer:

The correct option is C.

Step-by-step explanation:

The two patterns are defined as follows:

Form the two patterns as follows:

Pattern A : 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0

Pattern B : 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0

The first several terms of Patterns A and B are shown by:

Pattern A: 20, 18, 16, 14, 12, 10

Pattern B: 20, 19, 18, 17, 16, 15

Thus, the correct option is C.

Answer:

B. The second choice.

Step-by-step explanation:

A function cannot have two points with the same x-coordinate.

If you graph two different points that have the same x-coordinate, they will both lie on the same vertical line. Therefore, if in a relation, more than one point lie on the same vertical line, then the relation is not a function.

Answer:

Data Point B and Data point E

Step-by-step explanation:

Data point B and data point E are the farthest and are more distant away from the best line of fit compared to other data points. The more clustered data points are, the more the correlation that exists between the variables in question.

Therefore, data point B and data point E, will cause the correlation coefficient to decrease the most.

Answer:

28

Step-by-step explanation:

[tex]\frac{3}{4}-\frac{5}{7}[/tex]

Least Common Denominator of 4 & 7 is 4 * 7 = 28

[tex]\frac{3}{4}-\frac{5}{7}=\frac{3*7}{4*7}-\frac{5*4}{7*4}\\\\\\=\frac{21}{28}-\frac{20}{28}\\\\\\=\frac{21-20}{28}\\\\\\=\frac{1}{28}[/tex]

Multiplicative inverse of [tex]\frac{1}{28}[/tex] is [tex]\frac{28}{1} = 28[/tex]

Answer:

B

Step-by-step explanation:

So we have a table of values of a used car over time. At year 0, the car is worth $20,000. By the end of year 8, the car is only worth $3400.

We can see that this is exponential decay since each subsequent year the car depreciates by a different value.

To find the rate of change the car depreciates, we simply need to find the value of the exponential decay. To do this (and for the most accurate results) we can use the last term (8, 3400).

First, we already determined that the original value (year 0 value) of the car is 20,000. Therefore, we can say:

[tex]f(t)=20000(r)^t[/tex]

Where t is the time in years and r is the rate (what we're trying to figure out).

Now, to solve for r, use to point (8, 3400). Plug in 8 for t and 3400 for f(t):

[tex]3400=20000(r)^8\\3400/20000=17/100=r^8\\r=\sqrt[8]{17/100}\approx0.8[/tex]

In other words, the rate of change modeled by the function is 0.8.

As expected, this is exponential decay. The 0.8 tells us that the car depreciates by 20% per year.

Answer:

Step-by-step explanation:

Vertically opposite angles are equal

x = 25°

Answer:

water in quarts is in the first jar after 10th pour = 12/11

Step-by-step explanation:

Let X represent first jar and Y represents second jar.

Lets give the initial value of 2 to the first jar which is filled with water. Lets say there are two liters of water in first jar.

Lets give the initial value of 0 to the second as it is empty.

So before any pour, the values are:

X: 2

Y: 0

After first pour the value of jar X becomes:

Previously it was 2.

Now half of water is taken i.e. half of 2

2 - 1 = 1

So X = 1

The value of jar Y becomes:

The half from jar X is added to second jar Y which was 0:

After first pour the value of jar Y becomes:

0 + 1 = 1

Y = 1

After second pour the value of jar X becomes:

Previously it was 1.

Now third of the water in second jar Y is added to jar X

1 + 1/3

=  (3 + 1)/3

= 4/3

X = 4/3

After second pour the value of jar Y becomes:

Previously it was 1.

Now third of the water in Y jar is taken and added to jar X so,

1 - 1/3

=  (3 - 1)/3

= 2/3

Y = 2/3

After third pour the value of jar X becomes:

Previously it was 4/3.

Now fourth of the water in the first jar X is taken and is added to jar Y

= 3/4 * (4/3)

= 1

X = 1

After third pour the value of jar Y becomes:

Previously it was 2/3

Now fourth of the water in the second jar X is added to jar Y

= 2/3 + 1/4*(4/3)

= 2/3 + 4/12

= 1

Y = 1

After fourth pour the value of jar X becomes:

Previously it was 1

Now fifth of the water in second jar Y is added to jar X

= 1 + 1/5*(1)

= 1 + 1/5

=  (5+1) / 5

= 6/5

X = 6/5

After fourth pour the value of jar Y becomes:

Previously it was 1.

Now fifth of the water in Y jar is taken and added to jar X so,

= 1 - 1/5

= (5 - 1)  / 5

= 4/5

Y = 4/5

After fifth pour the value of jar X becomes:

Previously it was 6/5

Now sixth of the water in the first jar X is taken and is added to jar Y

5/6 * (6/5)

= 1

X = 1

After fifth pour the value of jar Y becomes:

Previously it was 4/5

Now sixth of the water in the first jar X is taken and is added to jar Y

= 4/5 + 1/6 (6/5)

= 4/5 + 1/5

= (4+1) /5

= 5/5

= 1

Y = 1

After sixth pour the value of jar X becomes:

Previously it was 1

Now seventh of the water in second jar Y is added to jar X

= 1 + 1/7*(1)

= 1 + 1/7

=  (7+1) / 7

= 8/7

X = 8/7

After sixth pour the value of jar Y becomes:

Previously it was 1.

Now seventh of the water in Y jar is taken and added to jar X so,

= 1 - 1/7

=  (7-1) / 7

= 6/7

Y = 6/7

After seventh pour the value of jar X becomes:

Previously it was 8/7

Now eighth of the water in the first jar X is taken and is added to jar Y

7/8* (8/7)

= 1

X = 1

After seventh pour the value of jar Y becomes:

Previously it was 6/7

Now eighth of the water in the first jar X is taken and is added to jar Y

= 6/7 + 1/8 (8/7)

= 6/7 + 1/7

= 7/7

= 1

Y = 1

After eighth pour the value of jar X becomes:

Previously it was 1

Now ninth of the water in second jar Y is added to jar X

= 1 + 1/9*(1)

= 1 + 1/9

=  (9+1) / 9

= 10/9

X = 10/9

After eighth pour the value of jar Y becomes:

Previously it was 1.

Now ninth of the water in Y jar is taken and added to jar X so,

= 1 - 1/9

=  (9-1) / 9

= 8/9

Y = 8/9

After ninth pour the value of jar X becomes:

Previously it was 10/9

Now tenth of the water in the first jar X is taken and is added to jar Y

9/10* (10/9)

= 1

X = 1

After ninth pour the value of jar Y becomes:

Previously it was 8/9

Now tenth of the water in the first jar X is taken and is added to jar Y

= 8/9 + 1/10 (10/9)

= 8/9 + 1/9

= 9/9

= 1

Y = 1

After tenth pour the value of jar X becomes:

Previously it was 1

Now eleventh of the water in second jar Y is added to jar X

= 1 + 1/11*(1)

= 1 + 1/11

= (11 + 1) / 11

= 12/11

X = 12/11

After tenth pour the value of jar Y becomes:

Previously it was 1.

Now eleventh of the water in Y jar is taken and added to jar X so,

= 1 - 1/11

=  (11-1) / 11

= 10/11

Y = 10/11

Answer:

6/11

Step-by-step explanation:

1/2 + (1/2)(2/11) = 6/11

sus

Answer:

67°

Step-by-step explanation:

CGE + AGC + AGG = 180 (angles on a straight line)

23°+90°+x=180°

x=67°

Answer:

240 minutes

Step-by-step explanation:

i divide 80 divided by 2 then multiply the answer which is 40 by 6 and get 240

Answer:

5/2 OR 2.5

Step-by-step explanation:

( x + 2y ) = 7 , ( x - 2y ) = 5

x = 7 - 2y , x = 5 + 2y

substitute the two eqns together:

7 - 2y = 5 + 2y

7 - 5 = 2y + 2y

2 = 4y

y = 1/2

when y = 1/2 ,

5y = 5(1/2)

= 5/2 OR 2.5

Answer:

$6125

Step-by-step explanation:

5000 x 3 x .075 = 1,125

5000 + 1125 = 6125

Answer:

The answer is 17.

Step-by-step explanation:

200/3 is approximately 67, and divided by 4 again to represent the second checkpoint will become 16.75. Obviously there can't be a fraction of a bag, so the answer is 17.

Answer:

16

Step-by-step explanation:

the lcm for 3 and 4 is 12

200 ÷ 12 = 16.667

≈16

First of all u will 9x^2-24xy+16y^2-12×16y-12=0 u will add the 9x^ then u will subtract 2-24