Find the sum of the first 274 natural numbers.

Answer:

5/6 and 1/4

Step-by-step explanation:

In order to add and subtract fractions, you have to first find a common denominator for both fractions. So, for your first question 1/3 + 1/2, your common denominator would be 6 because it is the least common multiple. So, multiply the top and bottom of 1/3 by 2 to get 2/6 and multiply the top and bottom of 1/2 by 3 in order to get 3/6. Next add your products together 2/6 + 3/6 but only add the numerator, not the denominator. Finally you get, 2/6 + 3/6 = 5/6.

For your second equation, you basically do the same thing, but for the last part, you subtract instead. First, find the least common multiple (common denominator) for 2 and 4, which is 4. Since, 3/4 already has a denominator of 4, you don't have to change that fraction at all, just change 1/2. Next multiply the top and the bottom of 1/2 by 2 to get 2/4. Finally, subtract 3/4 - 2/4 = 1/4.

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Answer:

1. 5/6

2. 1/4

Step-by-step explanation:

1. 1/3 + 1/2

Step 1. Find a common denominator for both fractions (by taking the denominator and finding their least common multiple)

Answer:

3: 3, 6, 9, 12, 15,…

2: 2, 4, 6, 8, 10,…

The least common multiple will be 6

So the new denominator for both fractions is 6

Step 2. Rewrite the fractions using the same denominator

Answer:

1/3 = ?/6 1/2 = ?/6

1/3 = 2/6 1/2 = 3/6

(To get the numerator of the fraction, note that to get the denominator by a number being multiplied by that number, that same number as to be multiplied to the numerator)

Step 3. Add (2/6 + 3/6)

Answer:

2/6 + 3/6 = 5/6

(Denominator stays the same when subtracting or adding)

——————————————————-

2. 3/4 - 1/2

Step 1. Find a common denominator for both fractions (by taking the denominator and finding their least common multiple)

Answer:

2: 2, 4, 6, 8, 10,…

4: 4, 8, 12, 16, 20,…

The least common multiple will be 4

So the new denominator for both fractions is 4

Step 2. Rewrite the fractions using the same denominator

Answer:

3/4 = ?/4 1/2 = ?/4

3/4 = 3/4 1/2 = 2/4

(To get the numerator of the fraction, note that to get the denominator by a number being multiplied by that number, that same number as to be multiplied to the numerator)

Step 3. Subtract (3/4 - 2/4)

Answer:

3/4 - 2/4 = 1/4

(Denominator stays the same when subtracting or adding)

•••••••••••••••••••••••••••••••••

=========================================================

Explanation:

Let

r = area devoted to residential use

This variable is some positive real number, and it represents the area in acres.

Your teacher says that " the area devoted to business use is 7,200 acres less than the area devoted to residential use"

This means the expression r-7200 represents the area for business use

Note the jump from 25% to 65% is 65/25 = 2.6, meaning that we multiply by 2.6 when going from the business area to the residential area.

So we'll multiply by 2.6 to go from r-7200 to r

We'll have this equation

2.6(r-7200) = r

because it's effectively saying

2.6*(business area) = residential area

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

Let's isolate r

2.6(r-7200) = r

2.6r-2.6*7200 = r

2.6r - 18720 = r

2.6r - r = 18720

1.6r = 18720

r = 18720/(1.6)

r = 11700

We'll use 11700 acres for the residential portion.

And also r-7200 = 11700-7200 = 4500 acres are set aside for the business district.

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

The largest region (residential) uses 11700 acres of land.

Note the jump from 10% to 65% involves a multiplier of 6.5 because 65/10 = 6.5

So if g is the amount of government land used, then,

6.5g = r

6.5g = 11700

g = 11700/(6.5)

g = 1800

1800 acres of land are for government use

This is why the answer is choice B.

The area, in acres, devoted to government use is 1800.

Option (B) is correct.

To find the area.

Percentage, a relative value indicating hundredth parts of any quantity.

Given that:

Let

r = area devoted to residential use

This variable is some positive real number, and it represents the area in acres.

This means the expression r-7200 represents the area for business use

Note the jump from 25% to 65% is 65/25 = 2.6, meaning that we multiply by 2.6 when going from the business area to the residential area.

To multiply by 2.6 to go from r-7200 to r

The equation is

2.6(r-7200) = r

because it's effectively saying

2.6*(business area) = residential area

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

Let's isolate r

2.6(r-7200) = r

2.6r-2.6*7200 = r

2.6r - 18720 = r

2.6r - r = 18720

1.6r = 18720

r = 18720/(1.6)

r = 11700

We'll use 11700 acres for the residential portion.

And also r-7200 = 11700-7200 = 4500 acres are set aside for the business district.

The largest region (residential) uses 11700 acres of land.

Note the jump from 10% to 65% involves a multiplier of 6.5 because 65/10 = 6.5

So if g is the amount of government land used, then,

6.5g = r

6.5g = 11700

g = 11700/(6.5)

g = 1800

So, the area, in acres, devoted to government use is 1800.

Learn more about percentage here:

https://brainly.com/question/24338898

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Answer:

10.2

Step-by-step explanation:

Length of arc=(2*pi*r)*(theta/360)

Length of arc=(2*pi*3)*(195/360)=10.2

Answer:

I don't really know

Step-by-step explanation:

Why don't u ask ur teacher for help that will help u more so in a test u can't use brainly

A number multiplied by a sum is the same as the sum of the number multiplied by each addend; a(b + c) = ab + ac

Answer:

the distributive property of binary operations generalizes the distributive law from elementary algebra, which asserts that one has always For example, one has One says that multiplication distributes over addition.

Answer:

Just to recap, an equation has no solution when it results in an incorrect "equation".

For  example:

Equation: x+3 = x+4

Subtract x: 3 = 4???

But clearly, 3 is not equal to 4, so this equation has NO SOLUTION.

Now onto our problem:

13y+2-2y = 10y+3-y

11y+2 = 9y+3

2y=1

y=1/2

9(3y+7)-2 = 3(-9y+9)

27y+61 = -27y+27

54y = -34

y = -34/54

32.1y+3.1+2.4y-8.2=34.5y-5.1

34.5-5.1=34.5y-5.1

5.1=5.1

infinite solutions

5(2.2y+3.4) = 5(y-2)+6y

11y+17 = 11y-10

17 = -10??

That's not true, so the option "5(2.2y+3.4) = 5(y-2)+6y" has no solution.

Let me know if this helps

Answer:um

Step-by-step explanation:

Answer:

y = 2x + 1

Step-by-step explanation:

y = mx + c

m = slope = 2

y = 2x + c

sub x = 1, y = 3

3 = 2(1) + c

c = 1

Answer:

Step-by-step explanation:

Note that the equation should be

f(t) = t^2 + 6t - 20

A. Completing the square

coefficient of the t term: 6

divide it in half: 3

square it: 3²

add 3² to complete the square and subtract 3² to keep the equation balanced:

f(t) = (t² + 6t + 3²) - 3² - 20

f(t) = (t+3)² - 29. This is the equation in vertex form.

:::::

B. Vertex (-3, -29)

The leading coefficient of the equation is +1. Since the leading coefficient is positive, the parabola opens upwards. Therefore, the vertex is a minimum.

:::::

The axis of symmetry is the vertical line passing through the vertex: x = -3

Step-by-step explanation:

y=mx+c

Answer:

y= 10x +14

Step-by-step explanation:

Distribute parenthesis:

7(x+2) + 3x = 7x +14 +3x

Then combine like terms:

7x + 3x = 10x +14

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

a) The first 5 partial sums are listed in the table in the attachment.

__

b) Sigma notation makes use of the general term shown:

  [tex]\displaystyle\sum_{n=1}^\infty{\frac{3^n+(-2)^n}{6^n}}[/tex]

__

c) The sum appears to be close to 3/4. (For large n, a calculator cannot evaluate the terms of the series--they are too small.) The attachment shows the 100th sum to be rounded to 3/4 (from 12 significant digits).

Answer:

A, B

Step-by-step explanation:

Square both sides

5x+1=sqr7        (sqr is square root)

Isolate x

x=sqr7-1/5

Because the square root can also be negative, -sqr7 is also an answer

Answer:

by doing the problem and you should get -24

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Three identical numbers whose product is 1000

10 * 10 * 10

50 - (16 + 19)

= 50 - 35

= 15m

Answer:

$101.44

Step-by-step explanation:

To calculate expected value, we can multiply each outcome by its probability. The probability that the female will pay is 100%, so to start, the expected value is (100%) * $220 = 1 * $220 = $220

Next, the only way the insurance loses or gains money outside of this value is if the female dies. The probability of this happening is 1 - 0.999544 (the probability that the female survives) = 0.000456 . Therefore, the expected value that the insurance company will pay to the woman is

(260000) * (0.000456) = 118.56

Overall, the insurance company is expected to gain $220 from the woman and lose $118.56. Adding these two up, we get

220-118.56 = $101.44 as the overall expected value of the policy to the insurance company

Step-by-step explanation:

Let find the distance of the diameter. using distance formula.

[tex](3 + 1) {}^{2} + ( - 2 + 6) {}^{2} = \sqrt{8} [/tex]

The diameter is sqr root of 8 units.

A circle equation is

[tex] {x}^{2} + {y}^{2} = {r}^{2} [/tex]

where r is the radius. The radius is half the diameter so

[tex]r = \frac{ \sqrt{8} }{2} = \frac{ \sqrt{8} }{ \sqrt{4} } = \sqrt{2} [/tex]

[tex] {r}^{2} = { \sqrt{2} }^{2} = 2[/tex]

So our radius is 2.

Now we need to find the midpoint or Center of the diameter.

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

[tex] \frac{3 - 1}{2} = 1[/tex]

So the center of the circle is (-4,1). So our equation of the Circle us

[tex](x + 4) {}^{2} + (y - 1) {}^{2} = ( \sqrt{2} ) {}^{2} [/tex]

Answer:

9/4 = 2 1/4

Hope this Helps!?

Answer:

(-1,4)

Step-by-step explanation:

The interval in which the function is decreasing is (-1, 4)

Answer:

The domain of a function is the set of all possible inputs for the function.

Using the table provided, the set of all possible inputs is the interval [-6 ; 4].

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. In plain English, the definition means: The range is the resulting y-values we get after substituting all the possible x-values.

Using the table provided, the range is estimated on the interval [-10;20]

The y-intercept is the value on the Y-axis where the function crosses the Y-axis.

Using the table provided, the function crosses the Y-axis for f(0)=18 so for the value y = 18 in the table.

The x-intercept is the value on the X-axis where the function crosses the X-axis.

It happens twice, for f(-6)=0 and f(3)=0.

We estimate the Maximum to be 20, and the Minimum -10.

The function is positive over the interval [-6, 3], and negative over (3;4]

The function is decreasing approximately at f(-1)=20 so at the estimated interval (-1;4]

9514 1404 393

Answer:

  58°

Step-by-step explanation:

The measure of arc HI is the supplement of the angle shown:

  arc HI = 180° -122° = 58°

Answer:

Our three numbers are 8, 48, and 16.

Step-by-step explanation:

Let the first, second, and third numbers be x, y, and z, respectively.

The sum of them is 72. In other words:

[tex]x + y + z = 72[/tex]

The second number y is three times the third number z. So:

[tex]y = 3z[/tex]

And the third number z is eight more than the first number x. So:

[tex]z = x + 8[/tex]

To find the numbers, solve for the system. We can substitute the last two equations into the first:

[tex]x + (3z) + ( x + 8) = 72[/tex]

Substitute again:

[tex]\displaystyle x + 3(x+8) + x+8 = 72[/tex]

Solve for x. Distribute:

[tex]x+3x+24+x+8=72[/tex]

Combine like term:

[tex]5x + 32 = 72[/tex]

Subtract:

[tex]5x = 40[/tex]

And divide:

[tex]x=8[/tex]

Thus, the first number is eight.

And since the third number is eight more than the first, the third number z is 16.

The second number is three times the third. Thus, the second number y is 3(16) or 48.

Our three numbers are 8, 48, and 16.

Step-by-step explanation:

You're going to break√12 into ✓4 and √3 because 4*3 = 12. Square rooting 4 will give you two, and now you can add since the argument of the roots are the same.

Answer:

2*√2

Step-by-step explanation:

You need to use the trigonometrical function of angle (You should use the side sqrt2 and x to find the x). Take any acute angle (for example, 60 degrees)

The cos of this angle is equal to the ratio of adjoined leg (sqrt2) to the hypotenude (the side opposite to right angle, it is x)

cos60degrees= sqrt2/ x

1/2= sqrt2/x

x= 2*sqrt2= 2*√2

When you evaluate [tex]3(\frac{4}{5})[/tex] you will have [tex]\frac{12}{5}[/tex]

In this exercise, you're required to evaluate the given whole number and fraction [tex]3(\frac{4}{5})[/tex]

First of all, you will notice that there is a bracket which signifies multiplication. Therefore, we would open up the bracket by multiplying the two numbers.

Opening the bracket;

[tex]3 * \frac{4}{5}[/tex]

Multiplying the whole number by the numerator;

[tex]3(\frac{4}{5}) = \frac{12}{5}[/tex]

Find more information on how to evaluate mathematical expressions: https://brainly.com/question/24373783

Answer:

243212

Step-by-step explanation:

Substitute the given value of t into the given formula. To find t, subtract 1997 from 2020.

2020−1997=23

Now substitute 23 into the equation for t and calculate.

N(t)N(23)==≈410(1.32)t410(1.32)23243,212

The number of unique visitors to the college website in the year 2020 was approximately 243,212.

Explanation:

Normally, y = cos(x) has a period of 2pi. This means that every 2pi horizontal units, the graph repeats itself. However, we can see that the period here is pi units instead.

One way to see this is to start at (0,1). This is a local max point. Move to its neighboring local max at (pi,1). We have moved pi units along the x axis and the cycle is finished, after which point the cycle repeats itself.

Since T = pi is the period, we then can say B = 2pi/T = 2pi/pi = 2

This is then plugged into y = A*cos(B(x-C))+D where

A = 1

C = 0

D = 0

That leads us to y = cos(2x)

Since the period is often connected to time values, it might help to think of this wave's oscillations occurring twice as often compared to y = cos(x). So that might help see why we replace the x with 2x.

Answer:

Step-by-step explanation:

Find GCF of 45 and 60:

GCF(45,60) = 3*5 = 15

Find Greatest common multiple or GCF

[tex]\\ \sf\longmapsto 45=3\times 3\times 5[/tex]

[tex]\\ \sf\longmapsto 60=2\times 2\times 3\times 5[/tex]

Now

[tex]\\ \sf\longmapsto GCF=3\times 5=15[/tex]

Answer:

a) -|x+4|

b) |x-1| -6

Step-by-step explanation:

First, we can compare the functions to f(x)

For (a), the graph seems to be

- flipped upside down

- moved to the left by 4 units (we can tell this because the x intercept is at -4 instead of 0)

First, -f(x) turns a function upside down. Therefore, we have -f(x) = -|x| (this is our new f(x) for (a)).  Then, f(x+b) shifts a function b units to the left, so we have f(x+4) = -|x+4|. Note that the 4 is inside the absolute values as it is f(x+b) and not f(x) + b. For f(x+b), we substitute x+b for x. For f(x)+b, we add a b at the end.

For (b), the graph seems to be

- moved to the right by 1 unit (the turning point in the slope is at x=1)

- moved down 6 units (the turning point in the slope is at y=-6)

First, f(x-b) shifts the function b units to the right, so we have f(x-1) = |x-1|

Then, f(x) - b shifts the function b units down, so we have f(x) - 6 = |x-1|-6