find the sum of 1+2-3+4+5-6+7+8-9+...+97+98-99

Answer:

Step-by-step explanation:

in the picture

Answer:

8 cups = 2 quarts

Step-by-step explanation:

Answer:

Eight cups will give you 2 quarts of water

The correct value of (3cis(pi/6))³ is 27i.

Complex numbers are numbers that consist of two parts — a real number and an imaginary number. Complex numbers are the building blocks of more intricate math, such as algebra.

Given the complex number in polar coordinate expressed as

z = r(cos∅+isin∅)

zⁿ =  {r(cos∅+isin∅)}ⁿ

According to DeMoivre’s Theorem;

zⁿ =  rⁿ(cosn∅+isinn∅)

Given the complex number;

(3cis(pi/6))³

= {3(cosπ/6 + isinπ/6)}³

Using  DeMoivre’s Theorem;

= 3³(cos3π/6 + isin3π/6)

=  3³(cosπ/2 + isinπ/2)

= 3³(0 + i(1))

= 27i

Thus, the correct value of (3cis(pi/6))³ is 27i.

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The equivalent expression of [tex]18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}[/tex] is [tex]3x^4\sqrt{2}[/tex]

The expression is given as:

[tex]18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}[/tex]

Start by dividing 18 by 6

[tex]3x^2\sqrt{14x^8} \div \sqrt{7x^4}[/tex]

Next, divide 14 by 7

[tex]3x^2\sqrt{2x^8} \div \sqrt{x^4}[/tex]

Take the square root of x^8 and x^4

[tex]3x^2 * x^4\sqrt{2} \div x^2[/tex]

Divide x^2 by x^2

[tex]3* x^4\sqrt{2}[/tex]

Evaluate

[tex]3x^4\sqrt{2}[/tex]

Hence, the equivalent expression of [tex]18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}[/tex] is [tex]3x^4\sqrt{2}[/tex]

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Answer: B or 3x^4 sqrt 2

explanation: only simplified answer above

The cost of installing a bush is $7 and the cost of installing a tree is $28

Represent the trees with t and the bushes with b.

So, we have the following equations:

13b + 7t = 287

8b + 12t = 392

Make t the subject in 13b + 7t = 287

t = (287 - 13b)/7

Substitute t = (287 - 13b)/7 in 8b + 12t = 392

8b + 12 * (287 - 13b)/7 = 392

Multiply through by 7

56b + 12 * (287 - 13b) = 2744

Expand

56b + 3444 - 156b = 2744

Collect like terms

56b - 156b = 2744 - 3444

-100b = -700

Divide both sides by -100

b = 7

Substitute b = 7in t = (287 - 13b)/7

t = (287 - 13*7)/7

Evaluate

t = 28

Hence, the cost of installing a bush is $7 and the cost of installing a tree is $28

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The equation c = 64 - d is a linear equation, and the value of c in the equation is 64 1/6

The equation is given as:

c = 64 - d

The value of d is given as:

d = -1/6

Substitute -1/6 for d in c = 64 - d

c = 64 - -1/6

Evaluate the difference

c = 64 1/6

Hence, the value of c in the equation is 64 1/6

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The range, standard deviation, and variance say about gas prices in 2018 discussed below

Variance is the average squared deviations from the mean, while standard deviation is the square root of this number.

As the variance in 2018 is 0.0121.

A model with low variance means sampled data is close to where the model predicted it would be.

As the standard deviation in 2018 is 0.1098.

Low standard deviation means data are clustered around the mean

A small range means low variability in a distribution.

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Answer:

358in²

Step-by-step explanation:

9 × 11 = Area of Face One = 99in²

99 × 2 = Face One + Face One on the opposite side = 198in²

4 × 11 = Area of Face Two = 44in²

44 × 2 = Face Two + Face Two on the opposite side = 88in²

9 × 4 = Area of Face Three = 36in²

36 × 2 = Area of Face Three + Face Three on the opposite side = 72in²

Total Surface Area = 198 + 88 + 72 = 358in²

Answer:

540° and x = 85°

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × 3 = 540°

2

sum the interior angles and equate to 540°

x + 115° + 95° + 115° + 130° = 540°

x + 455° = 540° ( sum 455° from both sides )

x = 85°

The probability that a student scored less than 55% on the exam is 0.134%.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have:

Mean of the sample = 70

Standard deviation = 5

= P(X<55%)

Z = (55-70)/5

Z = -3

P(X < -3)

From the Z table:

P(x<-3) = 0.0013499

or

P(x<-3) = 0.134%  

Thus, the probability that a student scored less than 55% on the exam is 0.134%.

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Answer:

2.46

Step-by-step explanation:

3.28/4=0.82(for one candy)

0.82×3=2.46(for 3 candies)

For proof of 3 divisibility, abc is a divisible by 3 if the sum of abc (a + b + c) is a multiple of 3.

The proof for divisibility of 3 implies that an integer is divisible by 3 if the sum of the digits is a multiple of 3.

111 = 1 + 1 + 1 = 3  (the sum is multiple of 3 = 3 x 1)  (111/3 = 37)

222 = 2 + 2 + 2 = 6 (the sum is multiple of 3 = 3 x 2)  (222/3 = 74)

213 = 2 + 1 + 3 = 6 ( (the sum is multiple of 3 = 3 x 2)  (213/3 = 71)

27 = 2 + 7 = 9  (the sum is multiple of 3 = 3 x 3)  (27/3 = 9)

Thus, abc is a divisible by 3 if the sum of abc (a + b + c) is a multiple of 3.

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The number of hours it will take to burn 4 1/4 inches of candle is 8.5 hours in decimal.

Using ratio to solve, find the ratio of candle length to the time taken to burn down

let

4 1/2 : 9 = 4 1/4 : x

9/2 ÷ 9 = 17/4 ÷ x

9/2 × 1/9 = 17/4 × 1/x

1/2 = 17/4x

1 × 4x = 2 × 17

4x = 34

x = 34/4

x = 8.5 hours

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Answer:

8%+10%=180 180÷100=1.8% grapefruit is heavier than Apple

Answer:

  B.  The function is nonlinear.

Step-by-step explanation:

A linear function graphs as a straight line. It is a polynomial function of degree 1. Any function that is not a linear function is a nonlinear function.

__

The function given is a polynomial function of degree 2. (Its highest-degree term is x^2, which has an exponent of 2.)

Since the degree is not 1, the function is nonlinear.

_____

Additional comment

A polynomial function will never be "linear at some points and nonlinear at other points." Such a description might apply to a piecewise-defined function.

Answer:

x=60

Step-by-step explanation:

First get x all alone on 1 side of the equation. Add 14.5 to both sides of the equation to cancel out the negative. You will then be left with

x/5= 12

Multiply both sides of the equation by 5 to cancel out the division and you'll get x=60

MN=2KM

MN+KM=24

As we can see

QP is almost greater than 3/4th MN

It's atleast 10+ or even 12+

So possible perimeter excluding QJ and KJ is atleast 34 to 36 .

So it can neither be 38 nor 28 .

Only one option yields that's 48(Option D)

Answer:

17.5%

Step-by-step explanation:

1879/10730=17.5%

Answer:

18%

Step-by-step explanation:

Locate the "receives aid" column and "graduate" row. The value 1879 is in this row and column combo.

There are 10730 students total as shown in the bottom right hand corner.

Roughly 1879/10730 = 0.1751 = 17.51% of the students are graduates who receive aid. This rounds to 18%

Answer:

B

Step-by-step explanation:

h(x) is the same as g(x), just that every y value of g(x) happens now at x instead of at x-3, so 3 units "later", and everything is therefore just moved 3 units to the right.

Answer:

y = 2x^2 + 8x + 3

Step-by-step explanation:

Step 1: use the vertex form of the quadratic equation

y = a*(x - h)^2 + k

vertex = (-2, -5) = (h, k)

y = a*(x + 2)^2 - 5

Step 2: determine a using the given point

point = (0, 3)

y = a*(x + 2)^2 - 5

3 = a*(0+2)^2 - 5

3 + 5 = a*(2)^2

8 = a*4

a = 2

vertex equation is now y = 2*(x + 2)^2 - 5

Step 3: simplify vertex equation to standard quadratic equation

quadratic equation = Ax^2 + Bx + C

y = 2*(x + 2)^2 - 5

y = 2*(x^2 + 4x + 4) - 5

y = 2x^2 + 8x + 8 - 5

y = 2x^2 + 8x + 3

The value of x is 1 , option B is the correct answer.

When two algebraic expressions are equated using an equal sign , the mathematical equation formed is called an Equation.

The equation is given by 3log₂(2x)=3

3log₂(2x)=3

log₂(2x) = 3/3

log₂(2x) = 1

The base of the logarithm is 2

it can also be written as

[tex]\rm 2^{log_{2}(2x)} = 2 ^1[/tex]

2x = 2

x = 1

Therefore the value of x is 1 , option B is the correct answer.

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Answer:

  rule: f(n) = n³

  missing numbers: 125, 216, 343, 512, 729

Step-by-step explanation:

Your familiarity with the cubes of small integers helps you recognize each of these numbers is a cube. Their sequence is the sequence of cubes of increasing natural numbers.

  1 = 1·1·1 = 1³

  8 = 2·2·2 = 2³

  27 = 3·3·3 = 3³

  64 = 4·4·4 = 4³

__

The rule is ...

  f(n) = n³

The cubes of 5 through 9 will complete the set of numbers ...

  1, 8, 27, 64, 125, 216, 343, 512, 729

The attached image represents the triangle after it has been enlarged

The given parameters are:

From the graph, the coordinates of the triangle are:

A = (-4,2)

B = (-4,-4)

C = (-1,-4)

The rule of dilation is calculated using:

[tex](x,y) \to (k(x - a) + a, k(y - b) + b)[/tex]

So, we have:

[tex]A' = (-\frac 13(-4 +1) - 1, -\frac 13(2 - 2) + 2)[/tex]

A' = (0, 2)

[tex]B' = (-\frac 13(-4 +1) - 1, -\frac 13(-4 - 2) + 2)[/tex]

B' = (0, 4)

[tex]C' = (-\frac 13(-1 +1) - 1, -\frac 13(-4 - 2) + 2)[/tex]

C' = (-1, 4)

See attachment for the image of the triangle, after it has been enlarged

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Answer:

the second option is correct.

Step-by-step explanation:

that is the solution above.

The value of b that causes the system of equations to have infinite solutions is -6.

For that, we will try solving it first using the method of substitution in which we express one variable in another variable's form and then you can substitute this value in another equation to get a linear equation in one variable.

If there comes a = a situation for any a, then there are infinite solutions.

If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.

In the given problem, our equations are:

y = 6x + b

-3x + (1/2)^y = -3

So the value of b needs to be such that these two equations must be equal.

In the second equation:

[tex](1/2)^y = -3 + 3x\\y = -3^2 + 3x^2 \\y = -6 + 6x[/tex]

Then we must have:

6x - 6 = 6x + b

-6 = b

Thus, the value of b that causes the system to have infinite solutions is -6.

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Answer:

-6

Step-by-step explanation:

trust

Answer:

x = 8

Step-by-step explanation:

Hello!

The missing angle in the triangle can be found by subtracting 90° and 45° from 180°. The missing angle is 45°.

This means that the triangle is isosceles, as there are two congruent base angles, 45° and 45°.

The side lengths opposite these two angles are congruent.

We can see that 8 is opposite 45°, and x is opposite 45°. Therefore, x must be equal to 8.

The value of x is 8.

Answer:

x = 8

Step-by-step explanation:

The interior angles of a triangle sum to 180°.

The given triangle is a right triangle, so the missing angle is 45°

⇒ 180° - 90° - 45° = 45°

As the triangle has 2 equal angles, this means it is an isosceles triangle (with its vertex at the right angle).  An isosceles triangle has legs of equal measure, therefore [tex]x=8[/tex].

Proof

This can be proven by using the tan trigonometric ratio to calculate the value of x.

Tan trig ratio

[tex]\sf tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

Substituting the given values into the equation and solving for x:

[tex]\implies \tan (45^{\circ})=\dfrac{8}{x}[/tex]

[tex]\implies x=\dfrac{8}{\tan (45^{\circ})}[/tex]

[tex]\implies x=\dfrac{8}{1}[/tex]

[tex]\implies x=8[/tex]

Answer:

Yes Ben is correct

Step-by-step explanation:

For example:

If n² is the greater of the two consecutive square numbers, then the difference will be 2n-1. So for example, if you have two consecutive squares with the values of 25, and 36, their difference will be 11. Notice though that 11=2×6–1, so it conforms to 2n-1.

The mass of hydrogen atoms that measures 54 u is 89.64 x 10^-24

Analysis:

If 1 u = 1.66 x 10^-24, then 54 u = 54 x 1.66 x 10^-24 = 89.64 x 10^-24

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