What is Half a cup in a fraction? .........

The series converges, since |8/9| = 8/9 < 1.

Let [tex]S_n[/tex] denote the n-th partial sum of the series,

[tex]S_n=\displaystyle\sum_{k=0}^n\left(\frac89\right)^k[/tex]

[tex]S_n=1+\dfrac89+\left(\dfrac89\right)^2+\cdots+\left(\dfrac89\right)^n[/tex]

Multiply both sides by 8/9:

[tex]\dfrac89S_n=\dfrac89+\left(\dfrac89\right)^2+\left(\dfrac89\right)^3+\cdots+\left(\dfrac89\right)^{n+1}[/tex]

Subtract this from [tex]S_n[/tex] to eliminate all but the first term in

[tex]S_n-\dfrac89S_n=1-\left(\dfrac89\right)^{n+1}[/tex]

Solve for [tex]S_n[/tex]:

[tex]\dfrac19S_n=1-\left(\dfrac89\right)^{n+1}[/tex]

[tex]S_n=9-9\left(\dfrac89\right)^{n+1}[/tex]

As [tex]n\to\infty[/tex], the exponential term vanishes, so that

[tex]\displaystyle\lim_{n\to\infty}S_n=\sum_{k=0}^\infty\left(\frac89\right)^k=\boxed{9}[/tex]

Steps to solve:

2 - 10 + 8 - (-2)

~Simplify

2 - 10 + 8 + 2

~Subtract

-8 + 8 + 2

~Add

0 + 2

~Add

2

Best of Luck!

Answer:

2

Step-by-step explanation:

first you do this first (-2) then the 2 - is gone then 10 + 8- is 2

Approximately 23. It is simple, but if you are asking because you don't know how to find it, divide the smaller number by the bigger number. Then, multiply this number by 100.

Hope I helped!

Answer:

It must contain carbon.

Step-by-step explanation:

get it right on test.

Answer: it must contain Carbon.

Step-by-step explanation: If a compound doesn’t contain carbon, it isn’t an organic compound

Answer:

x = 35

Step-by-step explanation:

Solve for x:

6 x - 15 = 4 x + 55

Hint: | Move terms with x to the left hand side.

Subtract 4 x from both sides:

(6 x - 4 x) - 15 = (4 x - 4 x) + 55

Hint: | Combine like terms in 6 x - 4 x.

6 x - 4 x = 2 x:

2 x - 15 = (4 x - 4 x) + 55

Hint: | Look for the difference of two identical terms.

4 x - 4 x = 0:

2 x - 15 = 55

Hint: | Isolate terms with x to the left hand side.

Add 15 to both sides:

2 x + (15 - 15) = 15 + 55

Hint: | Look for the difference of two identical terms.

15 - 15 = 0:

2 x = 55 + 15

Hint: | Evaluate 55 + 15.

55 + 15 = 70:

2 x = 70

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 2 x = 70 by 2:

(2 x)/2 = 70/2

Hint: | Any nonzero number divided by itself is one.

2/2 = 1:

x = 70/2

Hint: | Reduce 70/2 to lowest terms. Start by finding the GCD of 70 and 2.

The gcd of 70 and 2 is 2, so 70/2 = (2×35)/(2×1) = 2/2×35 = 35:

Answer: x = 35

Answer: 6

Step-by-step explanation:

Given, Jamie needs to ship 48 plates and 54 bowls to a store.

If she wants to ship the same number of items in each box such that plates and bowls are shipped separately. .

then the  greatest number of items she can ship in each box = GCD (48,54)

[GCD = Greatest common divisor]

Prime factorization of both numbers:

48 =  2 x 2 x 2 x 2 x 3

54 = 2 x 3 x 3 x 3

GCD (48,54)= 2 x 3 = 6

Hence, the greatest number of items she can ship in each box =6

Answer:6

Step-by-step explanation:

So here's the problem writen down.

48 =  2 x 2 x 2 x 2 x 3

54 = 2 x 3 x 3 x 3

GCD (48,54)= 2 x 3 = 6

Answer: A

Step-by-step explanation:

The formula for mass , m= ρ* V

Density, mass of a unit volume of a material substance.

The formula for density is d = M/V, where d is density, M is mass, and V is volume.

Given:

ρ = m/V

where

ρ = density, m = mass, and V = volume.

So, for solving for m we have

m= ρ* V

Hence,  formula for mass , m= ρ* V.

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Answer:

Step-by-step explanation:

Question (3)

The given expression is,

[tex]\frac{4(x-3)}{3}=20[/tex]

       Statements                Proof

1). [tex]\frac{4(x-3)}{3}=20[/tex]                1). Given

2). [tex]4(x-3)=60[/tex]           2). Multiplication property of equality

3). 4x - 12 = 60             3). Distributive property

4). 4x = 72                    4). Addition property of equality

5). x = 18                       5). Division property of equality

Question (4)

Equations are,

5x + 10 = 30 ------(1)

5(x + 10) = 30 ------(2)

From equation (1),

5x + 10 = 30

5x = 30 - 10

x = 4

From equation (2),

5(x + 10) = 30

(x + 10) = 6

x = 6 - 10

x = -4

Therefore, solutions of both the equations are different.

Answer:

3/10. 0/0_____________

The correct statement is line crosses the y-axis at 6 and the input increases, the output decreases.

It is required to choose the following statements are true.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers

Given:

The given line equation are

y=-3x+6

We have to find the which statement is true.

The line crosses the y-axis at 6.

As the input increases, the output decreases.

Therefore, the correct statement is line crosses the y-axis at 6 and the input increases, the output decreases.

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The graph of the equation is y = -3x + 6 and is plotted

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = -3x + 6

where the slope of the line is m = -3

Now , The line crosses the y-axis at 6:

True. To find the y-intercept, we set x = 0 and solve for y: y = -3(0) + 6. This gives y = 6. Therefore, the line crosses the y-axis at y = 6.

As the input increases, the output decreases:

True. Since the coefficient of x is negative, as x increases, the output y decreases.

Hence , the equation of line is solved

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Answer:

P=2(a+b)

=2(20+12)

=2×32

=64 feet

Step-by-step explanation:

The perimeter would equal 2l + 2w, which would lend to the equation 2(20) + 2(12), or 20 + 20 + 12 + 12 = perimeter.

Answer:

64ft.

Step-by-step explanation:

(20ft+20ft)+(12ft+12)= 64ft

Answer:

The lowest common denominator or least common denominator (abbreviated LCD) is the least common multiple of the denominators of a set of fractions. It is the smallest positive integer that is a multiple of each denominator in the set. Fractions write with fraction bar / like 3/4 .

Step-by-step explanation:

Answer:

there is no sufficient evidence to prove that viscosity is not 3000

Step-by-step explanation:

Let's state the hypothesis.

Null hypothesis; H0: μ = 3000

Alternative hypothesis; μ ≠ 3000

The sample mean is;

x = (2781 + 2900 + 3013 + 2856 + 2888)/5 = 2887.6

Standard deviation σ = √variance = √[(2781 - 2887.6)² + (2900 - 2887.6)² + (3013 - 2887.6)² + (2856 - 2887.6)² + (2888 - 2887.6)²)(1/(5 - 1))]

σ = √((1/4)(11363.56 + 153.76 + 15725.16 + 998.56 + 0.16)

σ = 84.026

Formula for test statistic is given as;

t = (x - μ)/σ

t = (2887.6 - 3000)/84.026

t = -1.338

From online p-value calculator from t value attached, using DF = 5 - 1 = 4, two tail and a significance level of 0.05,we have;

The p-value is 0.251896.

This is greater than the significance level of 0.05.

Thus, we will fail to reject the null hypothesis and conclude that there is no sufficient evidence to prove that viscosity is not 3000

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Hi there!

~

[tex]\sqrt{42}[/tex] ≈ [tex]6.4807406984087...[/tex]

So [tex]\sqrt{42}[/tex] is irrational (since the decimal portion doesn't terminate or repeat)

❀Hope this helped you!❀

☽------------❀-------------☾

(The other person copied there answer from google!)

Answer:it must be irrational and not rational

Step-by-step explanation:

Answer:

this is for the num 3 questions and above cuz im only in 4th grade and idk what this is: okay, 3: 6 times C. 4: x minus 1. 5. tdivided by 2. 6: 3 times t subtract 4

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

The 2 angles add up to 180°, as the definition of a line.

8x - 46 + 10x - 8 = 180

18x - 54 = 180

18x = 126

x = 7

Answer:

5.1 days

Step-by-step explanation:

[tex]3.4 \: miles = 1 \: day \\ 17.34 \: miles \: = x \: days[/tex]

Cross Multiply

[tex]3.4x = 17.34[/tex]

Divide both sides of the equation by 3.4

[tex] \frac{3.4x}{3.4} = \frac{17.34}{3.4} [/tex]

[tex]x = 5.1[/tex]

Answer:

5 Days and 1 Hour

Step-by-step explanation:

3,4 per day

So, for 17.34 miles;

      17.34/3.4 = 5 Days and 1 hour

Answer:

B: (5,1)

Step-by-step explanation:

So we have the system of equations:

[tex]x+y=6\text{ and}\\y+4=x[/tex]

We can solve this system using substitution.

Substitute the second equation into the first. Use x. So:

[tex](y+4)+y=6[/tex]

Combine like terms:

[tex]2y+4=6[/tex]

Subtract 4 from both sides:

[tex]2y=2[/tex]

Divide both sides by 2:

[tex]y=1[/tex]

So, the value of y is 1.

To find x, substitute this back into the second equation:

[tex]y+4=x[/tex]

Substitute 1 for y:

[tex]1+4=x[/tex]

Add:

[tex]x=5[/tex]

Therefore, our answer is (5,1).

The answer is B.

And we're done!

Answer:

235=30x-25

Step-by-step explanation:

235+25=30x-25+25

260=30x

260/30=30x/30

x=8.66 or 9 weeks

The equation is 30x + 25 = 235. And the number of weeks will be 7.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Greg is saving to purchase a tablet that costs $235. He as of now has $25 set aside. Every week, Greg procures $15 looking after children and $25 as a clerk, however, he burns through $10 on snacks.

Let x be the number of weeks. Then the equation is given as,

25x + 15x - 10x + 25 = 235

Simplify the equation, then the number of weeks is given as,

25x + 15x - 10x + 25 = 235

30x = 235 - 25

30x = 210

x = 210 / 30

x = 7 weeks

The equation is 30x + 25 = 235. And the number of weeks will be 7.

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Find the value of x by factoring.

What multiplies to -3 and adds to 2?

[tex]y=(x+3)(x-1)[/tex]

Meaning that the x-intercepts are at (-3,0) and (1,0).

Hope this helps.

頑張って!

Answer:

3(10)+30

(-30) (the amount she lost) +22 (the amount she gained)= -8

Glados lost 8 dollars while at the mall.

Answer:Multiply by the reciprocal, also sometimes referred to as "Keep, Change, Flip." Here is how it works. You rewrite the division question as a multiplication question by flipping the second fraction over. Next, keep the first number, change the division to multiplication and then flip the second fraction over.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

33x33x33333333

Answer:

Step-by-step explanation:

1) Two planes parallel to a third plane are parallel - True

2) Two lines parallel to a plane are parallel - False

3) Two lines orthogonal to a third line are parallel - False

4) Two lines parallel to a third line are parallel - True

5) Two planes parallel to a line are parallel - False

6) Two lines orthogonal to a plane are parallel - True

7) Two lines either intersect or are parallel - False

8) Two planes either intersect or are parallel - True

9) Two planes orthogonal to a line are parallel - True

10) A plane and a line either intersect or are parallel - True

11) Two planes orthogonal to a third plane are parallel - False

Answer:

v>5

Step-by-step explanation:

you will divide by negative 8 causing the value sign to flip and that gives you 5

The Answer is : -2f+121

Answer:

The answer is 18.

Step-by-step explanation:

Putting it straight into the calculator as you see it gives you 18.

Answer:

18

Step-by-step explanation:

Hope this helps : )