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So, the infinite sum can be determined in the geometric series a₁ = 5, r = -0.5.

For a geometric series the infinite sum is given by s = a/(1 - r) where a = first term, r = common ratio and |r| < 1.

For each of the geometic series given below, we need to determine if |r| < 1.

For a₁ = -0.25, r = - 3, |r| = |-3| = 3 > 1

For a₁ = 0.75, r = 4, |r| = |4| = 4 > 1

For a₁ = 3, r = 2, |r| = |2| = 2 > 1

For a₁ = 5, r = -0.5, |r| = |-0.5| = 0.5 < 1

Since we require |r| < 1 to find the infinite sum and |r| in the last geometric series |r| = 0.5 < 1, the infinite sum can be found in the geometric series a₁ = 5, r = -0.5..

So, the infinite sum can be determined in the geometric series a₁ = 5, r = -0.5.

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The distance from the top of the mirror to the ceiling once the mirror is hung on the wall is 21 inches

The dimension of the mirror is given as:

[tex]Height = 24\ in[/tex]

[tex]Width = 28\ in[/tex]

From the center of the mirror to the floor of the wall, the distance is:

[tex]Distance =5\frac14\ ft[/tex]

So, the distance to the top of the mirror will be:

[tex]Top = 5\frac 14\ ft + \frac 12 \times Height[/tex]

Substitute 24 for height

[tex]Top = 5\frac 14\ ft+ \frac 12 \times 24\ in[/tex]

[tex]Top = 5\frac 14\ ft+ 12 \ in[/tex]

Convert feet to inches

[tex]Top = 5\frac 14\times 12\ in+ 12 \ in[/tex]

[tex]Top = 63\ in+ 12 \ in[/tex]

[tex]Top = 75 \ in[/tex]

The distance from the top of the mirror to the ceiling is the difference between the height of the wall and 75 inches.

So, we have:

[tex]Distance = 8\ ft - 75\ in[/tex]

Convert feet to inches

[tex]Distance = 8\times 12\ in - 75\ in[/tex]

[tex]Distance = 96\ in - 75\ in[/tex]

[tex]Distance = 21\ in[/tex]

Hence, the distance is 21 inches

Read more about lengths at:

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Answer:

A. $4.25 per 1 kg of spice

B. 60 : 40 = 3 : 2

Step-by-step explanation:

200 g = 0.2 kg (÷100)

unit price formula: cost ÷ quantity

0.85 ÷ 0.2 = 4.25

set a proportion;

60 3

---- = ---

x 2

3÷60 = 0.05 2

2 ÷ 0.05 = 40

x = 40

hope this helps!

Answer:

You can! It's just a matter of personal choice.

Step-by-step explanation:

Answer:

Synthetic division is another way to divide a polynomial by the binomial x - c , where c is a constant.

Step-by-step explanation:

Set up the synthetic division.

Bring down the leading coefficient to the bottom row.

Multiply c by the value just written on the bottom row.

Add the column created in step 3.

5^-5, 5^0, 5^4

Explanation:

5^-5 would end up being in the negatives,

5^0 would end up equaling 5 or 0

5^4 is automatically more than 5^0 because 4 is greater than 0.

Step-by-step:

Use slope formula to find the slope. (y - y)/(x - x)

Make sure the x and y in front of the minus is a pair that goes together, as well as the x and y behind the minus sign. So

8 - -4 goes on top, that's 12

0 - -1 goes under, thats 1

12/1 is the slope which is just 12. Use either point to fill in the second x and the second y in the point-slope equation. m is the slope.

y - y = m(x - x)

y - 8 = 12(x - 0)

y - 8 = 12x

Step-by-step explanation:

we need to find how much 14/70 is equal to ? over 100

100/70=1.42857142857

14x1.42857142857=20

Therefore she drinks 20/100 she drinks before she goes on a ride.

or 20%

it's 20

I got it right on iready

Answer:

6.2

Step-by-step explanation: TOOK THE TEST

Answer:

[tex]x\approx4.5[/tex]

Step-by-step explanation:

In relation to ∠U, we are given the triangle's opposite side and adjacent side. Therefore, we should use the tangent function to determine the opposite side:

[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]

[tex]tan(34^\circ)=\frac{x}{6.7}[/tex]

[tex]6.7tan(34^\circ)=x[/tex]

[tex]x=6.7tan(34^\circ)[/tex]

[tex]x\approx4.5[/tex]

Answer:

x = (-b ± √b² - 4ac)/2a

Step-by-step explanation:

Answer:

20% of 2500 is 500

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

We need to determine 20% of 2500 now and the procedure explaining it as such

Step 1: In the given case Output Value is 2500.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 2500 = 100%.

Step 4: In the Same way, x = 20%.

Step 5: On dividing the pair of simple equations we got the equation as under

2500 = 100% (1).

x = 20% (2).

(2500%)/(x%) = 100/20

Step 6: Reciprocal of both the sides results in the following equation

x%/2500% = 20/100

Step 7: Simplifying the above obtained equation further will tell what is 20% of 2500

x = 500%

Therefore, 20% of 2500 is 500

Answer:

the answer is b -12 is closer to being a positive number making it worth more than -17. so you're answer would be -12>-17

Answer:

yes a 1/4 probability is 0.25

Answer:

Need more information

If you want put a graph or explain more your question

Hey there!

3^15/ 3^3

3^15

= 3*3*3*3*3*3*3*3*3*3*3*3*3*3*3

= 9*9*9*9*9*9*9*3

= 81*81*81*27

= 6,561 * 2,187

= 14,348,907

= 14,348,907/3^3

3^3

= 3*3*3

= 9*3

= 27

14,348,907/27

= 531,441

15 - 3 = 12

= 3^12

Because

3^12

= 3*3*3*3*3*3*3*3*3*3*3*3

= 9*9*9*9*9*9

= 81*81*81

= 6,561*81

= 531,441

531,441 ≈ 3^12

Therefore, your answer should be: 3^12

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

a resposta para a sua pergunta é 2.5 esperança que ajuda por favor marcar como mais inteligente se correto obrigado

x = 9

Scale size is 3 so multiply all terms in ABC by 3.

Answer:

well -5.5 is the left side of the graph then goes up 3 y which brings you to the -x positive y quadrant or the top left quadrant which is quadrant 2

Answer:

Negative Correlation

Step-by-step explanation:

Since the points are approximately lined up in a linear line pointing toward the bottom right, the slope of the best fit line would be a negative value. So the scatter plot shows a negative correlation.

Answer:

Question 2: 2/3

Question 1: 1/3

Question 3: 20

Step-by-step explanation:

Question 2: 8/4 = 2 & 12/4 = 3.

Question 1: 6/6 = 1 & 18/6 = 3.

Question 3: 10/10 = 1 & 20/10 = 2.

Answer:

[tex]x=-1[/tex] and [tex]x=-5[/tex]

Step-by-step explanation:

[tex]f(x)=(x+3)^2-4[/tex]

[tex]0=(x+3)^2-4[/tex]

[tex]0=(x^2+6x+9)-4[/tex]

[tex]0=x^2+6x+5[/tex]

[tex]0=(x+1)(x+5)[/tex]

[tex]x=-1[/tex] and [tex]x=-5[/tex]

Answer:

[tex]x=-1,\:x=-5[/tex]

Step-by-step explanation:

Solve the equation:

[tex]f(x)=\left(x+3\right)^2-4=0[/tex]

[tex]\left(x+3\right)^2-4=0[/tex]

[tex]\mathrm{Add\:}4\mathrm{\:to\:both\:sides}[/tex]

[tex]\left(x+3\right)^2-4+4=0+4[/tex]

[tex]\left(x+3\right)^2=4[/tex]

[tex]x+3=\sqrt{4}:x=-1[/tex]

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

[tex]x+3=2[/tex]

[tex]x+3-3=2-3[/tex]

[tex]x=-1[/tex]

[tex]x+3=-\sqrt{4}:x=-5[/tex]

[tex]x+3=-\sqrt{4}[/tex]

[tex]x+3=-2[/tex]

[tex]x+3-3=-2-3[/tex]

[tex]x=-5[/tex]

Now, look at the points plotted on the graph:

Answer:

180

Step-by-step explanation:

Answer and Explanation: We will find the area of the given shape:

To find the area, we will count the number of squares of the shaded area.

While calculating the area for a more accurate estimate, we count the square as “1” if the shaded region covers more than half of each square. By counting the squares, the area is approximately 50 square units.

Answer:

(4, -3)

Step-by-step explanation:

X is 4 units away from y=1, so 4 units further away is -3. The Y value of the point stays the same.

The true statement is (a) The rectangular prism boxes should be used because they will cost the company $2. 50 less than using the cylindrical containers.

The given parameters are:

[tex]Pencils = 2400[/tex] --- the pencils needed

The number of pencils the prism can hold is:

[tex]Prism =60[/tex]

Divide the number of pencils needed by the number of pencils in 1 rectangular prism, to calculate the number of prisms needed (n1)

[tex]n_1 = \frac{Pencils}{Prism}[/tex]

So, we have:

[tex]n_1 = \frac{2400}{60}[/tex]

[tex]n_1 = 40[/tex]

A rectangular prism costs $0.50.

So, the total cost is:

[tex]Total\ cost = 40 \times 0.50[/tex]

[tex]Total\ cost = \$20[/tex]

The number of pencils the cylinder can hold is:

[tex]Cylinder=80[/tex]

Divide the number of pencils needed by the number of pencils in 1 cylinder box, to calculate the number of cylinders needed (n2)

[tex]n_2 = \frac{Pencils}{Cylinder}[/tex]

So, we have:

[tex]n_2 = \frac{2400}{80}[/tex]

[tex]n_2 = 30[/tex]

A cylinder costs $0.75.

So, the total cost is:

[tex]Total\ cost = 30 \times 0.75[/tex]

[tex]Total\ cost = $22.5[/tex]

By comparison, the rectangular prism costs $2.5 less than the cylinder

Hence, the true statement is (a)

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Answer:

The answer is 11.6 cm

Step-by-step explanation:

The equation of a right triangle is a^2+b^2=c^2 (a and b being its legs and c its hypothenuse.)

Now we must input 16 cm into c and 11 cm into either a or b.

a^2+11^2=16^2 which is equal to a^2+121=256.

subtract 121 from both sides to get a^2 by itself

a^2+(121-121)=(256-121)

a^2=135

to get "a" by itself, we must find the square root of 135.

√a^2=√135

a=11.6

Answer:

x = 80

Step-by-step explanation:

4/5 = x/100

100 · 4/5 = 100 · x/100

100 · 4/5= x

80 = x

x = 80

Hence, The Answer is 80.

Answer:

35 degrees.

Step-by-step explanation:

Answer:

35 degrees

Step-by-step explanation:

27 - 35 = -8