What is the approximate length of y? round to the nearest tenth of an inch. 1.4 in. 2.0 in. 2.8 in. 3.5 in.

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

From the question, we have the following parameters that can be used in our computation:

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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Examine one full set:

12/8

simplify

3/2

filling in

3  2

9  6

12  8

18  12

To solve the equation in part a and determine the mystery weight, we used the following properties of equality:

Addition property: This property states that if we add the same number to both sides of an equation, the equality is preserved. In this case, we added 23 grams to both sides of the equation to isolate the variable.

Subtraction property: This property states that if we subtract the same number from both sides of an equation, the equality is preserved. In this case, we subtracted 8 grams from both sides of the equation to isolate the variable.

Multiplication property: This property states that if we multiply both sides of an equation by the same number, the equality is preserved. In this case, we multiplied both sides of the equation by 3 to isolate the variable.

Division property: This property states that if we divide both sides of an equation by the same number (excluding 0), the equality is preserved. In this case, we divided both sides of the equation by 2 to isolate the variable.

By using these properties of equality, we were able to manipulate the equation and isolate the variable to determine the mystery weight.

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Answer:

B

Step-by-step explanation:

6% is usually represented by 0.06

Hope this helped :)

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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Answer:

1. AD

2. 5.2 cm

3. x = 4

4. BC

5. 3

6. x = 12

Step-by-step explanation:

The respοnse tο the given questiοn wοuld be that As a result, it will take equatiοn arοund 9.7 days frοm the day Sandy placed her sandwich in her lοcker fοr 500 bacteria tο cοmpletely cοver it.

When twο statements are cοnnected by a mathematical equatiοn, the equals sign (=) implies equality. An equatiοn in algebra is a mathematical statement that prοves the equivalence οf twο mathematical expressiοns. Fοr instance, the equal sign separates the numbers in the equatiοn 3x + 5 = 14. It is pοssible tο determine the relatiοnship between the twο sentences οn either side οf a letter using a mathematical fοrmula. The lοgο fοr the particular piece οf sοftware is frequently the same. as 2x - 4 = 2, fοr dinstance.

This issue's expοnential equatiοn is as fοllοws:

N(t) = N0  × \(e^{(kt)\) ×  (kt)

We can utilise the abοve infοrmatiοn tο determine the values οf N0 and k:

N(4) = 71 × N(7) = 185

When we enter these numbers intο the equatiοn, we οbtain:

71 = N0  × \(e^{(4k)\)  × (4k)

185 = N0  × \(e^{(7k)\)   × (7k)

185/71 =  \(e^{(3k)\)  × (3k)

As a result, the equatiοn fοr this issue is:

N(t) = 23.77  × \(e^{(0.3056t)}\)  × (0.3056t)

We may set N(t) equal tο 500 and sοlve fοr t tο see hοw many days it will take fοr 500 germs tο grοw:

500 = 23.77  × \(e^{(0.3056t)}\) × (0.3056t)

9.7 days based οn t = ln(500/23.77) / 0.3056.

As a result, it will take arοund 9.7 days frοm the day Sandy placed her sandwich in her lοcker fοr 500 bacteria tο cοmpletely cοver it.

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Answer:

x = -4037/127

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

14x + 18 + x = -112(x + 36) + 13

Step 2: Solve for x

Answer:

The correct answer is a.) x=-6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Cost = Area Cylinder body* cost * 0.03 cm^3 + Area of 2 lids*cost 0.06 of cm^3

Volume = 300 cm^3

Volume = Base *h  

Volume = pi * r^2 * h = 300

h = 300/(pi * r^2 )

Area material =  2*pi * r * h * 0.03 + 2 pi r^2 * 0.06

Area material = 0.06*pi * r * 300/(pi* r^2) + 0.12 * pi * r^2

dmaterial/dr = (-1)18 r^-2 + 0.12 pi * 2*r

dmaterial/dr = -18 r^-2 + 0.24 pi * r

The minimum occurs when the right side = 0

18/r^2 = 0.24 *pi r

18 = 0.24*pi * r^3

18/(0.24 * pi) = r^3

23.89 = r^3

cube root (23.89) = cuberoot(r^3)

r = 2.88 cm

h = 300/pi * r^2

h = 300/(3.14 * 2.88^2)

h = 11.52

This isn't much of a check but we can try it.

Volume = 3.14 * 2.88^2 * 11.52

Volume = 302.01 which considering all the rounding is pretty close.

Here's a graph that confirms my answer.

Casey has 20 possible ways to pick the plants for the two pots.

Casey can choose one plant from the 5 available plants to put in the blue flower pot.

After selecting one plant for the blue pot, she will have 4 remaining plants to choose from for the red pot.

Therefore, the total number of possible ways she can pick plants for the two pots is:

Number of ways = Number of choices for the blue pot × Number of choices for the red pot

= 5× 4

= 20

Hence, Casey has 20 possible ways to pick the plants for the two pots.

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Answer:

x = 8.5

Step-by-step explanation:

In this question, we are to calculate the value of x.

To calculate this, we shall be utilizing one of the important properties of parallelogram.

This property is that opposite angles of a parallelogram are equal.

This means that mQSR = mSPQ = 4x + 90

Now to finally calculate x, we make use of another important parallelogram property which is that angles of parallelogram which faces each other are supplementary.

This means that they add up to be 180

Since mQSR faces mQRS

This means that;

4x + 90 + 9x -20 = 180

13x + 70 = 180

13x = 110

x = 110/13 which is approximately 8.5

Answer:

1. c 44

2. d 6

3. c 48

4. d. 107/1500

5. c. 19.50 pounds

6. a. 40

7. a. $113630

8. c. 217.06 poundspoundspounds

9. c. 1400

10. a. 48

Step-by-step explanation:

Answer:

1. To find the amount of gravel needed, we need to determine the fraction of the total mixture that represents gravel. The ratio of gravel to the total mixture is 4/(9+4+6) = 4/19. To find the amount of gravel for 209 cubic meters of patio, we multiply 209 by the fraction: 209 * (4/19) = 44.

Answer: c. 44

2. The ratio of girls to boys is 2:1, which means for every 2 girls, there is 1 boy. Since there are 3 boys, we can find the number of girls by multiplying 3 by 2: 3 * 2 = 6.

Answer: d. 6

3. The ratio of grapes to walnuts to oranges is 6:6:12, which simplifies to 1:1:2. The total number of fruits is 192, so we can divide it equally among the parts of the ratio: 192 / (1+1+2) = 192 / 4 = 48.

Answer: c. 48

4. To find the amount Tanya gets paid per square foot, we divide the total payment ($107.00) by the area of the building (1500 square feet): $107.00 / 1500 = $0.0713 per square foot (rounded to four decimal places).

Answer: The correct operation is not provided in the options. The answer is approximately $0.0713 per square foot.

5. The weight of the aluminum bar is proportional to its length. We can set up a proportion to find the weight of the 3 feet 3 inches long bar: (24 pounds) / (4 feet) = x / (3 feet + 3/12 feet). Solving for x, we get x = (24 pounds) * (3 feet + 3/12 feet) / (4 feet) = 29.54 pounds.

Answer: a. 29.54 pounds

6. The snail moves 5 inches in 6 minutes. To find how many inches it moves in 48 hours, we can set up a proportion: 5 inches / 6 minutes = x inches / (48 hours * 60 minutes per hour). Solving for x, we get x = (5 inches * (48 hours * 60 minutes per hour)) / 6 minutes = 240 inches = 20 feet.

Answer: a. 40

7. If the real estate agent receives 11 percent of the selling price, the amount the agent makes is 11 percent of $1,033,000: 0.11 * $1,033,000 = $113,630.

Answer: a. $113,630

8. Since both Dan and Evan have the same height/weight ratio, we can set up a proportion: (Dan's weight) / (Dan's height) = (Evan's weight) / (Evan's height). Solving for Evan's weight, we get Evan's weight = (Dan's weight) / (Dan's height) * (Evan's height) = (205 pounds) / (5 feet 8 inches) * (6 feet) ≈ 217.06 pounds.

Answer: c. 217.06 pounds

9. The ore contains 9 percent gold, which means that for every 100 tons of ore, there are 9 tons of gold. To obtain 126 tons of gold, we can set up a proportion: 9 tons / 100 tons = 126 tons / x tons. Solving for x, we get x = (100 tons * 126 tons) / 9 tons = 1400 tons.

Answer: c. 1400

10. If the catch of 4 bears, of which 2 are tagged, is representative, we can set up a proportion: (2 tagged bears) / (24 total bears) = (2 tagged bears) / (x total bears). Solving for x, we get x = (24 total bears) / (2 tagged bears) * (2 tagged bears) = 24.

Answer: b. 12

Step-by-step explanation:

The number of cube that can be packed in the rectangular prism is 30 cubes

Volume of the rectangular prism in terms of small cube and unit cube = 30(1 / 8) ft³

volume of rectangular prism = lwh

where

Therefore,

volume of rectangular prism = 3 / 2 × 1 × 5 / 2  = 15 / 4 ft³

volume of cube = 1 / 2 × 1 / 2 × 1 / 2  = 1 / 8 ft³

number of cube that can be packed in the rectangular prism = 15 / 4 × 8 =  30 cubes

Volume of the rectangular prism in terms of small cube and unit cube = 30(1 / 8) ft³

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Answer:

Number of large oranges: x

Number of small oranges: y

y < 6

x + y <= 10

The girl can buy a minimum of 3 oranges (either 3 large or 3 small) and a maximum of 10 oranges (a combination of large and small).

Let's represent the number of large oranges as "L" and the number of small oranges as "S."

From the given information, we have the following conditions:

At least three but fewer than nine large oranges: 3 ≤ L < 9

Fewer than six small oranges: S < 6

The maximum number of oranges she needs to buy is 10: L + S ≤ 10

Now, let's consider the possible combinations of L and S that satisfy these conditions:

L = 3, S = 0 (Total oranges = 3)

L = 4, S = 0 (Total oranges = 4)

L = 5, S = 0 (Total oranges = 5)

L = 6, S = 0 (Total oranges = 6)

L = 7, S = 0 (Total oranges = 7)

L = 8, S = 0 (Total oranges = 8)

L = 3, S = 1 (Total oranges = 4)

L = 4, S = 1 (Total oranges = 5)

L = 5, S = 1 (Total oranges = 6)

L = 3, S = 2 (Total oranges = 5)

L = 4, S = 2 (Total oranges = 6)

L = 3, S = 3 (Total oranges = 6)

As you can see, these are all the possible combinations of L and S that satisfy the given conditions. The girl can buy a minimum of 3 oranges (either 3 large or 3 small) and a maximum of 10 oranges (a combination of large and small).

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Answer:

3;4

Step-by-step explaining

do the first to ratios the 3rd doesnt matter

Answer:

y8x122

Step-by-step explanation:

Simplify this expression.

a.The probability that a randomly selected watch will be in working condition for more than five years is approximately 6.68%. b.Approximately 93.32% of the watches will be in operating condition after the warranty period. c. The maximum life expectancy of the middle 95% of the watches is approxiamately 63.68 months. d.The range of the middle 95% of the watches is from 32.32 months to 63.68 months. The range represents 95% of the watches, it means that 5%.

a. To find the probability that a randomly selected watch will be in working condition for more than five years, we need to convert the time to the same unit as the distribution. Since the mean is given in years and the standard deviation is given in months,

we need to convert five years to months.

Mean = 4 years = 4 x 12 months = 48 months

Standard deviation = 8 months

To calculate the probability, we need to find the area under the normal distribution curve to the right of 60 months (5 years).

Using a standard normal distribution table or a calculator, we can find the z-score corresponding to 60 months:

z = (x - μ) / σ

z = (60 - 48) / 8 = 12 / 8 = 1.5

The probability can be found by looking up the z-score in the standard normal distribution table or using a calculator. From the table or calculator, we find that the probability is approximately 0.0668, or 6.68%.

b. The warranty period for Timely brand watches is three years. To find the percentage of watches that will be in operating condition after the warranty period, we need to find the probability that a randomly selected watch will last longer than three years.

We need to convert three years to months:

Warranty period = 3 years = 3 x 12 months = 36 months

We calculate the z-score:

z = (x - μ) / σ

z = (36 - 48) / 8 = -12 / 8 = -1.5

Using the standard normal distribution table or a calculator, we find the area to the left of -1.5 is approximately 0.0668. The probability that a randomly selected watch will not last longer than three years is approximately 0.0668.

To find the percentage of watches that will be in operating condition after the warranty period, we subtract this probability from 1 (since we want the complementary probability):

Percentage = 1 - 0.0668 = 0.9332 = 93.32%

c. The middle 95% of the watches represents the range within which 95% of the watches' life expectancy falls. To find the minimum and maximum life expectancy of this range, we need to determine the z-scores that correspond to the cumulative probability of 0.025 and 0.975.

For the minimum life expectancy (lower bound), we look up the z-score that corresponds to a cumulative probability of 0.025. This z-score is approximately -1.96.

z = -1.96

Using the z-score formula, we can find the corresponding value in months:

x = μ + (z x σ)

x = 48 + (-1.96 * 8) = 48 - 15.68 = 32.32

The minimum life expectancy of the middle 95% of the watches is approximately 32.32 months.

For the maximum life expectancy (upper bound), we look up the z-score that corresponds to a cumulative probability of 0.975. This z-score is also approximately 1.96.

z = 1.96

Using the z-score formula, we can find the corresponding value in months:

x = μ + (z x σ)

x = 48 + (1.96 x 8) = 48 + 15.68 = 63.68

d. Ninety-five percent of the watches refer to the range between the 2.5th and 97.5th percentiles. We already calculated the z-scores corresponding to these percentiles in part c: -1.96 and 1.96.

To find the range in months,

we convert the z-scores back:

\(x_{1}\)= μ +\(z_{1}\) x σ = 48 + (-1.96) x 8 = 32.32 months,

and \(x_{2}\)= μ + \(z_{2}\) x σ

= 48 + 1.96 x 8

= 63.68 months.

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Exploring combinations.

A coin is tossed 5 times.

The results from (b) and (c) with the additional result of the one sequence of exactly 5 tails, which has at least 3 tails.

(a) Exactly 1 Tail?

Number of sequences/combinations of Heads/Tails that have exactly 1 Tail is 5.

For the 5 tosses, the single tail can occur in 5 different positions:

the first toss, second toss, third toss, fourth toss, or fifth toss.

(b) Exactly 4 Tails?

Number of sequences/combinations of Heads/Tails that have exactly 4 Tails is 5.

For the 5 tosses, the 4 tails can occur in 5 different positions:

the first 4 tosses, or the last 4 tosses, or the first 3 tosses and the last toss, or the first toss and the last 3 tosses, or the second toss and the last 3 tosses.

(c) Exactly 3 Tails?

Number of sequences/combinations of Heads/Tails that have exactly 3 Tails is 10.

For the 5 tosses, the 3 tails can occur in 10 different positions:

the first 3 tosses, or the last 3 tosses, or the first 2 tosses and the last toss, or the first toss and the last 2 tosses, or the second toss and the last 2 tosses, or the first toss and the second and last tosses, or the first and last 2 tosses, or the second and last 2 tosses, or the first and last tosses and the middle toss, or the middle toss and the first and last tosses.

(d) At least 3 Tails?

Number of sequences/combinations of Heads/Tails that have at least 3 Tails is 10 + 5 + 1 = 16.

We add the results from (b) and (c) with the additional result of the one sequence of exactly 5 tails, which has at least 3 tails.

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Answer:

4 centimetres per hour.

Step-by-step explanation:

The expansion of the function f = y'x + x'z with respect to x yields (x + y')(x + z'), and the expansion with respect to y gives (x' + y)(x + z').

(a) To expand the function f = y'x + x'z with respect to x, we use the distributive property and apply De Morgan's law to simplify the expression:

f = y'x + x'z

  = x'y + x'z

  = (x'y)'(x'z)'    [Using De Morgan's law]

  = (x + y')(x + z')   [Using De Morgan's law again]

(b) Designing the function using a 2-to-1 multiplexer for the case of expanding f with respect to x involves using the inputs x, y, and z as the select lines of the multiplexer. The inputs x + y' and x + z' will be connected to the data inputs of the multiplexer, and the output of the multiplexer will be the expanded function f.

(c) Similarly, for expanding f with respect to y, the expansion is:

f = y'x + x'z

  = xy' + x'z

  = (xy')'(x'z)'    [Using De Morgan's law]

  = (x' + y)(x + z')   [Using De Morgan's law again]

For this case, the inputs x', y, and z will serve as the select lines of the 2-to-1 multiplexer. The inputs x' + y and x + z' will be connected to the data inputs, and the output of the multiplexer will represent the expanded function f.

In both cases, the 2-to-1 multiplexer is used to implement the logic function by selecting the appropriate data inputs based on the select lines, which are derived from the expansion of the function with respect to the corresponding variable.

In conclusion, the expansion of the function f = y'x + x'z with respect to x yields (x + y')(x + z'), and the expansion with respect to y gives (x' + y)(x + z'). By utilizing 2-to-1 multiplexers, the expanded functions can be designed by connecting the appropriate data inputs to the multiplexer based on the select lines derived from the expansions. This allows for the implementation of the logic functions using multiplexers, providing a compact and efficient circuit design.

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The value of x is 10/7

Given:

4) Triangle ABC is similar to triangle DEF

side AB = 5, side BC = x

side EF = x + 2. side DE = 12

To find:

to draw the triangles, write the proportion and solve for x

First, we need to draw the triangles using the given information:

In similar triangles, the ratios of the corresponding sides are equal

For Triangle ABC similar to triangle DEF

AB corresponds to DE

BC corresponds to EF

AC corresponds to DF

The ratio of the corresponding sides will give the proportion:

Finally, we will solve for x:

Answer:

8v+3c

Step-by-step explanation:

Given 2v+6v+3c

1) Add all like terms

-Since both 2 and 6 have "v" and the two together

2) 8v+3c

Answer: 8v+3c

Hope this helps :)

Answer:

-6x-4

Step-by-step explanation:

2(-3x)-4

-6x-4

r F(x) is your frame function since it is on the outside, when every you get to an x in the F function you plug in the G function then solve as normal.

The missing side of a right triangle without using a calculator can be found by using the Pythagoras theorem .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the square of the hypotnuse (longest side) is equal to the sum of the square of the perpendicular and base .

that means : \(Hypotnuse^{2} = Perpendicular^{2} + Base^{2}\)  ;

let the missing side of the right triangle  be the hypotnuse ;

So , missing side can written as :  \(Hypotnuse = \sqrt{Perpendicular^{2} + Base^{2}}\) .

For Example : Let the right triangle has sides lengths as perpendicular = 6 and hypotnuse = 10

The length of side "base" is unknown.

So ,  to find length of side b, we put the known values into theorem:

\(10^{2} = 6^{2} + Base^{2}\) ;

\(base^{2} = 100 - 36\) ;

So , the missing side "base" = 8 ;

Therefore , the missing side without using calculator can be found by the Pythagoras Theorem .

The given question is incomplete , the complete question is

How do you find the missing side of a right triangle without a calculator when the other two sides are given ?

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Given:

Original price = $15.25

Tax rate = 7%

To find:

The total amount.

Solution:

We know that,

Total amount = Original price + Tax

According to the question,

Total amount = 15.25 + 7% of 15.25

\(\text{Total amount}=15.25+\dfrac{7}{100}\times 15.25\)

\(\text{Total amount}=15.25+1.0675\)

\(\text{Total amount}=16.3175\)

Round to the nearest cent (two decimal places).

\(\text{Total amount}\approx 16.32\)

Therefore, the total value is $16.32.

Answer:

It equals 5 /n2+4n+3

Answer:

C. 5 /n+3

Step-by-step explanation:

Answer:

x + y = 20

x - y = 4

Add the 2 equations and get

2x = 24

x = 24/2 = 12

Plug x=12 into either equation and get

y = 8

Answer:

Step-by-step explanation:

A+B=20

12 and 8

There is a difference of 4 between them and they add up to 20.

Answer: third number line

Step-by-step explanation: