Make a Prediction Predict the sum of -2 + 2. Explain

your prediction and check it using the number line.

Option a) $213.34 is the correct answer.

Given that, Suppose that you are 34 years old now and that you would like to retire at the age of 75. Furthermore, you would like to have a retirement fund from which you can draw an income of $70,000 annually. You plan to reach this goal by making monthly deposits into an investment plan until you retire. The amount to be deposited each month needs to be calculated. It is assumed that the annual interest rate is 8% and compounded monthly.

The formula for the future value of the annuity is given by, \(FV = C * ((1+i)n -\frac{1}{i} )\)

Where, FV = Future value of annuity

            C = Regular deposit

            n = Number of time periods

            i = Interest rate per time period

In this case, n = (75 – 34) × 12 = 492 time periods and i = 8%/12 = 0.0067 per month.

As FV is unknown, we solve the equation for C.

C = FV * (i / ( (1 + i)n – 1) ) / (1 + i)

To get the value of FV, we use the formula,FV = A × ( (1 + i)n – 1 ) /i

where, A = Annual income after retirement

After substituting the values, we get the amount to be deposited as $213.34.

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(a) After 4500 years, the sample will remain 3.9 mg.

(b) The sample will remain 15 mg after 1369 years.

The result is obtained by using the exponential decay equation.

The exponential decay equation can be used to calculate radioactive decay for the activity, the nuclei, and also the mass. The exponential decay equation for the mass is

\(m = m_{o} e^{-\lambda t}\)

Where

The half-life of radium-226 is 1600 years and the mass of a sample is 27 mg.

(a) What is the remaining mass after 4500 years?

(b) What is the decay time if the remaining mass is 15 mg?

First, let's calculate the decay constant.

λ = 0.693/T½

λ = 0.693/1600

λ = 0,000433

After 4500 years, the remaining mass is

\(m = m_{o} e^{-\lambda t}\)

\(m = 27 e^{-0.000433 \times 4500}\)

m = 27 × 0.142

m = 3.8 mg

If the remaining mass is 15 mg, the decay time is

\(m = m_{o} e^{-\lambda t}\)

\(15 = 27 e^{-0.000433 t}\)

\(ln \frac{15}{27} = ln (e^{-0.000433 t})\)

\(ln \frac{15}{27} = -0.000433 t\)

-0.588 = - 0.000433t

t = 1357.9 years

Hence,

(a) After 4500 years, the sample will remain 3.9 mg.

(b) The sample will remain 15 mg after 1369 years.

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Answer:2.7 - 1.1 = 1.6

Therefore, the factored form of the expression is:(2x - 1)(8x + 5)

Factor pairs of80 and 1, 40 and 2, 20 and 5, 16 and 8, and 10

In question 8 This requirement is met by the pair -8 and 24.

In question9 16x² - 8x + 24x - 5

7. We can list all the pairs of numbers that multiply to -80 in order to identify all the factor pairs for this number. These are a few of the pairs:

80 and 1, 40 and 2, 20 and 5, 16 and 8, and 10

The biggest integer that divides each of two or more numbers without producing a remainder is known as the greatest common factor (GCF).

For instance, 6 is the highest number that divides both 12 and 18 without producing a residual, making it the GCF of 12 and 18.

The highest common factor (HCF) and greatest common divisor (GCD) are other names for the GCF (HCF).

8. We can seek for two values in the list from question 7 that add up to 16 in order to get the factor pair for -80 that adds to the sum of 16. This requirement is met by the pair -8 and 24.

9. Applying the answer to question 8, we can write 16x2 + 16x - 5 in its expanded form as:

16x² - 8x + 24x - 5

The terms can then be categorised as follows:

(16x² - 8x) + (24x - 5) (24x - 5)

When we take the biggest thing in common between each group, we get:8x(2x - 1) + 5(4x - 1) (4x - 1)

10. As a result, grouping can factor the enlarged form of 16x2 + 16x - 5 as follows:

8x(2x - 1) + 5(4x - 1) (4x - 1)

10. Using the enlarged form from answer 9, we may factor the formula 16x2 + 16x - 5 by grouping:

8x(2x - 1) + 5(4x - 1) (4x - 1)

We can factor it out because we can see that the common factor for both terms is (2x - 1):

(2x - 1)(8x + 5)

As a result, the expression's factored form is as follows:

(2x - 1)(8x + 5)

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If the cost for 10 ounce of organic blueberry is $2. 70, the cost of 30 ounce of organic blueberry is represented by the equation x = 20y + 2.70 where y is the cost in dollars for one ounce of organic blueberry.

As x is the cost in dollar for 30 ounce of organic blueberry. For y is the cost in dollars for one ounce of organic blueberry, then

x = 30y + c

where c is the fixed cost

We know for 10 ounce of organic blueberry it costs $2.70. That is

2.70 = 10y + c

c = 2.70 - 10y

So x = 30y + 2.70 - 10y

x = 20y + 2.70

-- The question is incomplete, the complete question is as follows--

"The cost for 10 ounce of organic blueberry is $2. 70 which equation can be used to determine x the cost in dollars, for 30 ounces of organic blueberries.?"

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Answer:

\(4\frac{1}{5} cups\)

Step-by-step explanation:

Let's start by setting up a ratio for the recipe.

First, rewrite 2 and 4/5 as an improper fraction.

\(2\frac{4}{5} = \frac{14}{5}\)

We know that for every 2/3 cup of flour, we need 14/5 cups of sugar. So, our ratio will be:

\(\frac{2}{3} :\frac{14}{5}\)

We want to find how many cups of sugar we'd need for 1 cup of flour. Let s represent the cups of sugar. Let's set up another ratio (flour to sugar):

\(1:s\)

Now, since you're following the same recipe, let's set the ratios equal to make a proportion, like so:

\(\frac{2}{3} :\frac{14}{5} =1:s\)

Multiply the means and extremes, set their products equal, and solve.

\(\frac{2}{3}s=\frac{14}{5}*1=\\s=\frac{3}{2} *\frac{14}{5} =\\s=\frac{21}{5}\)

Let's turn 21/5 into a mixed number.

\(\frac{21}{5} =4\frac{1}{5}\)

So, if you used one cup of flour, you would need \(4\frac{1}{5}\) cups of sugar.

Therefore, the standard deviation for the number of people with the genetic mutation in groups of 500 is approximately 6.726.

To find the standard deviation for the number of people with the genetic mutation in groups of 500, we can use the binomial distribution formula.

Given:

Probability of having the genetic mutation (p) = 0.09

Sample size (n) = 500

The standard deviation (σ) of a binomial distribution is calculated using the formula:

σ = √(n * p * (1 - p))

Substituting the given values:

σ = √(500 * 0.09 * (1 - 0.09))

Calculating the standard deviation:

σ ≈ 6.726 (rounded to three decimal places)

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the vertical asymptοtes οf the functiοn are given by: x = 3 and x = -3.

Asymptοtes are lines that a curve apprοaches but dοes nοt intersect as it extends infinitely in οne οr mοre directiοns. They can be vertical, hοrizοntal, οr οblique.

Vertical asymptοtes οccur when the denοminatοr οf a ratiοnal functiοn is equal tο zerο and the numeratοr is nοt equal tο zerο. This creates a pοint οf discοntinuity in the functiοn, where the functiοn apprοaches infinity οr negative infinity as it apprοaches the vertical line.

The functiοn y = 5tan(0.1x) has vertical asymptοtes whenever the tangent functiοn is undefined, which οccurs at οdd multiples οf π/2.

the vertical asymptοtes οf y = 5tan(0.1x) are given by:

x = (2n+1)π/2*10, where n is an integer.

Fοr Explοratiοn 4.3.3, Questiοn 2, the given functiοn is:

\(y = (x^2 - 5x + 6)/(x^2 - 9)\)

Tο find the vertical asymptοtes οf this functiοn, we need tο determine where the denοminatοr becοmes zerο. This οccurs at x = 3 and x = -3.

Therefοre, the vertical asymptοtes οf the functiοn are given by: x = 3 and x = -3.

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Answer: The area of the square is 400sqf.

Answer 2: Area of circle = 509.31 square feet.

Answer 3: The circle because the circle's are is larger

Answers:

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

Explanation:

The rope forms the perimeter of each shape. This is the distance around the outer edges.

The square has all four sides the same length. Since we have 80 feet of rope, each side must be 80/4 = 20 feet long.

The area of the square is 20*20 = 400 square feet.

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

The circle has a circumference of 80 feet, which leads to a radius of...

C = 2*pi*r

r = C/(2pi)

r = 80/(2pi)

r = 12.732395

which is approximate. I used my calculator's stored version of pi so I could get the most accuracy possible.

Then use this to find the area of the circle

A = pi*r^2

A = pi*(12.732395)^2

A = 509.295782

This value is also approximate.

When rounding to the nearest whole number, we get A = 509

The area of the circle is about 509 square feet.

The circle has the largest area.

Answer:

Oh the answer is yes!

Step-by-step explanation:

If you graph (0,0) it will be in the gray area. Therefore, if the point is inside the gray, then the answer is yes.

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

1945 men and 2849 women register to audition for a singing competition. The number of participants who are not successful in their auditions what’s five times the number of those who are successful. There are 799  participants were successful.

The successful  participants  can be calculate by solving a linear equation as follows

First, it's crucial to understand linear equations.

Equation connects the two algebraic expressions with an equal to sign to demonstrate the equality between the two algebraic expressions.

Linear equations are those with one degree.

In this case, a linear equation must be resolved.

1945 for the men's total

Women are present in 2849.

Participants in total: 1945 + 2849 = 4794

Let x be the proportion of participants that were successful.

Men who failed were 5 times as numerous.

Participants in total: 5x + x = 6x

Due to the issue,

The linear formula is

6x = 4794

x = 4794/6

x = 799

799 of the participants had success.

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Answer:

15.5 is the median.

The mean of the data is 22

Step-by-step explanation:

First, the median of a data set is found by sorting the numbers in order, from least to greatest. Then you count inwards one at a time on both sides until you reach a center number.

4 , 12, 15, 16, 40, 45

     12, 15, 16, 40

          15, 16

               15.5

This means, 15.5 is the median

Next, to find the mean, you add up all the numbers and divide it by however many numbers there are. In this case there are 6 numbers, so we divide the total by 6.

40 + 4 + 12 + 15 + 45 + 16 = 132

132 / 6 = 22

The mean of the data is 22

Answer:

Mean: 22

Median: 15.5

Step-by-step explanation:

hope this helps :)

Answer:

The equation is y= 0.08 x+55

Step-by-step explanation:

Let's use total cost y= Variable cost + fixed cost.

Here fixed cost =$55

And variable cost  for each minute =0.08

That's variable cost for x minutes =0.08

So, total cost y=0.08 x+55

The median number of newspapers sold over seven weeks is 223.

The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.

The formula for the median is as follows:

Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)

We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288

The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.

Median = (215 + 231)/2

= 446/2

= 223

In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.

Hence, the median number of newspapers sold over seven weeks is 223.

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Answers:

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

Explanation:

The independent variable is always long the horizontal axis. Often this is x, but we are using t in this case.

The variable t represents the amount of time in minutes. For instance, t = 2 means 2 minutes have elapsed. At this time, 4 cookies have been eaten as shown by the point (2,4). As another example, the point (3,6) means that d = 6 cookies have been eaten at time t = 3 minutes.

The equation is d = 2t because the '2' represents the rate of change of "eating 2 cookies per minute". Whatever the time value (t) is, we double it to get the value of d, which is the number of cookies eaten.

Answer:

Because the sum of the length of any two sides of a triangle is greater than the length of the third side

Step-by-step explanation:

Why we Cannot construct a triangle of given sides as 5 cm 5 cm and 10 cm?.

5+5=10 (not possible)

The limit of a function at a point is defined as the value that the function approaches as its input values get arbitrarily close to the given point.

However, for an isolated point in the domain of the function, there are no other nearby points that approach the given point, so it does not make sense to talk about the limit of the function at that point.

To understand this concept better, let's consider an example. Suppose we have a function f(x) defined as follows:

f(x) = 1, if x = 2

0, otherwise

In this function, the point x = 2 is an isolated point in the domain of the function, because there are no other points close to 2 that are also in the domain of the function. Therefore, it does not make sense to talk about the limit of the function at x = 2.

In general, limits are only defined at points where the function is "approachable" from both sides, meaning that there exist values of the function that are arbitrarily close to the limit value as the input values approach the limiting point from both sides. Since an isolated point has no nearby points on either side, such behavior cannot be defined and the limit does not exist at such points.

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Answer:

yes

Step-by-step explanation:

First we should find a GCF for the number of boys and girls.

The gcf for the two would be 4.

Divide.

20/4 = 5

28/4= 7

therefore the ratio for boys to girls would be 5 to 7

Answer: A = 4400(1 + 0.0825 x 22)

Step-by-step explanation:

A = accumulated amount

P = original amount  unloaded- $4400

r = rate - 8.25% = 0.0825

t = years = 22

= 4400(1 + 0.0825 x 22)

Answer:

y = 25169.04

Step-by-step explanation:

Answer: The midpoint  is MZ midpoint = (0.5,1)

Step-by-step explanation:

\(MP= (\frac{x_1+x_2}{2}),(\frac{y_1+y_2}{2} ) \\MP= (\frac{-4+3}{2}),(\frac{-1+3}{2} )\\MP= (\frac{-1}{2}),(\frac{2}{2} ) \\\\MP= (-0.5 ,1)\)

Circumference of circle is 2πr

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter. A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14). How do you calculate a circle's circumference? The circle's radius is necessary to calculate the circumference: To calculate the diameter, multiply the radius by two. Divide the outcome by, or an estimate of 3.14. You have now successfully determined the circle's circumference.

Given,

Radius - r

Circumference of circle:

2πr

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The answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.To use a u-substitution to evaluate 0∫π/3 cos⁴xsinx dx, we will use the following steps:

Step 1: Choose a u-substitution that simplifies the integral. In this case, we will let u = cosx, which will allow us to rewrite the integral as 0∫1 u⁴(1-u²)du.

Step 2: Substitute the expression for u into the integral, and simplify. Using the substitution u = cosx, we have:

0∫π/3 cos⁴xsinx dx = 0∫1 u⁴(1-u²)du

Step 3: Evaluate the integral using standard integration techniques. Integrating u⁴(1-u²) with respect to u, we get:

∫ u⁴(1-u²)du = (1/5)u⁵ - (1/3)u³ + C

Step 4: Evaluate the integral from 0 to 1 using the substitution u = cosx. Substituting back, we have:

0∫π/3 cos⁴xsinx dx = (1/5)cos⁵x - (1/3)cos³x ∣₀ᴰ³/₃

Evaluating this expression at the limits of integration, we get:

(1/5)(cos⁵(π/3) - cos⁵(0)) - (1/3)(cos³(π/3) - cos³(0))

Simplifying, we get:

(1/5)(27/64 - 1) - (1/3)(3√3/8 - 1)

= -1/120 (27 - 64) - √3/24 + 1/3

= -5/24 - √3/24

Therefore, the answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.

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We need to find the probability of exactly three successes in six trials of a binomial experiment. Probability of success 50% (no success is 50%).

To find this probability, we need to use the following formula for Bernoulli Trials (or Binomial Experiment):

The combinations are given by:

Then, we have:

Thus, the probability of exactly three successes in six trials of a binomial experiment (which the probability of success is 50%) is 0.0625.

Rounding to the nearest tenth is about p = 0.1 (1/10) or 10%.

Answer:

4545w

;kjbStep-by-step explanation:

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Answer: A 6 hours 15 minutes

Step-by-step explanation:

Time = Distance / Speed

Time = 750 / 120

Time = 6.25

Answer:

A. 6 hours and 15 minutes

Step-by-step explanation:

=> 120 miles = 1 hour

=> 1 mile = 1/120 hour

Multiplying both sides by 750

=> 750 miles =  hours

=> 750 miles = 6.25 hours

=> 750 miles = 6 hours 15 minutes

We know that Ron's estimate for the number of messages he sent that day was 40% more than the actual number of messages he sent. To find out how many messages he estimated he sent, we need to undo this percentage increase.

If the actual number of messages Ron sent was 25, and his estimate was 40% more than that, we can use the following equation:

Estimated number of messages = Actual number of messages + (Actual number of messages * 40%)

We can then substitute in the known values and solve for the estimated number of messages:

Estimated number of messages = 25 + (25 * 40%)

Estimated number of messages = 25 + (25 * 0.4)

Estimated number of messages = 25 + 10

Estimated number of messages = 35

Therefore, Ron estimated that he sent 35 messages that day.

You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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Answer:

58 11/12

Step-by-step explanation:

Add up each item within the suitcase + the suitcase after taking out the items to find the weight of the suitcase at the beginning.

30 + 7 1/4 + 21 2/3

Convert the fractions to have a common denominator

30 + 7 3/12 + 21 8/12

Add these up to get 58 11/12.