factor to write an equivalent expression 36x-16

It will take approximately 2.55 years for the investment to grow to $4288, assuming no withdrawals are made.

What is an investment?

An investment is the purchase of an asset or item with the goal of generating income or appreciation in value over time. Investments can include a wide range of assets such as stocks, bonds, real estate, commodities, and more. The aim of investing is typically to grow wealth over the long term, although some investments may be made with a shorter-term goal in mind, such as generating income or protecting against inflation.

To solve this problem, we can use the formula for compound interest:

A = P[tex](1 + r/n)^{(nt)}[/tex]

where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, t is the time in years.

We can rearrange this formula to solve for t:

t = (1/n) × log(A/P) / log(1 + r/n)

where log denotes the natural logarithm.

In this problem, P = $4000, r = 0.04 (4% as a decimal), n = 4 (compounded quarterly), and A = $4288. Plugging in these values, we get:

t = (1/4) × log(4288/4000) / log(1 + 0.04/4)

t = (1/4) × log(1.072) / log(1.01)

t ≈ 10.18 quarters

Therefore, it will take approximately 10.18 quarters for the investment to grow to $4288. To convert this to years, we divide by 4 (since there are 4 quarters in a year):

t ≈ 2.55 years

So, it will take approximately 2.55 years for the investment to grow to $4288, assuming no withdrawals are made.

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Complete question is: Nicole deposited $4000 into an account with a 4% annual interest rate compounded quarterly assuming that no withdrawals are made  2.55 years will it take for the investment to grow to $4288.

Answer:

225°/360° = 5/8

Length of arc = (5/8)(2π)(1) = 5π/4 units, or about 3.927 units

The correct equation which represents the number of meters, M, swam to the number of laps, L is,

⇒ M = 25L

We have to given that;

The table shows the number of meters swam by a swimmer after a given number of laps.

Now, Take two points from table as;

⇒ (L, M) = (1, 25) and (2, 50)

Hence, We can find the rate of change as;

⇒ m = (50 - 25) / (2 - 1)

⇒ m = 25

Thus, The correct equation which represents the number of meters, M, swam to the number of laps, L is,

⇒ M - 25 = 25 (L - 1)

⇒ M - 25 = 25L - 25

⇒ M = 25L

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The probability that he has exactly 7 hits in his next 7 at bats is  0.0106%.

To find the probability that a baseball player with a batting average of 0.31 gets exactly 7 hits in his next 7 at-bats, we can use the binomial distribution formula:

P(X=k) = (n choose k) * [tex]p^{k}[/tex] * [tex](1-p)^{n-k}[/tex]

where:

P(X=k) is the probability of getting k hits in 7 at-bats

n is the number of trials (in this case, 7 at-bats)

k is the number of successes (in this case, 7 hits)

p is the probability of success on a single trial (in this case, the batting average of 0.31)

(n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials.

Using this formula, we can calculate the probability as follows:

P(X=7) = (7 choose 7) * [tex]0.31^{7}[/tex] * [tex](1-0.31)^{7-7}[/tex]

P(X=7) = 1 * [tex]0.31^{7}[/tex]* [tex]0.69^{0}[/tex]

P(X=7) = 0.000106288

Therefore, the probability that the baseball player with a batting average of 0.31 gets exactly 7 hits in his next 7 at-bats is approximately 0.000106 or 0.0106%.

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Concept testing is the test done before product launch, clients try a sample product and are then surveyed about whether they would buy the product again. So, option D is correct.

In concept testing, the companies will give newly launched products or new ideas or prototype products to the potential customers, to take reactions from them. This feedback is collected and assisted and analyze the feedbacks in order to improve their products sale.

The main aim of this concept testing is to collect information, patron needs, and assertions and can take powerful good decisions. This can gauge the market price and sale of the products through advertising.

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The complete question is:

type of test before product launch, customers try a sample product and are then surveyed about whether they would buy/use the product again. this process is known as:

a. premarket testing

b. alpha testing

c. prelaunch testing

d. concept testing

e. market testing.

When moving from a 95% confidence interval to a 90% confidence interval, the width of the interval will decrease. (option b).

To understand this, let's consider a simple example. Suppose we want to estimate the mean height of all high school students in a particular region. We take a sample of 100 students and calculate the mean height to be 65 inches, with a 95% confidence interval of (63, 67) inches. This means that if we were to repeat this process many times, we would expect the true population mean height to be within this interval 95% of the time.

Now, if we were to calculate a 90% confidence interval instead, we would obtain a narrower interval because we are now willing to accept a greater risk of being wrong.

It is important to note that the width of the confidence interval depends on the sample size and the variability of the data.

As the sample size increases or the variability decreases, the confidence interval will become narrower. Conversely, as the sample size decreases or the variability increases, the confidence interval will become wider.

Hence the correct option is (b)

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Answer:

63 more women than men.

Step-by-step explanation:

Let's start by finding out how many women and men on average buy tickets per day:

For women: (356 tickets) / (3 days) = 118.67 tickets per day

For men: (329 tickets) / (3 days) = 109.67 tickets per day

So on average, 9 more women than men buy tickets per day.

To find out how many more women than men will buy tickets during the first 7 days, we need to multiply the difference per day by the number of days:

9 (more women per day) x 7 (days) = 63

E = 2400/d is the equation for the illumination, E, in lux as a function of the source's distance, d, in meters.

From the given problem, we can let the illumination of light be 'E' and the distance from the source be 'd' such that if the illumination of a light source varies inversely with the square of the distance from that source, we will have:

E α 1/d

E = k/d

Given the following

d = 120 m

E = 20 lux

Substitute

20 = k/120
k = 2400

Determine the equivalent formula

E = 2400/d

Therefore  the formula for the illumination, E, in lux, as a function of the distance, d, from the source in meters is E = 2400/d

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Answer: 336in^3

Step-by-step explanation: In order to find the volume of a trapezoidal prism, you'll need to go by the formula of 1/2 (base 1 + base 2) x height x length.

In this case, you'll need to do 1/2 ( 10 + 4) x 6 x 8 and you should receive the answer of 336.

For two vectors u and v, the magnitude and direction of the sum of vectors, u +v, are equal to the 1.75 and 35.14°.

The formula to determine the magnitude of a vector (in two dimensional space) v = (x, y) is [tex]|v| =\sqrt {(x² + y²)}[/tex]. We have two vectors say v and u.

Magnitude of vector u = 5

direction of vector u = 265°

Magnitude of vector v = 8

direction of vector v = 105°

[tex]\vec u = ( 5cos(265°), 5sin(265°)) [/tex]

[tex]= (−0.436 , −4.981) [/tex]

[tex]\vec v = ( 8cos(105°), 8sin(105°)) [/tex]

[tex]= (−1.294 ,4.829 ) [/tex]

We have to determine the magnitude and direction of the sum, [tex] \vec u + \vec v[/tex]. Vector addition means putting two or more vectors together. Two vectors, a and b, can be added together using vector addition, and the resultant vector can be written as : a + b.

[tex] \vec u + \vec v = (-0.436 + (-1.294), -4.981 +4.829) [/tex]

[tex]= (- 1.730, -0.251) [/tex]

Now, the magnitude of the sum of two vectors is [tex]| \vec u + \vec v | = \sqrt{ {(u + v)_x}^{2} + {(u+v)_y}^{2} } [/tex]

[tex]= \sqrt{ 1.730² + 0.251²} [/tex]

[tex]= 1.74811355466 [/tex] ~ 1.75

Now, direction of vector which is sum of vectors : Let x be angle between componets of vector ( u + v) then direction is [tex]tan ( \theta) = \frac{-0.251}{-1.730} [/tex]

[tex]\theta = tan^{-1}(0.1451)[/tex]

= 35.14°

Hence, required value is 35.14°.

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Answer:

0.25

Step-by-step explanation:

The wellbeing of a community can be significantly harmed by poor service delivery. It may result in dangers to one's health and safety, a decline in quality of life, negative economic effects, and social unrest.

The quality of service that is rendered to the members of a community contributes to the level of development and self actualization of the members of the community.

As such, the community may suffer economically as a result of poor service delivery. Poor transportation infrastructure, for instance, can drive up the cost of goods and services, and bad water supply can have an impact on the local economy's agricultural and industry.

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The molarity of acetic acid in the vinegar is 0.561 M and the mass percent of acetic acid in the vinegar is 33.6%.

In this problem, we are given the volume and concentration of the base (NaOH) used to titrate a sample of vinegar, and we need to find the molarity of acetic acid in the vinegar and the mass percent of acetic acid.

To start, we can use the balanced chemical equation for the reaction between acetic acid and NaOH to find the moles of NaOH used in the titration:

CH₃COOH + NaOH → CH₃COONa + H₂O

From the equation, we can see that the ratio of moles of acetic acid to moles of NaOH is 1:1. Therefore, the number of moles of NaOH used is the same as the number of moles of acetic acid in the original vinegar sample.

Molarity of acetic acid in the vinegar:

moles of NaOH = concentration of NaOH × volume of NaOH used

moles of acetic acid = moles of NaOH

molarity of acetic acid = moles of acetic acid / volume of vinegar sample

Substituting the given values, we get:

moles of NaOH = 0.231 M × 0.02430 L = 0.00561 moles

moles of acetic acid = 0.00561 moles

molarity of acetic acid = 0.00561 moles / 0.0100 L = 0.561 M

Mass percent of acetic acid in the vinegar:

mass of acetic acid = density × volume × molarity × molecular weight

mass percent = (mass of acetic acid / mass of vinegar sample) × 100%

Substituting the given values and the molecular weight of acetic acid (60.05 g/mol), we get:

mass of acetic acid = 1.01 g/mL × 0.0100 L × 0.561 mol/L × 60.05 g/mol = 3.39 g

mass percent = (3.39 g / (1.01 g/mL × 0.0100 L)) × 100% = 33.6%

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Answer:  

a

Step-by-step explanation:

reflection acrossv y=-3

At the start of 2014 lucys house was worth $250,000.

Since the circle is divided into 12 equal sections by radii, the measure of any one of the 12 equal central angles would be:

360 degrees (total angle measure of a circle) ÷ 12 (number of sections) = 30 degrees

Therefore, any one of the 12 equal central angles would have a measure of 30 degrees.

The perimeter of the tiles is 53 inches.

The perimeter of the two dimensional figure is the sum of the whole sides of the figure,

Therefore, let's find the base of the other triangle and the height of the other as follows:

using trigonometric ratios,

cos 35  = adjacent / hypotenuse

cos 35 = x / 12

cross multiply

x = 12 cos 35

x = 9.82982453147 inches

sin 35 = opposite / hypotenuse

sin 35° = y / 12

cross multiply

y = 12 sin 35

y = 6.88291723621

Therefore, lets use Pythagoras's theorem to find the height of the other triangle.

9 + 6.88 = 15.88

Therefore,

15.88² - 8² = h²

252.267059932 - 64 = h²

h = √188.267059932

h = 13.7210422345

Therefore,

perimeter of the figure = 8 + 9 + 13.72 + 12 + 9.83

perimeter of the figure = 52.55

perimeter of the tiles = 53 inches

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The table that shows ta proportional relationship is the C. Minutes read.

The constant of proportionality is D. 20.

Given are three tables.

Proportional relationships are relationships for which the equations are of the form y = kx, where k is a constant.

Here k is also called constant of proportionality.

In a proportional relationships, the y values will be moving in a constant manner with that of x.

For the Minutes Read table,

Minutes read can be related to the number of days as,

Minutes read = 20 (Number of days).

So this is a proportional relationship.

Constant of proportionality = 20

Hence the table which shows a proportional is the c. Minutes Read table and the constant of proportionality is D. 20.

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The probabilities are given as follows:

The Poisson distribution was used, as we have only the mean of the distribution, and the Poisson distribution was then approximated to the normal.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For the Poisson distribution, the standard deviation is the square root of the mean, hence the mean and the standard deviation for the normal distribution are given as follows:

[tex]\mu = 150, \sigma = \sqrt{150} = 12.15[/tex]

The probability of less than 100 customers per day, using continuity correction, is one subtracted by the p-value of Z when X = 99.5, hence:

Z = (99.5 - 150)/12.15

Z = -4.16

Z = -4.16 has a p-value of 0.

The probability of more than 185 customers is one subtracted by the p-value of Z when X = 184.5, hence:

Z = (184.5 - 150)/12.15

Z = 2.84

Z = 2.84 has a p-value of 0.9977.

Hence:

1 - 0.9977 = 0.0023 = 0.23%.

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The baby's weight at birth is

The linear model's y-intercept (b) is required to ascertain the infant's birth weight.

We can determine the slope (m) of the line from given coordinates (1, 8) and (11, 12):

slope(m) = (y2 - y1)/(x2 - x1) = (12 - 8)/(11 - 1) = 0.4

To find the y-intercept, we then apply the previously computed slope with one point (1, 8):

y = mx + b

8 = 0.4(1) + b

b = 7.6

Therefore, it can be deduced that the baby weighed 7.6 pounds at its time of birth when x=0.

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Answer: x=25/3 or 8[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Since they are similar triangles the sides inc/dec by proportion

the longest sides of the triangle went from 48 to 16  which is 48/16=3

The larger triangle is 3 times bigger so each of the sides are 3 times bigger or you can look at it like the smaller triangle is 1/3 smaller than bigger.

so short side is 25 on bigger triangle and went down to x or 25/3=x

Answer: 16π square yards.

Step-by-step explanation:

The area of a circle is given by the formula:

A = πr^2

where r is the radius of the circle.

In this case, we are given the diameter of the circle, which is 8 yards. The radius is half the diameter, so:

r = d/2 = 8/2 = 4 yards

Substituting this value of r into the formula, we get:

A = π(4)^2 = 16π square yards

Therefore, the area of the circle is 16π square yards.

Answer: 50.24cm

Step-by-step explanation: Assuming π = 3.14, substitute the values into the equation πr^2

To get r we do 8/2 = 4

So 3.14 * 4^2 = 50.24

The account balance is b) $3,796.

To calculate the account balance after two years, we need to use the formula for the future value of an annuity due:

FV = Pmt x [[tex](1+r/n)^{nt}[/tex] - 1] x (1 + r/n)

where:

Pmt is the monthly payment ($150 in this case)

r is the annual interest rate (5.5%)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years (2 in this case)

Plugging in the numbers, we get:

FV = $150 x [[tex](1+0.055/12)^{(12*2)}[/tex] - 1] x (1 + 0.055/12)

FV = $150 x [1.1247 - 1] x 1.004583

FV = $150 x 0.1247 x 1.004583

FV = $18.69 x 1.004583 x 24

FV = $449.56

So the account balance after two years, rounded to the nearest dollar, is $450. Therefore, the closest answer is option B: $3,796.

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The area of the circle is 452.38 square inches.

An area in geometry is a measurement of how much space a two-dimensional form or surface takes up. Usually, it is expressed in square units like square meters or square feet.

The volume of space encircled by a circle's perimeter, or circumference, is its area.

The area of the circle is calculated by the formula,

Area = πr²

Here, r is the radius of the circle.

The given radius of the circle is 12 inches. The area of the circle is calculated as,

Area = πr²

Area = π x ( 12 )²

Area = 452.38 square inches

Therefore, the circle will have an area of 452.38 square inches.

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Answer:

The answer is

1)0.96 to 2d.p

2)0.28 to 2d.p

3)3.49 to 2d.p

Step-by-step explanation:

tan0=3/4

0=tan‐¹[3/4]

0=36.9°

0≈37°

1) sin2(0)

sin (2×37)=sin 74=0.96 to 2.dp

2)cos 2(37)

sin(2×37)=cos 74=0.28 to 2d.p

3) tan20

=tan(2×37)=tan74=3.49 to 2d.p

Rewriting multiplication of a sum or difference as an addition or subtraction problem is known as the distributive property.

The distributive property allows you to break down a multiplication problem involving a sum or difference into separate addition or subtraction problems. Here's a step-by-step explanation:
Step:1. Identify the sum or difference within the multiplication problem. For example, in the problem (a + b) * c, the sum is (a + b).
Step:2. Apply the distributive property by multiplying each term inside the parentheses by the outside term. In our example, this would be: a * c + b * c.
Step:3. The result is the rewritten problem as an addition or subtraction problem. In this case, it is a * c + b * c.

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Lines AC and RS are skew lines

Skew lines are lines that exist in different planes and are does not intersect each other directly.

The following are properties of skew lines;

1. They continue in two directions

2. They are in different planes

3. They are never parallel

4. They never intersect

5. They are never perpendicular

As we can see from the diagram, line AC and RS are not on thesame place and they are not parallel lines. They do not intersect each other.

This means that line AC and RS has shown skew lines property and they are therefore skew lines.

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