Polly has $10 in an account that earns 5% interest compounded annually.
To the nearest cent, how much will she have in 2 years?

Answer:

- 8

Step-by-step explanation:

the coefficient is the numeric value, including the sign, in front of the variable.

4a - 8b + c

the coefficient of b is - 8

The friend is correct. Split the 2D figure as indicated in the diagram below. The rectangle on the left rotates to form the cylinder. The triangle rotates to form the cone. Think of these as like a revolving door that carves out a 3D shape. Or you could think of propellers.

The upper bound of 206.264 to 3 decimal places would be 206.265.

What is upper bound?

In mathematics, an upper bound is a value that is greater than or equal to all of the values in a set. For example, if we have a set of numbers {1, 2, 3}, then 3 is an upper bound of this set because it is greater than or equal to all the numbers in the set.

An upper bound can be either a member of the set or not. If the upper bound is a member of the set, then it is called a maximum element of the set. If the upper bound is not a member of the set, then it is called a strict upper bound of the set.

In the context of rounding, the upper bound refers to the next highest value that a number could be rounded to. For example, if we are rounding a number to the nearest integer, the upper bound would be the next integer greater than the original number.

The upper bound of 206.264 to 3 decimal places would be 206.265.

This is because the third decimal place of the original number is 4, and any number greater than or equal to 5 in the next decimal place would round the number up to the next value. Therefore, rounding 206.264 to 3 decimal places gives 206.265.

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(a) The probability that the entire system works is  0.3136

(b) The probability that the component a is not working is 0.3

Probability is a scale between 0 and 1 that represents the possibility of an event happening. An event with probability 1 is guaranteed to happen, while an event with probability 0 is impossible. The number of favorable outcomes divided by the total number of potential outcomes in the sample space yields the probability of an event A, commonly denoted as P(A). The sample space, for a fair six-sided die, is the set of all potential outcomes, such as 1, 2, 3, 4, 5, and 6. The probability of rolling a 4 is 1/6. Numerous disciplines employ probability to make predictions, deduce conclusions, and make judgments in the face of uncertainty.

(a) To find the probability that the entire system works, we need to find the product of the probabilities of the individual components working.

For the components connected in series, A and B, the probability that both work is equal to the product of their individual probabilities:

P(A and B) = P(A) * P(B) = 0.7 * 0.8 = 0.56

For the components connected in series-parallel, C, D, and E, the probability that all three work is equal to the product of their individual probabilities:

P(C and D and E) = P(C) * P(D) * P(E) = 0.8 * 0.8 * 0.9 = 0.576

To find the probability of the entire system working, we need to find the product of the probability of A and B working and the probability of C, D, and E working:

P(system works) = P(A and B) * P(C and D and E) = 0.56 * 0.576 = 0.3136

(b) Given that the system works, the probability that component A is not working would be equal to 1 minus the probability that component A is working:

P(A not working | system works) = 1 - P(A working | system works) = 1 - 0.7 = 0.3

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The complete question is

Answer:

105, C

Step-by-step explanation:

16x + 1 + 40 = 27x - 3

This is because 180 - (27x - 3) = the missing angle in the triangle shown

16x + 1 + 40 = 27x - 3

1+ 40 = 41

16x + 41 = 27x - 3

        +3            +3

16x + 44 = 27x

-16x           -16x

44 = 11x

44/11 = x

x = 4

27x - 3 is equal to 27(4) - 3 = 108 - 3 = 105

Ans = 105

the cost is lower when using the service every 10 days, the hotel should use the pickup-and-delivery service every 10 days to minimize costs.

To determine how often the hotel should use the pickup-and-delivery service, we need to compare the costs of storing the dirty towels and clean towels with the costs of the pickup-and-delivery service.

Let's calculate the costs of storing the towels:

Dirty towel storage cost per day: 600 towels x $0.02 = $12 per day

Clean towel storage cost per day: 600 towels x $0.01 = $6 per day

Next, let's calculate the costs of the pickup-and-delivery service:

Fixed charge per pickup and delivery service: $81

Variable cost per towel: 600 towels x $0.60 = $360

Now, let's compare the costs:

If the hotel uses the pickup-and-delivery service every 10 days, the total cost would be:

10 days  ($12 + $6) + $81 + $360 = $267

If the hotel uses the pickup-and-delivery service every 9 days, the total cost would be:

9 days  ($12 + $6) + $81 + $360 = $255

Since the cost is lower when using the service every 10 days, the hotel should use the pickup-and-delivery service every 10 days to minimize costs.

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The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).

To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.

First, let's calculate the Z-score using the formula:

Z = (X - μ) / σ

Where:

X = consumption rate per day (1,155 pills)

μ = average consumption rate per day (1,155 pills)

σ = standard deviation (81 pills)

Z = (1,155 - 1,155) / 81

Z = 0

Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.

We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.

To find the probability of running out of sleeping pills, we subtract this probability from 1:

Probability of running out of sleeping pills = 1 - 0.5000

Probability of running out of sleeping pills = 0.5000

Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.

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\(4x+9=3x\)

......................

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

C and E are corre6

The expressions that are equivalent to 16^(5/2) is 16^(5/2) is 4^(5), √16^(5), 16^(2 + 1/2), 16^(2) 6^(1/2).

An exponent is a number or letter written above and to the right of a mathematical expression called the base. The exponent of a number says how many times to use that number in a multiplication.

Now the given expression is,

16^(5/2)

Since 4^2 = 16

Therefore we can write,

16^(5/2) = (4^2)^(5/2)

Using the exponent property,

a^b^(c) = a^(bc)

⇒ (4^2)^(5/2) = 4^{2*(5/2)}

⇒ (4^2)^(5/2) = 4^(5)

Thus,

16^(5/2) = 4^(5)

Now, Using the exponent property,

{a^(b)}^(c) = a^(bc)

Also, 16^(5/2) = 16^{5(1/2)}

⇒ 16^(5/2) = {16^(1/2)}^5

∵ 16^(1/2) = √16

⇒ 16^(5/2) = √16^(5)

Now, Using the exponent property,

a^(b)^(c) = a^{(b)(c)}

Also, 16^(5/2) = 16^(2 + 1/2)

Using the exponent property,

a^(b).a^(c) = a^{(b + c)}

16^(2 + 1/2) = 16^(2) 6^(1/2)

⇒ 16^(5/2) = 16^(2) 6^(1/2)

The expressions that are equivalent to 16^(5/2) is 4^(5), √16^(5), 16^(2 + 1/2), 16^(2) 6^(1/2).

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We can proved that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

Let's denote the vertices of the parallelogram as A, B, C, and D, with O as the midpoint of AC and BD.

First, we can see that triangles ABO and CDO are congruent by the Side-Side-Side (SSS) postulate, since they share side BD, and both have sides AB and CO of equal length due to O being the midpoint of BD. Therefore, angles AOB and COD are congruent, and we can denote their measure as θ.

Using the Law of Cosines in triangles ABO and CDO, we can express the squares of the diagonals AC and BD in terms of the sides of the parallelogram:

AC² = AB² + BC² - 2(AB)(BC)cosθ

BD² = AB² + BC² + 2(AB)(BC)cosθ

Adding these two equations together, we get:

AC² + BD² = 2(AB² + BC²)

which is the desired result. Therefore, we have shown that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

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Answer:

Got this from the internet.

Step-by-step explanation:

The vertical line dividing the parabola into two equal portions is called the line of symmetry. All parabolas have a vertex, the ordered pair that represents the bottom (or the top) of the curve. The vertex of a parabola has an ordered pair \begin{align*}(h, k)\end{align*}.

The inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

To find the inverse Laplace transform of each function, we need to express them in terms of known Laplace transforms. Here are the solutions for each function:

a)

\(F(s) = \large{\frac{2e^{-0.5s}}{s^2-6s+9}}\)

To find the inverse Laplace transform, we first need to factor the denominator of F(s). The denominator factors as (s - 3)². Therefore, we can rewrite F(s) as:

\(F(s) = \large{\frac{2e^{-0.5s}}{(s-3)^2}}\)

Now, we know that the Laplace transform of eᵃᵗ is 1/(s - a). Therefore, the inverse Laplace transform of

\(e^(-0.5s) \: is \: e^(0.5t).\)

Applying this, we get:

\(f(t) = 2e^(0.5t) * t \\

b) F(s) = \large{\frac{s-1}{s^2-3s+2}}\)

We can factor the denominator of F(s) as (s - 1)(s - 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{s-1}{(s-1)(s-2)}}\)

Simplifying, we have:

\(F(s) = \large{\frac{1}{s-2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(2t) \\

c) F(s) = \large{\frac{s-1}{s^2+s-2}}

\)

We factor the denominator of F(s) as (s - 1)(s + 2). The expression becomes:

\(F(s) = \large{\frac{s-1}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{1}{s+2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-2t) \\

d) F(s) = \large{\frac{e^{-s}(s-1)}{s^2+s-2}}\)

We can factor the denominator of F(s) as (s - 1)(s + 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{e^{-s}(s-1)}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{e^{-s}}{s+2}}\)

The Laplace transform of

\(e^(-s) \: is \: 1/(s + 1).\)

Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

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For a two-tailed binomial test with n = 144, alpha = 0.05, and a null hypothesis stating that p = 0.50, a score of X = 60 (option C) would be sufficient to reject the null hypothesis.

We will first calculate the critical values for a two-tailed binomial test with n = 144, alpha = 0.05, and a null hypothesis stating that p = 0.50.

Step 1: Identify the parameters.
n = 144 (sample size)
p = 0.50 (probability of success under the null hypothesis)
alpha = 0.05 (significance level)

Step 2: Calculate the critical values using a binomial test.
For a two-tailed test, we need to find the critical values in both tails. We can use a binomial calculator or statistical software to find these values. Divide the alpha by 2 (0.05/2 = 0.025) to get the significance level for each tail. The critical values are the number of successes at which we would reject the null hypothesis.

Using a binomial calculator, we find that the critical values are:
Lower critical value: X = 60 (below this value, we reject the null hypothesis)
Upper critical value: X = 84 (above this value, we reject the null hypothesis)

Step 3: Compare the critical values with the options given.
Option A: 75 falls within the range of accepting the null hypothesis (60 < 75 < 84).
Option B: 80 falls within the range of accepting the null hypothesis (60 < 80 < 84).
Option C: 60 falls at the lower critical value, which means we would reject the null hypothesis.
Option D: 7 is below the lower critical value, which means we would also reject the null hypothesis.

For a two-tailed binomial test with n = 144, alpha = 0.05, and a null hypothesis stating that p = 0.50, a score of X = 60 (option C) would be sufficient to reject the null hypothesis.

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Answer: C

Step-by-step explanation:

intersection of f(x) and g(x) is x=-3

f(-3)=g(-3)

Answer C

Answer:

The answer is f(-3)=g(-3)

Step-by-step explanation: just took the test hope it helps❤️

Answer:

They bought 3 softballs and they bought 2 baseballs which equals 24 dollars and 5 all together

Step-by-step explanation:

Since there is a 45 and 90 degree angle, this is a 45-45-90 triangle. The legs are equal in a 45-45-90 ttiangle. The hypotenuse sqr root of 2 times more than the legs. So this means the hypotenuse measure is

\(18 \sqrt{2} \)

So we can set up a equation.

\( {18}^{2} + {x}^{2} = ({18 \sqrt{2}) }^{2} \)

\(x = 18\)

So the missing side is 18

Answer:

(1/14)

Step-by-step explanation:

(6/7)/(12)              6/7 as a fraction divided by a whole of 12

(6/7)/(12/1)

(6/7)*(1/12)

(1/7)*(1/2)

(1/14)

Answer:

= \(\frac{1}{14}\)

Step-by-step explanation:

\(\frac{6}{7}\)÷12

\(\frac{6}{7}\)÷\(\frac{12}{1}\)

KFC for division with fractions

Keep

Flip

Change

Keep the first fraction ( \(\frac{6}{7}\) )

Flip the second fraction (          \(\frac{12}{1}\)→ \(\frac{1}{12}\) )  

Change the fraction symbol to a multiplication symbol (÷ →×)

   \(\frac{6}{7}\) × \(\frac{1}{12}\) = \(\frac{6}{84}\)

6 ÷ 6 = 1

84 ÷ 6 = 14

= \(\frac{1}{14}\)

Using the formula for the confidence interval and provided value for mean and the upper interval. The answer is 0.05.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

The alpha value is 0.025, and the associated critical value is 1.96 for a two-tailed 95% confidence interval. This indicates that we can subtract 1.96 standard deviations from the mean, or the mean, to determine the upper and lower boundaries of the confidence interval.

sample mean = 0.17

upper limit = 0.29

upper limit = sample mean + margin

margin = 0.29-0.17 = 0.12

lower limit = sample mean - margin

=0.17-0.12 = 0.05

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The sample is baised.

Since all the students who attended the football game will most likely want a football stadium to be built and those that do no want a stadium to be built are not proportionately represented in this sample

Step-by-step explanation:

We want to identify how to determine the x-factors for the graph of a function.

On some occasions, the x values for the function will be provided for you to solve for the y values. but on other occasions, the x values are not provided and you have to decide them yourself.

For a linear function, most times, you can pick values within any range of values, e.g from 0 to 5, or 2, 4, 6, 8, 10. Since it is a linear function, it will eventually result in a straight line that contains all other points.

For a quadratic function, the best practice is to pick points around the vertex of the function. The vertex of a function is either the minimum or maximum point of the function.

For example, if the vertex of a quadratic function is (4, 10), the x-coordinate of the vertex is 4. To pick your points, pick points that are some values below 4 and some values above 4, like 2, 3, 4, 5, 6 or 0, 2, 4, 6, 8 That way, you get points that are on either side of the vertex and that will make your plot easier.

Hope that helps!

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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The repeating decimal 0.29292929 can be expressed as a ratio of integers as 29/99

To express the repeating decimal 0.29292929 as a ratio of integers:  To do this Let x be the decimal you want to convert, which is 0.29292929.

Since the repeating part of the decimal has two digits (29), multiply x by 100:
100x = 29.29292929

Subtract the original x from the 100x value:
100x - x = 29.29292929 - 0.29292929
99x = 29

Divide by 99 to solve for x:
x = 29/99

Therefore the  repeating decimal 0.29292929 can be expressed as a ratio of integers as 29/99.

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Answer:

471.24 Inches

Step-by-step explanation:

The probability that exactly 30 drivers out of 600 say they read the newspaper while driving.

To find the probability that exactly 30 out of 600 randomly selected American drivers say they read the newspaper while driving, we can use the binomial probability formula.

The formula is P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where:
- P(X=k) is the probability of getting exactly k successes
- C(n,k) is the number of combinations of n items taken k at a time
- p is the probability of success for each trial
- n is the total number of trials

In this case, the probability of a driver reading the newspaper while driving is given as 5%, or 0.05. So p = 0.05, and the number of trials is 600 (n = 600). We want to find the probability of exactly 30 drivers saying they read the newspaper while driving (k = 30).

Using the formula, the probability is:
P(X=30) = C(600,30) * 0.05^30 * (1-0.05)^(600-30)

Calculating this value will give you the probability that exactly 30 drivers out of 600 say they read the newspaper while driving.

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Answer:

45

Step-by-step explanation:

9 of the 20 drawn were red

9/20 * 100 = 45

The prediction of the number of red marbles in the bag should be considered as the 45.

Since

A bag contains 100 marbles, some red and some purple.

The student has recorded 9 red marbles and 11 purple marbles.

So the total drawn be like

= 9 + 11

= 20

Now the red marbles be

\(= 9\div 20 \times 100\)

= 45

hence, The prediction of the number of red marbles in the bag should be considered as the 45.

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