Tara's retirement party will cost $12 if she invites 4 guests. What is the maximum number of guests there can be if Tara can afford to spend a total of $15 on her retirement party?

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Answer:

Answer is [tex](\frac{4}{-1})[/tex] option D is correct

The balance on the bank account at the end of the third quarter of the year is  2,630.80

How to find the compound interest?

Compound interest is defined as the interest calculated on the principal and the interest accumulated over the previous period.

Compound interest is found using the formula

A=P(1+r/n)ⁿˣ  where:

Therefore, the amount (A)=2630.80

The P=2500

interest rate is 0.17%

Number of interest applied per period is 365 periods and

number of time period is 3.

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Answer:

The length = 5x + 25

Step-by-step explanation:

A = l x w

The probability that exactly one insect will die is 142.611.

The subject of a random event is covered in the mathematical field of probability. For instance, if a coin is flung into the air, it could land on its Head or Tail. Probability is equal to the number of favorable outcomes (Total number of outcomes) P = n (E) / n (S) (S) E is the event, P is the probability, and S is the sample area.

Given,

P( an insect will die) = 0.60

q = 1 - p

q = 1 - 0.60

q = 0.40

Sample size,

n = 9

Binomial distribution:

P(X) = ⁿCₓ pˣ qⁿ⁻ˣ

Probability that exactly one insect will die = P(X = 1)

= ⁹C₁ × 0.6¹ × 0.4⁸

= 362880 × 0.6 × 0.000655

= 142.611

The probability that exactly one insect will die is 142.611.

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the required sample size for the interval estimate with a 95% level of confidence  is 385

since we are given the margin of error which is f $10 and a standard deviation which is $1,000,  and we are also given the level of confidence which is 95%

so the formula we are  referring to calculate the sample size is :

n=z(0..95)*s²/ E

here, E is the margin of error, S is the standard deviation

so z score of 0.95 is 1.96

so n = 1.96*1000^2/100

        = 384.16 ,which is almost 385

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Step-by-step explanation:

ratios are special fractions and follow therefore all the fraction rules.

e.g. they follow the rule that for transformations the same multiplications or divisions have to happen for the denominator and the numerator when bringing them to the same denominator.

and they follow the same division and multiplication rules.

2/3 : 1/6 : 5/2 = (2/3)×(2/2) : 1/6 : (5/2)×(3/3) =

4/6 : 1/6 : 15/6 = 4 : 1 : 15

The confidence interval for the population mean is 0.2896 , 0.3505)

The sample mean is x = 0.32

The sample standard deviation is s = 0.09

The sample size is n = 10

The population standard deviation is unknown and sample size is atleast 10.

Thus use the t distribution.

Replacing the values in the following formula, determine the 95% confidence interval.

95% C.I = x ± t₀.₉₅,ₙ₋₁ . Sm

= x ± t₀.₀₅/₂,₁₀₋₁ . s/√n

= 0.32 ± 2.03 . 0.09/√10

= (0.2896 , 0.3505)

Hence the confidence interval for the population mean is 0.2896 , 0.3505)

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Confidence interval for 68% confidence level = (0.548, 0.572)

Confidence interval for 95% confidence level = (0.536, 0.584)

Confidence interval for 99.99% confidence level = (0.523, 0.598)

The mean of this sample distribution is

Mean = μₓ = np = 0.61 × 1600 = 976

But the sample mean according to the population mean should have been

Sample mean = population mean = nP

= 0.56 × 1600 = 896.

To find the interval of values where the sample proportion should fall 68%, 95%, and almost all of the time, we obtain confidence intervals for those confidence levels. Because, that's basically what the definition of the confidence interval is; an interval where the true value can be obtained to a certain level. of confidence.

We will be doing the calculations in sample proportions,

We will find the confidence interval for the confidence levels of 68%, 95% and almost all of the time (99.7%).

Basically the empirical rule of 68-95-99.7 for standard deviations 1, 2, and 3 from the mean.

Confidence interval = (Sample mean) ± (Margin of error)

Sample Mean = population mean = 0.56

The margin of Error = (critical value) × (standard deviation of the distribution of sample means)

Standard deviation of the distribution of sample means = [tex]\sqrt{[p(1-p)/n]}[/tex] =

[tex]\sqrt{[(0.56\times0.44)/1600]}[/tex] = 0.0124

The critical value for 68% confidence interval = 0.999 (from the z-tables)

The critical value for 95% confidence interval = 1.960 (also from the z-tables)

Critical values for the 99.7% confidence interval = 3.000 (also from the z-tables)

Confidence interval for 68% confidence level

= 0.56 ± (0.999 × 0.0124)

= 0.56 ± 0.0124

= (0.5476, 0.5724)

Confidence interval for 95% confidence level

= 0.56 ± (1.960 × 0.0124)

= 0.56 ± 0.0243

= (0.5357, 0.5843)

Confidence interval for 99.7% confidence level

= 0.56 ± (3.000 × 0.0124)

= 0.56 ± 0.0372

= (0.5228, 0.5972)

Therefore,

Confidence interval for 68% confidence level = (0.548, 0.572)

Confidence interval for 95% confidence level = (0.536, 0.584)

Confidence interval for 99.99% confidence level = (0.523, 0.598)

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The number of pieces the bakery will sell is 16 and a half. The total amount of money they will make is $82.5.

To get the number of pieces of pies that they have to sell, we need to first determine how many 1/4 pies are in 4 and 8 pieces of bread. Going by that, we can see that:

1/4x of 4 = 16.

Also, 1/4x of 1/8 = 1/2.

So, the total number of pies that they have to sell is 16 and a half.

Now if 1/4 of a pie costs $5, then 4 1/8 will be equal to 33/8 × 5 ÷ 1/4.

This is equal to 165/8 × 4 = $82.5

So, the total amount of money that the bakery will make will be $82.5.

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There are 126 blue marbles.

Total marbles in the bag=150

There are 21 blue marbles for every 4 white marbles then the sequence will be⇒ 4+21+4+21+4+21+4+21+4+21+4+21=150

21 blue marbles appear 6 times for every 4 blue marbles

So 21×6=126 blue marbles and 4×6=24, then 126+24=150 total marbles

∴There will be a total of 126 blue marbles along with 24 white marbles among the 150 marbles.

The degree of the polynomial is 5, and the end behavior is:

as x → ∞, f(x) → -∞

as x → -∞, f(x) → ∞

For any given polynomial, we define the degree as the largest exponent on the polynomial.

On this case we have:

f(x) = 2x^3 - 3x^5 - x^2 + 1

We can see that the largest exponent is 5, so the degree is 5.

Now, for the ending behavior.

If we have an odd degree (like in this case) we will have opposite ending behaviors in both ends of the domain.

If the leading coefficient is negative (like in this case, it is -3) then the end behavior will be:

as x → ∞, f(x) → -∞

as x → -∞, f(x) → ∞

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When a bowling ball is propelled with a force of 22. 0 N and accelerates at a rate of 5. 5 [tex]ms^{-2}[/tex], its mass is 4. 0 kg.

Newton's Second Law of Motion states that force is the result of mass times acceleration.

[tex]F=m*a[/tex]

[tex]m = F / a[/tex]

A force of 22.0 Newtons (  [tex]kgms^{-2}[/tex] ) and an acceleration of 5.5 meters per second squared were used to drive the bowling ball.

F = 22.0 [tex]kgms^{-2}[/tex] and

a = 5.5 [tex]ms^{-2}[/tex]

Put the values in the formula as replacements.

M = 22 [tex]kgms^{-2}[/tex]/ 5.5 [tex]ms^{-2}[/tex]

Meters per second squared (m/s2) units cancel each other out.

M = 22 kg / 5.5

   = 4 kg

The bowling ball weighs 4 kilogram.

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Answer:

3

Step-by-step explanation:

[tex]4x + 5y = - 5 \\ 8 + 4x + 5y = {?} \\ 8 + - 5 \\ = 3 \\ 8 + 4x + 5y = 3[/tex]

Let x denote the score. Assuming x follows normal distribution with

mean m = 70 and SD = 5 ,

we first calculate P( x < or = 80)

The SNV is z = (x — m) /SD

When x = 80, Z = ( 80 — 70)/5 = 2

So, P( x < or= 80)

Given that total number of students is

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The number 1.41421356 is not a rational number.

What is a rational number?

A number that can be expressed as a ratio is called a rational number. This indicates that it may be expressed as a fraction, where the numerator (the number on top) and denominator (the number on the bottom) are both whole numbers.

The given number is 1.41421356

The square root of 2 has the approximate value of 1.41421356

The number is non-terminating and non-repeating decimals.

That's why the given number is not a rational number.

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The minimum cost will be 1091 units.

Define Vertex Formula.

When the graph crosses its symmetry axes, the vertex formula aids in determining the vertex coordinate of a parabola. The vertex point is often represented by (h, k).

We are aware that a parabola's conventional equation is y=ax²+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x² is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x² is negative.

Given expression is,

C = 70,000 - 120x + 0.055x²

For this equation, the graph will be parabola opening upward.

For that, the vertex will be the minimum cost

x = (-b) / 2a

Here, a = 0.055 , b = -120

Now, plug in the values and find 'x'

minimum cost (x) = ( -(-120) ) / ( 2 * 0.055 )

                            = 120 / 0.11

                            = 120 / 0.11

                            = 1090.90  or 1091 units

Therefore, the minimum cost will be 1091 units.

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The expression that is equivalent is 6(y + 1) and 6y + 6.

The expression that are not equivalent are 3(x + 3) and 3x + 6 and x(x + 4) and x² + 4.

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.

Now, let's check if the expression are equivalent by simplifying it.

3(x + 3) and 3x + 6

3x + 9 and 3x + 6

Therefore, the expressions are not equivalent.

6(y + 1) and  6y + 6

6y + 6 and 6y + 6

They are equivalent expression.

x(x + 4) and x² + 4

x² + 4x and x² + 4

They are not equivalent expression.

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Answer:

Step-by-step explanation:

15 ile 25 arasında toplam 10 tam sayı var,
buna 25-15=10 şeklinde ulaşabiliriz. Ardından tek sayılar sorulduğu için ve bu 10 tam sayı içerisinde hem tek hemde çift olduğu için sayıyı ikiye böleriz
10/2=5 ve ardından en sonda bulunan 25 sayısını çıkarırız yani, 5-1=4

cevaplar: 17, 19,21,23

Answer:

20

Step-by-step explanation:

do parenthesis first

1/5(3+2+ 5)² =

1/5(10)² =

then exponent

1/5(10)² =

1/5(100) =

20

Answer: when the value on each side of the equal sign is the same

Step-by-step explanation: for example, 9=9 is a true equation. 5+4 = 9 is a true equation

The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.

Hence, The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.

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The equation of the line that passes through the points (-2,-6) and (1,2) is y = 8x/3-2/3.

According to the question,

We have the following information:

Points through which line is passing =  (-2,-6) and (1,2)

Now, we have the following values:

x1 = -2, y1 = -6

x2 = 1 and y2 = 2

We know that the following formula is used to find the slope of the line:

m = (y2-y1)/(x2-x1)

m = (2+6)/(1+2)

m = 8/3

Now, the following formula is used to find the equation of the line:

y-y1 = m(x-x1)

y+6 = 8/3(x+2)

y+6 = 8x/3+16/3

Subtracting 6 from both sides:

y = 8x/3+16/3-6

y = 8x/3-2/3

Hence, the equation of the line that passes through the points (-2,-6) and (1,2) is y = 8x/3-2/3.

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If the amount after 4 years is 844.13. Then the rate of the compound interest will be 3%.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Hannah contributes £750 and following 4 years has £844.13. Then the compound interest rate is given as,

844.13 = 750 (1 + r)⁴

(1 + r)⁴ = 1.1255

1 + r = 1.02999

r = 0.0299

r = 2.99%

r ≈ 3%

If the amount after 4 years is 844.13. Then the rate of the compound interest will be 3%.

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The exponential function has an equation of f(x) = 2(3)^x

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

(0, 2) and (1,6)

Also, we understand that

Function type = Exponential function

An exponential function is represented as

f(x) = ab^x

At point (0, 2), we have

2 = ab^0

Evaluate

a = 2

Substitute a = 2 in f(x) = ab^x

f(x) = 2b^x

At point (1, 6), we have

6 = 2b^1

This gives

2b = 6

Divide

b = 3

So, we have

f(x) = 2(3)^x

Hence, the equation of the exponential function is f(x) = 2(3)^x

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The number of views in the four weeks round to the whole number is 48.

Here it is given that the initial number of views for a reader board was 25 and it gets increased at the rate of 18% per week.

We have to find the number of views in the fourth week.

On the first week the increase = 25 + 25× 18%

                                                   = 25 + 25 × 18/100

                                                   = 25 + 4.5

                                                   = 29.5

The second week increase = 29.5 + 29.5 × 18%

                                              = 29.5 + 5.31

                                                = 34.81

The third week increase = 34.81 + 34.81 × 18%

                                         = 34.81 + 6.2658

                                         = 41.0758

The fourth week increase = 41.0758 + 41.0758 × 18%

                                           = 41.0758 + 7.393644

                                            = 48.469444

Therefore the number of views in the four weeks is 48.

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The time taken by peregrine falcon dove at its maximum speed to cover half a mile is 9 sec.

For the given question;

The maximum speed of peregrine falcon dove is 200 mph.

Time of travel  = 0.5 miles.

The relation of distance and speed is;

speed = distance/time

200 mph = 0.5 miles / time

Time = 0.5 miles / 200 mph

Time = 0.5 × 60 × 60  miles / 200 m/ sec

Time = 9 sec

Thus, time taken by peregrine falcon dove at its maximum speed to cover half a mile is 9 sec.

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