Write a formula that describes the value of an initial investment of $1,200, growing an interest rate of 4% compounded continuously.​

The required function that represents the situation is [tex]y=800(\frac{1}{4} )^t[/tex]

The standard exponential function is expressed as:

[tex]y=ab^x[/tex] where:

Given the following parameters:

a = 800

b = 1/4

Substitute into the formula to have;

[tex]y=800(\frac{1}{4} )^t[/tex]

Hence the required function that represents the situation is [tex]y=800(\frac{1}{4} )^t[/tex]

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Answer:

It's 800(3/4)^t

Step-by-step explanation:

The Murphy family spend $ 700

Solution:

Given that,

Murphy family has 4 members and they went to 7 games

Let "x" be the cost of each game

Murphy family cost: [tex]4 \times 7 \times x = 28x[/tex]

Chen family has 5 members and they went to 4 games

Chen family cost: [tex]5 \times 4 \times x = 20x[/tex]

In total, the two families spent $1200

Therefore,

28x + 20x = 1200

48x = 1200

Divide both sides by 48

x = 25

How much did the Murphy family spend?

Murphy family cost = 28x = 28(25) = 700

Thus murphy family spend $ 700

Answer: The quotient is 2x² - x + 1

Step-by-step explanation:

We would apply the long division method to find the quotient of

(2x^3 + x^2 + 1)/(x + 1)

The attached photo shows the step by step calculations

Answer:

The answer is:

22 tacos per tray

Step-by-step explanation:

Number of trays:

Number of Tacos is 88:

Put 22 Taco's in each tray:

Tray 1.  22 Tacos

Tray 2. 22 Tacos

Tray 3. 22 Tacos

Tray 4. 22 Tacos

Example of dividing:

All 4 trays Add up to 88 tacos total

I hope this helped! <3

Answer: the function is

A = 120000(1.055)^x

Step-by-step explanation:

A homes value increases at an average rate of 5.5% each year. The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

A = P(1 + r/n)^ nt

Where

A represents the value of the home after t years.

n represents the period of growth

t represents the number of years.

P represents the initial value of the home.

r represents rate of increase in value.

From the information given,

P = 120000

r = 5.5% = 5.5/100 = 0.055

n = 1

Therefore

A = 120000(1 + 0.055/1)^ x × 1

A = 120000(1.055)^x

Answer: B. Population X will require a larger sample size

Step-by-step explanation:

Given : Two population distributions labeled X and Y.

Distribution X → highly skewed

Distribution Y → slightly skewed.

Since Distribution X more skewed so , we will need a larger sample size of population X as compared to Y.

Hence, the correct answer is B. Population X will require a larger sample size

The correct option is B. Population X will require a larger sample size.

According to the Central Limit Theorem, the sampling distribution of the sample mean will tend to be normally distributed as the sample size becomes larger, regardless of the shape of the population distribution. However, the rate at which the sampling distribution approaches normality depends on the degree of skewness in the population distribution.

For a population distribution that is highly skewed (like Distribution X), a larger sample size is needed for the sampling distribution to approximate a normal distribution compared to a population distribution that is only slightly skewed (like Distribution Y). This is because the effects of skewness are more pronounced and take longer to "average out" in larger samples.

Therefore, to achieve the same degree of normality in their respective sampling distributions, Population X, with its high skewness, will require a larger sample size than Population Y, which is only slightly skewed.

Answer:

c)

Step-by-step explanation:

α also known as type I error depicts the probability of rejecting the true null hypothesis. So, when α=0.05 then it means that there is 5% probability or chance of rejecting the true null hypothesis.

So, in hypothesis testing α=0.05 means that there is a maximum 5 percent chance that a true null hypothesis will be rejected.

Answer:

P=1/12

Step-by-step explanation:

From Exercise we have  ten people are in a room wearing badges marked 1 through 10.

For first man we conlude that  the probability that is 5/10,  that  his number at least 6.

For second man we conlude that  the probability that is 4/9,  that  his number at least 6.

For third man we conlude that  the probability that is 3/8,  that  his number at least 6.

Therefore, the probability is

P=5/10 · 4/9 · 3/8 = 1/12

P=1/12

Answer:

Step-by-step explanation:

Triangle VWX is a right angle triangle.

From the given right angle triangle,

VX represents the hypotenuse of the right angle triangle.

With m∠X as the reference angle,

WX represents the adjacent side of the right angle triangle.

VW represents the opposite side of the right angle triangle.

To determine m∠X, we would apply

the tangent trigonometric ratio. It is expressed as

Tan θ = opposite side/adjacent side. Therefore,

Tan X = 2/1 = 1

m∠X = Tan^-1(1)

m∠X = 45°

The inequality representing Marisa's goal to buy a phone costing at least $200, with $125 already saved and a plan to save $10 each week, is 125 + 10w \\geq 200, where w is the number of weeks of additional savings.

To write an inequality that represents Marisa's situation, we need to consider the amount she has already saved, the additional amount she plans to save weekly, and the minimum amount she needs for the phone. Marisa wants a phone that costs at least $200 and has saved $125. She plans to save $10 each week. We can use the variable w to represent the number of weeks she will save additional money.

Marisa's current savings plus the additional amount she plans to save for w weeks needs to be at least $200. This situation can be represented by the following inequality:

125 + 10w \\geq 200

Here, 125 represents the amount already saved, 10w represents the additional amount saved after w weeks, and the inequality symbol \\geq (greater than or equal to) establishes that Marisa's total savings must be at least $200.

Answer:

[tex]p(x) = {x}^{4} + {x}^{3} - 7 {x}^{2} - x + 6[/tex]

Step-by-step explanation:

The polynomial function has zeros

x=1, x=2,x=-3,x=-1

This means the factored form of the polynomial is

[tex]p(x) = (x - 1)(x + 1)(x + 3)(x - 2)[/tex]

We expand to get:

[tex]p(x) = ( {x}^{2} - 1)( {x}^{2} + x - 6)[/tex]

We expand further to get:

[tex]p(x) = {x}^{2}( {x}^{2} + x - 6) - 1({x}^{2} + x - 6)[/tex]

[tex]p(x) = {x}^{4} + {x}^{3} - 6 {x}^{2} - {x}^{2} - x + 6[/tex]

This simplifies to:

[tex]p(x) = {x}^{4} + {x}^{3} - 7 {x}^{2} - x + 6[/tex]

This is the standard form of the polynomial since it is written in descending powers of x.

Answer: Julia is 48 years

The oldest child is 16 years

The youngest child is 12 years

Step-by-step explanation:

Let x represent the age of the youngest child.

Let y represent the age of the oldest child.

Let x represent Julia's age.

The sum of the ages of Julia and her 2 kids is 76 years. This means that

x + y + z = 76- - - - - - - - - - -1

Julia has 2 children who are 4 years apart in age. This means that

y = x + 4

Julia is four times older than her youngest child. This means that

z = 4x

Substituting z = 4x and y = x + 4 into equation 1, it becomes

x + x + 4 + 4x = 76

6x = 76 - 4 = 72

x = 72/6 = 12

y = x + 4 = 12 + 4

y = 16

z = 4x = 4 × 12

z = 48

Answer:

what?

Step-by-step explanation:

Answer:

seven eights mean; 8888888

they can repave one fifty six mile per hour; 156/hour

Step-by-step explanation:

To calculate total time to repave

8888888/156 = 56980.02 hours require

Answer:

The Final answer will be [tex]x^2-x+1[/tex] with remainder 0.

Step-by-step explanation:

We have attached the division for your reference.

Given:

Dividend = [tex]x^4+x^3+7x^2-6x+8[/tex]

Divisor = [tex]x^2+2x+8[/tex]

Explaining the division we get;

Step 1: First when we divide the Dividend [tex]x^4+x^3+7x^2-6x+8[/tex] with divisor  [tex]x^2+2x+8[/tex] we will first multiply [tex]x^2[/tex] with the divisor then we get the Quotient as [tex]x^2[/tex]  and Remainder as [tex]-x^3-x^2-6x+8[/tex]

Step 2: Now the Dividend is [tex]-x^3-x^2-6x+8[/tex] and Divisor [tex]x^2+2x+8[/tex] is  we will now multiply [tex]-x[/tex] with the divisor then we get the Quotient as [tex]x^2-x[/tex] and Remainder as [tex]x^2+2x+8[/tex]

Step 3: Now the Dividend is [tex]x^2+2x+8[/tex] and Divisor is [tex]x^2+2x+8[/tex] we will now multiply 1 with the divisor then we get the Quotient as [tex]x^2-x+1[/tex]  and Remainder as 0.

Hence The Final answer will be [tex]x^2-x+1[/tex] with remainder 0.

Answer:

5/6

Step-by-step explanation:

The ratio 35:42 represents the fraction:

                                                       [tex]\dfrac{35}{42}[/tex]

Now we have to cancel this fraction - we will divide numerator and denominator by 7:

35/7 = 5

42/7 = 6

Therefore,

                       [tex]\dfrac{35}{42} = \dfrac{7\cdot 5}{7\cdot 6} =\dfrac{5}{6}[/tex]

Answer:

Are there like any images or opinions for your question

Answer:

Option b) Sample                                                            

Step-by-step explanation:

We are given the following in the question:

Survey:

356 surveys on television-viewing habits of American adolescents.

Result:

Average of 3.1 hours per day.

Population and sample:

For the given survey, those who responded to the survey forms a a sample as it is a part of 356 surveys that is a subset of population.

The correct answer is

Option b) Sample

Answer:yes

Step-by-step explanation:

Answer:

should be the 3rd choice

Step-by-step explanation:

even though the 2nd choice is technically correct for a rhombus, but this property does not explain the first part of this 2 part question.

We are looking for an answer that supports pert 1 of the question.

by definition, a rhombus is a parallelogram with 4 sides of equal length, which means 2 adjacent sides will have the same length, which explains the answer in the first part because JK and KL are adjacent sides

Step-by-step explanation:

By Wien’s Law we have

              [tex]\lambda =\frac{2898}{T}[/tex]

          where λ is in μm and T is in K

Given that

             T = 6000 K

Substituting

              [tex]\lambda =\frac{2898}{6000}=0.483\mu m[/tex]

Option C is the correct answer.

Final answer:

By using Wien's Law with the given temperature of the Sun (6000K), we calculate the peak emission wavelength as 0.483 micrometers, which corresponds to option c. 0.48 µm.

Explanation:

The student asked about the wavelength most emitted by the Sun as predicted by Wien's Law, given the temperature of 6000K using the equation λ = 2898/T, where λ is the wavelength in micrometers and T is the temperature in Kelvin. According to Wien's displacement law, the temperature and peak wavelength of emission of an object are inversely proportional.

Plugging in the given temperature (T = 6000K) into the equation λ = 2898/T, we calculate the peak emission wavelength to be 2898/6000 = 0.483 µm.

So, the correct answer is c. 0.48 µm.

Answer:

24 ways

Step-by-step explanation:

4x3x2

12x2

24

Answer:

A) We are extrapolating. Extrapolation is dangerous because the pattern of data may change outside the x range.

Step-by-step explanation:

When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions? (Choose one)

A) We are extrapolating. Extrapolation is dangerous because the pattern of data may change outside the x range.

B) We are interpolating. There are no concerns about interpolation.

C) We are interpolating. Interpolation is dangerous because the pattern of data may change inside the x range.

D) We are extrapolating. There are no concerns about extrapolation.

The answer is A

assuming we are looking for the value of y within the range of x, we are interpolating. Take for instance, the range of  xi between 60 and 65, what is the value of y at point 62.5. This is interpolation.

But then we have the data sets of temperature of a particular place within 1 to 15 days in a month. if we are asked to look for its temperature on the 31st of that particular month, we are extrapolating, which might take a different pattern from the line of best bit

Using a least-squares line to predict y values for x values beyond the range of the data is called extrapolation. This process is risky because the pattern of data may change outside of the existing range, leading to inaccurate predictions.

When using a least-squares line to predict y values for x values beyond the range of x values found in the data, we are extrapolating. This is because we are making predictions outside of the range of the existing data set. However, extrapolation comes with certain risks. The pattern of the data may not remain constant beyond the data we have, leading to inaccurate predictions.

Therefore, answer A is the most accurate: 'We are extrapolating. Extrapolation is dangerous because the pattern of data may change outside the x range.'

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Answer:

the order is Helen Olivia Francessca

Step-by-step explanation:

ik im late but i hop this helps C:

The order of percentage of correct questions from least to greatest.

80% < 84% < 88%

Helen < Olivia < Francesca.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of questions in the test = 25.

Helen:

Percentage of the number of questions correct.

= 20/25 x 100

= 80%

Francesca:

Percentage of the number of questions correct.

= 22/25 x 100

= 88%

Olivia:

Percentage of the number of questions correct.

= 84%

Thus,

Arranging the percentage in increasing order.

80% < 84% < 88%

Helen < Olivia < Francesca.

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The coordinates of X are (5, 11).

Solution:

Given points of the line segment are P(2, 2) and T(7, 17)  

Let X be the point that partitions the directed line segment PT in the ratio 3 : 2

Using section formula, we can find the coordinate of the point that partitions the line segment.

Section formula:

[tex]$X(x, y)=\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}\right)[/tex]

Here, [tex]x_{1}=2, y_{1}=2, x_{2}=7, y_{2}=17[/tex] and m = 3, n =2

Substitute these in the section formula,

[tex]$X(x, y)=\left(\frac{3 \times 7+2 \times 2}{3+2}, \frac{3 \times 17+2 \times 2}{3+2}\right)[/tex]

            [tex]$=\left(\frac{21+4}{5}, \frac{51+4}{5}\right)[/tex]

           [tex]$=\left(\frac{25}{5}, \frac{55}{5}\right)[/tex]

           [tex]=(5, 11)[/tex]

X(x, y) = (5, 11)

The coordinates of X are (5, 11).

Answer:

100

Step-by-step explanation:

Answer:

25,000

Step-by-step explanation:

For the described uniform distribution, the probability that a fish is between 0.25 and 2 feet long can be found by calculating the area under the probability density function graph, which gives a result of 43.75%.

The given situation implies a uniform distribution as the probability density function is constant (equal to 1/4) for fish lengths between 0 and 4 feet, and zero otherwise. For such a distribution, the probability that the length x is in an interval can be found by calculating the area under the probability density function graph for that interval. As the graph is a rectangle, this is as simple as length times width.

Here, the interval is from 0.25 to 2 feet. The length of this interval is (2 - 0.25)= 1.75 feet. The width of the rectangle is the constant probability density function value of 1/4. Hence, the probability that a fish caught by the sports fishermen is between 0.25 and 2 feet long is 1.75 * 1/4 = 0.4375 or 43.75%.

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Answer: there are 25 red flowers in Sakura's garden.

Step-by-step explanation:

In Sakura's garden, for every 5 red flowers, there are 10 yellow flowers. This means that if there are 10 red flowers, there would be 20 yellow flowers. if there are 20 red flowers, there would be 40 yellow flowers. Therefore, the ratio of red flowers to yellow flowers in the garden is

5/10 = 10/20 £= 20/40 = 1/2 = 1:2

Total ratio = 2 + 1 = 3

If there are 75 total red and yellow flowers, then the total number of red flowers are in Sakura's garden would be

1/3 × 75 = 25

Answer:

25

Step-by-step explanation:

Step-by-step explanation: Understand it as a ratio. 5:10. Add both ratios together, 15. Make an expression, 15x=75. x=5, Then multiply 10 and 5 by 5 and that will give you the ratio of 25:50 red to yellow flowers.

Answer:

Ethan can type 12 pages before the meeting starts.

Step-by-step explanation:

Given:

Number of pages he can type =2

Number of hours he can type 2 pages = [tex]\frac{1}8\ hrs[/tex]

We need to find number of pages he can type in [tex]\frac34\ hrs[/tex]

Solution:

Now first we will  find number of pages in 1 hour

So we can say;

In [tex]\frac{1}8\ hrs[/tex]  = 2 pages

In 1 hour = number of pages he can type in 1 hour

By Using Unitary method we get;

number of pages he can type in 1 hour = [tex]\frac{2}{\frac18} =\frac{2\times8}{1}=16\ pages[/tex]

Now we can say that;

In 1 hour = 16 pages

So [tex]\frac34\ hrs[/tex] = number of pages he can type in [tex]\frac34\ hrs[/tex]

Again By using Unitary method we get;

number of pages he can type in [tex]\frac34\ hrs[/tex] = [tex]16\times \frac34 = 12\ pages[/tex]

Hence Ethan can type 12 pages before the meeting starts.

Final answer:

Ethan has 3/4 hours to type and can complete two pages every 1/8 hour, resulting in a total of 12 pages typed before the meeting starts.

Explanation:

Ethan can type two pages every 1/8 hour. To find out how many pages he can type before the start of the meeting, we need to calculate the total pages he can type in the waiting time of 3/4 hours. Here's the step-by-step calculation:

Calculate the number of 1/8 hour intervals in 3/4 hours by dividing: (3/4) ÷ (1/8) = (3/4) × (8/1) = 6.

Since he types two pages every 1/8 hour, we find the total number of pages by multiplying the number of intervals by 2: 6 × 2 = 12 pages.

Therefore, Ethan can type a total of 12 pages before the meeting starts.

Answer:

The action required by the submarine to get back to the surface is to rise 195 feet

Step-by-step explanation:

we know that

The ocean's surface or sea level is at an elevation of 0 feet.

we have

1) A submarine dives 270 feet below the ocean's surface

In this moment the position of the submarine is

-270 ft ---> is negative because is below the sea level

2) It then rises 90 feet

In this moment the position of the submarine is

-270+90=-180 feet

3) rises another 40 feet,

In this moment the position of the submarine is

-180+40=-140 feet

4) Finally dives 55 feet

In this moment the position of the submarine is

-140-55=-195 feet

therefore

The action required by the submarine to get back to the surface is to rise 195 feet

Final answer:

The submarine initially dives to 270 feet below the surface and undergoes a series of rises and dives. After all movements, it is at a depth of 195 feet. To return to the surface, it needs to rise 195 feet.

Explanation:

A student asked: A submarine dives 270 feet below the ocean's surface. It then rises 90 feet, rises another 40 feet, and finally dives 55 feet. What action is required by the submarine to get back to the surface?

To solve this problem, we will sum up the changes in the submarine's depth and find out how much more it needs to rise to reach the surface.

Summing up these changes: -270 + 90 + 40 - 55 = -195 feet.

The submarine is currently 195 feet below the surface. Therefore, to get back to the surface, the submarine needs to rise 195 feet.

Answer:

a. Mean = 6

Variance = 2.4

Standard Deviation = 1.55

b. P(X=16) = 0.124

Step-by-step explanation:

Given

n = Total shots = 10

p = Probability of success = 60%

p = 60/100

p= 0.6

q = Probability of failure

q = 1-p

q = 1 - 0.6

q = 0.4

a.

Mean = np

Mean = 10 * 0.6

Mean = 6

Variance = npq

Variance = 10 * 0.6 * 0.4

Variance = 2.4

Standard Deviation = √Variance

Standard Deviation = √2.4

Standard Deviation = 1.549193338482966

Standard Deviation = 1.55 --------- approximated

b.

We have X = 16

x = 10

Assume that the events "success" on the various throws are independent.

The 10th success came on the 16th attempt

So, the player had exactly 10 successes and 6 failures on 16th trial

So Probability = nCr 0.6^10 * 0.4^6

Where n = 15 and r = 9 (number of attempts and success before the 16th trial)

15C9 * 0.6^10 * 0.4^6

= 5005 * 0.0060466176 * 0.004096

= 0.123958563176448

= 0.124 ------ Approximated

A. The mean, variance, and standard deviation of x are: Mean: 16.67, Variance: 11.11 and  Standard deviation: 3.33.   B. The probability that the player will need exactly 16 attempts to make 10 successful shots is approximately 0.123

Given that a basketball player can make a free throw 60% of the time, we are to determine the minimum number of free throws that this player must attempt to make a total of 10 shots.

Since each shot is independent and has a 60% chance of being successful, this scenario follows a negative binomial distribution.

(a) Calculating the mean, variance, and standard deviation:

Mean:

[tex]\[ \mathbb{E}[X] = \frac{r}{p} = \frac{10}{0.60} = \frac{10}{0.6} = 16.67 \][/tex]

Variance:

[tex]\[ \text{Var}(X) = \frac{r(1-p)}{p^2} = \frac{10(1-0.60)}{0.60^2} = \frac{10 \cdot 0.40}{0.36} = \frac{4}{0.36} = 11.11 \][/tex]

Standard deviation:

[tex]\[ \sigma = \sqrt{\text{Var}(X)} = \sqrt{11.11} \approx 3.33 \][/tex]

So, the mean, variance, and standard deviation of x are: Mean: 16.67, Variance: 11.11 and  Standard deviation: 3.33

(b) Finding  P(X = 16)

The probability mass function of a negative binomial random variable  \is given by:

[tex]\[ P(X = k) = \binom{k-1}{r-1} p^r (1-p)^{k-r} \][/tex]

[tex]\[ P(X = 16) = \binom{15}{9} (0.60)^{10} (0.40)^{6} \][/tex]

Calculating the binomial coefficient:

[tex]\[ \binom{15}{9} = \frac{15!}{9!(15-9)!} = \frac{15!}{9!6!} \][/tex]

This can be computed as follows:

[tex]\[ \binom{15}{9} = \frac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10}{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 5005 \][/tex]

Combining these:

[tex]\[ P(X = 16) = 5005 \cdot 0.0060466 \cdot 0.004096 \approx 0.123 \][/tex]

Therefore:

[tex]\[ P(X = 16) \approx 0.123 \][/tex]

So, the probability that the player will need exactly 16 attempts to make 10 successful shots is approximately 0.123