QUESTION 10 ..... [1.5 marks]
You are testing two random samples of 25 (group 1) people and 27 (group 2) people and you found that
those in the first group are spending in average $38.6 a day and those in the second group re spending in
average $37.4 a day. Assume that the population standard deviation for the first group is $5.3 and the
population standard deviation for the second group is $6.8.
At a = 0.01, can you conclude that there is a significant difference in the average amount on money
each group is spending every day?
Justify your answer by stating what is
(a) the null hypothesis and alternative hypothesis. Explain what test (left-tailed, right-tailed or two-tailed)
you are using. Also find
(b) critical z-value (not the p-value!)
(c) test value

The missing value that completes the frequency table is 100.

A frequency table is a statistical tool that summarizes data by displaying the frequency (or count) of each category or interval in a data set. It is commonly used in data analysis to organize and understand categorical or numerical data.

The missing value is the frequency for the value range between 28 and 30 (i.e 28 ≤ x ≤30). Looking at the histogram, you will notice that the frequency for the value between 28 and 30 is 100 (Check the attached image).

Therefore, the missing value is 100.

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To choose a simple random sample assign different numbers to the house and visit by choosing randomly.

To choose a simple random sample of the 3 homes to survey,

Jerome could assign each home a number from 1 to 10,

And then use a random number generator or a table of random numbers to select three numbers.

He would then visit the homes corresponding to those numbers for the survey.

For example,

if he assigned the following numbers to each home,

1, 2, 3, 4, 5, 6, 7, 8, 9 ,10

He could use a random number generator or table of random numbers to select three numbers, such as 2, 5, and 9.

He would then visit the homes at 2, 5, 9 for the survey.

If someone is not home when Jerome visits,

He should make a note of it and try to arrange a time to come back and conduct the survey.

If it is not possible to arrange another time,

He should make a note that the household was not surveyed and move on to the next household in the sample.

It is important to keep track of which households were surveyed and which were not.

And to try to minimize any biases that may arise from nonresponse.

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(a) We can rewrite 32 as 2^5, so we have:

8^(2x) = (2^5)^(x+3)

Simplifying the right side, we get:

8^(2x) = 2^(5x+15)

(b) Now we can use the fact that 8 is 2^3, so we can rewrite the left side as (2^3)^(2x) = 2^(6x), giving us:

2^(6x) = 2^(5x+15)

Since the bases are equal, we can equate the exponents and solve for x:

6x = 5x + 15

x = 15

Therefore, the solution is x = 15.

Answer:

linear

Step-by-step explanation:

yw

Answer:

Step-by-step explanation:

The equation of the polynomial using finite difference is y = 18x^3 - 126x^2 + 269x - 163 and other solutions are shown below

To find the equation of the polynomial table using finite difference, we need to calculate the differences.

The differences are obtained by subtracting each value of y from the next value of y and this is repeated for the differences

So, we have

x   1   2   3   4   5

y  -2  15  -4  49  282

1st 17 -19  53 233

2nd -36 72 180

3rd 108 108

Since the third differences are all the same, this indicates that the original data can be represented by a cubic polynomial.

We can use the formula for a cubic polynomial:

y = ax^3 + bx^2 + cx + d

Using the table of values, we have:

a + b + c + d = -2

8a + 4b + 2c + d = 15

27a + 9b + 3c + d = -4

64a + 16b + 4c + d = 49

Using a graphing calculator, we have

a = 18, b = -126, c = 269 and d = -163

So, we have

y = 18x^3 - 126x^2 + 269x - 163

We can use the formula for a cubic polynomial:

y = a(x - x1)(x - x2)(x - x3)

Using the ordered pairs, we have:

y = a(x + 3)(x + 1)(x - 2)

At (0, -12), we have

a(0 + 3)(0 + 1)(0 - 2) = -12

a = 2

So, we have

y = 2(x + 3)(x + 1)(x - 2)

Expand

y = 2x^3 + 4x^2 - 10x - 12

We can use the formula for a cubic polynomial:

y = a(x - x1)(x - x2)(x - x3)

Using the ordered pairs, we have:

y = a(x + 10)(x + 5)(x - 4)

At (-8, -2), we have

a(-8 + 10)(-8 + 5)(-8 - 4) = -2

a = -1/36

So, we have

y = -1/36(x + 10)(x + 5)(x - 4)

Expand

[tex]y = -\frac{x^3}{36}-\frac{11x^2}{36}+\frac{10x}{36}+\frac{200}{36}[/tex]

We have

g(x) = -9x^5 + 3x^4 + x^2 - 7

g(x) is a polynomial function of odd degree (5), so it will have at least one real root.

Also, the leading coefficient is negative;

So, g(x) has at least one root in the interval (-∞, ∞).

Since g(0) = -7 < 0 and g(1) = -12 < 0, and g(x) is continuous, there exists a root of g(x) in the interval (0, 1).

Similarly, since g(-1) = 6 > 0 and g(-2) = 333 > 0, there exists a root of g(x) in the interval (-2, -1).

Since g(x) is a polynomial of odd degree, it cannot have an even number of real roots.

Therefore, g(x) has exactly one real root.

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The value of M - N is [tex]8x^2[/tex] + 11x - 9 by subtracting the value of N from the value of M.

To find the value of M - N, we first need to subtract the second polynomial N from the first polynomial M.

M - N = ([tex]5x^2[/tex] + 7x - 4) - ([tex]-3x^2[/tex] - 4x + 5)

To subtract the polynomials, we need to add the opposite of the second polynomial (i.e., add the negative of N) to the first polynomial M:

M - N = [tex]5x^2[/tex] + 7x - 4 + [tex]3x^2[/tex] + 4x - 5

Now we can combine like terms:

M - N = ([tex]5x^2 + 3x^2[/tex]) + (7x + 4x) + (-4 - 5)

M - N = [tex]8x^2[/tex] + 11x - 9

Therefore, the value of M - N is [tex]8x^2[/tex] + 11x - 9.

In summary, we found the value of M - N by subtracting the polynomial N from the polynomial M and then combining like terms. The resulting polynomial is [tex]8x^2[/tex] + 11x - 9.

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The value of x in the given similar triangles is 30.8.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are described as items with the same shape but varying sizes, such as two or more figures. A hula hoop and the wheel of a bicycle are two examples of things whose forms are similar to one another.

Given that the triangles are similar, thus the ratio of their sides are equal.

Here, 28/10 = x / 11

Using cross multiplication we have:

x = 28 / 10 (11)

x = 30.8

Hence, the value of x in the given similar triangles is 30.8.

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[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 20\%\to \frac{20}{100}\dotfill &0.2\\ t=\textit{elapsed time} \end{cases} \\\\\\ A = 50(1 + 0.2)^{t} \implies \boxed{A =50(1.2)^t}[/tex]

Answer:

X = 3,2

Step-by-step explanation:

1)Expand.

[tex]x^{2}[/tex] - 8X+3X - 24 = -30

2)Simplify [tex]x^{2}[/tex]-8X+3X-24 to [tex]x^{2}[/tex]-5X - 24.

[tex]x^{2}[/tex] – 5X – 24 = –30

3)Move all terms to one side.

[tex]x^{2}[/tex] - 5X - 24+ 30 = 0

4)Simplify [tex]x^{2}[/tex]–5X-24+30 to [tex]x^{2}[/tex] - 5X + 6.

[tex]x^{2}[/tex] - 5X + 6 = 0

5)Factor [tex]x^{2}[/tex]–5X+6.

(X-3)(X-2) = 0

6)Solve for X.

X = 3,2

a) The time that Rodrigo spent practicing during the third week is 5.42 hours.

b) The equation that represents the problem is 15¹/₃ = 5¹/₄ + 4²/₃ + x.

An equation is a mathematical statement showing that two or more mathematical or algebraic expressions are equal or equivalent.

Equations are represented using the equal symbol (=), unlike algebraic expressions that contain variables, constants, numbers, and values.

The time spent during the first week = 5¹/₄ hours

The time spent during the second week = 4²/₃ hours

The total time spent during the three weeks period = 15¹/₃ hours

Let the time spent during the third week = x

15¹/₃ = 5¹/₄ + 4²/₃ + x

x = 15¹/₃ - (5¹/₄ + 4²/₃)

x = 5.41663

Thus, solving the equation, Rodrigo spent 5.42 hours practicing the guitar during the third week.

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Answer: it slithers

Step-by-step explanation:

To further explain it They move by dragging their body throughout in the form of loops. Hence, snakes have a crawling or slithering type of movement

Answer:

Overlapping belly scales provide friction with the ground that gives snakes a preferred direction of motion, like the motion of wheels or ice skates.

Step-by-step explanation:

Hope this helps! =D

Mark me brinaliest!=D

Answer:

36

Step-by-step explanation:

The value of length of side of triangle AD using the angle bisector theorem is obtained as: AD = 4.68.

Angles are measurements created by joining two lines, also known as the vertex. Geometric forms such as triangles but also rectangles contain internal angles produced by their sides.

Using the angle bisector theorem in the given triangles:

The ratios of the sides will be equal.

AB / BC = AD / DC

AB = 9 ; BC = 11.7 AD = 3.6

Put the values.

9/11.7 = 3.6 / AD

AD = 3.6*11.7 / 9

AD = 4.68

Thus, the value of length of side of triangle AD using the angle bisector theorem is obtained as: AD = 4.68.

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The final amount earned on the investment after 4 years is $900.40.

An investment of $800 is made at an annual interest rate of 3% compounded yearly for 4 years. To calculate the final amount earned on the investment after 4 years, we can use the formula for compound interest:

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

where:

A = the final amount

P = the principal investment, which is $800 in this case

r = the annual interest rate, which is 3% or 0.03 as a decimal

n = the number of times the interest is compounded per year, which is once per year in this case

t = the number of years, which is 4 in this case

Plugging in the values, we get:

A = 800(1 + 0.03/1)¹ˣ⁴

A = 800(1.03)⁴

A = 800(1.1255)

A = $900.40

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Answer:

(v+8) x (v+9)

We can multiply v into the other two terms in the second bracket, then we can do the same with 8.

(v*v + v*9) + (8*v + 8*9)

v² + 9v + 8v + 72

v² + 17v + 72.

I'm sorry, but I don't see a question or any context for your statement. Could you please provide more information or clarify your request?

Answer:

x = 8

Step-by-step explanation:

the angle between the tangent and the radius at the point of contact A is 90°

then Δ ABP is right at A

using Pythagoras' identity in the right triangle

BP² = AP² + AB² , that is

(x + 9)² = x² + 15² ← expand parenthesis on left side using FOIL

x² + 18x + 81 = x² + 225 ( subtract x² from both sides )

18x + 81 = 225 ( subtract 81 from both sides )

18x = 144 ( divide both sides by 18 )

x = 8

Answer:

Step-by-step explanation:

The local minimum value of a graph is the point where the graph changes from a decreasing function to an increasing function.

Answer:

Step-by-step explanation:

Any value of x may be substituted into this function. So the domain is:

          [tex]D=(-\infty , \infty)[/tex]   or   D=all real [tex]x[/tex]

I am not sure the format how you have been taught to write the answer.

The exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

Prοbability can be defined as ratiο οf number οf favοurable οutcοmes and tοtal number οutcοmes.

(a) Tο find the exact prοbability that there wοuld be exactly 70 accidents at the intersectiοn in οne year, we can use the Pοissοn distributiοn fοrmula:

P(X = k) =( [tex]e^{(-λ)[/tex] * [tex]λ^k[/tex]) / k!

where X is the number of accidents, λ is the average rate of accidents per week (1.4), and k is the number of accidents we're interested in (70).

To find the probability of 70 accidents in one year, we need to adjust the value of λ to reflect the rate over a full year instead of just one week. Since there are 52 weeks in a year, the rate of accidents over a year would be 52 * λ = 72.8.

So, we have:

P(X = 70) = ([tex]e^{(-72.8)[/tex]* [tex]72.8^(70)[/tex]) / 70!

Using a calculatοr οr sοftware, we can evaluate this expressiοn and find that:

P(X = 70) ≈ 0.00382

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

(b) Tο use the nοrmal distributiοn as an apprοximatiοn, we need tο assume that the Pοissοn distributiοn can be apprοximated by a nοrmal distributiοn with the same mean and variance. Fοr a Pοissοn distributiοn, the mean and variance are bοth equal tο λ, sο we have:

mean = λ = 1.4

variance = λ = 1.4

Tο use the nοrmal apprοximatiοn, we need tο standardize the Pοissοn randοm variable X by subtracting the mean and dividing by the square rοοt οf the variance:

[tex]Z = (X - mean) / \sqrt{(variance)[/tex]

Fοr X = 70, we have:

Z = (70 - 1.4) / [tex]\sqrt{(1.4)[/tex] ≈ 57.09

We can then use a standard nοrmal table οr calculatοr tο find the prοbability that a standard nοrmal randοm variable is greater than οr equal tο 57.09. This prοbability is extremely small and practically 0, indicating that the nοrmal apprοximatiοn is nοt very accurate fοr this particular case.

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

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The approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

(a) Using the Poisson distribution, the probability of exactly 70 accidents at this intersection in one year (i.e., 52 weeks) is:

P(X = 70) = (e^(-λ) * λ^x) / x!

where λ = average rate of accidents per week = 1.4

and x = number of accidents in 52 weeks = 70

Therefore, P(X = 70) = (e^(-1.4) * 1.4^70) / 70! ≈ 3.33 x 10^-23

(b) We can use the normal approximation to the Poisson distribution to approximate the probability that there would be exactly 70 accidents at this intersection in one year. The mean of the Poisson distribution is λ = 1.4 accidents per week, and the variance is also λ, so the standard deviation is √λ.

To use the normal distribution approximation, we need to standardize the Poisson distribution by subtracting the mean and dividing by the standard deviation:

z = (x - μ) / σ

where x = 70, μ = 1.452 = 72.8, σ = √(1.452) ≈ 6.37

Now we can use the standard normal distribution table to find the probability that z is less than or equal to a certain value, which corresponds to the probability that there would be exactly 70 accidents at this intersection in one year:

P(X = 70) ≈ P((X-μ)/σ ≤ (70-72.8)/6.37)

≈ P(Z ≤ -0.44)

≈ 0.3300

Therefore, the approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

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Answer:

Step-by-step explanation: We know that ,

Area of circle =πr² and

r = radius of circle.

Now,

Diameter of circle =56 cm [given]

So, radius of circle=D/2=56/2

Radius of circle=28

Now,

Area of circle=πr²

Area of circle=22/7 ×(28)² [π=22/7]

Area of circle=22×4×28

Area of circle=2464cm²

Hence, Area of circle is 2464cm²

I hope it's help you.

Answer:

48 cm²

Step-by-step explanation:

Area of circle formula:  A = πr²

                                          = π (d/2)²

                                          = 3.14 * (4)²

                                          = 50.24

The area of the circle is closest to Option D, 48 cm²

Answer:

a) 675

b) 12

c) y = 12x + 675

d) y = 12 (500) + 675 = $6,675

Answer:

  428.75π ft³

Step-by-step explanation:

You want the exact volume of a cylinder 35 ft high with a radius of 3.5 ft.

The volume is given by the formula ...

  V = πr²h

  V = π(3.5 ft)²(35 ft) = 428.75π ft³ . . . . . use the given values

The exact volume of the cylinder is 428.75π ft³.

The probability of Carrie randomly selecting a gold short sleeve top on Monday and a red short sleeve tank on Tuesday is 2/15.

To find the probability of Carrie randomly selecting a gold short sleeve top on Monday and a red short sleeve tank on Tuesday, we need to multiply the probabilities of these two events occurring.

The probability of selecting a gold short sleeve top on Monday is 2/6, or 1/3. There are 2 gold short sleeve tops out of a total of 6 uniforms.

After selecting a gold short sleeve top on Monday and not replacing it, there are 5 uniforms left, of which 2 are red short sleeve tanks. Therefore, the probability of selecting a red short sleeve tank on Tuesday is 2/5.

To find the probability of both events occurring, we multiply the probabilities together:

(1/3) * (2/5) = 2/15

Therefore, the probability of Carrie randomly selecting a gold short sleeve top on Monday and a red short sleeve tank on Tuesday is 2/15.

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Answer:

C

Step-by-step explanation:

The appropriate z-value to use in the situation given in the question is 1.28.

Given,Total number of adults in the sample = 2092

Number of adults using the internet = 1318

Number of internet users who expect businesses to have websites that give product information = 1041

Probability of internet users who expect businesses to have websites that give product information as per the teacher's statement = 80% = 0.8

To find the appropriate z-value to use in this situation, we need to calculate the standard error of proportion, which is given by:

SEp = √[p(1-p)/n]

where p is the proportion of internet users who expect businesses to have websites that give product information and n is the sample size.

Substituting the given values in the formula,

SEp = √[(1041/1318)(1-1041/1318)/1318]SEp = 0.019

z-value is given by:

z = (p - P)/SEp

where P is the proportion of internet users who expect businesses to have websites that give product information as per the teacher's statement.

Substituting the given values in the formula,

z = (0.8 - 1041/1318)/0.019

z = - 1.28

The appropriate z-value to use in this situation is -1.28.

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After following all the listed steps, you can determine that it will be a graph with lines going through the y-int of -6.

The function g(x)=3^x change over the interval from x=8 to x=10 by a factor of 9

The function g(x)=3^x is an exponential function. As x increases, the value of g(x) increases at an increasing rate.

Therefore, over the interval from x=8 to x=10, g(x) will increase at an increasing rate.

To see this, we can calculate g(8) and g(10) and observe the difference between the two values.

g(8) = 3^8 = 6561

g(10) = 3^10 = 59049

So, the rate is

Rate = 59049/6561

Rate = 9

This means that the rate is by a factor of 9

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