the first term of a geometric sequence of positive numbers is 12 , and the fourth term is 24 . find the 10th term of the geometric sequence.

The Result of the research done by the dermatologists is Option (b): The researcher has statistical evidence to conclude that the sample mean shower length for high school students is greater than 10 minutes.

Statistical hypothesis testing involves testing hypotheticals about a population grounded on a sample of data and determining whether those hypotheticals are statistically significant or simply passed by chance. The selection of a significance position is a pivotal part of this process, as it represents the probability of rejecting the null hypothesis when it's actually true.

In the given problem, dermatologists carried out a study to determine whether the average shower length of high academy scholars exceeded 10 minutes. The null hypothesis( H ₀) assumes that the population mean shower length equals 10 minutes, while the Indispensable hypothesis      ( H ₁) assumes that the population mean shower length is lesser than 10 twinkles. The experimenters named a arbitrary sample of 125 high academy scholars and set up that the average shower length was14.7 twinkles.

The p- value provides a measure of the substantiation against the null thesis. In this case, a p- value of0.0000 suggests that the liability of observing an average shower length of 14.7 minutes or further, assuming the null thesis is true, is extremely low. The significance position( α) was set at 0.05, indicating that the experimenters were willing to reject the null hypothesis if the liability of observing an average shower length of 14.7 minutes or lesser was lower than or equal to0.05.

Grounded on the p- value and significance position, the experimenters have statistical substantiation to reject the null thesis and accept the indispensable thesis. therefore, it's applicable to conclude that the sample mean shower length for high academy scholars is lesser than 10 twinkles. Option( b) directly reflects this conclusion

To know more about Hypothesis Testing here

https://brainly.com/question/30588452

#SPJ4

Complete Question

Most dermatologists recommend that the ideal shower lasts approximately 10 minutes. A researcher suspects that the average shower length of high school students is greater than 10 minutes. To test the belief, the researcher surveyed 125 randomly selected high school students and found that their average shower length was 14.7 minutes. With all conditions for inference met, a hypothesis test was conducted at the significance level of α=0.05, and the test produced a p-value of 0.0000. Which of the following is an appropriate conclusion?

a. The test was flawed because the p-value cannot equal 0.

b. The researcher has statistical evidence to conclude that the sample mean shower length for high school students is greater than 10 minutes.

c. The researcher does not have statistical evidence to conclude that the sample mean shower length for high school students is greater than 10 minutes.

d. The researcher has statistical evidence to conclude that the population mean shower length for high school students is greater than 10 minutes.

e. The researcher does not have statistical evidence to conclude that the population mean shower length for high school students is greater than 10 minutes.

The solutions for x, y, z, and w in terms of a, b, c, d, e, and f are: x y = - (a b c d)^-1 (e f z w), z w = - (a b c d)^-1 (e f x y)

To solve for x, y, z, and w in terms of a, b, c, d, e, and f given the equality a b c d x y i 0 = e f z w,

we can rearrange the equation as follows: x y i 0 = - (a b c d)^-1 (e f z w).

Then we can solve for x and y by multiplying both sides by the matrix

(1 0 0 0; 0 1 0 0; 0 0 0 1; 0 0 0 1)

to obtain x y = - (a b c d)^-1 (e f z w).

Finally, we can solve for z and w by multiplying both sides by the matrix (

0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0) to obtain z w = - (a b c d)^-1 (e f x y).

Thus, the solutions for x, y, z, and w in terms of a, b, c, d, e, and f are:

x y = - (a b c d)^-1 (e f z w)

z w = - (a b c d)^-1 (e f x y)

To learn more about matrix  click here

brainly.com/question/29132693

#SPJ11

Checking the given predicates, there are unifiers in (i), (ii), (iii) and (iv) but not in (v).

Unifier is a substitution that allows two expressions or terms to be made equal by replacing variables with suitable values. A unifier is used to find a common instance or solution to a set of logical expressions or predicates.

A unifier is useful in fields like natural language processing, and artificial intelligence.

From the given question, to know if Unifier exists,

i. Yes, a unifier exists. One possible unifier is:

x = Bob, y = John

ii. Yes, a unifier exists. One possible unifier is:

x = Bob, y = x

iii. Yes, a unifier exists. One possible unifier is:

x = Mary

iv. Yes, a unifier exists. However, there are multiple possible unifiers, since the predicates do not constrain any variables to specific values. For example:

x = y, z = Bob

v. No, a unifier does not exist, since the predicates are contradictory. One predicate states that Bob is shorter than John, while the other states that Bob is shorter than Mary. These two statements cannot be true at the same time, so the predicates cannot be unified.

Learn more about unifier logic here:

https://brainly.com/question/4692301

#SPJ1

The equation of parabola is x² = 12y and the endpoints of the latus rectum are (-6, 3) and (6, 3).

Hence the correct option is (C).

We know that for parabola, any point on parabola is equidistance from the directrix and the focus.

Given that the focus of the required parabola is = (0, 3)

The directrix is y = -3.

Let the locus of the point on parabola be (h, k).

The distance between (h, k) and (0, 3) = √((h - 0)² + (k - 3)²) = √(h² + (k - 3)²)

The distance of the point (h, k) from y = -3 is = k + 3.

According to properties,

k + 3 = √(h² + (k - 3)²)

(k + 3)² = h² + (k - 3)²

k² + 6k + 9 = h² + k² - 6k + 9

h² = 12k

Since (h, k) is an arbitrary point.

So the equation of the parabola is, x² = 12y

We know that the endpoints of the latus rectum of parabola x² = 4ay are given by (2a, a) and (-2a, a).

Here a = 3.

So the endpoints of the latus rectum are (6, 3) and (-6, 3).

Hence the correct option is (C).

To know more about parabola here

https://brainly.com/question/25651698

#SPJ4

The expression w / 6 represents the number of new watercolor palettes on each table

Let's assume that Mr. Chen bought a total of "w" new watercolor palettes.

Since he wants to distribute an equal number of palettes on each of the 6 tables, we can divide the total number of palettes by the number of tables.

Expression: (number of new watercolor palettes) ÷ (number of tables)

Expression: w / 6

This expression represents the number of new watercolor palettes on each table, given that there are "w" total palettes and 6 tables in Mr. Chen's class.

Learn more about Expressions here :

brainly.com/question/21751419

#SPJ1

Follow these procedures to calculate the mean absolute deviation.

1. Determine the data's mean by adding all of the values and dividing by the number of values in the data set.

2. Subtract the mean from each of the data points.

3. Make each difference a good one.

4. Add up all of the positive differences.

5. Subtract this total from the amount of data values in the collection.

This is the  mean absolute deviation.

A data set's average absolute deviation is the sum of its absolute departures from a central point. It is a statistical dispersion or variability summary statistic.

The average distance between the values in a data collection and the set's mean is described by mean absolute deviation. A data collection with a mean average deviation of 3.2, for example, has values that are 3.2 units away from the mean on average.

Learn more about mean absolute deviation:
https://brainly.com/question/10528201
#SPJ1

A total of 1470 boxes are there all together if there are seven separate, equal-size boxes, and inside each box there are six separate small boxes, and inside each of the small boxes there are five even smaller.

Starting from the smallest boxes, we have 5 boxes inside each of the 6 small boxes, giving us a total of 5 x 6 = 30 boxes in each of the 7 medium boxes.

Therefore, there are a total of

30 x 7 = 210 boxes in the medium boxes.

Finally, we have 7 of these medium boxes, giving us a total of

210 x 7 = 1470 boxes in all.

Thus, there are a total of 1470 boxes altogether in the seven separate, equal-size boxes, each containing six separate small boxes, and each small box containing five even smaller boxes.

To learn more about boxes click on,

https://brainly.com/question/14623769

#SPJ4

Answer:

7

Step-by-step explanation:

OB bisects CB

So,

AD = DC

2x + 5 = 3x - 2

 3x - 2 = 2x + 5

3x - 2x = 5 + 2

         x = 7

B. real Gross Domestic Product (GDP) will rise by $100 billion.

When autonomous investment increases by $100 million, it leads to an increase in the aggregate demand for goods and services.

The increase in aggregate demand causes a chain reaction of increases in national income and output, which is known as the multiplier effect.

The size of the multiplier effect depends on the marginal propensity to consume (MPC), which is the fraction of any additional income that is spent on consumption.

In this case, the MPC is given as 0.75. So, for every $1 increase in autonomous investment, there will be an increase in total spending by $1.75 (i.e., $1 increase in consumption and $0.75 increase in savings).

Therefore, the total increase in spending due to the increase in autonomous investment of $100 million will be $175 million ($100 million x 1.75).

This increase in spending will lead to an increase in real GDP, which is the total value of goods and services produced in an economy, by $100 billion (i.e., $175 million x 1000/1 million).

To learn more about million click here

brainly.com/question/29262446

#SPJ11

The conversion factor that you should use is; 60 minutes =  1 hour. Option A

A conversion factor is a ratio used in mathematics to change a measurement's unit of measurement. It is a fraction with two different units that yet has the value 1. Both the fraction's numerator and denominator are identical measurements expressed in different units.

If 60 minutes make 1 hour

x minutes make 3.5 hours

x = 3.5 * 60/1

x = 210 minutes

Thus 3.5 hours is the same as 210 minutes.

Learn more about conversion ratio:https://brainly.com/question/24166407

#SPJ1

The correct statements of probability are:

C. The experimental probability of getting two red marbles is less than the theoretical probability.

D. The theoretical probability of getting two blue marbles is 2/10 or 20%.

E. The experimental probability of getting two blue marbles is i/4 or 25%.

The true probability statements are determined as follows:

Probability of blue = 3/6 or 1/2

Probability of red = 2/6 or 1/3

Probability of yellow = 1/6

Without replacement:

Experimental probability of BB = 15/60 or 1/4

Experimental probability of RR = 5/60 or 1/12

Experimental probability of YY = 0

The theoretical probability of BB = 1/5

The theoretical probability of RR = 1/15

The theoretical probability of YY = 0

Hence the true statements are:

Learn more about probability at: https://brainly.com/question/13604758

#SPJ1

Therefore, there are 5,040 ways to assign 7 volunteers to 7 booths for a charity bazaar. The answer is option C: 5,040 ways.

To determine how many ways seven volunteers can be assigned to seven booths for a charity bazaar, we need to use the formula for permutations. A permutation is an arrangement of objects in a specific order, and it is calculated using the following formula:

nPr = n! / (n - r)!

Where n is the total number of objects and r is the number of objects being arranged. In this case, we have 7 volunteers and 7 booths, so n = 7 and r = 7. Plugging these values into the formula, we get:
7P7 = 7! / (7 - 7)!
7P7 = 7! / 0!
7P7 = 7!
So there are 7! (7 factorial) ways to assign 7 volunteers to 7 booths. To find the actual value, we can calculate:

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
7! = 5,040

Therefore, there are 5,040 ways to assign 7 volunteers to 7 booths for a charity bazaar. The answer is option C: 5,040 ways.

To know more about permutation visit:-

https://brainly.com/question/30649574

#SPJ11

Here is a box and whisker plot for the given numbers: 48, 111, 121, 125, 126, 141, 149, 198, 223, 224, 238, 263, 292, 327, 330. The plot shows a box from Q1 (121) to Q3 (263) with a median (149) and whiskers extending to the minimum (48) and maximum (330) values.

Arrange the numbers in ascending order:

48, 111, 121, 125, 126, 141, 149, 198, 223, 224, 238, 263, 292, 327, 330

Find the minimum and maximum values:

Minimum value: 48

Maximum value: 330

Find the median:

To find the median, we need to locate the middle value. In this case, since we have an odd number of data points, the median will be the middle value, which is the 8th number: 149.

Find the lower quartile (Q1):

To find Q1, we need to locate the median of the lower half of the data. Since we have an odd number of data points below the median, the lower quartile will be the middle value of the lower half, which is the 4th number: 121.

Find the upper quartile (Q3):

To find Q3, we need to locate the median of the upper half of the data. Since we have an odd number of data points above the median, the upper quartile will be the middle value of the upper half, which is the 12th number: 263.

Calculate the interquartile range (IQR):

IQR = Q3 - Q1

IQR = 263 - 121

IQR = 142

Determine the outliers:

To identify any outliers, we need to find any values that are below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR. However, in this case, there are no values that fall outside this range.

Create the box and whisker plot:

Using the minimum value, Q1, median, Q3, and maximum value, we can now create the box and whisker plot. The plot consists of a box with a line inside representing the median, "whiskers" extending from the box representing the minimum and maximum values, and any outliers plotted individually if present.

for such more question on median

https://brainly.com/question/14532771

#SPJ11

Answer: J.C

1/9

::1/10 :: 2/8

Step-by-step explanation: good day! hope i helped love helping. bye

Answer:

148.9ft underwater

Step-by-step explanation:

Substract the ft the submarine dove minus the ft the submarine came up.

Ex. ft of dive-ft of coming up

Which would be 363.5-214.6=

148.9ft

The points on the curve x = 9cos(t) with a slope of -3 are approximately (7.81, y) and (-3.81, y), where y can vary based on the corresponding x-values obtained from the equation of the curve.

The given curve is x = 9cos(t), where t is the parameter. To find the points on the curve with a given slope, we need to find the derivative of x with respect to t:

dx/dt = -9sin(t)

We can then solve for t to find the values of the parameter that correspond to the given slope. For example, if we are given a slope of m = -3, we can set dx/dt = -3 and solve for t:

-3 = -9sin(t)

sin(t) = 1/3

There are two solutions for t in the interval [0, 2π] that satisfy this equation:

t = arcsin(1/3) ≈ 0.34 or t = π - arcsin(1/3) ≈ 2.8

To find the corresponding points on the curve, we can substitute these values of t into the equation x = 9cos(t)

When t = arcsin(1/3):

x = 9cos(arcsin(1/3)) ≈ 7.81

When t = π - arcsin(1/3):

x = 9cos(π - arcsin(1/3)) ≈ -3.81

Therefore, the points on the curve with a slope of -3 are approximately (7.81, y) and (-3.81, y), where y can be any value of the y-coordinate that satisfies the equation of the curve for the corresponding value of x.

To know more about slope:

https://brainly.com/question/3605446

#SPJ4

The reasonable estimate for the forecast value for January using exponential smoothing would be 208 cat trees.

Exponential smoothing is a statistical technique used for time series forecasting. It involves a weighted average of past observations, with more recent observations given greater weight than older ones.

The level of smoothing is controlled by a smoothing parameter, which determines the extent to which past observations influence the forecast.

Here we have

Chairman cat products produces cat trees that are sold by several large pet stores. They sold 190, 210, and 208 cat trees in january, february, and march, respectively.

To estimate the forecast value for January using exponential smoothing, we need to use the following formula:

F₁ = A × D₀ + (1 - A) × F₀

Where:

F₁ = forecast for January

D₀ = actual demand for December (last period)

F₀ = forecast for December (last period)

A = smoothing factor (a value between 0 and 1)

Since we do not have a forecast for December, we can assume that F₀ is equal to the actual demand for December.

Therefore, we can use the following formula to estimate F₁:

F₁ = A × D₀ + (1 - A) × F₀

We need to choose a value for A.

This value represents the weight or importance that we give to the most recent demand observation when making the forecast.

A smaller value of A gives more weight to past observations, while a larger value of A gives more weight to the most recent observation.

A reasonable estimate for A would be between 0.1 and 0.3.

Let's assume we choose A = 0.2.

Using the given data, we have:

D₀ = 208 (demand for March)

F₁ = 0.2 × 208 + (1 - 0.2) × 208

= 0.2 × 208 + 0.8 × 208

= 208

Therefore,

The reasonable estimate for the forecast value for January using exponential smoothing would be 208 cat trees.

Learn more about Exponential smoothing at

https://brainly.com/question/31358866

#SPJ4

The volume of the object is 695.75 units²

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Generally, the volume of a prism is expressed as;

V = base area × height

base area = area of rectangle + area of triangle

area of rectangle = l× w

= 11 × 5

= 55 units²

area of the triangle = 1/2 bh

= 1/2 × 11 × 1 = 5.5 units²

area of tht base = 55+5.5 = 60.5 units²

The radius of the semi circle is the height of the semicircle = 5.5 units

total height of the object = 5.5 + 5 = 11.5

Volume = 60.5 × 11.5

= 695.75 units².

learn more about volume from

https://brainly.com/question/27710307

#SPJ1

The man is standing about 40.44 feet away from the base of the streetlight and  height of the streetlight is 32 ft

We can use the fact that the man's height and shadow length are proportional to the streetlight's height and shadow length.

Let the streetlight's height be "h".

(6 ft) / (15 ft) = h / (80 ft)

Simplifying this proportion, we get:

h = (6/15) × 80

h = 32 ft

Now we have found the height of the streetlight.

We can use trigonometry to find the distance from the man to the base of the streetlight.

Let's call this distance "d".

We know the angle of elevation is 52.5 degrees, and we can use the tangent function:

tan(52.5) = h / d

Solving for d, we get:

d = h / tan(52.5)

d = 32 / tan(52.5)

d ≈ 40.44 ft

Therefore, the man is standing about 40.44 feet away from the base of the streetlight.

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ1

21 inch²

we splitthe two shapes, find the areas by multiplying the two sides and we add both of the answers, 15+6

Answer:

2(3) + 2(6) = 6 + 12 = 18 square feet

The association of the graph scatterplot is a negative nonlinear association

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

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be scattered and they do not follow a particular direction

Also, we can see that

As the x values change, the y values do not follow a pattern

This represents a nonlinear association.

Hence, the association is a negative nonlinear association

Read more about scatter plot at

brainly.com/question/16920148

#SPJ1

[tex]\cfrac{a-3}{10}+\cfrac{a-5}{5}=\cfrac{1}{2}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}}{10\left( \cfrac{a-3}{10}+\cfrac{a-5}{5} \right)=10\left( \cfrac{1}{2} \right)} \\\\\\ (a-3)+2(a-5)=5\implies a-3+2a-10=5\implies 3a-13=5 \\\\\\ 3a=18\implies a=\cfrac{18}{3}\implies a=6 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{2}{n-3}+\cfrac{2}{n+5}=\cfrac{5n-7}{n^2+2n-15}\implies \cfrac{2}{n-3}+\cfrac{2}{n+5}=\cfrac{5n-7}{(n-3)(n+5)} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{(n-3)(n+5)}}{(n-3)(n+5)\left( \cfrac{2}{n-3}+\cfrac{2}{n+5} \right)=(n-3)(n+5)\left( \cfrac{5n-7}{(n-3)(n+5)} \right)} \\\\\\ (n+5)2~~ + ~~(n-3)2=5n-7\implies 2n+10+2n-6=5n-7 \\\\\\ 4n+4=5n-7\implies 4=n-7\implies 11=n[/tex]

The valid arithmetic operators are division (÷), exponentiation (^), multiplication (×), addition (+), and subtraction (-). The invalid arithmetic operator in the given options is modulas division (mod).

Modulas division (mod) is not a valid arithmetic operator. Modulas division is used to find the remainder when one number is divided by another. It is denoted by the symbol "%". However, in the given options, the modulas division (mod) is marked as invalid, which means it is not recognized as a valid arithmetic operator.

The other arithmetic operators listed, such as division (÷), exponentiation (^), multiplication (×), addition (+), and subtraction (-), are all valid and commonly used arithmetic operators in mathematics and programming languages. They have well-defined operations and are widely recognized and utilized for various calculations and computations.

Learn more about Arithmetic Operators here: brainly.com/question/30553381

#SPJ

If this month's blend used three times as many pounds of type B coffee as type A, for a total cost of $621.00, Keisha used 30 pounds of type A coffee to make the blend.

Let's assume that Keisha used x pounds of type A coffee to make the blend.

Since the blend uses three times as many pounds of type B coffee as type A, then the amount of type B coffee used would be 3x pounds.

The total cost of the blend is $621.00. We can write an equation in terms of x for the total cost:

4.20x + 5.50(3x) = 621

Simplifying and solving for x:

4.20x + 16.5x = 621

20.7x = 621

x = 30

To check, we can find the amount of type B coffee used:

3x = 3(30) = 90 pounds

And we can verify that the total cost is $621.00:

4.20(30) + 5.50(90) = 621

126 + 495 = 621

So the answer is that Keisha used 30 pounds of type A coffee.

To learn more about pounds click on,

https://brainly.com/question/30671860

#SPJ4

Complete question is:

Keisha's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Keisha $4.20 per pound, and type B coffee costs $5.50 per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $621.00. How many pounds of type A coffee were used?

Answer:

[tex]\huge\boxed{\sf \$144}[/tex]

Step-by-step explanation:

1 dozen = 12 pieces

So, 3 dozen candies = 3 × 12

3 dozen candies = 36 candies

Given that,

9 candies = $36

Using unitary method

1 candy = $36/9

1 candy = $4

36 candies = $4 × 36

[tex]\rule[225]{225}{2}[/tex]

Scale factor = 5/3, AB = 4√5 cm, and perpendicular distance of scale factor is so A'B' = (20/3)√5 cm.

To find A'B, we want to initially decide the scale element of the growth. We know that Promotion = 12 cm and A'D' = 20 cm, so the scale factor is:

scale factor = A'D'/Promotion = 20 cm/12 cm = 5/3

This implies that each side of A'B'C'D' is 5/3 times the length of the relating side of ABCD.

To find A'B, we can zero in on the level side of the square, which relates to Stomach muscle in ABCD. We know that |DC| = 8 cm, so |BC| = |DC| = 8 cm. Since the scale factor is 5/3, we have:

|A'B'| = (5/3) * |AB|

We can utilize the Pythagorean hypothesis to track down |AB|. Let x be the length of |AB|, then, at that point:

[tex]x^2 + 8^2 = 12^2[/tex]

Working on this situation, we get:

[tex]x^2 = 144 - 64 = 80[/tex]

Taking the square base of the two sides, we get:

x = √80 = 4√5

Hence:

|A'B'| = (5/3) * |AB| = (5/3) * 4√5 = (20/3)√5

So the length of A'B' is (20/3)√5 cm.

To learn more about perpendicular distance, refer:

https://brainly.com/question/21406061

#SPJ1

If a Member is taking 40mg twice monthly, they will need a total of 80mg per month. Given that the pre-filled syringe contains 40mg per 0.4mL, this means that the Member will need 0.8mL per month.

Since there are 4 weeks in a month, the Member will need to take the medication every 2 weeks. This means that they will need 2 pre-filled syringes per month. It's important to note that the Member should always follow the instructions of their healthcare provider and only use the medication as directed. They should also check with their insurance provider to ensure that the medication is covered and to learn about any potential cost-saving options, such as a copay card.

Learn more about medication here:

https://brainly.com/question/30714139

#SPJ11

The mean lifetime of the machine part, given that it survives less than ten years, is 2.568 years. So, correct option is C.

The problem requires calculating the conditional mean of an exponential distribution. The formula for conditional mean is given as:

Conditional Mean = (Integral of x * f(x|condition)) / P(condition)

where f(x|condition) is the probability density function of x given the condition, and P(condition) is the probability of the given condition.

In this case, the given condition is that the machine part survives less than ten years. The probability of this condition is P(condition) = F(10), where F is the cumulative distribution function of the exponential distribution.

The probability density function of the exponential distribution with a mean of five years is given as:

f(x) = (1/5) * [tex]e^{(-x/5)[/tex]

Therefore, the conditional probability density function can be calculated as:

f(x|condition) = f(x) / F(10) = (1/5) * [tex]e^{(-x/5)[/tex] / (1 - e⁻²)

The integral in the numerator can be evaluated as:

Integral of x * f(x|condition) dx = (1/F(10)) * [tex]\int\limits^{10}_0 {x} \, f(x) dx[/tex]

Simplifying the above expression, we get:

Conditional Mean = (10/3) * (1 - e⁻²) / (1 - e⁻²)

Evaluating this expression gives the answer as 2.568, which is option C.

To learn more about exponentially distributed click on,

https://brainly.com/question/13949595

#SPJ4