The temperature at a point (x, y) on a flat metal plate is given by T(x, y) = 31/(3 + x^2 + y^2), where T is measured in °C and x, y in meters.
(a) Find the rate of change of temperature with respect to distance at the point (3, 9) in the x- direction.
(b) Find the rate of change of temperature with respect to distance at the point (3, 9) in the y- direction.

Answer:

111

Step-by-step explanation:

-The occupancy rate index is calculated using the following formula:

[tex]Index=\frac{Hotel \ OCC}{Competitive \ OCC}\times 100[/tex]

-The Hotel OCC is the property's occupancy rate given as 85%

-The Competitive OCC, is the competitive set's occupancy rate calculated as;

[tex]Occupancy \ Rate=\frac{Room \ Sold}{Rooms \ Available}\\\\\\=\frac{115000}{150000}\\\\=76.67\%[/tex]

-We then substitute to solve for the occupancy rate index:

[tex]Index=\frac{Hotel \ OCC}{Competitive \ OCC}\times 100\\\\=\frac{0.85}{0.7767}\times 100\\\\=110.86\\\approx 111[/tex]

Hence, the occupancy rate index is 111

Answer:

Part A) [tex]QR=2\sqrt{5}\ units[/tex]

Part B) [tex]PR=2\sqrt{13}\ units[/tex]

Step-by-step explanation:

The complete question in English is

Observe the isosceles PQRS trapeze in the Cartesian plane.

A) How long is the QR side?

B) What is the distance between points P and R?

The picture of the question in the attached figure

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Part  A) How long is the QR side?

we have the coordinates

Q(7,6) and R(9,2)

substitute in the formula

[tex]d=\sqrt{(2-6)^{2}+(9-7)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(2)^{2}}[/tex]

[tex]d_Q_R=\sqrt{20}\ units[/tex]

simplify

[tex]d_Q_R=2\sqrt{5}\ units[/tex]

Part B) What is the distance between points P and R?

we have the coordinates

P(3,6) and R(9,2)

substitute in the formula

[tex]d=\sqrt{(2-6)^{2}+(9-3)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(6)^{2}}[/tex]

[tex]d_P_R=\sqrt{52}\ units[/tex]

simplify

[tex]d_P_R=2\sqrt{13}\ units[/tex]

Answer:

Part A: The null hypothesis failed to be rejected.

Part B: The null hypothesis failed to be rejected.

Step-by-step explanation:

We have an hypothesis test with null and alternative hypothesis H0: p = 0.5 versus Ha: p > 0.5, which has the test statistic z=1.15.

Part A: If the significance level is 0.05, the conclusion depends on the P-value.

If the P-value is below 5%, the null hypothesis is rejected.

The P-value for this right-tailed tes and z=1.15 is:

[tex]P-value=P(z>1.15)=0.125[/tex]

The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis is failed to be rejected.

Part B: In this case, the significance level is 0.01 and, as the alternative hypothesis is defined with an unequal sign, the test is two-tailed.

This changes the way we calculate the P-value, as we need to compute the two tails.

The P-value is:

[tex]P-value=2P(z>1.15)=0.25[/tex]

The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis is failed to be rejected.

Null hypothesis of a sample suggest that there is no statistical relationship exists in a set of provided single observed variable. The null hypothesis is failed to be rejected for both part A and part B of the question.

Using the hypothesis test we have,

[tex]H_o; p=0.5[/tex]

[tex]H_ap>0.5[/tex]

[tex]z=1.15[/tex]

Null hypothesis of a sample suggest that there is no statistical relationship exists in a set of provided single observed variable.

Part A: The conclusion to draw at the 5% significance level-

In the right tailed test or upper test the p value for the z score can be given form z table which is,

p-value[tex]=0.125[/tex]

Here the p value 0.125 is bigger than the significance level 0.05. Thus the effect is not significant and the null hypothesis is failed to be rejected.

Part B: If the alternative hypothesis is Ha: p ≠ 0.5, the conclusion to draw at the 5% significance level-

Here for the unequal sign 2-test is performed. The p value for the 2-test is,

p- value[tex]=0.25[/tex]

Here the p value 0.25 is bigger than the significance level 0.05. Thus the effect is not significant and the null hypothesis is failed to be rejected.

Hence, the null hypothesis is failed to be rejected for both part A and part B of the question.

For more about the null hypothesis, follow the link below-

https://brainly.com/question/4454077

The question is asking to find an equation of how many customers the waiter served.

Given: 12 customers at lunch; 5 per hour for dinner

Find: number of customers served at lunch AND dinner

We use variables for this, x and y. A general equation is usually y=ax+b, where y is the solution, x is the variable, and a and b are numbers.

Knowing this information, since it is already given that 12 customers were served, the equation turns into y=ax+12

Additionally, since we don't know how many hours she worked, we can use that as a variable. y=5x+12

x=how many hours the waiter worked at dinner

y=overall hours the waiter worked at both lunch and dinner

slope=5, means customers are going up 5 every hour

y-intercept=12, the given/starting point on the y-axis

Answer:

see below

Step-by-step explanation:

x-1>2

Add 1 to each side

x-1+1>2+1

x >3

There would be an open circle at 3 and a line to the right

Answer:

x = 111°

Step-by-step explanation:

We know that angles in a triangle add up to 180°

Step 1: Find angle supplementary to x

82 + 29 + x = 180

111 + x = 180

x = 69°

Step 2: Find angle x

Both the angles are supplementary, meaning they add up to 180°.

x + 69 = 180

x = 111°

Answer:

Easy = 111 degrees

Step-by-step explanation:

Answer:

The answer of this question is 1/4

Step-by-step explanation:

Total no of cookies=12+6+6=24

No.sugar cookies=6

Probability= Possible outcomes/total no of outcomes

= 6/24

= 1/4

Answer:

A. The statement that the random variable X is normally distributed with parameters is often abbreviated.

Step-by-step explanation:

The X is normally distributed with parameters u and  is often distributed as X ≈N (u 2 ). The correct answer is a. The statement that the random variable is normally distributed.

Step-by-step explanation:

Step 1

From the given information,

number of ferrous-type substance, n = 5

Let [tex]\mu_1[/tex] and [tex]\mu_2[/tex] are the true population average for laboratory chemical and X-ray flourescence analysis

Level of significance, [tex]\alpha = 0.05[/tex]

state the null and alternative hypotheses

[tex]H_0 : \mu_1 - \mu_2 = 0\\\\H_1 : \mu_1 - \mu_2 \neq 0[/tex]

Attached are steps 2 to 7 of the remaining solution

Yes, the two methods of analysis give, on average, the same result and this can be determined by using the given data.

Given :

The mean of the first sample is:

[tex]\bar{X_1} = \dfrac{\sum X_1}{n_1}[/tex]

[tex]\bar{X_1} = \dfrac{ 10.8}{5}=2.16[/tex]

Now, the standard deviation of the first sample is:

[tex]S_1 =\sqrt{\dfrac{\sum(X_1-\bar{X_1})^2}{n_1-1}}[/tex]

[tex]S_1 =\sqrt{\dfrac{0.132}{4}}=0.182[/tex]

The mean of the second sample is:

[tex]\bar{X_2} = \dfrac{\sum X_2}{n_2}[/tex]

[tex]\bar{X_2} = \dfrac{ 11.3}{5}=2.26[/tex]

Now, the standard deviation of the second sample is:

[tex]S_2 =\sqrt{\dfrac{\sum(X_2-\bar{X_2})^2}{n_2-1}}[/tex]

[tex]S_2 =\sqrt{\dfrac{0.212}{4}}=0.230[/tex]

Now, the hypothesis test is given below:

Null Hypothesis  --  [tex]H_0:\mu_1=\mu_2[/tex]

Alternative Hypothesis  --  [tex]H_a:\mu_1\neq \mu_2[/tex]

The degree of freedom is calculated as:

[tex]df=n_1+n_2-2\\df=8[/tex]

Now, the formula of the test statistics is given below:

[tex]t = \dfrac{(\bar{X_1}-\bar{X_2})-(\mu_1-\mu_2)}{\sqrt{\dfrac{S^2_1}{n_1}+\dfrac{S^2_2}{n_2}} }[/tex]

[tex]t = \dfrac{2.16-2.26}{\sqrt{\dfrac{(0.182)^2}{5}+\dfrac{(0.230)^2}{5}} }[/tex]

[tex]t = -0.76238688[/tex]

Now, according to the t-value, the p-value is 0.46771. Therefore, the null hypothesis is not rejected.

So, yes the two methods of analysis give, on average, the same result.

For more information, refer to the link given below:

https://brainly.com/question/2695653

Answer:

25/36

Step-by-step explanation:

P(1) = 1/6

P'(1) = 5/6

5/6 * 5/6 = 25/36

Answer:

10x-48y

Step-by-step explanation:

It is appropriate to use the correlation coefficient to describe the strength of the relationship between "Time" and "Fish Quality" in this study. The correlation coefficient measures the strength and direction of the linear relationship between two variables.

It is appropriate to use the correlation coefficient to describe the strength of the relationship between "Time" and "Fish Quality" in this study. The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, "Time" and "Fish Quality" are both continuous variables, and a scatterplot can be used to visually represent their relationship.

In the scatterplot, if the data points form a clear pattern or trend, it suggests a strong relationship between the variables. The correlation coefficient quantifies this relationship, ranging from -1 (perfect negative relationship) to 1 (perfect positive relationship), with 0 indicating no linear relationship. By calculating the correlation coefficient, we can determine the strength and direction of the relationship between "Time" and "Fish Quality" in the study.

Keywords: correlation coefficient, relationship, variables, scatterplot, strength, direction, linear, continuous

https://brainly.com/question/15577278

#SPJ11

Answer:

Option C - Matched-Pairs t-test

Step-by-step explanation:

Looking at the options given,

-Two-Sample t-test for means is used to test the difference (d0) between two population means. A common application is to determine whether the means are equal. This can't apply to the question as it determine if this treatment was effective.

- Two-Sample z-test for means is used to test the null hypothesis that there is no difference between the means of two independent populations. This doesn't determine if this treatment was effective

-Matched-Pairs t-test is used to test whether there is a significant mean difference between two sets of paired data. This will be sufficient to determine if this treatment was effective

-Two-Sample z-test for proportions is used when we want to know whether two populations or groups (e.g., males and females; theists and atheists) differ significantly on some single (categorical) characteristic - for example, whether they are vegetarians. This can't be used to determine if this treatment was effective

The only correct option is Matched-Pairs t-test

To evaluate the effectiveness of Omega-3 tablets for lowering cholesterol, a Matched-Pairs t-test should be used, as it compares the cholesterol levels before and after treatment in the same individuals.

To determine the effectiveness of taking Omega-3 tablets to lower a person's cholesterol, one should use a statistical hypothesis test that compares two related samples. In this case, the comparison is between cholesterol levels before and after the 6-week course. Since the same individuals are tested twice, the appropriate test is the Matched-Pairs t-test (also known as the paired sample t-test or dependent sample t-test). This test is utilized when you have two sets of related data and want to assess if their means differ. The differences between each pair will follow a normal distribution if certain conditions are met, which is assumed in a matched-pairs t-test.

https://brainly.com/question/15365572

#SPJ3

Answer:

48

Step-by-step explanation:

32+16=48

48-16=32

Answer:

48

Step-by-step explanation:

add 32 and 16 to get 48

Answer:

[tex](B) \dfrac{dM}{dt} = kM[/tex]

Step-by-step explanation:

Given the mass M(a decreasing function) of a sample of a radioactive element at time t.

The rate of change of the sample’s mass [tex]\dfrac{dM}{dt}[/tex], is proportional to the mass, M of the sample.

This is written as:

[tex]\dfrac{dM}{dt} \propto M[/tex]

Introducing the decay constant k,

[tex]\dfrac{dM}{dt} = kM[/tex]

This is the equation which model the relationship between the mass of the sample and the rate of change of the sample’s mass.

The other options are therefore invalid.

[tex](A)\dfrac{dM}{dt} = kt (C)\dfrac{dM}{dt} = \dfrac{k}{t} (D)\dfrac{dM}{dt} = \dfrac{k}{M}[/tex]

The correct differential equation is [tex]\(\frac{dM}{dt} = kM\)[/tex], option B) indicating the rate of change of mass is proportional to the mass.

1. Understanding the Problem Statement:

  - The mass [tex]\(M\)[/tex]of a sample of a radioactive element is a decreasing function of time [tex]\(t\).[/tex]

  - The rate of change of the sample's mass is proportional to the mass of the sample itself.

2. Translating the Statement into a Mathematical Form:

  - When a quantity is said to change at a rate proportional to its current value, we can express this mathematically as:

[tex]\[ \frac{dM}{dt} \propto M \][/tex]

  - This means the rate of change of [tex]\(M\)[/tex] with respect to time [tex]\(t\)[/tex] is proportional to [tex]\(M\).[/tex]

3. Introducing a Proportionality Constant:

  - To express this proportionality as an equation, we introduce a constant of proportionality [tex]\(k\):[/tex]

[tex]\[ \frac{dM}{dt} = kM \][/tex]

  - Here, [tex]\(k\)[/tex] is a constant that determines the rate at which [tex]\(M\)[/tex] changes with respect to [tex]\(t\).[/tex]

4. Evaluating Given Differential Equations:

  - We need to find which of the provided differential equations matches the relationship [tex]\(\frac{dM}{dt} = kM\).[/tex]

  The given differential equations are:

[tex]\[ \begin{aligned} & \frac{dM}{d} = kt \\ & \frac{dM}{dt} = kM \\ & \frac{dM}{d} = \frac{A}{2} \\ & \frac{dM}{d} = \frac{k}{M} \end{aligned} \][/tex]

5. Matching with the Correct Equation:

  - Comparing each option with [tex]\(\frac{dM}{dt} = kM\):[/tex]

[tex]- \(\frac{dM}{d} = kt\)[/tex] does not match since it suggests the rate of change depends on [tex]\(t\), not \(M\).[/tex]

[tex]- \(\frac{dM}{dt} = kM\)[/tex] matches our derived equation perfectly.

[tex]- \(\frac{dM}{d} = \frac{A}{2}\)[/tex]  suggests a constant rate of change, which does not depend on [tex]\(M\).[/tex]

[tex]- \(\frac{dM}{d} = \frac{k}{M}\)[/tex] suggests an inverse relationship, which is incorrect.

6. Conclusion:

  - The differential equation that models the relationship between the mass of the sample and the rate of change of the mass is:

[tex]\[ \frac{dM}{dt} = kM \][/tex]option B)

Complete Question:

Answer:

  16

Step-by-step explanation:

You want the mean of {20, 15, 19, 16, 10}.

The mean is the sum of the numbers, divided by the number of numbers.

  (20 +15 +19 +16 +10)/5 = 80/5 = 16

The mean is 16.

Final answer:

The mean of tickets sold by Helena for the Willowbrook School play is calculated by adding the total tickets sold (80) and dividing by the number of homerooms (5), resulting in a mean of 16 tickets.

Explanation:

To calculate the mean of tickets sold for the Willowbrook School play, we need to add up the number of tickets sold in each homeroom and then divide by the number of homerooms. The data given is:

Adding these together, we get 20 + 15 + 19 + 16 + 10 = 80 tickets sold in total. As there are 5 sets of data, we divide the total by 5 to find the mean.

Therefore, the mean number of tickets sold is 16 tickets.

Answer:

75.36

Step-by-step explanation:

To find the diameter, take the radius and multiply it by two, or use the diameter, and then multiply by pi. The formula, in this case, would be pi x 24. I hope this helps. I used 3.14, the shorter version, but a more precise answer would be 75.3982236862, or 75.4 rounded.

Answer:

This type of data are not measurement of anything , so it is not feasible  to calculate their average(Mean)

Step-by-step explanation:T

The data are at the level of measurement that are Nominal

In level of nominal measurement, letters, numeric and alpha-numeric, words, symbols are used to classify data in the example stated.

Now we recall that,

Brown hair = 100,

Blond hair = 200,

Black hair = 300

Anything else = 400

Thus,  100, 200, 300, 400 are used as code numbers for hair colors and does not have any importance to their  values numerically.

There is no arithmetic solutions such as  average, total which cannot be solved  using these numbers.

Therefore the average mean  calculated is not feasible

Answer:

The level of measurement of the date is: nominal level of measurement.

Such data are not counts or measures of​ anything, so it makes no sense to compute their average​ (mean)

Step-by-step explanation:

The given data are at the nominal level of measurement. Nominal data is not measurable and cannot be ordered as well. It is qualitative in nature and not quantitative. For example this nominal data type can be measured of categorized as yes or no, high or low, mild, moderate or severe, male or female etc. So there is no point of calculating average of such qualitative data and nominal level of measurement deals with qualitative variables.

Answer:

$800  [((1.005)18 - 1)/.005]

$800 x [(1.0939 - 1)/.005]

$800 x (0.0939/0.005)

$800 x 18.785

~ $15,028

The savings plan is 15,028.

Step-by-step explanation:

The savings plan balance on the account after 18 months is $3651.46.

Basically, the savings plan balance means the total amount of money saved and accumulated in a designated account or investment over a period of time.

The savings plan balance will be found using annuity formula [tex]P * [(1 + r)^n - 1] / r[/tex]

Data:

The plan balance will be:

= 200 * [(1 + 0.00166667)^18 - 1] / 0.00166667

= 200 * 18.2572814188

= 3651.45628376

= 3651.46.

Read more about plan balance

brainly.com/question/35585538

#SPJ3

Answer:

The answer is C. x=In(5/3)-2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The moments of inertia are [tex]\( I_x = I_y = \frac{\pi \rho a^4}{4} \)[/tex] and [tex]\( I_0 = \frac{\pi \rho a^4}{2} \).[/tex]

Example 4 involves finding the moments of inertia [tex]\( I_x \)[/tex], [tex]\( I_y \)[/tex], and [tex]\( I_0 \)[/tex] of a homogeneous disk [tex]\( D \)[/tex] with density [tex]\( \rho(x, y) = \rho \)[/tex], centered at the origin, and radius [tex]\( a \)[/tex].

To compute [tex]\( I_0 \)[/tex], we integrate [tex]\( (x^2 + y^2) \rho \)[/tex] over the disk [tex]\( D \)[/tex] using polar coordinates. The bounds for [tex]\( \theta \)[/tex] are [tex]\( 0 \)[/tex] to [tex]\( 2\pi \)[/tex], and for [tex]\( r \)[/tex] are [tex]\( 0 \)[/tex] to [tex]\( a \).[/tex]

[tex]\[ I_0 = \int \int_D (x^2 + y^2) \rho \, dA = \rho \int_0^{2\pi} \int_0^a r^3 \, dr \, d\theta = \frac{2\pi \rho a^4}{4} = \frac{\pi \rho a^4}{2} \][/tex]

Since the disk is symmetric about both the x-axis and y-axis, [tex]\( I_x = I_y = \frac{I_0}{2} = \frac{\pi \rho a^4}{4} \).[/tex]

The answer is [tex]\( I_0 = \frac{1}{2} \rho a^4 \pi \).[/tex]

To find the moments of inertia[tex]\( I_x \) and \( I_y \) of a homogeneous disk \( D \) with density \( \rho(x, y) = \rho \),[/tex] centered at the origin, and radius \( a \), we use the following formulas:

[tex]\[ I_x = \int \int_D y^2 \rho(x, y) \, dA \]\[ I_y = \int \int_D x^2 \rho(x, y) \, dA \]where \( dA \) represents the differential area element in polar coordinates.[/tex]

For a disk, we use polar coordinates [tex]\( (r, \theta) \), where \( r \) represents the radius and \( \theta \)[/tex] represents the angle.

The density [tex]\( \rho \)[/tex] is constant, so it can be pulled out of the integrals.

We integrate over the disk, which has a radius [tex]\( a \), and \( \theta \) ranging from \( 0 \) to \( 2\pi \).[/tex]

[tex]Let's calculate \( I_x \):\[ I_x = \int_0^{2\pi} \int_0^a (r \sin \theta)^2 \rho \cdot r \, dr \, d\theta \]\[ = \rho \int_0^{2\pi} \int_0^a r^3 \sin^2 \theta \, dr \, d\theta \]\[ = \rho \int_0^{2\pi} \left[ \frac{1}{4} r^4 \sin^2 \theta \right]_0^a \, d\theta \]\[ = \rho \int_0^{2\pi} \frac{1}{4} a^4 \sin^2 \theta \, d\theta \]\[ = \rho \cdot \frac{1}{4} a^4 \int_0^{2\pi} \sin^2 \theta \, d\theta \]\[ = \rho \cdot \frac{1}{4} a^4 \cdot \pi \][/tex]

Using the trigonometric identity [tex]\( \sin^2 \theta = \frac{1 - \cos(2\theta)}{2} \) and integrating from \( 0 \) to \( 2\pi \), the integral of \( \sin^2 \theta \) over one period is \( \pi \), and thus, the integral over \( 2\pi \) periods is \( 2\pi \).[/tex]

[tex]So, \( I_x = \rho \cdot \frac{1}{4} a^4 \cdot \pi \).Similarly, for \( I_y \), the integral will be:\[ I_y = \rho \int_0^{2\pi} \int_0^a (r \cos \theta)^2 \rho \cdot r \, dr \, d\theta \]\[ = \rho \int_0^{2\pi} \int_0^a r^3 \cos^2 \theta \, dr \, d\theta \]\[ = \rho \cdot \frac{1}{4} a^4 \cdot \pi \]Thus, \( I_y = \rho \cdot \frac{1}{4} a^4 \cdot \pi \), which is the same as \( I_x \).[/tex]

Now, for the moment of inertia \( I_0 \) about the origin:

[tex]\[ I_0 = I_x + I_y = 2 \rho \cdot \frac{1}{4} a^4 \cdot \pi \][/tex]

So, [tex]\( I_0 = \frac{1}{2} \rho a^4 \pi \).[/tex]

For complete question refer to image:

Answer:

0.6915

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 88, \sigma = 4[/ex]

What is the probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG?

This is 1 subtracted by the pvalue of Z when X = 86. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{86 - 88}{4}[/tex]

[tex]Z = -0.5[/tex]

[tex]Z = -0.5[/tex] has a pvalue of 0.3085

1 - 0.3085 = 0.6915

The answer is 0.6915

Answer:x+21

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that :

The enormous sinkhole that appeared in the middle of Guatemalan neighborhood in the year 2010  swallowed a three story building above it and the  sinkhole has an estimated depth of about 100 feet

How much material is needed to fill the sinkhole?

Then , the material needed to fill the sinkhole will be dependent on the volume of the sinkhole.

Determine what information is needed to answer the question.

The information that is needed to answer this question are:

the base area of the sinkhole will be required; &

the height should also be known

if the base area is determined then we can proceed to determine how much material is needed to be calculated.

Do you think your estimate is more likely to be too high or too low

No, the estimate is not likely to be too high or too low rather the estimate of the material required will be almost  equal to the volume of the sinkhole, but that does not implies that it will be exactly the same since the sinkhole is not uniform and regular in shape.

Answer:

60.15

Step-by-step explanation:

if he needs to pay 170 and he has 109.85

170-109.85=60.15

so he needs 60 dollars and 15 cents to reach his goal

Answer:

Step-by-step explanation:

The null hypothesis is the hypothesis that is assumed to be true. It is an expression that is the opposite of what the researcher predicts.

The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected.

From the given situation,

Historically, on average, clementine have 10.25 segments. This is the null hypothesis.

The fruit lover wonders if the actual mean number of segments is more than the historic value. This is the alternative hypothesis.

Therefore, the correct null and alternative hypotheses are

H0: μ = 10.25 and HA: μ > 10.25

The null hypothesis for the test is that the population mean number of clementines segments is equal to the historic value (μ = 10.25). The alternative hypothesis is that the population mean number of clementines segments is greater than the historic value (μ > 10.25). The test will determine whether to accept or reject the null hypothesis.

In conducting a hypothesis test, the null hypothesis is the statement that is assumed to be true, whereas the alternative hypothesis is what the test is attempting to prove. In this instance, if we are questioning whether the actual mean number of segments in a clementine is more than the historic value, we set our null and alternative hypothesis as follows:

In this context, μ represents the population mean number of segments, whilst '10.25' is the historical mean number of segments. The test will determine if there is strong enough evidence to reject the null hypothesis in favour of the alternative hypothesis, hence proving that the mean number of segments is indeed greater than 10.25.

https://brainly.com/question/34171008

#SPJ3

Answer:

Mathematical  200

reasonable 0,200

Step-by-step explanation:

i got it right on the test

Answer:  (a). Passwords = 48620250

               (b). Passwords = 3111696000

Step-by-step explanation:

The question reads that 'A certain organization recommends the use of passwords with the following format':

Consonant, Vowel, Consonant, Consonant, Vowel, Consonant, Number, Number (for example, pinray45​).

The number of consonants is 21, the number of vowels is 5 and the numbers are 10 (0 to 9).

Since, there are 21 consonants and 5 vowels and repetition is allowed.

Use the general multiplication rule for each characters in the sequence.

Multiply by 21 consonants, 5 for vowels and 10 for numbers.

Assuming that the passwords are not case sensitive.

i.e. upper case & lower case letters are same.

Thus, the number of possible passwords is:

Passwords = Consonant * Vowel * Consonant * Consonant * Vowel * Consonant * Number * Number

Passwords = 5 x 21 x 21 x 21 x 5 x21 x 10 = 48620250

(b). Assuming that the passwords are case sensitive

Passwords = 10 x 42 x 42 x 42 x 10 x 42 x 10 = 42 x 420³ = 3111696000

cheers i hope this helps!!!!

The total number of possible passwords is 95,887,125,000.

To calculate the number of possible passwords, we need to consider the number of choices for each position in the password. In the given format, we have 5 positions for consonants, 2 positions for vowels, and 1 position for a number. Let's break it down:

For the 1st consonant position, we have 21 choices (since there are 21 consonants).

For the 1st vowel position, we have 5 choices (since there are 5 vowels).

For the 2nd consonant position, we have 21 choices.

For the 2nd vowel position, we have 5 choices.

For the 3rd consonant position, we have 21 choices.

For the number position, we have 10 choices (since there are 10 numbers).

For the 4th consonant position, we have 21 choices.

For the 3rd vowel position, we have 5 choices.

For the 5th consonant position, we have 21 choices.

Finally, for the last consonant and the last vowel positions, we have 21 and 5 choices respectively.

To find the total number of possible passwords, we multiply the number of choices for each position:

Total number of passwords = 21 * 5 * 21 * 5 * 21 * 10 * 21 * 5 * 21 * 5 = 95,887,125,000.

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 82

For the alternative hypothesis,

µ ≠ 82

This is a 2 tailed test

Since the sample mean and sample standard deviation is given, the t test would be used to determine the test statistic. The formula is

t = (x - µ)/(s/√n)

Where

x = sample mean = 87

µ = population mean = 82

s = samples standard deviation = 10

n = 25

t = (87 - 82)/(10/√25) = 2.5

α = 1 - Confidence level

α = 1 - 0.95 = 0.05

Since α = 0.05, the critical value is determined from the t distribution table.

For the left, α/2 = 0.05/2 = 0.025

For the right of 0.025 = 1 - 0.025 = 0.975

To determine the t score from the t distribution table, we would find the degree of freedom, df and look for the corresponding α value.

df = n - 1 = 25 - 1 = 24

t score = critical value = ±2.064

In order to reject the null hypothesis, the test statistic must be smaller than - 2.5 or greater than 2.5

Since - 2.064 > - 2.5 and 2.064 < 2.5, we would fail to reject the null hypothesis.

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

Margin of error = z × s/√n

Where

s = sample standard deviation

z = t score

Margin of error = 2.064 × 10/√25

= 4.13

Confidence interval = 87 ± 4.13

the lower limit of this confidence interval is

87 - 4.13 = 82.87

the upper limit of this confidence interval is

87 + 4.13 = 91.13

Answer:

0.09312

Step-by-step explanation:

15C9×0.4⁹×0.6⁶ + 15C10×0.4¹⁰×0.6⁵ × 15C11×0.4¹¹×0.6⁴

0.09311963893