Please help with this easy 5th grade math! Tysm!

Answer:

x = 0

Step-by-step explanation:

To solve this equation you would need to get x by itself on one side

1/2 (x+4)^2 - 5 = 3

1.) add 5 to both sides

1/2 (x+4)^2 = 8

2.) divide each side by 1/2

(x+4)^2 = 16

3.) find the square root of both sides

(x+4) = 4

4.) subtract 4 from both sides

x = 0

The app "Photomath" is a great way to solve problems like these and it gives a step by step explanation that might be easier to understand than mine :)

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:

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.

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Answer:

10x-48y

Step-by-step explanation:

Answer:

0.09312

Step-by-step explanation:

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

0.09311963893

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:

120

Step-by-step explanation:

I=prt . Where: P = Principal Amount; I = Interest Amount; r = Rate of Interest per year in decimal and time t should be in the same time units such as months or years.

I=500(.08)(3)

Answer:

8% of 500 is 40, For the first year is 540. 8% of 540 is 43.20 dollars. 8% of 583.2 is 46.656. So the total is 630 by rounding but the actual amount is 629.956. The interest is 129.956

P.S

Have an Amazing Day!

-Faker/Tosrel

Answer:

a) [tex]f(401) = 3010[/tex], b) [tex]f(400.5) = 3005[/tex], c) [tex]f(399) = 2990[/tex], d) [tex]f(398) = 2980[/tex], e) [tex]f(399.75) = 2997.5[/tex]

Step-by-step explanation:

The estimation of each value can be found by the following value:

[tex]f(x + \Delta x) = f(x) + f'(x)\cdot \Delta x[/tex]

a) [tex]f(401) = 3000 + 10\cdot (401-400)[/tex]

[tex]f(401) = 3010[/tex]

b) [tex]f(400.5) = 3000 + 10\cdot (400.5 - 400)[/tex]

[tex]f(400.5) = 3005[/tex]

c) [tex]f(399) = 3000 + 10\cdot (399 - 400)[/tex]

[tex]f(399) = 2990[/tex]

d) [tex]f(398) = 3000 + 10\cdot (398-400)[/tex]

[tex]f(398) = 2980[/tex]

e) [tex]f(399.75) = 3000 + 10\cdot (399.75-400)[/tex]

[tex]f(399.75) = 2997.5[/tex]

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:

[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:

There is no sample given, please provide us with an attachment for your answer.

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.

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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:

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:

there is no any number to caculate social security tax.

Step-by-step explanation:

Social Security taxes are calculated using a deduction rate of 6.2% and 1.45% for Medicare from an employee's gross annual income. Employers also contribute matching amounts. However, the economic impact of employers' contributions often invariably impact employees indirectly.

To calculate social security taxes, you need to consider a standard deduction rate of 6.2% for the Social Security and 1.45% from Medicare. These deductions are generally taken directly out of the employee's gross annual income. Employers also contribute matching percentages. However, it is important to note that in reality, the burden of the employer's contribution may in effect fall on the employee as it can result in lower wages. For instance, for those considered as independent contractors or members of the 'gig economy' receiving a 1099 tax statement, the individual must pay both the employer and employee portion of the social security and Medicare taxes.

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Answer:

1) H0: p=0.3

Ha: p≠0.3

2) 0.48

3)•2.78

•0.0054. So, we reject H0.

• No, we cannot conclude

•

Step-by-step explanation:

1) To formulate the null and alternative hypothesis:

• Null hypothesis:

[tex] H_0: p=0.3 [/tex]

•Alternative hypothesis:

Ha: p≠0.3

2) Point estimate of the population proportion stocks that went up:

Since sample is 50 stocks and 24 went up, we have phat as:

[tex]phat = \frac{24}{50} = 0.48[/tex]

3) • Hypothesis test using 0.01 as level of significance:

Test statistic =

[tex] Z = \frac{phat-p}{\sqrt{\frac{p*(1-p)}{n}}}[/tex]

[tex] = \frac{0.48-0.3}{\sqrt{\frac{0.3*0.7}{50}}}[/tex]

= 2.78

•Using standard normal table

P value =

2*(P>2.78) = 0.0054

• The p value (0.0054) is less than level of significance (0.01), we reject null hypothesis H0.

• No, we cannot conclude that the proportion of stocks going up is not .30

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

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]

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Answer:x+21

Step-by-step explanation:

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

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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:

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:

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:

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.

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

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The equivalent expression to 16(w+q) is 16w + 16q, but none of the given options A, B, C, or D are correct as they do not accurately represent this distribution. The closest option would be C (16w + 9), though it is still incorrect because it has 9 instead of 16q.

The question asks which expression is equivalent to 16(w+q). The correct way to distribute a constant over a sum inside parentheses is to multiply each term inside the parentheses by that constant. So, 16 must be multiplied by both w and q.

Therefore, the equivalent expression is 16w + 16q. Looking at the provided options:

Since none of the given options are exactly 16w + 16q, no available option is a correct equivalent expression to 16(w+q).

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.

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Answer:

The probability that the person is more than 30 years old is 0.153

Step-by-step explanation:

We can obtain the probability that the person sampled is more than 30 years old by dividing the amount of peope with more than 30 years old with the total amount of people that visited the library that Saturday, in other owrds, 1086.

The number of people with more than 30 years old can be obtained by substracting from 1086 (the total amount) the total amount of people with 30 years or less.

There are 269 (under 10) + 466 (between 10 and 18) + 185 (between 19 and 30) = 920 people under 30 years old. Therefore, the total amount of people with more than 30 years old is 1086-920 = 166, and the probability that a person selected is from that group is 166/1086 = 0.153

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:

I'd say go to Wikipedia and look it up.  It is something that cannot be summarized into just a few words.

Step-by-step explanation: