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## A random sample of 25 statistics examinations was taken. the average score in the sample was 76 with a standard deviation of 12. assuming the scores are normally distributed, the 99% confidence interval for the population average examination score is:

Since the sample size is less than 30, therefore we use
the t statistic.

Let us define the given variables:

N = sample size = 25

X = average score = 76

s = standard deviation = 12

99% Confidence interval

Degrees of freedom = n – 1 = 24

The formula for confidence interval is given as:

CI = X ± t * s / sqrt N

using the standard distribution table, the t value for DF
= 24 and 99% CI is:

t = 2.492

Therefore calculating the CI using the known values:

CI = 76 ± 2.492 * 12 / sqrt 25

CI = 76 ± 5.98

CI = 70.02, 81.98

Answer: The average score ranges from 70 to 82.

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## An 8.65-g sample of an unknown group 2a metal hydroxide is dissolved in 85.0 ml of water. an acid-base indicator is added and the resulting solution is titrated with 2.50 m hcl(aq) solution. the indicator changes color signaling that the equivalence point has been reached after 56.9 ml of the hydrochloric acid solution has been added.

The molar mass of metal hydroxide = 121.66 g/ mole

The formula is Sr(OH)2

Explanation;

M(OH)2 + 2 HCl = MCl2 + 2 H2O

Moles of the acid = 2.5 x 56.9 / 1000 = 0.14225

Therefore; moles of hydroxide at the eq point = 0.0711 moles

These have a mass of 8.65g

Thus; mass of 1 mole = 8.65 / 0.0711

= 121.66 g / mole

That means the compound is Sr (OH)2 ..

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## The durations of a random sample of 16 commercials are below (in seconds). find the mean, median, and mode of these durations. 30, 12, 26, 7, 14, 35, 20, 30, 55, 8, 35, 18, 42, 15, 30, 10

First arrange in ascending order of time:-

7, 8, 10, 12, 14, 15, 18, 20, 26, 30, 30, 30, 35, 35, 42, 55

MOde is the value occuring mos  = 30.

Median is the mean of 2 middle numbers = (20 + 26) / 2 = 23

Mean = sum of the 16 numbers  / 16  =  387/16  = 24.2

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## . What is the mass, in grams, of a sample of 7.83 × 1024 atoms of helium (He)?

. What is the mass, in grams, of a sample of 7.83 × 1024 atoms of helium (He)?

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## Li designed a survey to determine how comfortable students at her middle school are with fractions. There are 600 students in her middle school. The students are equally distributed among grade levels. She selected a sample of 28 students in her first-period class. Which best explains Li’s sample?

The correct answer to this is:

Nonrandom and biased

The method of Li’s sampling has a
tendency that some elements or portion in the population has no chance of
selection. Further, it was not stated which portion of the population she
obtained the sample thus we cannot accurately determine the probability of
selection. This kind of sampling results in a bias. A biased sampling is a type
of nonrandom sampling.

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## A 150ml sample of hydrochloric acid completely reacted with 60.0mL of a 0.100 M NaOH solution. What was the original concentration of the HCl solution

A 150ml sample of hydrochloric acid completely reacted with 60.0mL of a 0.100 M NaOH solution. What was the original concentration of the HCl solution

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## Which statement is true? A sample statistic can never be equal to the population parameter. Point estimates are defined for both samples and populations. To calculate a sample proportion, we need to know the population size. To calculate a point estimate, we need to know the sample size

Option C is true. To calculate a sample proportion, we need to know the population size.

Step-by-step explanation:

To calculate a sample proportion, we need to know the population size. – This is the true statement.

A sample statistic can never be equal to the population parameter. This is false. A statistic is a feature of sample and a parameter is a feature of  population. Every sample of the selected size has an equal chance of being used.

Point estimates are defined for both samples and populations. This is false. A point estimate is used to estimate the population parameter.

To calculate a point estimate, we need to know the sample size. This is false. Population is needed.

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## A sample of gas occupies 7.80 liters at 425°C? What will be the volume of the gas at 35°C if the pressure does not change? 4.65 liters 3.65 liters 3.44 liters 7.65 liters 5.89 liters

A sample of gas occupies 7.80 liters at 425°C? What will be the volume of the gas at 35°C if the pressure does not change? 4.65 liters 3.65 liters 3.44 liters 7.65 liters 5.89 liters

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## Julie has a juice stand where she sells apple juice, orange juice, and carrot juice. She sells her cups of juice in two sizes: large and small. Draw a tree diagram showing the sample space of possible juice orders.

Julie has a juice stand where she sells apple juice, orange juice, and carrot juice. She sells her cups of juice in two sizes: large and small. Draw a tree diagram showing the sample space of possible juice orders.

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## What price do farmers get for the peach crops? in the third week of June, a random sample of 40 farming regions gave a sample mean of \$6.88 per basket. assume that the standard deviation is known to be \$1.92 per basket. find a 90% confidence interval for the population mean price per basket that farmers in this region get for their peach crop

Given:
Sample size, n = 40
Sample mean, xb = \$6.88
Population std. deviation, σ = \$1.92 (known)
Confidence interval = 90%

Assume normal distribution for the population.
The confidence interval is
(xb + 1.645*(σ/√n), xb – 1.645*(σ/√n)
= (6.88 + (1.645*1.92)/√40, 6.88 – (1.645*1.92)/√40)
= (7.38, 6.38)

Answer: The 90% confidence interval is (7.38, 6.38)

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## A sample of water is mixed with a surfactant what will most likely happen to the viscosity of the water

If a sample o water is mixed with a surfactant, the most likely result is that the viscosity of the water will increase. This is because of the property of the surfactant which is generally viscous; and becomes more viscous when mixed with water.

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## Two fair coins are flipped and a fair number cube is rolled. What is the sample space of possible outcomes?

Two fair coins are flipped and a fair number cube is rolled. What is the sample space of possible outcomes?

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## Samples of size n = 90 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the variance is found for each sample. What is the distribution of the sample variances?

chi square distribution with df = n-1

Step-by-step explanation:

Given that sample of size n=90  are randomly selected from the population of numbers (0 through 9) produced by a random-number generator

Since sample size is large and randomness is followed we can assume that the variable follows a normal distribution.

Hence the sample variance would follow a chi square distribution with degree of freedom =

This is because we have is standard normal hence square will be a chisquare variate.  When we sum n variates we get chi square distribution with df n-1

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## A chunk of gold and copper in the ratio 20:7. How much gold is in this 200g sample of gold

A chunk of gold and copper in the ratio 20:7. How much gold is in this 200g sample of gold

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## Read this excerpt from a student's essay and answer the question below. "Having a brother with autism can be really stressful. You never know how he's going to react. It takes a lot of patience sometimes. You love him but sometimes he drives you crazy." What is the BEST description of the tone in this student sample? A. passive B. protective C. empathetic D. determined

Read this excerpt from a student’s essay and answer the question below. “Having a brother with autism can be really stressful. You never know how he’s going to react. It takes a lot of patience sometimes. You love him but sometimes he drives you crazy.” What is the BEST description of the tone in this student sample? A. passive B. protective C. empathetic D. determined

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## 1. If 500 ML of a 3 L sample of 0.20 M sodium chloride solution is spilled, what is the concentration of the remaining solution? A. 300 M B. .033 M C. 15.2 M D. .20 M

D. 0.2 MThe concentration of a solution is basically the ratio of the solute present to the solvent in the solution. This is an intrinsic property, independent of the amount of solution that is present. A similar example is that of density. No matter the size of a sample, the density and concentration of that sample remain constant.

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## A sample of carbon dioxide gas, co2 (g), occupies a volume of 5.75 l at 0.890 atm. if the temperature and the number of moles remain constant, calculate the volume when the pressure a. increased to 1.25 atm b. decrease to 0.350 atm

According to Boyle’s law;
P1V1 = P2V2
P1 is the pressure of the gas in the first case.
V1 is the volume of the gas in the first case.
P2 is the pressure of the gas in the second case.
V2 is the volume of the gas in the second case.

P1 = 0.890 atm, V1 = 5.75l

a. P2 = 1.25 atm,
0.890*5.75 = 1.25*V2
V2 = 4.094 l

b. P2 = 0.350 atm,
0.890*5.75 = 0.350*V2
V2 = 14.621 l.

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## A 47.3 ml sample of alcohol has a mass of 37.32 g. what is its density in g/ml?

A 47.3 ml sample of alcohol has a mass of 37.32 g. what is its density in g/ml?

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## A gas sample is heated from -20.0°c to 57.0°c and the volume is increased from 2.00 l to 4.50 l. if the initial pressure is 0.140 atm, what is the final pressure

A gas sample is heated from -20.0°c to 57.0°c and the volume is increased from 2.00 l to 4.50 l. if the initial pressure is 0.140 atm, what is the final pressure

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## Pon heating, a 5.41 g sample of a compound decomposes into 2.37 g n 22 and 3.04 g h 22 o. if the molar mass of the compound is 64.06 g/mol, what is the chemical formula of the compound

The unknown of this problem is the experimental percent of water in the compound in order to remove the water of hydrogen, given the following:

Mass of crucible, cover and contents before heating                               23.54 g
Mass of empty crucible and cover                                                            18.82 g
Mass of crucible, cover, and contents after heating to constant mass     20.94 g

In order to get the answer, determine the following:

Mass of hydrated salt used                          = 23.54 g – 18.82 g = 4.72 g
Mass of dehydrated salt after heating          = 20.94 g – 18.82 g = 2.12 g
Mass of water liberated from salt                 = 4.72 g – 2.12 g = 2.60 g

Then solve the percent of water in the hydrated salt by:

% water = (mass of water / mass of hydrated salt) x 100
% water = 2.60 g / 4.72 g x 100
% water = 55.08 % in the compound

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## A 12-g sample of cooking oil, which is a fat, contains ________ kcal. (energy value for fat = 9 kcal/g)

25) Answer is: less metallic and more nonmetallic.

Electronegativity increases from left to right across a period, atoms have tendency to attract electrons.

Electronegativity (χ) is a property that describes the tendency of an atom to attract a shared pair of electrons.

Radioisotope has an unstable atomic nucleus and emit energy and particles when it changes to a more stable form.

Francium (Fr) is element with atomic number 87 (87 protons and 87 electrons).

Boiling is the temperature at which the vapour pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding atmosphere.

The Celsius scale was based on 0°C for the freezing point of water and 100°C for the boiling point of water at 1 atm pressure.

There are two types of reaction:

1) endothermic reaction (chemical reaction that absorbs more energy than it releases, ΔH>0).

2) exothermic reaction (chemical reaction that releases more energy than it absorbs).

For example, the breakdown of ozone is an endothermic process. Ozone has lower energy than molecular oxygen (O₂) and oxygen atom, so ozone need energy to break bond between oxygen atoms.

The average kinetic energy of molecules depends on the temperature.

As temperature increases, molecules gain more energy from surrounding and move faster.

Kinetic energy (standard unit is the joule J) depends on speed of the molecule.

Solid gains kinetic energy to become a liquid and then becomes a gas.

This was famous Rutherford’s Gold Foil Experiment: he bombarded thin foil of gold with positive alpha particles.

Rutherford observed the deflection of alpha particles on the photographic film.

Alpha particles are helium atom particles, consist of two protons and two neutrons.

According to Rutherford model of the atom: atoms have their charge concentrated in a very small nucleus.

For example, calcium oxide.

Calcium oxide (CaO) has ionic bonds between calcium cations (Ca²⁺) and oxygen anions (O²⁻).

Because it has strong ionic bonds, it has high melting point (around 2600°C).

Ionic bond is the electrostatic attraction between oppositely charged ions (cations and anions).

32) Answer is: a scientific model.

A scientific model is a representation of an idea, an object, a process or a system that is used to describe and explain phenomena that cannot be experienced directly.

33) Answer is: the superscript is mass number and the subscript is atomic number.

Atomic number(Z) is the number of protons, which is characteristic of a chemical element..

Mass number (A) is the total number of protons and neutrons in a nucleus.

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## Find the sample standard deviation and the population standard deviation of the data set. 70, 58, 70, 37, 58, 47, 58, 76, 77, 67, 66, 77, 33, 74, 57

Employee                                 Mary      Zoe         Greg         Ann           Tom

Cumulative Pay                       \$6,800   \$10,500  \$8,400    \$66,000   \$4,700

Pay subject to FICA S.S.         \$421.60  \$651.00  \$520.80 \$4092.00 \$291.40
6.2%, (First \$118,000)

Pay subject to FICA Medicare \$98.60 \$152.25    \$121.80    \$957.00    \$68.15
1.45% of gross

Pay subject to FUTA Taxes      \$40.80  \$63.00     \$50.40    \$396.00  \$28.20
0.6%

Pay subject to SUTA Taxes   \$367.20  \$567.00  \$453.60  \$3564.00 \$253.80
5.4% (First \$7000)

Totals                                     \$928.20 \$1,433.25 \$1,146.60 \$9,009.00 \$641.55

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## A sample of gold has a mass of 38.6 grams and a volume of 2 cm3. What is the density of gold?

This problem is to apply Roult’s Law.

Roult’s Law states that the vapor pressure, p, of a solution of a non-volatile solute is equal to the vapor pressure of the pure solvent, Po solv, times the mole fraction of the solvent, Xsolv

p = Xsolv * Po sol

X solv = number of moles of solvent / number of moles of solution

The solvent is water and the solute (not volatile) is glycerin.

Number of moles = mass in grams / molar mass

mass of water = 132 ml * 1 g/ml = 132 g

molar mass of water = 18 g/mol

=> number of moles of water = 132 g / 18 g/mol = 7.33333 mol

mass of glycerin = 27.2 g

molar mass of glycerin:, C3H8O3: 3 * 12 g/mol + 8 * 1 g/mol + 3*16 g/mol = 92 g/mol

number of moles of glycerin = 27.2g / 92 g/mol = 0.29565

total number of moles = 7.33333 moles + 0.29565 moles = 7.62898 moles

=> X solv = 7.33333 / 7.62898 = 0.96125

=> p = 0.96125 * 31.8 torr ≈ 30.57 torr ≈ 30.6 torr.

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## A sample of hydrated magnesium sulfate has a mass of 4.052 g. After it is heated, it has a mass of 1.979 g. What is the percentage by mass of water in the hydrate?

This problem is to apply Roult’s Law.

Roult’s Law states that the vapor pressure, p, of a solution of a non-volatile solute is equal to the vapor pressure of the pure solvent, Po solv, times the mole fraction of the solvent, Xsolv

p = Xsolv * Po sol

X solv = number of moles of solvent / number of moles of solution

The solvent is water and the solute (not volatile) is glycerin.

Number of moles = mass in grams / molar mass

mass of water = 132 ml * 1 g/ml = 132 g

molar mass of water = 18 g/mol

=> number of moles of water = 132 g / 18 g/mol = 7.33333 mol

mass of glycerin = 27.2 g

molar mass of glycerin:, C3H8O3: 3 * 12 g/mol + 8 * 1 g/mol + 3*16 g/mol = 92 g/mol

number of moles of glycerin = 27.2g / 92 g/mol = 0.29565

total number of moles = 7.33333 moles + 0.29565 moles = 7.62898 moles

=> X solv = 7.33333 / 7.62898 = 0.96125

=> p = 0.96125 * 31.8 torr ≈ 30.57 torr ≈ 30.6 torr.