g suppose 50 students took an exam and the average score was 70 with a standard deviation of 10. use 68-95-99.7 rule for questions dealing with normal distribution. if the distribution of scores is perfectly normal, how many students would you expect to get an a? (a score between 90 and 100) round up to nearest whole number.

Approximately 68% of the area under the normal distribution curve falls within 1 standard deviation above and below the mean. This is known as the empirical rule, also called the 68-95-99.7 rule.

Approximately 95% of the area under the normal distribution curve falls within 2 standard deviations above and below the mean.

Approximately 99.7% of the area under the normal distribution curve falls within 3 standard deviations above and below the mean.

It's important to note that these values apply to a standard normal distribution (mean = 0, standard deviation = 1). For any normal distribution with a different mean and standard deviation, you can use the standard score (z-score) to transform the data into the standard normal distribution, and then use the standard normal distribution to find probabilities.

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People cannot tell if infrared lights have been turned on in a dark environment. A good method to test this theory is to ask a group of people if an infrared light had been turned on while they were in a room that was lit by infrared radiation.

The experimenter's measurement of the control variable is the independent variable. Independent and dependent variables are the two different categories. These two things might be related in a cause-and-effect manner. The dependent variable is impacted by changes to the independent variable.

Dependent variables are variables that are examined or evaluated as a part of a study.Participants' test scores would be the dependent variable in a study looking at how tutoring affects test results because that is what is being measured.

Two of the most crucial terms in scientific study are "causing" and "effect. It is essential to recognise the independent and dependent variables.A "complex hypothesis" is one that describes a relationship between two or more variables. This equation, as its name implies, has a minimum of two independent variables and a minimum of two dependent variables. These illustrations can aid in your understanding of a challenging theory.

To find out if a theory holds up under inspection, anyone can conduct an experiment. This technique enables you to explain why a theory is unsupported by the evidence. Experimental data, however, can sometimes be interpreted in a nebulous or unclear way.

The amount of sunshine a plant receives determines how large it will become. The dependent variable changes when the independent variable changes. To get valid findings from this experiment, all other factors must be kept constant or under control.

By comparing the probability of the two independent random variables, you may determine their independence. If the collision has no effect on these variables' probabilities, they are regarded as independent.

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Write an equation using x to represent the cost of socks and y to represent the cost of shoes is 5x+2y=100.

As according algebra, an equations is a statement that illustrates the equivalence of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14. a formula that illustrates the relationship between the two expressions on either side of a sign. Every equation is a formula. Not all equations have formulas. It is the purpose of equations to be solved for a variable. We analyze formulas. An expression is made up of a number, a variable, or a combination of a number, a variable, and operation symbols. Two expressions are combined into one equation by using the equal symbol.

Let the cost of sock be $x.

Let the cost of shoes be $y.

According to question

[tex]5x+2y=100[/tex]

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The time it takes a 100g sample of woosterium-21 to decay to 1/3rd of its original amount is 3.002 hours.

The initial amount of woosterium-21 (Ni) that is provided is 100g

The half life of woosterium-21 (t1/2) is given as 3 hours

The final time (t) is provided as 10 hours

The equation for half life is given by the equation:

Nt =  Ni * (1/2)^(t/t₁/₂)

Where, Nt = the final amount of woosterium-21 after 10 hours.

Therefore, Nt = 100 * (1/2)^(10/3) = 100 * 0.5^3.33 = 100 * 0.09944 = 9.944g

Let third life of woosterium-21 be t₁/₃

Substituting values in equation Nt =  Ni * (1/2)^(t/t₁/₂)

9.944 = 100 * (1/2)^(10/t₁/₃)

0.9944 = (1/2)^(10/t₁/₃)

Taking log on both sides,

log 0.9944 = 10/(t₁/₃) log 0.5

-1.0026 = 10/(t₁/₃) * (-0.301)

1.0026 = 3.01/(t₁/₃)

t₁/₃ = 3.002 hours

Therefore, the third life of woosterium-21 was found to be 3.002 hours.

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Complete Question: Suppose that Woosterium-21 is a radioactive substance that has a half-life of 3 hours. (Woosterium-21 does not, as far as I know, exist in real life.) Suppose the initial amount of Woosterium-21 is 100 mg. How much Woosterium-21 remains after 10 hours? Round your answer to three decimal places. (Enter only a number. Do not include units.) |What is the third-life of Woosterium-21? That is, find the time it takes a sample of Woosterium-21 to decay to 1/3 of its original amount. Round your answer to three decimal places. (Enter only a number. Do not include units.

The measure of the angle opposite to the side 'x' is 49.6177°. Then the value of the variable 'x' will be 6.856 units.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The measure of the hypotenuse of the upper triangle is given as,

h² = 5² + 3²

h² = 25 + 9

h² = 34

h = 5.8309

Then the measure of the angle opposite to the side 'x' is given as,

cos ∅ = 5.8309 / 9

cos ∅ = 0.64788

      ∅ = 49.6177°

Then the value of the variable 'x' is given as,

sin 49.6177° = x / 9

0.7617 = x / 9

x = 6.856 units

The measure of the angle opposite to the side 'x' is 49.6177°. Then the value of the variable 'x' will be 6.856 units.

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Answer:

The ratio to represent the relationship between Hallie's donation of blue jeans and Mattie's donation of blue jeans is 4 : 6, or 2 : 3.

Answer:

3/7

Step-by-step explanation:

Answer: 3/7

Step-by-step explanation:

By increasing his speed to 10.4 km/h, he saves 0.175 - 0.16875 = 0.00625 hours or 0.375 minutes.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

If a man runs at the speed of 10 km/h, it will take him 1.75 / 10 = 0.175 hours or 10.5 minutes to cover 1.75 km.

If he increases his speed to 10.4 km/h, it will take him 1.75 / 10.4 = 0.16875 hours or 10.13 minutes to cover the same distance.

So, by increasing his speed to 10.4 km/h, he saves 0.175 - 0.16875 = 0.00625 hours or 0.375 minutes.

Hence, by increasing his speed to 10.4 km/h, he saves 0.175 - 0.16875 = 0.00625 hours or 0.375 minutes.

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Answer: 20% would be the answer

The volume of the new square-based right pyramid will be reduced by 96%.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given a  square-based right pyramid,

and base dimensions are 10 feet by 10 feet

base length = 10 feet

height = 12 feet

the volume of a square-based right pyramid is given by,

V = 1/3b²h

V = 1/3(10)²(12)

V = 400 cubic feet

and if the dimensions of the base are reduced to one-fifth,

The new dimensions for the base is 10/5 feet by 105 feet

base length = 2 feet

and no change in height, h = 12 feet

v = 1/3b²h

v = 1/3(2)²(12)

v = 16 cubic feet

change in volume = V - v

change in volume = 400 - 16

change in volume = 384 cubic feet

percent change in volume = 100*384/400

percent change in volume = 96%

Hence the volume is reduced by 96%.

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An equation which can not be used to find the value of x include the following: B. 11x + 25x = 180.

In Mathematics, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

Furthermore, the sum of the angles in a triangle is equal to 180. This ultimately implies that, we would sum up all of the angles as follows;

m∠D + m∠E + m∠F = 180

Substituting the given parameters into the mathematical expression, we have the following;

(11x)° + (25x)° + (9x°) = 180°

(36x)° + (9x°) = 180° or (11x)° + (34x°) = 180°

45x = 180

x = 4.

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Using the triangle sum theorem, the equation that can NOT be used to find x is:

11x + 25x = 180

The triangle sum theorem says that all interior angles of a triangle is always equal to 180 degrees.

Therefore, to solve for the value of x, the equation below can be created by adding all angles in the triangle which gives 180 degrees:

11x + 25x + 9x = 180

36x + 9x = 180

45x = 180

x = 180/45

x = 4

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The values of the indicated measures are:

i. EF = 44 units

ii. FG = 36 units

iii. DF = 62 units

A straight line that divides a given line into two equal parts and which is at right angle is called a perpendicular bisector of a line segment.

So that to determine the values of indicated measures, we have:

FE = ED

7x + 9 = 9x - 1

collect like terms

1 + 9 = 9x - 7x

10 = 2x

x = 10/ 2

x = 5

Also,

FG = GD

7y + 8 = 10y - 4

collect like terms,

4 + 8 = 10y - 7y

12 = 3y

y = 12/ 3

y = 4

Therefore;

i. EF = 7x + 9

       = 7(5) + 9

       = 35 + 9

EF = 44 units

ii. FG = 7y + 8

        = 7(4) + 8

        = 28 + 8

FG = 36 units

iii. DF = 2(3x + 4y)

         = 2(3*5 + 4*4)

         = 2(15 + 16)

         = 2(31)

DF = 62 units

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Answer: B. 2 quarts

Step-by-step explanation: 16 divided by 8 is 2 so you multiply 2 by 1 and you get 2. :)

The correct response is b. 47.06 minutes. the shortest wait time that would still be in the longest 15% of wait times is 47.06 minutes.

A minute is a unit of time equal to 60 seconds and one-sixtieth of an hour. (See leap second; certain uncommon minutes have 59 or 61 seconds.) The minute is acceptable for use with SI units even though it is not a SI unit. In mathematics, time is defined as a continuous and ongoing sequence of events that occur one after another in the past, present, and future. Time can be used to quantify, contrast, or even rank the length of events or the gaps between them. When you say something has to be done, you are emphatically stating that it should happen or be done right away.

Mean, μ[tex]=38.12[/tex]

Standard deviation,σ[tex]=8.63[/tex]

Waiting times that are longer are worse than those that are shorter. Therefore, the 15% of wait times that are the worst fall into this category. The inferred level of confidence is 0.85.

The z value corresponding to the right tail probability of 0.15 is

[tex]z=1.03[/tex]

But

Z= x−μ/σ

x=Z∗σ+μ

[tex]=1.03∗8.63+38.12=47.06[/tex]

The quickest waiting period that would still fall into the worst 15% of waiting periods is 47.06 minutes.

​

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The required probability for the parts which are examined for defects are ;

1. Probability of both the parts are good is equal to 0.375.

2. Probability represents exactly one part has major defect is 0.2333.

Total number of parts to be examined for defects = 16

Number of good parts = 10

Number of parts with minor defects = 4

Number of parts with major defects = 2

Number of parts to be chosen at random without replacement = 2

Total number of outcomes = ¹⁶C₂

                                             = (16!) / ( 16 - 2 )!2!

                                             = 120

1. Probability of both the parts to be good

Number of favourable outcomes = ¹⁰C₂

                                                        = 10! / (8!)(2!)

                                                        = 45

Required Probability = 45 / 120

                                   = 0.375

2. Probability of exactly one major defect

Number of favourable outcomes= ²C₁ × ¹⁴C₁

                                                      = 2 × 14

                                                      = 28

Required Probability = 28/ 120

                                   = 0.2333

Therefore, the probability of both are good is 0.375 and probability of exactly one major defect is 0.2333.

The above question is incomplete, the complete question is:

'16 parts are examined for defects. It is found that 10 are good, 4 have minor defects, and 2 have major defects. Two parts are chosen at random from the 16 without replacement; that is; the first part chosen is not returned to the mix before the second part is chosen:

1. What is the probability that both parts are good?

2. What is the probability that exactly one part has major defect?'

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The equation of the line graph is y = -3/8x + 5/2

A line is defined as the shortest distance between two points. The equation of a line in slope intercept form is expressed as:"

y = mx + b where:

m is the slope

b is the intercept

Using the coordinate points (-4, 4) and (4, 1)

Slope = 1-4/4-(-4)
Slope = -3/8

Determine the y-intercept

1 = -3/8(4) + b

1 = -3/2 + b

b = 1 + 3/2

b = 5/2

The required equation of the graph is y= -3/8x + 5/2

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There's no guaranteed way to make someone fall in love with you.

Love is a complex and deeply personal emotion that is influenced by a wide range of factors, including a person's upbringing, life experiences, and individual preferences and values.

The best approach is to simply be yourself, be kind and respectful, and let the relationship develop naturally over time. It's important to understand that you cannot control someone else's feelings, and trying to force or manipulate someone into falling in love with you is unlikely to result in a healthy and happy relationship.

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The order of the numbers from least to greatest is as follows:

4.427 , 4.42 , 4.325 , 4.63

A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32, etc.

Given here: The numbers containing fractions and decimal numbers.

To get a clarity on the magnitude of the numbers, let's convert every fraction to decimal numbers

Thus 4⁷/₁₁=4.63

37/8=4.625

Hence, The order of the numbers from least to greatest is as follows:

4.427 , 4.42 , 4.325 , 4.63

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The number of tons of strawberries they should order is; 2 Tons

The parameters in the question are;

Quantity of flavor used = 10 pounds for every 16-jars

Number of jars of classic strawberry = 4000 jars

Number of jars of Tropical strawberries = 2400 jars

If 16 jars = 10 pounds

Then 4000 jars = 4000 * 10/16 = 2500 pounds

Similarly;

2400 jars = 2400 * 10/16

= 1500 pounds

Total pounds = 2500 + 1500

= 4000 pounds

From conversion factors;

1 pound = 0.0005

Thus;

4000 pounds = 4000 * 0.0005

= 2 pounds

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The probability mass function of x is p(x) = 4/52 * (48/51)^(x-1) * (1/51)^(52-x) for x = 1, 2, ..., 52.

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

x denote the number of cards removed

This means that

x = 1, 2, ..., 52

The probability of selecting an ace is

P(Ace) = 4/52

This means that

P(Ace') = 48/51 ----- the card is selected without replacement

When x Aces are selected, the remaining cards is 52 - x

Using the above as a guide, we have the following:

PMF = 4/52 * (48/51)^(x-1) * (1/51)^(52-x) for x = 1, 2, ..., 52.

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Answer:

Step-by-step explanation:

you get 5000 and divide 21and it equals 238 people

Michael is 3 33 times as old as brandon. 18 1818 years ago, michael was 9 99 times as old as brandon so michael is 272454 years old.

Since we have given that

Michael is 3 times as old as Brandon .

Let the age of Brandon be 'x'.

Let the age of Michael be 333x

According to question, 181818 years ago, Michael was 999 times as old as Brandon.

181818 years ago,

Age of Brandon was x-181818

Age of Michael was 333x-181818

So, our equation becomes,

999( x- 181818) = 333x - 181818

999x - 181636182 = 333x - 181818

666x = 181454364

x = 272454

Hence, Age of Brandon is 272454 years.

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The probability that both motors from the particular supplier are assigned to the first line is 1/126.

To explain this further, the numerator of the equation is the number of ways to choose two motors from the nine available, and the denominator is the number of ways to assign the nine motors to the three production lines. The denominator is calculated by multiplying the number of ways to assign three motors to the first line, three motors to the second line, and three motors to the third line. This is why the denominator is 3C2*3C2*3C2, which simplifies to 126.

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Step-by-step explanation:

（3*10＾9）（2.3*10＾7）

＝

[tex]6.9 \times {10}^{16 \\} [/tex]

The alumni giving rates would represent a nominal variable, as it is a categorical variable representing donors and non-donors.

An appropriate graph to depict these data would be a bar graph. The bar graph would show the number of alumni who donated (the numerator) and the number of alumni who did not donate (the denominator) in a given year. The formula for this calculation would be,

Alumni Giving Rate = (Number of Alumni Donors / Total Number of Alumni) x 100

For example, if 10 alumni donors out of 100 total alumni donated, the alumni giving rate would be 10%. The graph would show the percentage of alumni that donated in a given year.given year. The formula for this calculation would be,

Alumni Giving Rate = (Number of Alumni Donors / Total Number of Alumni) x 100

For example, if 10 alumni donors out of 100 total alumni donated, the alumni giving rate would be 10%. The graph would show the percentage

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The solution of the graph are x=1 and y=11.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

In the first graph the one line is passing through points (-1, -3) and (0,4)

m=4+3/0+1=7

4=7(0)+b

b=4

y=7x+4..(1)

Now other line passing through points (-4, 0) and (0, -4)

m=-4/4=-1

0=-1(-4)+b

b=-4

y=-x-4..(2)

-x-4=7x+4

Take all the variables on one side.

-x-7x=8

-8x=8

x=1

Now let us find y value

y=7+4=11

Hence, the solution of the graph are x=1 and y=11.

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The frequency distribution looks to have a normal distribution because (A) the frequencies start off low, rise to one or two high frequencies, then fall to a low frequency, and the distribution is fairly symmetric.

Frequency tables or charts are used to represent frequency distributions. Frequency distributions can display the proportion of observations or the actual number of observations that fall inside each range.

The distribution is known as a relative frequency distribution in the latter case.

Frequency distribution that is cumulative.

Frequency distribution relative. distribution of the relative cumulative frequency.

Measurements of position and central tendency (mean, median, mode) Dispersion metrics (range, variance, standard deviation) How much symmetry or asymmetry there is (skewness) The peakedness or flatness (kurtosis).

Because the frequencies begin low, rise to one or two high frequencies, then fall to a low frequency, and the distribution is roughly symmetric, the frequency distribution appears to have a normal distribution.

Therefore, the frequency distribution looks to have a normal distribution because (A) the frequencies start off low, rise to one or two high frequencies, then fall to a low frequency, and the distribution is fairly symmetric.

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The probability of having a pile with 4 cards, another pile with 3 cards, another pile with 2 cards, and the smallest pile with 1 card is 17.36%.

The probability of a pile having 4 cards, another pile having 3 cards, another pile having 2 cards, and the smallest pile having 1 card can be calculated using the formula [tex]$\frac{n!}{n_1! n_2! n_3! n_4!}$[/tex]. In this case,

n = 10, n1 = 4, n2 = 3, n3 = 2 and n4 = 1.

Therefore, the probability of this particular combination of piles is [tex]$\frac{10!}{4! 3! 2! 1!} \\= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{4 \cdot 3 \cdot 2 \cdot 1 \cdot 4 \cdot 3 \cdot 2 \cdot 1 \cdot 2 \cdot 1} \\ = \frac{5040}{288} = 17.36$[/tex].

This means that the probability of having this particular combination of piles is 17.36%.

The probability of having a pile with 4 cards, another pile with 3 cards, another pile with 2 cards, and the smallest pile with 1 card is 17.36%.

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Answer:

see explanation

Step-by-step explanation:

∠ 1 and ∠ 2 are corresponding angles and are congruent , then

7x - 27 = 4x + 18 ( subtract 4x from both sides )

3x - 27 = 18 ( add 27 to both sides )

3x = 45 ( divide both sides by 3 )

so

∠ 1 and ∠ 2 = 7x - 27 = 7(15) - 27 = 105 - 27 = 78°

∠ 2 and ∠ 3 are corresponding angles and are congruent , then

∠ 3 = 78°

∠ 3 and ∠ 4 are same- side interior angles and sum to 180° , that is

78 + 4y + 2 = 180

4y + 80 = 180 ( subtract 80 from both sides )

4y = 100 ( divide both sides by 4 )

y = 25

thus

∠ 4 = 4y + 2 = 4(25) + 2 = 100 + 2 = 102°

in conclusion

x = 15 , y = 25 , ∠ 1 = 78° , ∠ 4 = 102°

The area of the waxed hardwood floor is 35/9 yards square.

The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.

Given here: Total area of the floor = 4³/₈ yards² and he waxed 8/9 part of the total area.

Now 8/9 of the total area is

Waxed area= 8/9×35/8   ( 4³/₈ =35/8)

                  =35/9

Thus the area in square units that Jahdiel waxed is 35/9 yards²

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