A=3.14r^2, If A=49, find r?

The probability that a student scored less than 55% on the exam is 0.134%.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have:

Mean of the sample = 70

Standard deviation = 5

= P(X<55%)

Z = (55-70)/5

Z = -3

P(X < -3)

From the Z table:

P(x<-3) = 0.0013499

or

P(x<-3) = 0.134%  

Thus, the probability that a student scored less than 55% on the exam is 0.134%.

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The probability of event A occurring is 1/3, the probability of event B occurring is 5/18, and the probability of event AB occurring is 1/9.

The probability of an event occurring is the number of favorable outcomes divided by the total number of possible outcomes. In this case, we have an unfair die where the even numbered sides are twice as likely as the odd numbered sides. We can use this information to find the probabilities of events A and B.

Event A = {odd numbered side} = {1, 3, 5, 7, 9, 11}

Event B = {4, 5, 6, 7, 8}

(a) To find the probability of event A occurring, we need to find the number of favorable outcomes and the total number of possible outcomes. There are 6 odd numbered sides on the die, so the number of favorable outcomes is 6. However, since the even numbered sides are twice as likely as the odd numbered sides, we need to account for this in the total number of possible outcomes. The total number of possible outcomes is 12 + 6 = 18. Therefore, the probability of event A occurring is 6/18 = 1/3.

(b) To find the probability of event B occurring, we need to find the number of favorable outcomes and the total number of possible outcomes. There are 5 sides in event B, so the number of favorable outcomes is 5. The total number of possible outcomes is the same as in part (a), which is 18. Therefore, the probability of event B occurring is 5/18.

(c) To find the probability of event AB occurring, we need to find the intersection of events A and B. The intersection of events A and B is {5, 7}, so the number of favorable outcomes is 2. The total number of possible outcomes is the same as in parts (a) and (b), which is 18. Therefore, the probability of event AB occurring is 2/18 = 1/9.

So, the probability of event A occurring is 1/3, the probability of event B occurring is 5/18, and the probability of event AB occurring is 1/9.

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Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

"Meta Analysis" is a quantitative statistical analysis that compares and combines the results of individual but similar studies.

A quantitative statistical analysis of numerous distinct but related experiments or research to assess the statistical significance of the pooled results.

Some characteristics of meta analysis are-

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Answer:

The statement is false.

Step-by-step explanation:

A parallelogram is a figure of four sides, such that opposite sides are parallel

A rectangle is a four-sided figure such that all internal angles are 90°

Here, the statement is:

"A rectangle is sometimes a parallelogram but a parallelogram is always a

rectangle."

Here if we found a parallelogram that is not a rectangle, then that is enough to prove that the statement is false.

The counterexample is a rhombus, which is a parallelogram that has two internal angles smaller than 90° and two internal angles larger than 90°, then this parallelogram is not a rectangle, then the statement is false.

The correct statement would be:

"A parallelogram is sometimes a rectangle, but a rectangle is always a parallelogram"

The number of tablespoons Debnil has is 2 tablespoons

Number of teaspoons of salt with Debnil = 6

Ratio = 3:1

Ratio: mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent."

Let x represent the total number of teaspoons and the tablespoons

Therefore,

6 = 3/4x

x = (6*4)/3

x = 8

So, there are a total of 8 spoons

Now, the number of tablespoons is 1/4 of the total

Hence, the number of tablespoons will be 2

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By using the concept of Probability, 0.771 is the probability by which worker 1 will outproduce worker 2

Let Xi be the random variable representing the number of units the first worker produces in day i.

Define X = X₁+ X₂ + X₃ + X₄ + X₅ as the random variable representing the number of units the first worker produces during the entire week.

We know that Mean =(Sum of all quantities)/(Number of quantities)

Mean=75 and number of quantities =5(given)

Therefore, from the formula

=>Sum of all quantities=75×5

or We can Say that X₁+ X₂ + X₃ + X₄ + X₅=375--------------------------------(eq1)

Now, talking about the standard deviation of first worker

We know that standard deviation = \(\frac{\sqrt{(Each quantity - Mean)^{2} } }{\sqrt{Total Number of quantities} }\)

We are given standard deviation of first worker as 20,

Therefore 20×\(\sqrt{Total Number of quantities}\) = \(\sqrt{(Eachquantity -Mean)^{2} }\)

20√5 = √[(X₁ - Mean)²+(X₂ - Mean)²+(X₃ - Mean)²+(X₄ - Mean)²+(X₅ - Mean)²]-(eq2)

Therefore, from eq1 and eq2,

we get Mean(µx) =375 and standard deviation(σ\(x\)) =20√5

Similarly, define random variables Y₁, Y₂, . . . , Y₅ representing the number of units produces by the second worker during each of the five days and define Y = Y₁ + Y₂ + Y₃ + Y₄ + Y₅.

From the Mean formula,

we get  Y₁ + Y₂ + Y₃ + Y₄ + Y₅=(65×5)--------------------------------(eq3)

Standard deviation of second worker = 21(given),

So using the standard deviation formula, we get

Therefore 21×\(\sqrt{Total Number of quantities}\)=\(\sqrt{(Eachquantity -Mean)^{2} }\)

21√5=√[(Y₁ - Mean)²+(Y₂ - Mean)²+(Y₃ - Mean)²+(Y₄ - Mean)²+(Y₅ - Mean)²]-(eq4)

Therefore, from eq3 and eq4,

we get Mean(µy) =325 and standard deviation(σy) =21√5

Of course, we assume that X and Y are independent. The problem asks for P(X > Y ) or in other words for P(X − Y > 0).

It is a quite surprising fact that the random variable U = X −Y , the difference between X and Y ,is also normally distributed with mean µU = µx−µy = 375−325 = 50 and standard deviation σu ,where σ\(u^{2}\) = σ\(x^{2}\)+σ\(y^{2}\) =400·5+441·5 = 841·5 = 4205

It follows that  σu=√4205.

Now probability of first worker(P₁)=375/√4205

probability of second worker(P₂) =325/√4205

We can clearly see P₁>P₂

Difference in Probability of both workers(P)=P₁-P₂

=>P=[(375/√4205)-(325/√4205)]

=>P=50/√4205

=>P=50/64.84

=>P=0.771

Hence, probability by which worker 1 will outproduce worker 2 is 0.771.

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So, the simpler form of the radical expression 4 sqrt 1296 x^16y^12 is 144x^14y^14 sqrt (x) sqrt (y).

To simplify the radical expression 4 sqrt 1296 x^16y^12, we need to first factor the number inside the radical. 1296 can be factored into 36 x 36, which simplifies to 6^4. So, the expression becomes 4 sqrt (6^4 x^16y^12).
Next, we can simplify the expression further by using the property of exponents that says a^m x a^n = a^(m+n). This means that we can combine the exponents of x and y, which gives us 4 sqrt (6^4 x^(16+12) y^(12+16)). Simplifying this, we get 4 sqrt (6^4 x^28 y^28).
Now, we can simplify the radical expression even further by using the property that says sqrt (a x b) = sqrt (a) x sqrt (b). Applying this to our expression, we get 4 x 6^2 x sqrt (x^28) x sqrt (y^28). Simplifying this further, we get 144x^14y^14 sqrt (x) sqrt (y).
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Answer:

x ≈ 27.86

Step-by-step explanation:

Supplement means 180 degrees.

7x - 15 = 180

~Add 15 to both sides

7x = 195

~Divide 7 to both sides

x ≈ 27.86

Best of Luck!

The values of the positive integers k and a as required to be determined in the task content are; 3 and 5 respectively.

Since it follows from the task content that the values of the positive integers k and a are to be determined.

First, the equation given in the task content is;

(4 + √a)(7 − √a) = 23 + k√a

By expansion; it follows that we have;

28 - 4√a + 7√a - a = 23 + k√a

(28 - a) + 3√a = 23 + k√a

It therefore follows from comparison of coefficients that we have;

3 = k

and

28 - a = 23

a = 28 - 23

a = 5

Consequently, since the positive values of the integers k and. a are to be determined, it follows that the values of k and a are; 3 and 5 respectively.

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Answer:

8z - 1

Step-by-step explanation:

Given

3 + 4(2z - 1) ← multiply each term in the parenthesis by 4

= 3 + 8z - 4 ← collect like terms

= 8z - 1

Answer:

-1 + 8z

Step-by-step explanation:

First use the distributive property of multiplication (Just multiply 4 with all numbers in the parenthesis):

3 + 4(2z - 1)

3 + 8z - 4

Group like terms:

3 + 8z - 4

-1 + 8z

The answer is -1 + 8z

Hope this helped.

Harry will have a gross margin of $5,290.

If the cost of each shirt is $12.90 and 1,000 shirts are purchased, then the total cost of 1,000 shirts is:

$12.90 x 1,000 = $12,900

If Harry sells 800 shirts at a 50% markup, then he sells them for:

$12.90 x 1.5 = $19.35

Harry sells the 200 remaining shirts at a 30% reduction from the selling price:

$19.35 x 0.7 = $13.55

The gross margin (markup) is the difference between the selling price and the cost per shirt. For the 800 shirts sold at a markup, the gross margin per shirt is:

$19.35 - $12.90 = $6.45

So the gross margin for the 800 shirts is:

$6.45 x 800 = $5,160

For the 200 shirts sold at a discount, the gross margin per shirt is:

$13.55 - $12.90 = $0.65

So the gross margin for the 200 shirts is:

$0.65 x 200 = $130

Therefore, the total gross margin for all 1,000 shirts is:

$5,160 + $130 = $5,290

Harry will have a gross margin of $5,290.

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Answer:

A

Step-by-step explanation:

Answer:

I’m not sure if I’m right but here I go.

Step-by-step explanation:

Each line goes from zero and down, look at the ponies where they are and find the coordinates.

The probability that z is divisible by 2 is 12/16, which simplifies to 3/4 or 0.75.

To calculate the probability that z = xy is divisible by 2, we will first analyze the possible outcomes of rolling the pair of 4-sided fair dice. Since each die has 4 sides, there are a total of 4x4 = 16 possible outcomes.

We are interested in the cases where z = xy is divisible by 2, meaning that either x or y (or both) are even numbers. On a 4-sided die, half of the outcomes (2 sides) are even numbers, specifically 2 and 4.

There are three possible scenarios for z to be divisible by 2:
1. x is even and y is odd.
2. x is odd and y is even.
3. x and y are both even.

For scenario 1, there are 2 even outcomes for x and 2 odd outcomes for y, resulting in 2x2 = 4 possibilities.
For scenario 2, there are 2 odd outcomes for x and 2 even outcomes for y, also resulting in 2x2 = 4 possibilities.
For scenario 3, there are 2 even outcomes for both x and y, resulting in 2x2 = 4 possibilities.

In total, there are 4+4+4 = 12 possible outcomes where z is divisible by 2. Thus, the probability that z is divisible by 2 is 12/16, which simplifies to 3/4 or 0.75.

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The probability that z is divisible by 2 is 12/16, which simplifies to 3/4 or 0.75.

To calculate the probability that z = xy is divisible by 2, we will first analyze the possible outcomes of rolling the pair of 4-sided fair dice. Since each die has 4 sides, there are a total of 4x4 = 16 possible outcomes.

We are interested in the cases where z = xy is divisible by 2, meaning that either x or y (or both) are even numbers. On a 4-sided die, half of the outcomes (2 sides) are even numbers, specifically 2 and 4.

There are three possible scenarios for z to be divisible by 2:
1. x is even and y is odd.
2. x is odd and y is even.
3. x and y are both even.

For scenario 1, there are 2 even outcomes for x and 2 odd outcomes for y, resulting in 2x2 = 4 possibilities.
For scenario 2, there are 2 odd outcomes for x and 2 even outcomes for y, also resulting in 2x2 = 4 possibilities.
For scenario 3, there are 2 even outcomes for both x and y, resulting in 2x2 = 4 possibilities.

In total, there are 4+4+4 = 12 possible outcomes where z is divisible by 2. Thus, the probability that z is divisible by 2 is 12/16, which simplifies to 3/4 or 0.75.

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Answer:

Step-by-step explanation:

Math nerds, algebros?

Answer:

20

Step-by-step explanation:

The condition for the equation (∂U/∂V)T = (∂U/∂P)T = (∂H/∂V)T = 0 to be true is that the system described must be in a state of mechanical, thermal, and chemical equilibrium.

Let's break down the conditions for each partial derivative:

1. (∂U/∂V)T = 0: This condition implies that the internal energy of the system does not change with respect to volume at constant temperature.

It indicates mechanical equilibrium, where the system is in balance and no work is being done on or by the system due to volume changes.

2. (∂U/∂P)T = 0: This condition suggests that the internal energy of the system does not change with respect to pressure at constant temperature.

It indicates thermal equilibrium, where the system is in balance and there is no transfer of energy as heat due to pressure changes.

3. (∂H/∂V)T = 0: This condition implies that the enthalpy of the system does not change with respect to volume at constant temperature.

It also indicates mechanical equilibrium, where the system is in balance and there is no work being done on or by the system due to volume changes.

In summary, the condition (∂U/∂V)T = (∂U/∂P)T = (∂H/∂V)T = 0 is true when the system is in a state of mechanical, thermal, and chemical equilibrium, where there are no changes in internal energy, pressure, and enthalpy with respect to volume at constant temperature.

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Answer:

Step-by-step explanation:

221/17= 13 miles per hour over

30 limit + 13 over = 43mph

Answer:

43

Step-by-step explanation:

Possibly measurement error are recording error, differences in environmental conditions at the time of measurement.

Given in a famous experiment carried out in 1882, Michelson and Newcomb obtained 66 observations on the time it took for light to travel between two locations in Washington, D.C. A few of the measurements (coded in a certain manner) were 31, 23, 32, 36, 22, 26, 27, and 31.

An error in measurement is the difference between a taken measurement and the known actual value (the accepted true measurement) of what is being measured.

Here experiment was conducted to study the time taken for light to travel from one place to another place.

From the given problem obtained 66 observations are obtained.

Since the experiment conducted in different times, the density of the material changes with temperature/environmental conditions which may result the difference in measurement.

So possibly measurement error, recording error, differences in environmental conditions at the time of measurement, etc.

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So possibly measurement error, recording error, differences in environmental conditions at the time of measurement

Given In a famous experiment carried out in 1882, Michelson and Newcomb obtained 66 observations on the time it took for light to travel between two locations in Washington, D.C. A few of the measurements (coded in a certain manner) were 31, 23, 32, 36, 22, 26, 27, and 31.

Here experiment was conducted to study the time taken for light to travel from one place to another place.

From the given problem obtained 66 observations are obtained.

Since the experiment conducted in different times, the density of the material changes with temperature/environmental conditions which may result the difference in measurement.

So possibly measurement error, recording error, differences in environmental conditions at the time of measurement, etc.

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21124

Answer:

  34 square units

Step-by-step explanation:

You want the area of the triangle with vertices X(6, 8), Y(3, 3), and Z(13, -3).

There are several ways the area of a triangle can be calculated from the coordinates of the vertices. One relatively easy method is to find half the absolute value of the sum of the determinants of adjacent pairs of points.

This calculation is shown in the second attachment.

The area of ∆XYZ is 34 square units.

A slope calculation will tell you side XY is perpendicular to side YZ. This means you can find the area from the lengths of these two sides. The distance formula can tell you the lengths.

  XY = √((3 -6)² +(3 -8)²) = √(9 +25) = √34

  YZ = √((13 -3)² +(-3 -3)²) = √(100 +36) = 2√34

 Area = 1/2bh = (1/2)(√34)(2√34) = 34 . . . . square units

Pick's theorem tells you the area of a polygon with vertices on grid points can be found by counting the grid points on the boundary and interior to the boundary.

  A = i + (b/2) -1

This triangle has the three given vertices on grid points, along with point (8, 0), which is the midpoint of YZ. There are 33 interior points, so the area is ...

  A  = 33 +(4/2) -1 = 34 . . . . square units

The length of XZ is ...

  XZ = √((13 -6)² +(-3 -8)²) = √(49 +121) = √170

Heron's formula tells you the area is given by ...

  A = √(s(s -a)(s -b)(s -c)) . . . . . . where s = (a+b+c)/2, the semiperimeter

The third attachment shows this calculation gives an area of 34 square units.

__

Additional comments

The slope calculation tells you the slope of XY is ...

  m = (y2 -y1)/(x2 -x1) = -5/-3 = 5/3

and the slope of YZ is ...

  m = -6/10 = -3/5 . . . . . . . . the opposite reciprocal of the slope of XY

Hence these sides are perpendicular, as we noted above.

We like Pick's theorem for finding the areas of small figures with irrational side lengths (such as this one). It just involves counting, which is often easier than using a bunch of different formulas for slope or length.

The determinant formula is easy to compute, but tedious to enter on a calculator. It is much easier to program a spreadsheet for this. As with Pick's theorem, the method applies to a polygon with any number of vertices.

  \(\left|\begin{array}{cc}a&b\\c&d\end{array}\right|=ad-bc\)

In these 2×2 matrices, the coordinates can be listed in rows or in columns. It makes no difference to the calculation. The key is to work in one direction around the figure. (Here, we went CCW.)

The triangle is drawn in the first attachment. The geometry program that drew it also calculated its area to be 34 square units.

You may have noticed that the "determinant" method and Pick's theorem guarantee that the area of any polygon with integer coordinates will be an integer multiple of 1/2 square unit. That is, it will never be irrational. (You might not see that using Heron's formula.)

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Answer:

1,1,2

Step-by-step explanation:

The solution to the given system of equations are:{ x = 1, y = 1, z = 2} which is the corrrect answer would be option (A).

The equation is defined as a mathematical statement with at least two terms that contain variables or values that are equal.

We have been given the system of equations as:

2x − y − z = −1

3x + y − z = 2

x + y − 5z = −8

Isolate the term of x in the equation 2x − y − z = −1, and we get

x = (- 1 + y +z)/2

Substitute the value of x = (- 1 + y +z)/2 in the above both equations,

3(- 1 + y +z)/2 + y − z = 2

(- 1 + y +z)/2 + y − 5z = −8

Simplify the equation to you get,

(5y + z - 3) / 2 = 2

(3y - 9z - 1) / 2 = -8

Isolate the term of y : (5y + z - 3) / 2 = 2 ⇒ y = (-z +7 )/5

Substitute the value of y = (-z +7 )/5 in the equation (3y - 9z - 1) / 2 = -8

(3(-z +7 )/5 - 9z - 1) / 2 = -8

Simplify the equation to you get,

8(-3z + 1)/d = -8

Isolate the term of z : 8(-3z + 1)/d = -8 ⇒ z = 2

Substitute the value of z = 2 in the equation y = (-z + 7) / 5 to simplify to get

⇒ y = 1

Substitute the values of y = 1 and z = 2 in the equation x = (-1 + y + z) / 2 to simplify to get

⇒ x = 1

The solution to the given system of equations are:

{ x = 1, y = 1, z = 2}

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Answer:

Answer is B

Step-by-step explanation:

Remember, perpendicular lines have opposite slopes. In order to do this, you just need to flip the sign (Change it to the opposite. For example, if it is 3, it would be -3), and change the slope to its reciprocal (For example, if it is 3, it would 1/3). Finally, since the equation is y = 1/2x + 10, the slope would change to -2x... so your answer is B

Answer:

the picture is really blurry I can't read it

Using the binomial distribution, it is found that he is most likely to get 99 blues.

For each spin, there are only two possible outcomes, either it lands on blue, or it does not. The probability of a spin landing on blue is independent of any other spin, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability of a success on each trial.  

The expected value of the binomial distribution is:

\(E(X) = np\)

In this problem:

Thus, the expected value is:

\(E(X) = np = 297\frac{1}{3} = 99\)

He is most likely to get 99 blues.

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The possible data in the question does not provide sufficient evidence available to support the alternative hypothesis that there is a difference between Mr. Starnes and Ms. McGrail's AP Statistics classes and Mr. Starnes did not stack the class.

In statistics, a hypothesis test is the performance of a test on an assumption made about a population parameter.

The possible data in the question, obtained from a similar online question, using MS Excel, indicates;

The mean of the Starnes GPA ≈ 3.212867

The standard deviation of Starnes GPA ≈ 0.364249

Mean of McGrail GPA ≈ 3.134722

The standard deviation of McGrail's GPA ≈ 0.357995

The null hypothesis is H₀: μ₁ - μ₂ = 0

The alternative hypothesis is Hₐ: μ₁ - μ₂ ≠ 0

The test statistic is found using the following formula;

\(t_0 = \dfrac{(\overline{x_1} - \overline{x_2})-(\overline{\mu_1}-\overline{\mu_2})}{\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2} } }\)

The decision rule is obtained with α = 0.05 and the null hypothesis is rejected t₀ ≤ -1.96 or t₀ ≥ 1.96

Therefore, we get;

\(t_0 = \dfrac{(3.212867 - 3.134722)-0}{\sqrt{\dfrac{0.364249^2}{15}+\dfrac{0.357995^2}{18} } } \approx 0.618\)

The parameter for the degrees of freedom is 15 - 1 = 14

The critical value obtained from the t-table, at t.₉₅ is 1.761 which is larger than 0.618, therefore, we fail to reject the null hypothesis, and the evidence is insufficient to suggest that there is a difference in the average score of the two AP Statistics classes.

Taking the variance to be the same, we get;

\(S_p^2= \dfrac{(n_1-1)\cdot s_1^2+(n_2-1)\cdot s_2^2}{n_1+n_2-2}\)

Therefore;

\(S_p^2= \dfrac{(15-1)\times 0.364249^2+(18-1)\times 0.357995^2}{15+18-2}\approx 0.1302\)

\(t_0 = \dfrac{(\overline{x_1} - \overline{x_2})-(\overline{\mu_1}-\overline{\mu_2})}{\sqrt{s_p^2 \times\left(\dfrac{1}{n_1}+\dfrac{1}{n_2} }\right) }\)

\(t_0 = \dfrac{(3.212867 - 3.134722)-0}{\sqrt{0.1302\times \left(\dfrac{1}{15}+\dfrac{1}{18} }\right) } \approx 0.6195\)

df = 15 + 18 - 2 = 31

From the t-table, the critical value is about 1.697, which is larger than 0.6195, therefore, the null hypothesis cannot be rejected and the evidence available is not enough to suggest that there is a difference between the grade point averages of Mr. Starnes and Ms. McGrail AP Statistics classes and Mr. Starnes did not stack the class

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SOLUTION

From the diagram, the total outcome is 4

Probability of spinning A is

Probability of spinning B is

So probability of spinning A or B becomes

Hence the answer is

Respuesta:

B) x = 4 e y = 8

Explicación paso a paso:

Busque la imagen de la pregunta adjunta a continuación;

Tomando la razón de los lados similares y equiparándolos a una constante k dará;

De los triángulos dados;

AC = PR y BC = QR

Si AC = PR, entonces;

9 = 2x + 1

Intercambio

2x + 1 = 9

2x = 9 - 1

2x = 8

x = 8/2

x = 4

De manera similar, si BC = QR, entonces;

y - 3 = 5

y = 5 + 3

y = 8

Por lo tanto, los valores de xey son 4 y 8 respectivamente.

Answer:

-2/45

Step-by-step explanation:

-3/5 - (-5/9)

Subtracting a negative is like adding

-3/5 + 5/9

Then we need a common denominator of 45

-3/5 * 9/9    + 5/9 *5/5

-27/45   + 25/45

-2/45

Answer:

x=-1.34

Step-by-step explanation:

x=-1.34

We can see that the triangle is given as one of the angles is 90 degrees . The triangle is a right-angle triangle, and scalene also.

A right-angled triangle is a triangle having one of its angles with measure of 90°

The slanted side of that triangle is called Hypotenuse and it is the longest side in that triangle.

We can see that the triangle is given as one of the angles is 90 degrees and the other two angles are 36 and 54 degrees.

If one of the angles is 90°  then the triangle is a right-angled triangle.

Also, the length of the two sides is given as 8.66 units and 5.1.

We have already concluded that the triangle is a right-angle triangle, so all the three sides of the triangle must be different.

This implies that the triangle is scalene also.

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