a track team earned a total of 98 points at a track meet. A first place medal earned 6 points, a second place medal earned 3 points, and a third place medal earned 1 point. there were a total of 24 track team members who received medals. the number of first place winners was equal to the number of second and third place medal winners combined. how many second place medals did the team receive?


A.) 24
B.) 12
C.) 5
D.) 10
E.) 7

We need to find the probability that John waits less than 20 minutes for the train.

To find this probability, we need to calculate the area under the density curve from 0 to 20:

P(X < 20) = ∫[0,20] (1/30) dx

P(X < 20) = [x/30] from 0 to 20

P(X < 20) = 20/30 - 0/30

P(X < 20) = 2/3

Therefore, the probability that John waits less than 20 minutes for the train is 2/3 or approximately 0.67.

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Answer:

Part A

Scale factor

= 1 : 175

Part B

52.5 mm

Part C

99.4%

Step-by-step explanation:

Justin is working with a microscope that magnifies objects to 175 times their actual size.

Part A

Enter a number in each box to determine the scale factor for the microscope.

= 1 : 175

Part B

The diameter of an amoeba cell is 0.30 millimeter. How big will the cell appear to Justin under the microscope?

Scale factor =

1 : 175

Diameter of the Amoeba cell = 0.3mm

1mm = 175 mm

0.3mm = x

Cross Multiply

x = 0.3 × 175

x = 52.5 mm

Part C

What is the percent increase of the area of the amoeba cell under the microscope?

Increase = 52.5 mm - 0.3mm

= 52.2 mm

Percent increase

= 52.2/52.5 × 100

= 99.4%

The lights on or off in the daytime is the independent variable. (option c).

The variable that you manipulate or control in your study is called the independent variable. In your case, the independent variable is whether the drivers have their headlights on or off during the daytime.

The dependent variable, on the other hand, is the variable that you observe or measure in your study. It is dependent on the independent variable, as it is expected to be affected by it.

A confounding variable is a variable that is not controlled for in a study and can affect the dependent variable. It is a potential source of bias that can make it difficult to determine whether the independent variable truly has an effect on the dependent variable.

Finally, the fact that the independent variable in your study is a random variable means that it is not under your control, but is determined by chance.

This is because you will randomly assign the drivers to the two groups, with some having their headlights on and others having their headlights off.

So, the correct option is (c).

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The sample size needed to achieve a power of 90% with an alpha of 0.05 is 25. The true beta with this sample size is 10%.

The first step to solving this problem is to determine the z-scores that correspond to the two specifications. The specification that the mean burning rate must be 50 cm/s is equivalent to the null hypothesis, so the z-score for this specification is 0.

The specification that the mean burning rate can differ from 50 cm/s by as much as 1 cm/s is equivalent to the alternative hypothesis, so the z-score for this specification is 1.

Once we have the z-scores, we can use the following formula to determine the sample size:

n = (z_1 - z_0)^2 / (sigma^2 * (1 - alpha)^2)

Plugging in the values from the problem, we get the following:

n = (1 - 0)^2 / (1.5^2 * (1 - 0.05)^2) = 25

The true beta with this sample size is 1 - 0.9 = 10%. This means that there is a 10% chance of rejecting the null hypothesis when it is actually true.

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The correct option is B) x[] = {36, 78, 12, 24} and y[] = {36, 78, 12, 24}.

The results after the given code was executed is x[] = {36, 78, 12, 24} and y[] = {36, 78, 12, 24}.

An array is a group of elements the same type that are stored in adjacent memory locations and may be accessed individually by using a reference to a unique identifier.

Some key features regarding the array are-

Now, for the given programme,

for(int a = 0; a < x.length; a++)

{

x[a] = y[a];

y[a] = x[a];

}

After execution of the programme, the result obtain will be;

x[] = {36, 78, 12, 24}

y[] = {36, 78, 12, 24}.

Therefore, the output of the given programme is obtained.

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The complete question is-

What would be the results after the following code was executed?

int[] x = {23, 55, 83, 19};

int[] y = {36, 78, 12, 24};

for(int a = 0; a < x.length; a++)

{

x[a] = y[a];

y[a] = x[a];

}

A) x[] = {36, 78, 12, 24} and y[] = {23, 55, 83, 19}

B) x[] = {36, 78, 12, 24} and y[] = {36, 78, 12, 24}

C) x[] = {23, 55, 83, 19} and y[] = {23, 55, 83, 19}

D) This is a compilation error.

Answer:

C

Step-by-step explanation:

Th explicit formula of a geometric sequence has the following format:

\(x_n=a(r)^{n-1}\)

Where a is the initial term and r is the common ratio.

From the recursive formula, we can see that each subsequent term is multiplied by 13. Thus, the common ratio is 13.

Also, we are given that the first term is 7.

So, substituting these in, we have:

\(x_n=7(13)^{n-1}\)

Our answer is C

And we're done!

The graphed function is the one in option D.

\(F(x) = \frac{1}{(x + 3)*(x - 2)}\)

We can see two vertical asymptotes in our graph, these ones appear at the values:

x = -3

x = 2

So we must have a denominator that becomes zero in these values, this is something like:

(x + 3)*(x - 2)

Then the correct option is D, where the function has a denominator exactly like the one written above.

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Answer:

So they would pave 3×215=3 ×23 ×5=25 mile/hr.

Step-by-step explanation:

Word form One hundred three and five hundred three thouandth

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The graph will be a downward-facing curve that approaches but never reaches the x-axis as t increases. The area under the curve is equal to 1, and the probability distribution is normalized. The mean of this distribution is infinity.

a. To sketch the probability distribution function, we can start by plotting the function for several values of t. For t = 0, f(t) = 1. As t increases, f(t) decreases and approaches 0 asymptotically. The graph will be a downward-facing curve that approaches but never reaches the x-axis as t increases.

b. To show that the probability distribution is normalized to 1, we need to show that the area under the curve is equal to 1. To do this, we can integrate the function from 0 to infinity:

∫f(t) dt = ∫1 - e^(-t/to) dt

= t - to*e^(-t/to) |0 to infinity

= infinity - 0

= 1

Therefore, the area under the curve is equal to 1, and the probability distribution is normalized.

c. To evaluate the mean of the distribution, we can use the formula for the mean of a continuous distribution:

mean = ∫t f(t)dt

= ∫t(1 - e^(-t/to)) dt

= t^2/2 - tote^(-t/to) |0 to infinity

= infinity - 0

= infinity

Therefore, the mean of this distribution is infinity.

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The equation that represents the number of pages Ben can read per minute is p = (3/4)m.

The two quantities are said to be in a directly proportionate relation when the connection between them is such that if we increase one, the other will also increase, and if we reduce one, the other quantity will also drop.

If x and y are in direct proportion then

=>  x ∝ y

=>  x = ky  [ where k is constant ]

Here we have,

Ben reads 6 pages in 8 minutes

9 pages can be read in 12 minutes

30 pages can be read in 40 minutes

And the number of minutes = m

Number of pages = p

If observe the given data,

When the number of pages increases, the number of minutes are also increasing, So here we can conclude that the number of minutes is directly proportional to the number of pages

=> p ∝ m

=> p = km --- (1)  

[ where k is constant ]  

From the given data,

At p = 6 pages, m = 8 minutes

=> 6 = k(8)

=> k = 6/8 = 3/4

From (1)

=> p = (3/4)m

Therefore,

The equation that represents the number of pages Ben can read per minute is p = (3/4)m

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For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic at least as unlikely as or more unlikely than that provided by the sample.

What is two tailed test ?

In statistics, a two-tailed test is a procedure that determines whether a sample is greater than or less than a specific range of values by using the critical area of a distribution that is two-sided.

Main body:

Hence the p-value is the probability of obtaining a value for the test statistic at least as unlikely as or more unlikely than that provided by the sample.

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Total Time = t1 + t2 = (D / 1.4) + (D / 0.8) hours.

To find the time it takes for Dae to hike downhill and uphill, we can use the formula:

Time = Distance / Speed

1. For the downhill hike, Dae's speed is 1.4 miles per hour. Let's assume the distance is D miles. So the time it takes for the downhill hike is t1 = D / 1.4 hours.

2. For the uphill hike, Dae's speed is 0.8 miles per hour. The distance is still D miles. So the time it takes for the uphill hike is t2 = D / 0.8 hours.

Now, if we add the time it takes for the downhill hike (t1) and the uphill hike (t2), we get the total time for the round trip:

Total Time = t1 + t2 = (D / 1.4) + (D / 0.8) hours.

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In given word problem ending time of the play is 10.50 AM.

What is word problem?

 A comprehensive list of math word problems focuses on addition, subtraction, multiplication, division and more specific operations. life scenario. This means that children must be familiar with vocabulary associated with familiar mathematical symbols in order to understand word problems.

Here starting time of play = 9:05 AM

It took 1 hour 45 minutes to end the play. Then ,

=> 9 hour  05 minutes

    1 hour   45 minutes +

=> 10 hour 50 minutes.

Hence ending time of the play is 10.50 AM.

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Answer:

1 subtracted from the variable w.

:)

Answer:

\(→ \frac{8 {a}^{( - 5) } {b}^{(4)} }{12 {a}^{( - 6)} {b}^{( - 2)} } = \frac{2 {a}^{(6 - 5)}{b}^{(4 + 2)} }{3} = \boxed{ \frac{2}{3}a {b}^{6} }✓ \\ \)

Answer:

x = 4/5

Step-by-step explanation:

1) Group like terms

   4x + 7x + 5x - 2 - 10 = x

2) Add similar elements

   16x - 2 - 10 = x

3) Subtract

   16x - 12 = x

4) Add 12 to both sides

   16x - 12 + 12 = x + 12

5) Simplify

   16x = x + 12

6) Subtract x from both sides

   16x - x = x + 12 - x

7) Simplify

   15x = 12

8) Divide both sides by 15

    15x/15 = 12/15

9) Simplify

   x = 4/5

The simplified trigonometric expression in this problem is defined as follows:

sin(3x)/sin²(x) = 3csc(x) - 4sin(x).

The trigonometric expression in this problem is defined as follows:

sin(3x)/sin²(x).

The equivalent expression for the sine of 3x is given as follows:

sin(3x) = 3sin(x) - 4 sin³(x).

Then the expression can be written as follows:

(3sin(x) - 4 sin³(x))/sin²(x)

The subtraction is in the numerator, hence the expression can be simplified as follows:

3sin(x)/sin²(x) - 4sin³(x)/sin²(x)

3/sin(x) - 4sin(x)

One divided by the sine is equivalent to the cossecant, hence:

3/sin(x) - 4sin(x) = 3csc(x) - 4sin(x).

Meaning that the first option among those given on the image at the end of the answer is correct.

The problem is given by the image shown at the end of the answer.

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The density of glycerin at 60°C is approximately 19.9592 g/cm³.

To find the density of glycerin at 60°C, we can use the volume expansion coefficient and the given density at 20°C.

The formula for volume expansion is:

ΔV = β * V₀ * ΔT

where:

ΔV is the change in volume,

β is the volume expansion coefficient,

V₀ is the initial volume, and

ΔT is the change in temperature.

In this case, we want to find the change in density, so we can rewrite the formula as:

Δρ = -β * ρ₀ * ΔT

where:

Δρ is the change in density,

β is the volume expansion coefficient,

ρ₀ is the initial density, and

ΔT is the change in temperature.

Given:

ρ₀ = 20 g/cm³ (density at 20°C)

β = 5.1 x 10⁻⁴ °C⁻¹ (volume expansion coefficient)

ΔT = 60°C - 20°C = 40°C (change in temperature)

Substituting the values into the formula, we have:

Δρ = - (5.1 x 10⁻⁴ °C⁻¹) * (20 g/cm³) * (40°C)

Calculating the expression:

Δρ = - (5.1 x 10⁻⁴) * (20) * (40) g/cm³

≈ - 0.0408 g/cm³

To find the density at 60°C, we add the change in density to the initial density:

ρ = ρ₀ + Δρ

= 20 g/cm³ + (-0.0408 g/cm³)

≈ 19.9592 g/cm³

Therefore, the density of glycerin at 60°C is approximately 19.9592 g/cm³.

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The drawing that creates a line of reflection that takes the point A to point B is; D: Draw a line parallel to line AB.

A line of reflection is a line that lies in a position between two identical mirror images so that any point on one image is the same distance from the line as the same point on the other flipped image.

Let us look at the given options;

A) Draw the perpendicular bisector of segment AB; A perpendicular bisector will NOT create a line of reflection that takes point A to point B but rather it will divide the line AB in two equal parts

B) Draw a line through B perpendicular to segment AB; A line through B perpendicular to segment AB will NOT Create a line of reflection that takes point A to point B

C) Draw the line passing through A and B;

A line passing through A and B will NOT create a line of reflection that takes point A to point B but rather will create Line A and B again and not its reflection

D) Draw a line parallel to line AB;

A line parallel to line AB will create a line of reflection that takes point A to point B because a parallel line never meet thereby creating the direct imagery of Line AB.

Thus, the drawing that create a line of reflection that takes the point A to point B is; D: Draw a line parallel to line AB.

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(a) To satisfy (*) with X ~ N(0, 1) and Z ~ N(0, 2), we can rearrange the equation as follows: Y = Z - X. Since X and Z are normally distributed, their linear combination Y = Z - X is also normally distributed.

The mean of Y is the difference of the means of Z and X, which is 0 - 0 = 0. The variance of Y is the sum of the variances of Z and X, which is 2 + 1 = 3. Therefore, Y ~ N(0, 3). The joint distribution of X, Y, and Z is multivariate normal with means (0, 0, 0) and covariance matrix:

```

   [ 1  -1  0 ]

   [-1   3 -1 ]

   [ 0  -1  2 ]

```

(b) i. To show that X and Y are dependent, we need to demonstrate that their covariance is not zero. Since Y = aX, the covariance Cov(X, Y) = Cov(X, aX) = a * Var(X) = a * 2 ≠ 0, where Var(X) = 2 is the variance of X. Therefore, X and Y are dependent.

ii. For Y = aX to hold, we require a ≠ 0. If a = 0, Y would always be zero regardless of the value of X. The variance of Y can be obtained by substituting Y = aX into the formula for the variance of a random variable:

Var(Y) = Var(aX) = a^2 * Var(X) = a^2 * 2

iii. The smallest variance that Y can have is 2, which is achieved when a = ±√2. This occurs when Y = ±√2X.

iv. To find the joint distribution of X, Y, and Z such that Y assumes the variance bound of 2, we can substitute Y = √2X into the covariance matrix from part (a). The resulting covariance matrix is:

```

   [ 1   -√2   0 ]

   [-√2   2   -√2]

   [ 0   -√2   2 ]

```

The determinant of this covariance matrix is -1. Therefore, the determinant of the covariance matrix of the random vector (X, Y, Z) is -1.

Conclusion: In part (a), we found that Y follows a normal distribution with mean 0 and variance 3 when X ~ N(0, 1) and Z ~ N(0, 2). In part (b), we demonstrated that X and Y are dependent. We also determined that Y = aX is possible for any a ≠ 0 and found the corresponding variance of Y to be a^2 * 2. The smallest variance Y can have is 2, achieved when Y = ±√2X. We constructed a joint distribution of X, Y, and Z where Y assumes this minimum variance, resulting in a covariance matrix determinant of -1.

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The statement that described the triangle properties is that the segment YZ and segment Y"Z" should be proportional when the dilation is done and it should be congruent when the translation should be done.

Given that,

Based on the above information,

Therefore we can conclude that option d is correct.

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Answer:

7

Step-by-step explanation:

You divide the number of visits and the price. 14÷2=7

Answer:

2c + 15 = 25

Step-by-step explanation:

The total he wants to earn is $25, so we know the equation must be an expression that equals 25.

____ = 25

He earns a fixed $15. He also earns $2 per customer.

The total he earns is the sum of the fixed amount ($15) and the amount he earns per customer. Let the number of customers be c. The amount he earns from the number of customers is 2c.

fixed amount + amount per customer = 25

15 + 2c = 25

2c + 15 = 25

Answer: 2c + 15 = 25

Answer:

0.1136

Step-by-step explanation:

Total number of possible outcomes:

You start with 12 cards in the box. After selecting the first card, 11 cards remain. Total number of possible outcomes is 12 x 11 = 132.

Number of favorable outcomes:

There are six even numbers (2, 4, 6, 8, 10, 12) among the twelve cards.

To find the number of ways to choose two even numbers out of six use the formula for combinations:

C(n, r) = n! / (r!(n-r)!)

n = the total number of items = 6

r = the number of items to be chosen = 2

C(6, 2) = 6! / (2!(6-2)!)

= 6! / (2! * 4!)

= (6 * 5 * 4!) / (2! * 4!)

= (6 * 5) / (2 * 1)

= 15

Therefore, the number of favorable outcomes = 15

Probability = Number of favorable outcomes / Total number of possible outcomes

= 15 / 132

≈ 0.1136

Answer:

223

Step-by-step explanation:

expand/solve 111×2 and 112×2

this will be 222 and 224

the question asks about the numbers between so 222 and 224 are not counted

so the number between is 223

Answer: 4y+4z

Step-by-step explanation:

Answer:

what could be written?

Answer:

The correct answer is 7¹⁰

Step-by-step explanation:

I think you wrote 1.7 because i wrote 1. 7¹⁰

but I meant that 1. as the first question i was answering, sorry if I wasn't clear

Answer:

B

Step-by-step explanation:

sine = opposite/hypotenuse

sin45 = x/4

sin45/1 = x/4

cross multiply

1 × x = 4 × sin45

x = 4sin45

x = 2.828427125

x = 2 × square root of 2 = 2.828427125

Answer:

B )  2\(\sqrt{2}\)

Steps:

α = 90°, β = 45°, a = 4: b = 2.82842. . .

β = 45°

a = 4

α = 90°

b =  \(\frac{4sin(45)}{sin(90)}\)

b = 2.82842. . .

2\(\sqrt{2}\) = 2.82842. . .