Ziyionnah forgot her locker combination. She thinks the first number is a 2, 3, 4 or 5. She is pretty sure the second number is 19 or 20. How many possible locker combinations are there?

The probability that more boys than girls are chosen is 0.4590

as we know,

Probability of any event P(E) = \(\frac{Number of favorable outcomes}{Total number of outcomes}\)

We have to chose five students to do presentations and also number of boys must be greater than the girls.

In classroom there are 12 boys and 13 girls.

So, Possible arrangements can be: B - Boys, G - Girls

(3B, 2G) , (4B, 1G) , (5B, 0G).

Note: nCr = n! / ( (r!) x (n-r)! ) also see the attached figure.

To choose 5 students out of 25 students to do the presentation 25 C 5

25 C 5 = 25! / (5! x 20!) = 53,130

(3B, 2G) :

To chose 3 Boys out of 12 Boys 12 C 3 = 12! / (3! x 9!) = 220

To chose 2 Girls out of 13 Girls 13 C 2 = 13! / (2! x 11!) = 78

(4B, 1G) :

To chose 4 Boys out of 12 Boys 12 C 4 = 12! / (4! x 8!) = 495

To chose 1 Girl out of 13 Girls 13 C 1 = 13! / (1! x 12!) = 13

(5B, 0G) :

To chose 5 Boys out of 12 Boys 12 C 5 = 12! / (5! x 7!) = 792

To chose 0 Girl out of 13 Girls 13 C 0 = 13! / (0! x 13!) = 1

here, 0! is equal to 1.

Now, the probability that more boys than girls are chosen =

\(\frac{(220 *78) + (495 * 13) + (792 * 1) }{53,130}\)

P(E) = 0.4590

Hence, the probability that more boys than girls are chosen is 0.4590.

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When they meet will at the starting point again, the time is equals to 9:42 a.m.

Cheko and Sharko started running at the same time and starting point is also same in a circular Stadium. Time taken by Cheko to complete the one round of circular stadium = 7 minutes

Time taken by Sharko to complete the one round of circular stadium = 6 minutes.

At 9.00 a.m, both are start running together. We have to calculate time they will meet at the starting point again. So, they will starting together after LCM (7, 6) minutes. LCM stands for least common multiple of 7 and 6. The factors of 7 and 6 are written as

=> 7 = 1x7

=> 6 = 2x 3 x 1

So, LCM (6,7) = 2x3x7x1 = 42 minutes

Thus, the time they meet at starting point

= 9:00 a.m. + 42 minutes = 9: 42 a.m.

Hence, the required time is 9: 42 a.m.

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The correlation is a significant non-zero value.

The number of samples is n.

n = 25

The correlation of the coefficient is r.

r = -0.40

When correlation is significant,

\(H _{0} : p = 0\)

When correlation is non-zero,

\(H _{ \alpha } : p ≠0\)

The test statistic is,

\(TS = \frac{r \times \sqrt{n - 2} }{ \sqrt{1 - r {}^{2} } } \)

\( = \frac{0.4 \times \sqrt{25 - 2} }{ \sqrt{1 - ( - 0.4) ^{2} } } \)

\( = \frac{ - 1.918 }{ \sqrt{0.84} } \)

= -2.093

The test statistic is -2.093.

The correlation is,

\(H _{ \alpha } : - 2.93 ≠0\)

The correlation is not equal to zero and is significant.

Therefore, the correlation is a significant non-zero value.

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1) Yes L1 is context free language.

2) Yes L2 is context free language.

3)  Yes L2 belongs to \(\sum0\)  .

1. Yes L1 is context free language.

Because if a=2 then L1=011001 and when a=1 then L1=0101

When a=3 then L1=01110001

And there is a context free grammar to generate L1.

S=0A|1A|epsilon

A=1S|epsilon

2. Yes L2 is context free language.

Because there exists a context free grammar which can generate L2.

Because when a=2 L2=1101100100

And S=1A|0A|epsilon

And A=1S|0S|epsilon can derive L2.

3. Yes L2 belongs to \(\sum0\)  because sigma nought is an empty string and when a=0 L2 will have empty string.

Because it's given that a ≥ 0.

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It is used in situations where there are only two outcomes, such as heads or tails, success or failure, and so on. The normal approximation to the binomial is used when the sample size is large and the probability of success is not too close to 0 or 1.

As far as the random variable is concerned in this question, it satisfies the assumptions for the normal approximation to the binomial based on the results. The coin looks like it is fair based on the assumption that the null hypothesis is correct. The probability that a number of heads that large or larger occurs under the assumptions is approximately 0.321.

The standard deviation of the number of heads under the assumptions is approximately 15.811. The expected value of the number of heads under the assumptions is 500. Thus, these are the answer options to match with the given phrases. Let's elaborate on the normal approximation to the binomial.The normal approximation to the binomial is a statistical approximation used to compute binomial probabilities.

The normal distribution has a bell shape and is symmetrical about its center. When the sample size is large, the normal distribution approximates the binomial distribution. A sample size is considered large if np and nq are both greater than or equal to 10. When the sample size is small, the binomial distribution is used instead of the normal distribution.The binomial distribution can be used to determine the likelihood of a specific number of successes in a certain number of trials.

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Answer:

(1.5, 0)

(0, 1)

Scatter plots are used to show the correlation between the measured variables

The table entries are given as:

Day         1    2     3     4     5     6

Hours     3    2     1      0    2.5   3.5

Height -0.4  0.1  0.2  0.5  -0.3 -0.5

Next, we represent the hours on the x-axis and the height on the y-axis.

So, we have the following ordered pairs

(x,y) = (3,-0.4) (2,0.1) (1,0.2) (0.0.5) (2.5,-0.3) and (3.5,-0.5)

See attachment for the scatter plot

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Answer:

The correct answer would be 3693

Step-by-step explanation:

9 + 180 + 2,700 + 804

3693

1200 pages were numbered using a total of 3693 digits.

Total digits equal =  the digits in the 1 - digit page numbers + the 2 digit page numbers - digit page numbers  + 3 digit page numbers - digit page numbers.

Then simplify,

9 + 180 + 2,700 + 804

= 3693

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The resulting disjoint sets after the operation union({7, 4}) would be: {5, 7, 9, 1, 11, 4, 2, 3, 6, 8, 10}.

The union of two sets A and B is denoted by A ∪ B and is defined as the set of all elements that are either in A or in B or in both. Therefore, the resulting disjoint sets after the operation union({7, 4}) would be:

{5, 7, 9, 1, 11, 4, 2, 3, 6, 8, 10}.

To calculate the union, we can use the following formula:

A ∪ B = {x : x ∈ A or x ∈ B}

Therefore, the union of {7, 4} can be calculated as:

{7, 4} ∪ {7, 4} = {x : x ∈ {7, 4} or x ∈ {7, 4}}

= {7, 4}

Therefore, the resulting disjoint sets after the operation union({7, 4}) would be: {5, 7, 9, 1, 11, 4, 2, 3, 6, 8, 10}.

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Answer:

The SF is 3

Step-by-step explanation:

The sides are 3x the length of the sides of ∆ABC

The volume of the solid obtained by rotating the region in the first quadrant bounded by the curve 4 - (x - 10)^2 about the y-axis is (2560π/3) cubic units.

To find the volume of the solid, we can use the method of cylindrical shells. The curve 4 - (x - 10)^2 represents a parabola with its vertex at (10, 4) and opening downwards.

1. First, let's determine the limits of integration. Since the region is in the first quadrant, it is bounded by the x-axis and the curve. To find the x-values where the curve intersects the x-axis, we set 4 - (x - 10)^2 = 0 and solve for x:

  (x - 10)^2 = 4

  x - 10 = ±2

  x = 8, 12

  So the limits of integration are x = 8 to x = 12.

2. Next, let's consider a small strip or "shell" of width Δx at a distance x from the y-axis. The height of this shell is given by the equation 4 - (x - 10)^2.

3. The circumference of the shell is given by 2πx, as it is being rotated about the y-axis.

4. The volume of the shell is calculated by multiplying the height, circumference, and width together: ΔV = (4 - (x - 10)^2) * 2πx * Δx.

5. To find the total volume, we integrate the expression ΔV from x = 8 to x = 12:

  V = ∫[8,12] (4 - (x - 10)^2) * 2πx dx.

6. Evaluating the integral, we obtain:

  V = 2π ∫[8,12] (4x - (x - 10)^2x) dx

    = 2π ∫[8,12] (4x^2 - x^3 - 20x + 100) dx

    = 2π [4/3 x^3 - 1/4 x^4 - 10x^2 + 100x] |[8,12]

    = 2π [(4/3 * 12^3 - 1/4 * 12^4 - 10 * 12^2 + 100 * 12) - (4/3 * 8^3 - 1/4 * 8^4 - 10 * 8^2 + 100 * 8)]

7. Simplifying the expression, we find:

  V = 2π [(4/3 * 12^3 - 1/4 * 12^4 - 10 * 12^2 + 100 * 12) - (4/3 * 8^3 - 1/4 * 8^4 - 10 * 8^2 + 100 * 8)]

    ≈ (2560π/3).

Therefore, the volume of the solid obtained by rotating the region in the first quadrant bounded by the curve 4 - (x - 10)^2 about the y-axis is approximately (2560π/3) cubic units.

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Answer:

(0 , 25)

Step-by-step explanation:

y = 4x + 25 is our equation.

The formula used is y = mx + b where:

m = slope

x = independent variable

b = constant/y - intercept

Based on that knowledge we can tell that 25 is our y intercept.

Answer:

1568.16

Step-by-step explanation:

................

Answer:

8 x (5 - 2) = ( 8 x 5) - ( 8 x 2)

Step-by-step explanation:

8 x (5 - 2) = ( _ x 5) - ( _ x 2)

Distribute

8 x (5 - 2) = ( 8 x 5) - ( 8 x 2)

Yes, there is a correlation between the number of hours per week a student works outside of school and how many units the student takes in a quarter.

The cluster sample of 482 students is chosen in order to examine the relationship between these two variables. The statistical relationship between two variables is known as correlation.

The correlation coefficient r is used to determine the degree and direction of the correlation between two variables. The correlation coefficient is a numerical value that ranges from -1 to +1.

A negative correlation exists when one variable decreases as the other variable increases. A positive correlation exists when both variables increase or decrease together.

In this case, if the number of hours per week a student works outside of school increases, the number of units the student takes in a quarter may decrease, indicating a negative correlation between the two variables. Similarly, if the number of hours per week a student works outside of school decreases, the number of units the student takes in a quarter may increase, indicating a positive correlation between the two variables.

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The equation of the tangent line to f(x)=ln(x) at x=2 is given by y = 1/2x - ln(2).

To find the formula for the tangent line to f(x)=ln(x) at x=2, we first need to take the derivative of the function:

f'(x) = 1/x

At x=2, the derivative is:

f'(2) = 1/2

The equation of the tangent line at x=2 is given by:

y - f(2) = f'(2)(x - 2)

Substituting the values of f(2) and f'(2) gives:

y - ln(2) = 1/2(x - 2)

Simplifying this equation gives us the equation of the tangent line:

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

Therefore, the equation of the tangent line to f(x)=ln(x) at x=2 is given by y = 1/2x - ln(2).

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Answer: If there are 198 calories in 4 ounces if ice cream it will be 396

Step-by-step explanation:

Answer:

m<BXY = 36degrees

Step-by-step explanation:

If XY bisects ∠AXB, then;

<AXY + <BXY = <AXB

Given

m∠AXY = (3x^2 - 12)°

m∠AXB = -18x°

Required

Find m∠BXY.

From the formula above;

Find m∠BXY = <AXB - <AXY

m<BXY = -18x - (3x^2-12)

m<BXY = -18x - 3x^2 + 12

m<BXY =  -3x^2 -18x + 12

Also <AXY = m<BXY

3x^2 - 12 =   -3x^2 -18x + 12

6x^2 + 18x -24 = 0

x^2+3x-4 = 0

Factorize

x = -3±√9+16/2

x = -3±5/2

x = -3+5/2 and -3-5/2

x = 2/2 and -8/2

x = 1 and -4

Substitute x = 1 into m<BXY

m<BXY =  -3x^2 -18x + 12

m<BXY =  -3(1)^2 -18(1) + 12

m<BXY =  -3 -18+ 12

m<BXY =  -9

when x= -4

m<BXY =  -3(-4)^2 -18(-4) + 12

m<BXY =  -3(16) +72+ 12

m<BXY =  -48+84

m<BXY = 36degrees

To create a valid matched pair test, the researcher should consider random assignment, similarity, blinding, sample size, and duration.

To create a valid matched pair test, the researcher should consider the following:

Random assignment: The pairs should be randomly assigned to the treatment and control groups to avoid bias.

Similarity: The pairs should be matched based on similar characteristics that could affect the outcome, such as age, gender, prior algebra performance, and socioeconomic status.

Blinding: The researcher should ensure that the students do not know which group they are assigned to, and the person administering the test should also be blinded to the group assignments.

Sample size: The sample size should be large enough to provide sufficient statistical power to detect a meaningful difference between the two groups.

Duration: The length of the study should be sufficient to allow for meaningful differences to occur between the groups, but not so long that other factors could interfere with the outcome.

By considering these factors, the researcher can create two groups that are well-matched and comparable, allowing for a valid matched pair test to be conducted.

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This inequality will intersect x axis at -2 and y axis at 100.

An inequality in the algebra is called mathematical statement that employs the inequality symbol to represent how two expressions relate to one another. The data on each side of an inequality symbol are nonequal. Relation  between two algebraic expressions that are represented by the inequality symbols are known as literal inequalities.

"A limk is referred an inequality if two real numbers  are connected by the symbols ">," "," "," or "."

Example: 3≤x<8 ( x is greater than or equal to 3 and less than 8)

y<50x+100

For x=0;

y<100

For y=0;

x>-2

The graph of the inequality is attached below:

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Step-by-step explanation:

The volume = 15 × 4.2 × 9.9 = 623.7

please give me a brainliest answer

Answer:

Triangle JKE and Triangle KEJ

Step-by-step explanation:

You have to look at each answer choice for this. For example, for A, it starts at K and then goes to E then to j. That forms a triangle. Whatever answer choice makes a complete triangle is your answer.

The value of x from the equation is 4

These are mathematical expressions that are known to be made of variables, factors, constants, coefficients and terms.

Algebraic expressions are also composed of mathematical to arithmetic operations, such as;

From the information given, we have;

2x+6= 7x - 14

collect the like terms

2x - 7x = -14 - 6

subtract the values

-5x = -20

Make 'x' the subject of formula

x = 4

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Answer:

Step-by-step explanation:

-23=-3X-8

The approximate probability that the number of heads is at least 25 when a fair coin is flipped 40 times is approximately 0.9222.

It involves steps:
Step 1: Calculate the mean and standard deviation
- The mean (μ) of a binomial distribution is equal to the number of trials (n) multiplied by the probability of success (p). In this case, n = 40 (number of flips) and p = 0.5 (probability of getting heads in a fair coin).
   μ = n * p = 40 * 0.5 = 20
- The standard deviation (σ) of a binomial distribution is equal to the square root of n multiplied by p multiplied by (1-p).
   σ = √(n * p * (1-p)) = √(40 * 0.5 * (1-0.5)) = √(10) ≈ 3.16

Step 2: Convert the problem into a standard normal distribution
- We want to find the probability of getting at least 25 heads, which is equivalent to finding the probability of getting more than or equal to 24.5 heads. We use the continuity correction here.
- We calculate the z-score for 24.5 heads using the formula:
   z = (x - μ) / σ
   where x is the number of heads and μ is the mean, and σ is the standard deviation.
   z = (24.5 - 20) / 3.16 ≈ 1.42

Step 3: Find the probability using the standard normal distribution table
- We use the z-score calculated in the previous step to find the probability using the standard normal distribution table. The probability corresponds to the area under the curve to the right of the z-score.
- From the standard normal distribution table, we find that the probability corresponding to a z-score of 1.42 is approximately 0.9222.

Therefore, using the De Moivre-Laplace theorem, the approximate probability that the number of heads is at least 25 when a fair coin is flipped 40 times is approximately 0.9222.

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Beau can wrap 32 inches of ribbon outside the mirror.

Area of Beau Thai's mirror is 60 sq. inches.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The word "area" refers to a free space. A shape's length and width are used to compute its area.

Given information:

Length of mirror = 6 inches

Width of mirror = 10 inches

To Find:

The amount of ribbon Beau could wrap around the outside of the mirror.

Perimeter of the mirror = 2(6+10)

                                       = 2(16)

                                       = 32 inches

The area of Beau Thai's mirror.

Area of the mirror = 6*10

                              = 60 sq. inches

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Step-by-step explanation:

the volume of a 3D object is always calculated in some way by multiplying the 3 dimensions with each other.

so, if every dimension is then changed by a factor f (4 in our case), then the volume changes by f×f×f = f³, as the factor has to be included in the calculation for each dimension. and as they are multiplied with each other, so are the scaling factors in each case.

in our case the prism is dilated by the factor 4.

that means that every side length, every height, ..., each dimension is increased by the factor 4.

and therefore, the volume increases by the factor 4³ = 64.

so, the volume of the new image is

244 × 64 = 15,616 cm³

Volume changes by f × f × f = f³

Volume increases by the factor of 4³ = 64

The volume of the new image exists 244 × 64 = 15616 cm³.

The volume of a 3D object exists always computed in some form by multiplying the 3 dimensions by each other.

The volume changes by f × f × f = f³, as the factor, contains to be included in the calculation for each dimension and as they exist multiplied with each other, so exist the scaling factors in each case.

Here, the prism exists dilated by factor 4 which indicates that every side length, every height and each dimension exists increased by factor 4.

Volume increases by the factor of 4³ = 64

The volume of the new image exists 244 × 64 = 15,616 cm³.

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The amplitude of the trigonometric function is the distance from the middle line (or axis) to the highest point on the graph, which is 4 in this case. The period is the distance between two consecutive peaks (or troughs) on the graph, which is 2π in this case.

Therefore, the correct answer is D) 4;2π.
The graph of a trigonometric function: Its amplitude is _ and its period is _. Based on the provided options, the correct answer is D) 4;2π. This means that the amplitude of the trigonometric function is 4, and its period is 2π.

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