PLEASE ANSWER QUICK!!!!! 25 POINTS
Find the probability of exactly one successes in five trials of a binomial experiment in which the probability of success is 5%
round to the nearest tenth

To find the total number of different routes from town A to town C, we can first find the number of different routes from A to B and then multiply it by the number of different routes from B to C. There are 7 different roads between A and B and 4 different roads between B and C. Therefore, the total number of different routes from A to C is 7 x 4 = 28.

(b) To find the total number of different routes from town A to town C and back, we can use the product rule. There are 28 different routes from A to C (as calculated in part a) and 28 different routes from C to A (since we can use any road once in each direction). Therefore, the total number of different routes from A to C and back is 28 x 28 = 784.

(c) To find the total number of different routes from town A to town C and back in part (b) that visit town B at least once, we can use the principle of inclusion-exclusion. There are 28 different routes from A to C and 28 different routes from C to A. However, we need to subtract the routes that do not visit B at all. To find this number, we can use the product rule again, since there are 5 different roads between A and C that do not go through B (2 from A to C and 3 from C to A). Therefore, the number of routes that do not visit B at all is 2 x 3 = 6. So, the total number of different routes from A to C and back in part (b) that visit B at least once is 28 x 28 - 6 = 784 - 6 = 778.

(d) To find the total number of different routes from town A to town C and back in part (b) that do not use any road twice, we can use the principle of permutations. Since we cannot use any road twice, we need to find the number of permutations of the roads. There are 7 roads between A and B, 4 roads between B and C, and 2 roads between A and C. Therefore, the total number of different routes from A to C and back in part (b) that do not use any road twice is 7P2 x 4P2 x 2P2 = 126 x 12 x 2 = 3024.

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Answer:
The correct is 60%

Step-by-step explanation:

The total number of marbles in the bag is:

2 + 4 + 10 + 9 = 25

The probability of selecting a yellow marble from the bag is:

P(yellow) = 10/25 = 2/5

Therefore, the probability of not selecting a yellow marble (i.e., selecting a red, green, or purple marble) is:

P(not yellow) = 1 - P(yellow) = 1 - 2/5 = 3/5 = 60%

Therefore, the answer is 60%.

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

The answer is -90.

Given G(s) = w2n/s^2+w2n

To find the asymptotically minimum value of phase in the Bode plot, we can use the formula for the phase of a transfer function in the Laplace domain:

Φ(w) = -atan(w/w2n)

where atan is the arctangent function.

To find the minimum value of Φ(w), we need to find the value of w that maximizes the term inside the arctangent function. Taking the derivative of the term inside the arctangent with respect to w, we get:

d/dw (w/w2n) = 1/w2n

Setting this derivative equal to zero, we get:

1/w2n = 0

which has no real solution. Therefore, there is no frequency that maximizes the term inside the arctangent function, and the minimum value of Φ(w) in the Bode plot is -90 degrees, which occurs at high frequencies as w → infinity.

Thus, the answer is -90.

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Answer:

246 boys like to play outdoors

Step-by-step explanation:

82% = 0.82

0.82 x 300 = 246

Answer:

246 boys like to play outdoors

Step-by-step explanation:

82% = 0.82

0.82 x 300 = 246

Oni walked at a rate of 66.67 miles per minute on the way home.

We have,

Let's use the formula:

distance = rate x time

Let x be the rate at which Oni walked on the way home (in miles per minute).

On the way to her sister's house,

Oni walked at a rate 25% faster than x, or 1.25x miles per minute.

The distance to her sister's house is half a mile, so it took her:

Time to get there

= distance/rate

= 0.5 / 1.25x

= 0.4x minutes

On the way back home, she walked at a rate of x miles per minute, and it took her:

Time to get back

= distance/rate

= 0.5 / x

= 0.5x minutes

The total time for the round trip was 60 minutes, so we can set up an equation:

Time to get there + time to get back = 60

0.4x + 0.5x = 60

0.9x = 60

x = 66.67 (rounded to two decimal places)

Therefore,

Oni walked at a rate of 66.67 miles per minute on the way home.

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The area of the window is 2122.64 ft².

Given that a window has a diameter of 26 feet, we need to find the area of the window,

Since, the window is circular so the area will be = π × radius²

= 3.14 × 26²

= 2122.64 ft²

Hence, the area of the window is 2122.64 ft².

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a. The test is a left-tailed test. b. What is the test statistic is -1.73.

a. The test is a left-tailed test because we are testing the claim that less than 10% of treated subjects experienced headaches.

b. To find the test statistic, we'll use the normal distribution as an approximation to the binomial distribution. Here are the steps:

Step 1: Determine the null and alternative hypotheses.
H0: p = 0.10 (The proportion of treated subjects experiencing headaches is equal to 10%.)
H1: p < 0.10 (The proportion of treated subjects experiencing headaches is less than 10%.)

Step 2: Calculate the sample proportion (p-hat).
p-hat = number of subjects with headaches / total subjects = 19 / 276 ≈ 0.0688

Step 3: Determine the standard error.
SE = sqrt((p * (1 - p)) / n) = sqrt((0.10 * (1 - 0.10)) / 276) ≈ 0.0180

Step 4: Calculate the test statistic (z-score).
z = (p-hat - p) / SE = (0.0688 - 0.10) / 0.0180 ≈ -1.73

So, the test statistic is -1.73 (rounded to two decimal places).

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Yes Kevin's comparison in the number line is correct because 10.9 is less than 11.5.

A number line is described as a picture of a graduated straight line that serves as visual representation of the real numbers.

We can agree with Kevin  after referencing the decimal value chart or decimal comparisons below.

o   t     h

10  9

11   5

A number line can also be referred to as a  pictorial representation of numbers on a straight line that is used for  comparing and ordering numbers.

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We would expect about 4 students to respond that rock is their favorite music if we randomly select 20 students from the population.

We need to first calculate the proportion of students in the population who prefer rock music.

We can do this by adding up the number of students who prefer rock music in both samples, and then dividing by the total sample size:

Number of students who prefer rock music = 19 + 23 = 42

Total sample size = 100 + 100 = 200

Proportion of students who prefer rock music = 42 / 200 = 0.21

Next, we can use the proportion to estimate the number of students who would prefer rock music in a sample of 20.

To do this, we multiply the proportion by the sample size:

Expected number of students who prefer rock music in a sample of 20

= 0.21 x 20 = 4.2

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a. A result between -0.08 and 0.08 has a probability of around 0.1562.

b. Using the standard normal distribution table the value of a is 19.4.

c. After using z-score to find the value of a, we got 28.2.

(a) To find P(19.6 < X < 20.4), we need to standardize the values and use the standard normal distribution table:

z1 = (19.6 - 20) / √(25) = -0.4 / 5 = -0.08

z2 = (20.4 - 20) / √(25) = 0.4 / 5 = 0.08

Using the standard normal distribution table, the probability of a value falling between -0.08 and 0.08 is approximately 0.1562. Therefore:

P(19.6 < X < 20.4) = 0.1562

(b) To find the value of a such that P(X > a) = 0.5517, we need to use the standard normal distribution table to find the z-score that corresponds to a cumulative probability of 0.5517:

P(X > a) = 1 - P(X ≤ a) = 0.5517

P(X ≤ a) = 1 - 0.5517 = 0.4483

Using the standard normal distribution table, the z-score that corresponds to a cumulative probability of 0.4483 is approximately -0.12. We can use this z-score to solve for a:

z = (a - μ) / σ

-0.12 = (a - 20) / 5

-0.6 = a - 20

a = 19.4

Therefore, a = 19.4.

(c) To find the value of a such that P(X > a) = 0.05, we need to use the standard normal distribution table to find the z-score that corresponds to a cumulative probability of 0.95:

P(X > a) = 0.05

P(X ≤ a) = 1 - 0.05 = 0.95

Using the standard normal distribution table, the z-score that corresponds to a cumulative probability of 0.95 is approximately 1.64. We can use this z-score to solve for a:

z = (a - μ) / σ

1.64 = (a - 20) / 5

8.2 = a - 20

a = 28.2

Therefore, a = 28.2.

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First estimate: To estimate the miles per gallon, we can round 280 miles to 300 miles and round 9.2 gallons to 10 gallons. So, the first estimated miles per gallon would be 30 mpg.

Exact answer: To calculate the exact miles per gallon, we need to divide the total miles traveled (280 miles) by the total gallons of gas used (9.2 gallons).

280 miles ÷ 9.2 gallons = 30.43478261 mpg

Rounded to three decimal places, the exact answer is 30.435 mpg.

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The Intermediate Value Theorem concludes that for a continuous function on a closed interval, if there are two points in the interval such that the function takes on two different values, then there must be at least one point in the interval where the function takes on every value between those two values.

Assuming its assumptions are met, the Intermediate Value Theorem (IVT) concludes that:

If a continuous function, f(x), is defined on a closed interval [a, b], and k is any value between f(a) and f(b), then there exists at least one value c in the interval (a, b) such that f(c) = k.

In other words, if a function is continuous on a closed interval and k is a value between the function's values at the endpoints of the interval, the function must take on the value k at least once within that interval. This theorem is particularly useful in determining the existence of roots or zeroes for a function in a specified interval.

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Answer: x +

Step-by-step explanation:

the correct expression is:

5 x (8 + 4)

when expanded, this would give you:

5x8 + 5x4

so the blanks should be filled with x and +

Estimating the square root of the number -√7 gives -2 and -2.6

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

-√7

To estimate the number is to approximate the number

When the square root of 7 is evaluated, we have

-√7 = -2.64575131106

Approximate to the nearest integer

-√7 = -2

Approximate to the nearest tenth.

-√7 = -2.6

Hence, the estimates are -2 and -2.6

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The 30th term of the given sequence 156, 153, 150, ... is 69.

The given sequence is as follows: 156, 153, 150,...

To locate the 30th term in this sequence, we must first determine the series's pattern. We can observe that each term is dropping by three, resulting in a common difference of -3. As a result, the nth term of this series can be written as a = a1 + (n - 1)d, where a1 represents the first term, d represents the common difference, and n represents the nth term.

We can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n-1)d

In this case, we have:

a1 = 156 (the first term)

d = -3 (the common difference)

n = 30 (the number of terms)

Using the formula, we can calculate the 30th term:

a30 = 156 + (30-1)(-3)

a30 = 156 + (-87)

a30 = 69

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The frequencies of the dominant red allele, the recessive white allele, and the incomplete dominance allele that produces pink flowers are 0.425, 0.475, and 0.55, respectively.

To solve for the alleles, we need to first determine the possible genetic combinations that could result in the observed flower colors. Let's use the following notation: R for the dominant red allele, r for the recessive white allele, and P for the incomplete dominance allele that produces pink flowers when paired with either R or r.

If we assume that the inheritance of flower color follows Mendelian genetics, we can use the Punnett square to determine the expected ratios of offspring for each possible combination of alleles. Here are the possible genetic combinations and their expected ratios:

RR (red) x RR (red) = 100% RR (red)
RR (red) x RP (pink) = 50% RR (red), 50% RP (pink)
RR (red) x rr (white) = 100% Rr (pink)
RP (pink) x RP (pink) = 25% RR (red), 50% RP (pink), 25% rr (white)
RP (pink) x rr (white) = 50% Rr (pink), 50% rr (white)

Using these ratios, we can calculate the expected number of each genotype based on the observed number of flowers:

RR (red) = 100
RP (pink) = 0.5 x (800 + 100) = 450
Rr (pink) = 2 x 100 = 200
rr (white) = 0.25 x 800 + 0.5 x 100 = 250

Therefore, the allele frequencies can be calculated as follows:

R = (2 x RR) + RP + Rr = (2 x 100) + 450 + 200 = 850
r = (2 x rr) + RP + Rr = (2 x 250) + 450 + 200 = 950
P = RP + (0.5 x Rr) = 450 + (0.5 x 200) = 550

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A graph which represent the points (-1, -3) and (1, -2) is shown in the image below.

In Mathematics and Geometry, an ordered pair is a pair of two elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

Based on the cartesian coordinate (grid) below, the coordinates points and quadrants should be identified as follows;

Point (-1, -3) → quadrant 3.

Point (1, -2) → quadrant 4.

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Complete Question:

Plot the points (-1, -3) and (1, -2)

The transformations that take the graph of f(x) = 5^x to the graph of g(x) = 5^x+7 — 2 are;

a) The graph is translated left 7 units.

b) The graph is translated down 2 units

The function originally is given as:

f(x) = 5^(x)

Now, after transformation it becomes:

g(x) = (5^(x + 7)) - 2

We know that:

If the function f(x) is translated by a units to the right, the we have: 5^(x - a)

If the function f(x) is translated by a units to the left, the we have: 5^(x +a)

If the function f(x) is translated by b units up , the we have: 5^(x) + b

If the function f(x) is translated by b units down , the we have: 5^(x) - b

Thus, the transformation occurring is:

The graph is translated left 7 units

The graph is translated down 2 units

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If the chi-square test shows that there is a significant association, then it can be concluded that older students tend to make more complaints over minor details compared to their younger counterparts.

The most appropriate statistical test to utilize in addressing the hypothesis that older students tend to make more complaints over minor details compared to their younger counterparts would be the chi-square test.

The chi-square test is used to analyze the categorical data and determine whether there is a significant association between two categorical variables. In this case, the two categorical variables would be the age group of the students (older vs. younger) and the frequency of complaints over minor details.

The researchers could collect data by randomly selecting a sample of older and younger students and recording the number of complaints made by each student over minor details. This data could then be organized into a contingency table with rows representing the age group of the students and columns representing the frequency of complaints.

Once the data is organized in this way, the chi-square test can be used to determine if there is a significant association between age group and frequency of complaints. If the chi-square test shows that there is a significant association, then it can be concluded that older students tend to make more complaints over minor details compared to their younger counterparts.

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The cost of Legos, given that this is based on vowels and consonants would be $ 19.

The vowels and consonants can be arranged such that:

Doll - 1 vowel (o), 3 consonants ( d , l , l ) - $ 17

Kite - 2 vowels ( i, e ) , 2 consonants ( k, t) - $ 14

Skates - 2 vowels ( a, e ), 4 consonants ( s, k , t , s) - $24

Using this, we can solve for vowels and consonants such that cost per vowel is $2, and the cost per consonant is $5.

The cost of Legos is based on 2 vowels (e, o) and 3 consonants (L, g, s)

= ( 2 x 2 ) + ( 5 x 3 )

= $ 19

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The computed value of a line integral, [tex]I = \int_C ( x \: e^y dx + x² y) dy [/tex] is equals to the 32

The line integrals form that we can work with the involvement of rewriting in terms of a single variable. During the integrating over a path where one of the variables is constant, then that variable is not actually variable at all, and there is no need to do more. We have a line

integral is [tex]I = \int_C ( x \: e^y dx + x² y) dy [/tex]

We have to determine its value along line segment x = 4

Now, the line segment is x = 4 that means, dx = 0 and 0≤y≤4. So, substitute all known values in above integral, [tex]I = \int_C ( x \: e^y dx + x² y) dy [/tex]

[tex]= \int_{ 0}^{2} x² y dy + 0[/tex]

[tex]= [ x² \frac{ y²}{2}]_{0}^{2}[/tex]

[tex]= [ x² \frac{ 2²}{2} - 0][/tex]

[tex]= 2x²[/tex]

= 2× 4² = 32

Hence, required value is 32.

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Mr. Well has a class of 24 students who were given an assignment to complete. Once they completed the assignment, they were allowed to play math games at the end of class. At the end of class, it was observed that 40% of the class was playing math games. This means that 60% of the class was not playing math games.

To find out what percentage of the class was still taking the test, we subtract 40% (those playing math games) from 100%. Thus, 100% - 40% = 60% of the class was still taking the test.

This information can be useful in determining how much time is needed to complete the test, and how much time can be allotted for math games. It is important to ensure that enough time is given to complete the test, while also allowing for some fun activities to keep the students engaged and motivated.

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The amount in the account after 12 years is approximately $466,197.. The amount of interest earned over 12 years is approximately $139,725.

We can use the formula for the future value of an annuity to calculate the amount in the account after 12 years:

FV = PMT * ((1 + r/12)^n - 1) / (r/12)

where PMT is the monthly deposit, r is the annual interest rate (as a decimal), n is the total number of payments, and FV is the future value of the annuity.

In this case, we have:

PMT = $2,449

r = 0.048

n = 12 * 12 = 144

Plugging these values into the formula, we get:

FV = $2,449 * ((1 + 0.048/12)^144 - 1) / (0.048/12)

FV ≈ $466,197

Therefore, the amount in the account after 12 years is approximately $466,197.

To calculate the amount of interest earned, we can subtract the total amount of deposits over 12 years from the total amount in the account:

Interest = FV - (PMT * n)

Interest = $466,197 - ($2,449 * 144)

Interest ≈ $139,725

Therefore, the amount of interest earned over 12 years is approximately $139,725.

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Answer:

When data has a narrow range and we want to see the shape of the data, the best way to display the data is through a line plot. A line plot is a graphical display of data that uses dots placed above a number line to show the frequency of values in a set of data. It is useful for showing the distribution of a small set of data, especially when the data has a narrow range of values. The line plot allows us to see how many times each value occurs and to identify the mode(s) of the data.

When data has a narrow range and we want to see its shape, a stem-and-leaf plot is the best way to display it. In a stem-and-leaf plot, the data is divided into two parts: the stem and the leaf. The stem is the leftmost digit(s) of each data point, and the leaf is the rightmost digit. This plot allows us to quickly see the distribution of the data and identify any outliers or patterns.

Answer:

19

Step-by-step explanation:

Let's call the number we're trying to find "x".

According to the problem:

4x + 25 = 6x - 13

To solve for x, we can start by isolating the x term on one side of the equation. Let's subtract 4x from both sides:

4x + 25 - 4x = 6x - 13 - 4x

25 = 2x - 13

Next, let's add 13 to both sides:

25 + 13 = 2x - 13 + 13

38 = 2x

Finally, we can divide both sides by 2 to solve for x:

38/2 = 2x/2

19 = x

The coordinates of the vertices after a reflection over the x-axis would be:

Reflecting a figure over the x-axis causes the y-coordinates of its vertices to change signs, while their respective x-coordinates remain unchanged.

To apply this principle to the given triangle, we flip the y-coordinate of point A from -3 to 3, that of point B from -1 to 1 and also for point C changing from -2 to 2 respectively. The outcome is as follows: A (0, 3), B (0, 1) and C (6, 2). It's noted that the x-coordinate remains constant across all points of the newly transformed shape.

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Answer:

The function is f(x)=2x

Step-by-step explanation:

Since every single y is 2 times x, it will be 2x. This function just doubles whatever x you put in.

Answer:

Step-by-step explanation:

Those are coordinate points on a line but they are written in table form.

For the first point,  when x=1, y=2  (that's given from the table) but it's a point on the line (1, 2)

The next point (2,4),

(3,6) and so forth.

The format for a line is

y=mx+b (slope-intercept form)

or

[tex]y-y_{1} = m(x-x_{2})[/tex]   (point-slope form)

They did not give you the y-intercept (that's when x=0) in the chart.  You may have been able to figure it out by looking at the pattern but if not we will use the second formula, point slope form, because we know a point from the chart and we can find slope

[tex]slope=m=\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]    

pick any 2 points from the chart to find slope.  I will pick (1,2) and (2,4)

[tex]m=\frac{4-2}{2-1 } =\frac{2}{1} =2[/tex]

Now that i know slope m=2  and i will pick (1,2) to plug into formula

[tex]y-y_{1} = m(x-x_{2})[/tex]

y-2=2(x-1)       distribute 2

y-2=2x-2          add 2 to both sides

y=2x

The function is increasing at a rate of 2 and the y-intercept is 0.