You buy a sheet with 10 stamps. Some are 45 cents and some are 30 cents. If it cost $4. 20 how many of each did you get

(A) Total number of points served by Samson and multiply by 100  (B) Null hypothesis(H0) and Alternative hypothesis (Ha) (C)  there would be a 24% chance of observing a difference in performance as extreme as the one observed in the data.

(D) Based on the p-value of 0.24, we do not have strong evidence to reject the null hypothesis. (E) it would be a Type II error. (F) Type II error would mean that we concluded there is no difference in Samson's performance when serving and when his opponent is serving, but in reality, there is a difference. (G) To reduce the likelihood of a Type II error occurring, we can increase the sample size (H)  No, we cannot conclude that Samson's serving is the cause of the difference in his ability to win points when serving compared to when his opponent is serving

a) The difference in the percentage of points won when serving and when the opponent is serving can be calculated by subtracting the percentage of points won when the opponent is serving from the percentage of points won when serving.  To find the percentage of points won when serving, we divide the number of points won when serving by the total number of points served by Samson and multiply by 100. Similarly, to find the percentage of points won when the opponent is serving, we divide the number of points won when the opponent is serving by the total number of points served by the opponent and multiply by 100.

b) The hypotheses we are interested in testing are:
- Null hypothesis (H0): There is no difference in Samson's performance when serving and when his opponent is serving.
- Alternative hypothesis (Ha): Samson performs better when serving compared to when his opponent is serving.

c) A p-value of 0.24 indicates that if the null hypothesis were true, there would be a 24% chance of observing a difference in performance as extreme as the one observed in the data. In other words, the p-value represents the probability of obtaining the observed difference in performance or a more extreme difference, assuming that there is no actual difference in Samson's performance when serving.

d) Based on the p-value of 0.24, we do not have strong evidence to reject the null hypothesis. This means that the data does not provide convincing evidence that Samson plays better when serving compared to when his opponent is serving.

e) If our conclusion from part d was in error, it would be a Type II error. This occurs when we fail to reject the null hypothesis even though it is false. In this case, it would mean that there is a difference in Samson's performance when serving, but we failed to detect it.

f) In the context of this question, a Type II error would mean that we concluded there is no difference in Samson's performance when serving and when his opponent is serving, but in reality, there is a difference. This could potentially lead to underestimating Samson's ability to perform better when serving.

g) To reduce the likelihood of a Type II error occurring, we can increase the sample size. By collecting more data, we can increase the power of our test and improve our ability to detect a difference in performance if it truly exists. Additionally, we can also adjust the significance level of our test (e.g., from 0.05 to 0.01) to make it more likely to detect smaller differences.

h) No, we cannot conclude that Samson's serving is the cause of the difference in his ability to win points when serving compared to when his opponent is serving. The data provided only shows an association between serving and winning points, but it does not establish a causal relationship. Other factors, such as skill, strategy, or the opponent's performance, could also contribute to the difference observed. To establish causality, further investigation and controlled experiments would be needed.

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Answer: 83r^2 - 59 + 60

Step-by-step explanation:

R^2 - 59R - 82r^2 + 60

= 83r^2 - 59 + 60

Answer:

8

Step-by-step explanation:

2×2×2=8

Answer:

8

Step-by-step explanation:

Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

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Answer:

x=17 degrees

Step-by-step explanation:

All 3 angles = 180 degrees

So 90 + 54 + (x+19) = 180

Combine like terms

163 + x = 180

Subtract 163 from both sides

x = 180-163

x = 17

Answer:

√104

Step-by-step explanation:

missing side = \(\sqrt{15^2-11^2} = \sqrt{225-121} = \sqrt{104}\)

Answer:

The square root of 20 is 4.472.

Step-by-step explanation:

Answer:

74

Step-by-step explanation:

50+33+20−16−6−10+3=74

Answer:

B)

Step-by-step explanation:

exponential function given by:

\( \displaystyle f(x )= a \cdot{b}^{x} \)

where:

since the function crosses y-axis at (0,4) point

to find a we can consider (1,8) point it tells us when x is 1 then y is 8 thus:

\( \displaystyle 8= 4 \cdot{b}^{1} \)

\( \displaystyle 8= 4 \cdot{b}^{} \)

divide both sides by 4:

\( \displaystyle \boxed{b = 2}\)

altogether substitute:

\( \displaystyle f(x)= 4 \cdot{2}^{x} \)

hence our answer is B)

Answer:

That kind of depends what x is...the theta angle? the hypotenuse? the base?

But i'll solve it for the missing value of the hypotenuse

5^2 +{ 12^2=c^2

169=c2

c=169 root

c=13 inches

the radial form is, 6 times the eight root of x to the fifth power.

Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.

here, given that,

6x^5/8

now,

the radial form is,

6 times the eight root of x to the fifth power.

Hence, the radical form is, 6 times the eight root of x to the fifth power.

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The solution to the equation 3x + 7 = 16 - 2x is x = 9/5.

Option A is the correct answer.

We have,

To solve the equation 3x + 7 = 16 - 2x for x, we need to isolate the variable x on one side of the equation.

Let's solve it step by step:

Start with the original equation:

3x + 7 = 16 - 2x

- Add 2x to both sides of the equation to get rid of the -2x on the right side: 3x + 2x + 7 = 16 - 2x + 2x

- Simplifying, we have: 5x + 7 = 16

- Next, subtract 7 from both sides of the equation to isolate the term with x: 5x + 7 - 7 = 16 - 7

- Simplifying, we have: 5x = 9

- Finally, divide both sides of the equation by 5 to solve for x: (5x)/5 = 9/5

- Simplifying, we have: x = 9/5

Therefore,

The solution to the equation 3x + 7 = 16 - 2x is x = 9/5.

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The complete question:

Solve the following equation for x: 3x + 7 = 16 - 2x

a) x = 9/5

b) x = 5

c) x = 4

d) x = 6

The dimensions of the rectangle with the largest perimeter that can be inscribed inside the given ellipse are:

Length: 2a = 2(18/5) = 36/5

Width: 2b = 2(32/5) = 64/5

To find the dimensions of the rectangle with the largest perimeter that can be inscribed inside the ellipse x^2/36 + y^2/64 = 1, we can use Lagrange multiplier techniques.

Let's denote the sides of the rectangle as 2a and 2b, with a and b representing half the length and half the width, respectively. The perimeter of the rectangle is given by P = 2(2a + 2b) = 4(a + b).

We need to maximize P subject to the constraint x^2/36 + y^2/64 - 1 = 0, which represents the equation of the ellipse.

Using Lagrange multipliers, we set up the following equations:

∇P = λ∇f(x, y), where ∇P is the gradient of the objective function P and ∇f(x, y) is the gradient of the constraint function f(x, y).

f(x, y) = x^2/36 + y^2/64 - 1 = 0.

The gradient of P is given by:

∇P = (4, 4)

The gradient of f(x, y) is given by:

∇f(x, y) = (2x/36, 2y/64)

Setting up the equations:

2 = λ(2x/36)

2 = λ(2y/64)

x^2/36 + y^2/64 - 1 = 0

Simplifying the first two equations:

x = 18λ

y = 32λ

Substituting these values into the third equation:

(18λ)^2/36 + (32λ)^2/64 - 1 = 0

324λ^2/36 + 1024λ^2/64 - 1 = 0

(9λ^2 + 16λ^2) - 1 = 0

25λ^2 - 1 = 0

25λ^2 = 1

λ^2 = 1/25

λ = 1/5 or λ = -1/5

Considering the positive value, λ = 1/5, we can solve for x and y:

x = 18(1/5) = 18/5

y = 32(1/5) = 32/5

Therefore, the dimensions of the rectangle with the largest perimeter that can be inscribed inside the given ellipse are:

Length: 2a = 2(18/5) = 36/5

Width: 2b = 2(32/5) = 64/5

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Answer:

answer it yourself

Step-by-step explanation:

The area of this region is equal to \(\pi \cdot (\sqrt{35})^2 = 35\pi\)

The equation for the set of complex numbers z such that the real part of 1/z is equal to 1/6 is given by:

Re(1/z) = 1/6

Since 1/z = 1/x + i/y,

Where x and y are the real and imaginary parts of z, respectively,

we can write the equation as:

(1/x)=(1/6) and \($\frac{y}{x^2 + y^2} = \frac{1}{6}$\)

From the first equation,

we have x = 6.

Substituting this value into the second equation, we get:

\($\frac{y}{36 + y^2} = \frac{1}{6}$\)

Solving for y,

we find that \($y = \pm \sqrt{35}$\).

So, the set of complex numbers z that satisfies the equation forms a circle centred at 6 + 0i with radius \($\sqrt{35}$\).

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Check the picture below.

we know the diameter MK is 9 units, so the radius must be half that, or 4.5.

\(\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4.5\\ \theta =218 \end{cases}\implies \begin{array}{llll} s=\cfrac{(218)\pi (4.5)}{180}\implies s=5.45\pi \\\\\\ s\approx 17.1 \end{array}\)

To determine whether the sequence {an} = 5n/4n + 1 is convergent or divergent, we can analyze its behavior as n approaches infinity.

First, let's rewrite the expression for the nth term of the sequence:

an = 5n / (4n + 1)

As n approaches infinity, the denominator 4n + 1 becomes dominant compared to the numerator 5n. Therefore, we can simplify the expression by neglecting the term 5n:

an ≈ n / (4n + 1)

Now, we can consider the limit of the sequence as n approaches infinity:

lim(n→∞) n / (4n + 1)

To evaluate this limit, we can divide both the numerator and denominator by n:

lim(n→∞) (1 / 4 + 1/n)

As n approaches infinity, the term 1/n approaches zero, leaving us with:

lim(n→∞) 1 / 4 = 1/4

Since the limit of the sequence is a finite value (1/4), we can conclude that the sequence {an} = 5n/4n + 1 is convergent.

In other words, as n gets larger and larger, the terms of the sequence {an} get closer and closer to the limit of 1/4. This indicates that the sequence approaches a fixed value and does not exhibit wild oscillations or diverge to infinity. Therefore, we can say that the sequence is convergent.

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Answer:

Θ = 5 radians

Step-by-step explanation:

arc length is calculated as

arc = circumference of circle × fraction of circle

here arc length = 15 , then

2πr × \(\frac{0}{2\pi }\) = 15 ( r is the radius )

2π × 3 × \(\frac{0}{2\pi }\) = 15 ( cancel 2π on numerator/ denominator )

3Θ = 15 ( divide both sides by 3 )

Θ = 5 radians

Answer:

The answer is (4,1). Substitute the x and y values into the system and you should have the answer.

Answer:

option one

Step-by-step explanation:

Answer:

What math stuff??

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\\)

From the question the points are

(1, -3) and (3, -5)

The slope is

\(m = \frac{ - 5 - - 3}{3 - 1} = \frac{ - 5 + 3}{2} = - \frac{2}{2} = - 1 \\ \)

We have the final answer as

Hope this helps you

Answer:

3 and negative 5

Step-by-step explanation:

Answer:  13.46 km/h

Step-by-step explanation:

7 1/2 hr= 450 min

6057/450= 13.46

(a) The graph of the linear functions is as attached.

(b) The equation of the linear function in slope-intercept form is; y = x

(c) The equation of the transformed function in slope-intercept form is;

y = x + 2 and y = x - 3

Functions are defined as the relationship between sets of values. For example, in the function; y = f(x), for every value of x there exists a set of y values.

x is the independent variable.

y is the dependent variable.

If the linear function is; y = x,

The equation of the transformation in slope-intercept form is given as;

For translation of 2 units up, we have;

y = x + 2

For a translation of 3 units down, we have;

y = x - 3

Thus, the required graph has been attached and the solution is determined.

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A student's probability of having a sister are 1/2 or 0.5 if they do not have a brother.

Using the above data table, we must determine the likelihood that a student without a brother also has a sister. Analysing the table now

has a sibling: 5

possesses no sisters: 2

has an 18-year-old brother

possesses no brothers: 4

We are looking for the likelihood that a student has a sister and neither a brother (as indicated by the statement "Does not have a brother"). In this instance, there are two children who do not have a brother but do have a sister, making that number the number of positive outcomes.

No matter whether a student has a sister or not, the total number of outcomes is equal to the number of students who do not have a brother. According to the table, there are 4 students without brothers.

As a result, the likelihood that a student who doesn't have a brother will have a sister can be determined as follows:

Probability is calculated as the ratio of the number of favourable outcomes to all possible outcomes.

Probability equals 2/4

Probability equals 0.5 or half.

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Answer:

root(7/2) and root (-7/2) are the roots then (x-root(7/2))(x-root(-7/2))= some quadratic polynomial then divide f(x) by this quadratic polynomial to get the other two roots

Step-by-step explanation:THE QUESTION IS HARD

Javid travelled by bus for 3 days using a simultaneous equation

What is simultaneous equation?

This refers to equations that are solved together in order to determine the values of unknown variables.

In this case, the total amount spent on daily bus or train can be determined as the fare price multiplied by the number of days

Let  X be the number of days that Javid took bus

total spent on bus=2.50X

Let Y be the number of days that Javid took train

total spent on train=3.50Y

Total spent=2.50X+3.50Y

14.50=2.50X+3.50Y

Secondly, X plus Y gives 5 days

5=X+Y

multiply the second equation by 2.50 and the first by 1

14.50=2.50X+3.50Y

12.50=2.50X+2.50Y

subtract the second equation from first

2=Y

substitute for Y

5=X+Y

5=X+2

X=5-2

X=3

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The number of days that he travelled by bus is; 3 days

Let  x be the number of days that Javid travelled by bus.

Let y be the number of days that Javid travelled by train.

Thus;

Total spent on bus = 2.50x

Total spent on train = 3.50y

Overall total spent is;

2.5x + 3.5y = 14.50   -----(1)

Total number of days is 5 days and so;

x + y = 5    -----(2)

Making x the subject in eq 2 gives us;

x = 5 - y     -----(3)

Put eq 3 in eq 1 to get;

2.5(5 - y) + 3.5y = 14.50

12.5 - 2.5y + 3.5y = 14.5

y = 14.5 - 12.5

y = 2 days

Thus;

x = 5 - 2

x = 3 days

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The Taylor series for f(x)=sin(x) at x=π/2 is ∑n=0[infinity]cn(x-π/2)n, where cn=(-1)n/(n!) if n is even and cn=0 if n is odd.

So, c0=0, c1=(-1)1/(1!)= -1, c2=0, c3=1/(3!)=1/6, c4=0.
Therefore, the first five coefficients are c0=0, c1=-1, c2=0, c3=1/6, c4=0.
Note that the odd coefficients are all 0, which is because the function f(x)=sin(x) is an odd function and its derivatives evaluated at π/2 are all 0. The Taylor series for a function f(x) is given by ∑n=0∞(f^(n)(a)(x-a)^n)/n!, where f^(n)(a) is the nth derivative of f(x) evaluated at x=a. In this case, f(x) = sin(x) and a = π/2.
To find the first five coefficients, we need the first five derivatives evaluated at x = π/2:
f(x) = sin(x)
f'(x) = cos(x)
f''(x) = -sin(x)
f'''(x) = -cos(x)
f^(4)(x) = sin(x)
Now, evaluate them at x = π/2:
f(π/2) = 1
f'(π/2) = 0
f''(π/2) = -1
f'''(π/2) = 0
f^(4)(π/2) = 1
Finally, apply the Taylor series formula:
c0 = f(π/2)/0! = 1
c1 = f'(π/2)/1! = 0
c2 = f''(π/2)/2! = -1/2
c3 = f'''(π/2)/3! = 0
c4 = f^(4)(π/2)/4! = 1/24

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Answer:

Step-by-step explanation:

y - 2 = 2(x + 3)

y - 2 = 2x + 6

y = 2x + 8

Answer:

geometric

x=number of terms

∑ 2(-5)^(k-1)

k=1

Step-by-step explanation:

the sequence has a ratio of -5 (2*-5=-10, -10*-5=50)

x=number of terms

∑ 2(-5)^(k-1)

k=1

for this i don't know what the last term is since it doesn't show in the question but just find 2(-5)^x and x will be the top term