What is the slope passing through the points (11,-5) and (1,20)

Answer:

32.5

Step-by-step explanation:

23x6÷4-2 and that's how you get your answer

Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test the claim about the population mean μ at the level of significance α, we can perform a one-sample t-test.

Given:

Claim: μ > 29 (right-tailed test)

α = 0.05

σ = 1.2 (population standard deviation)

Sample statistics: x = 29.3 (sample mean), n = 50 (sample size)

We can follow these steps to conduct the hypothesis test:

Step 1: Formulate the null and alternative hypotheses.

The null hypothesis (H₀): μ ≤ 29

The alternative hypothesis (Hₐ): μ > 29

Step 2: Determine the significance level.

The significance level α is given as 0.05. This represents the maximum probability of rejecting the null hypothesis when it is actually true.

Step 3: Calculate the test statistic.

For a one-sample t-test, the test statistic is given by:

t = (x - μ) / (σ / √(n))

In this case, x = 29.3, μ = 29, σ = 1.2, and n = 50. Plugging in the values, we get:

t = (29.3 - 29) / (1.2 / √(50))

= 0.3 / (1.2 / 7.07)

= 0.3 / 0.17

≈ 1.76

Step 4: Determine the critical value.

Since it is a right-tailed test, we need to find the critical value that corresponds to the given significance level α and the degrees of freedom (df = n - 1).

Looking up the critical value in a t-table with df = 49 and α = 0.05, we find the critical value to be approximately 1.684.

Step 5: Make a decision and interpret the results.

If the test statistic (t-value) is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value is approximately 1.76, which is greater than the critical value of 1.684. Therefore, we reject the null hypothesis.

hence, Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

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The answer to the trigonometry question in the picture attached is:

   = cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

Simplify 1-csc θ as follows:

1 - csc θ = (1 - csc θ)(1 + csc θ) / (1 + csc θ)

= 1 - csc^2 θ / (1 + csc θ)

= 1 - 1/sin^2 θ / (1 + 1/sin θ)

= 1 - sin^2 θ / (sin θ + 1)

= (sin θ - sin^2 θ) / (sin θ + 1)

Simplify 1+csc θ as follows:

1 + csc θ = (1 + csc θ)(1 - csc θ) / (1 - csc θ)

= 1 - csc^2 θ / (1 - csc θ)

= 1 - 1/sin^2 θ / (1 - 1/sin θ)

= 1 - sin^2 θ / (sin θ - 1)

= (sin θ + sin^2 θ) / (sin θ - 1)

Substitute the above simplifications in the expression cos θ/(1-csc θ) * 1+csc θ/(1+ csc θ) to get:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

Simplify the expression by canceling out the sin^2 θ terms:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

= cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

Simplify further by factoring out common terms in the numerator and denominator:

cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

= cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

Finally, simplify the expression by factoring out a sin θ term from the denominator:

cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

= cos θ * (1 + sin θ) / [sin θ * (1 - sin θ) * (sin θ + 1)]

= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

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Answer:

189.992

Step-by-step explanation:

divide the speed value by 2.237

Answer:

Step-by-step explanation:

1176=7 weeks

3 weeks=504

The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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Answer:

\( \underline{\boxed{Part \: A}}: \\ \: \\the \: function \: is \: a \: \boxed{ geometric \: sequence} \\ \\ \underline{\boxed{Part \: B}}: \\\boxed{T_n = a( {r})^{(n - 1)}} \\ \\ \underline{\boxed{Part \: C}}: \\ \boxed{T_4 = T_3( { - 3})^{(1)}} \\ \\ \underline{\boxed{Part \: D}}: \\ \boxed{ T_9 = 26,244}\)

Step-by-step explanation:

\( \underline{\boxed{Part \: A}}: \\ \: \\the \: function \: is \: a \: \boxed{ geometric \: sequence} \\ this \: due \: to \: their \: common \: ratio (r)= \boxed{- 3} \\ \\ \underline{\boxed{Part \: B}}: \\ \\ let \: the \: required \: term \: be \to \: T_n \\ let \: the \: first \: term \: be \to \: a \\ let \: the \:common \: ratio \: be \to \: r \\ hence : \boxed{T_n = a( {r})^{(n - 1)}} \\ where \: n \: is \: the \: number \: of \: term. \\ \\ \underline{\boxed{Part \: C}}: \\ let \: the \: required \: term \: be \to \: T_4 \\ hence : \boxed{T_4 = T_3( { - 3})^{(1)}} \\ \\ \underline{\boxed{Part \: D}}: \\if \: a = 4 : r = ( - 3) : n = 9 \\ hence : \boxed{T_9 = 4( { - 3})^{(9 - 1)}} \\ hence : \boxed{T_9 = 4( { - 3})^{(8)}} \\T_9 = 4( 6,561) \\ \boxed{ T_9 = 26,244}\)

The product of -7 and p³ is determined as - 7p³.

The product of two numbers is obtained by multiplying the two numbers.

In other words, product of numbers implies the multiplicative result of the numbers.

The product of -7 and p³ is calculated as follows;.

= -7 x p³

= - 7p³

Thus, the product of -7 and p³ is obtained by multiplying the numbers together, since 7 is the only digit in the expressions, we simply attach 7 as the coefficient of p³.

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A marketing company is testing eight different page designs for its new catalogue of clothing. The analysis is most appropriate is ANOVA

The best analysis to use to determine whether there is a noticeable difference in sales amounts between the eight various page designs in the marketing company's new clothing catalogue is Analysis of Variance. In this instance, the averages of the sales figures for each of the eight page designs were compared using the statistical technique known as an ANOVA.

If there is a statistically significant difference between the group means, then at least one of the patterns may be linked to a higher degree of revenue than the others. This can be determined using an ANOVA. The marketing firm can use this data to identify the page designs that are most successful at driving purchases and change their catalogue as necessary to maximise income.

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Answer:

It's simply just subtract the these two numbers

451,202

- 239,021

= 212,181

Hope u doubt is cleared

Answer:

75%

Step-by-step explanation:

Step-by-step explanation:

quarter = 25¢

dime = 10¢

nickel = 5¢

1 quarter (25¢) + 3 dimes (3 x 10¢, which is 30¢) + 4 nickels (4 x 5¢, which is 20¢)

25 + 30 + 20

25 + 50

75¢

1 dollar is 100¢

75/100 = 75%

Answer:

The answer is A, D, and E. The first answer and then the last two.

Step-by-step explanation:

The first answer and then the last two.

Answer:

  (x/9)² +(y/3)² = 1 . . . P = (x, y)

Step-by-step explanation:

You want the equation of the locus of a point P that is 3 cm from the x-axis end of a 12 cm rod whose ends are on the x- and y-axes.

Let the x- and y-intercepts of the rod ends be represented by 'a' and 'b', respectively. The fixed length of the rod tells us ...

  a² +b² = 12²

according to the Pythagorean theorem.

The location of point P is 3/12 = 1/4 of the way from the x-intercept to the y-intercept. Its coordinates in terms of 'a' and 'b' are ...

  P = 3/4(a, 0) +1/4(0, b) = (3a/4, b/4)

If we define the point P as having coordinates (x, y), then we have ...

  3a/4 = x   ⇒   a = 4/3x

  b/4 = y   ⇒   b = 4y

Using these values in the above relation between 'a' and 'b', we have ...

  (4/3x)² +(4y)² = 12²

We can divide by 12² to get the following equation of the ellipse that is the locus of P.

  (x/9)² +(y/3)² = 1 . . . . . . useful domain/range: 0≤x≤9; 0≤y≤3.

The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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3/4, the negatives cancel each other out so you add them

Answer:

Use the number line and the additive inverse to find the difference.

Step-by-step explanation:

3/4

Answer:

0.5 < x < 15.5

Step-by-step explanation:

Triangle Inequality Theorem

Let y and z be two of the side lengths of a triangle. The length of the third side x cannot be any number. It must satisfy all the following restrictions:

x + y > z

x + z > y

y + z > x

Combining the above inequalities, and provided y>z, the third size must satisfy:

y - z < x < y + z

The two side lengths given in the triangle of the figure are y=8.5, z=8.0, thus the possible values of x lie in the interval

8.5 - 8.0 < x < 8.5 + 8.0

0.5 < x < 15.5

Answer:

B is the wrong way, If it were correct it would be 31 14/29

"The mean will be higher than the median in any distribution that" ;

has a positively skewed distribution

A positively skewed distribution is one in which the majority of data values are clustered towards the lower end of the range, while the rest of the values are spread out towards the higher end of the range. As a result, the mean (the average of all the data values) will be higher than the median (the middle value of the data set).

This is because the mean is affected by the higher values in the distribution, while the median is not.

Positively skewed distributions are common in real-world data sets and are often seen in income distributions, stock market returns, and other economic data.

For example, a distribution of incomes may have a few very high earners pushing up the mean, while the majority of people make much lower amounts, resulting in a median that is lower than the mean.

Similarly, stock market returns may have a few very large returns that pull the mean up, while the majority of returns are much lower, resulting in a median that is lower than the mean.

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Answer:

Step-by-step explanation:

so the first condition is

therefore

26 is our subject

and the second condition is

it means 16 students have already signed up

let's x be more students

therefore

according to the question

the inequality is

Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.

Answer:

the area of the isosceles triangle is approximately 104.49 cm^2.

Step-by-step explanation:

The perimeter of the triangle is 100 cm, so we can write an equation using the lengths of the sides:

x + x + (x + 10) = 100

3x + 10 = 100

3x = 90

x = 30

So the equal sides of the triangle have length 30 cm and the side that is 10 cm greater has length 40 cm.

To find the area of the triangle, we can use the formula for the area of an equilateral triangle:

Area = (sqrt(3) / 4) * (side length)^2

Area = (sqrt(3) / 4) * 30^2

Area = (sqrt(3) / 4) * 900

Area = (sqrt(3) / 4) * 30 * 30

Area = (sqrt(3) / 4) * 900

Area = (30 * sqrt(3)) / 2

Area = 45 sqrt(3)

Answer:

\(Area = 129.5m^2\)

\(Perimeter = 48m\)

Step-by-step explanation:

Given

See attachment

Required

Determine the area and the perimeter of the garden

Calculating Area

First, we calculate the \(area\ of\ the\ rectangle\)

\(A_1 = L * B\)

Where:

\(L = 20-(3.5 +3.5)\)

\(B = 7\)

So:

\(A_1 = (20 - (3.5 + 3.5)) * 7\)

\(A_1 = (20 - 7) * 7\)

\(A_1 = 13 * 7\)

\(A_1 = 91\)

Next, we calculate the area of the two semi-circles.

Two semi-circles = One Circle

So:

\(A_2 = \pi r^2\)

Where

\(r = \frac{7}{2}\)

\(A_2 = \frac{22}{7} * (\frac{7}{2})^2\)

\(A_2 = \frac{22}{7} * \frac{49}{4}\)

\(A_2 = \frac{22}{1} * \frac{7}{4}\)

\(A_2 = \frac{22*7}{4}\)

\(A_2 = \frac{154}{4}\)

\(A_2 = 38.5\)

Area of the garden is

\(Area = A_1 + A_2\)

\(Area = 91 + 38.5\)

\(Area = 129.5m^2\)

Calculating Perimeter

First, we calculate the perimeter of the rectangle

But in this case, we only consider the length because the widths have been covered by the semicircles

\(P_1 = 2 * L\)

Where:

\(L = 20-(3.5 +3.5)\)

So:

\(P_1 =2 * (20-(3.5 +3.5))\)

\(P_1 =2 * (20-7)\)

\(P_1 =2 * 13\)

\(P_1 =26\)

Next, we calculate the perimeter of the two semi-circles.

Two semi-circles = One Circle

So:

\(P_2 = 2\pi r\)

Where

\(r = \frac{7}{2}\)

\(P_2 = 2 * \frac{22}{7} * \frac{7}{2}\)

\(P_2 = \frac{2 * 22 * 7}{7 * 2}\)

\(P_2 = \frac{308}{14}\)

\(P_2 = 22\)

Perimeter of the garden is

\(Perimeter = P_1 + P_2\)

\(Perimeter = 26 + 22\)

\(Perimeter = 48m\)

Answer:

Step-by-step explanation:

Answer:

2, 3, 5

Step-by-step explanation:

Because I said so

The initial size of the bacteria culture was approximately 202.02.

To solve this problem, we can use the formula for exponential growth:

N(t) = N0 * e^(kt)

where N(t) is the size of the culture at time t, N0 is the initial size of the culture, k is the growth rate, and e is the natural logarithmic base.

We can use the given information to set up two equations:

300 = N0 * e^(k10)

1400 = N0 * e^(k40)

Dividing the second equation by the first equation gives:

1400/300 = e^(k40) / e^(k10)

Simplifying:

4.67 = e^(k*30)

Taking the natural logarithm of both sides:

ln(4.67) = k*30

Solving for k:

k = ln(4.67) / 30

Substituting back into the first equation:

300 = N0 * e^(ln(4.67)/3)

300 = N0 * 1.484

Solving for N0:

N0 = 300 / 1.484

N0 ≈ 202.02

Therefore, the initial size of the bacteria culture was approximately 202.02.

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The negative exponent becomes the denominator

\( {4}^{ - 2} = \frac{1}{ {4}^{2} } = \frac{1}{16} = 0.0625\)

I hope I helped you^_^

To find the derivative of a function by computing the first few derivatives and looking for a pattern, we can apply this method to the functions sin(x) and cos(x) for the given values of x.

1. dx970 (sin x):

Let's start by computing the first few derivatives of sin(x):

d(sin x)/dx = cos(x)

d²(sin x)/dx² = -sin(x)

d³(sin x)/dx³ = -cos(x)

d⁴(sin x)/dx⁴ = sin(x)

By observing the pattern, we can see that the derivatives of sin(x) repeat every four derivatives. Since 970 is divisible by 4, we can conclude that the derivative dx970 (sin x) is equal to sin(x).

2. d987 (cos x):

Similarly, let's compute the first few derivatives of cos(x):

d(cos x)/dx = -sin(x)

d²(cos x)/dx² = -cos(x)

d³(cos x)/dx³ = sin(x)

d⁴(cos x)/dx⁴ = cos(x)

Again, we notice that the derivatives of cos(x) repeat every four derivatives. As 987 is divisible by 4, we can conclude that the derivative d987 (cos x) is equal to cos(x).

3. dx987 (COS x):

By using the same pattern as before, we can determine the derivatives of cos(x):

dx(cos x)/dx = -sin(x)

d²x(cos x)/dx² = -cos(x)

d³x(cos x)/dx³ = sin(x)

d⁴x(cos x)/dx⁴ = cos(x)

Once again, we observe that the derivatives of cos(x) repeat every four derivatives. Therefore, dx987 (cos x) is equal to cos(x).

4. dx987 (CoS x):

Since "CoS x" appears to be a typographical error (cosine function is typically written as "cos x"), we can assume that it refers to cos(x). Therefore, the derivative dx987 (cos x) would also be equal to cos(x).

In summary, by computing the first few derivatives of sin(x) and cos(x) and observing the pattern of their derivatives, we find that dx970 (sin x) is sin(x), d987 (cos x) is cos(x), dx987 (COS x) is cos(x), and dx987 (CoS x) is also cos(x).

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Answer:

4800 ft²

Step-by-step explanation:

Given that :

Area of cabin = 800 ft²

Width of cabin = 20 feets

Side yard setback of building = 20 feets

Depth of lot = 80 feets

The cabin is a rectangle :

Area of rectangle = Length * Width

800 = length * 20

Length = 800 / 20 = 40 feets

Hence,

Width of lot = side yard + Width of cabin = (20 + 20) = 40 feets

Length of lot = depth +. Length of cabin = (80 + 40) = 120 feets

Area of lot = Length of lot * width of lot

Area of lot = 120 ft * 40 ft = 4800 ft²

Answer:

I THINK the domain is

Negative infinity to infinity

and I THINK the range is..

0 to infinity

Step-by-step explanation:

im not sure im sorry if im wrong : ) hope this helps

Answer:

Step-by-step explanation:

negative infinity to infinity

0 to infinity

pt2

negative infinity to infinity

3 to infinity

Answer:

8 lb.10 oz.

9 minus 1 equals 8 15 minus 5 equals 10