Using Pythagoras' theorem, calculate the length of XY. Give your answer in centimetres (cm) to 1 d.p. 16 cm X Z 5 cm​

The sample size needed to obtain a 99% confidence interval with a margin of error of 0.05 for the true proportion of homes in the city that are heated by oil is 666.

To calculate the required sample size, we need to use the formula n = [tex](z^2 * p * q) / e^2[/tex], where z is the z-score for the desired confidence level (2.58 for 99% confidence), p is the estimated proportion of homes heated by oil, q is 1-p, and e is the desired margin of error (0.05).

Using the information given in the question, we can estimate p as 0.5 (assuming equal probability of homes being heated by oil or other means) and q as 0.5. Plugging these values into the formula, we get n = [tex](2.58^2 * 0.5 * 0.5) / 0.05^2[/tex], which simplifies to n = 665.64. Therefore, we would need a sample size of at least 666 homes to obtain a 99% confidence interval with a margin of error of 0.05 for the true proportion of homes in the city that are heated by oil.

Thus, the answer is 666.

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Answer:

D

Step-by-step explanation:

I  assume you meant   (-i)^6

  (-i) (-i)     * (-i)(-i)     *  (-i)(-i)  =

     i^2      *   i^2      *    i^2

       -1       *   -1       *    -1

            = -1

To convert polar coordinates (r,θ) to rectangular coordinates (x,y). Therefore, the rectangular coordinates of the point with polar coordinates (1,116) are approximately (-0.211, 0.978).

we use the following formulas:

x = r cos(θ)

y = r sin(θ)

In this case, the polar coordinates are (1,116). Therefore, we have:

r = 1

θ = 116°

Converting θ from degrees to radians, we get:

θ = 116° * π/180 = 2.025 radians

Substituting these values into the formulas above, we get:

x = r cos(θ) = 1 cos(2.025) ≈ -0.211

y = r sin(θ) = 1 sin(2.025) ≈ 0.978

Therefore, the rectangular coordinates of the point with polar coordinates (1,116) are approximately (-0.211, 0.978).

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The domain and the range of the graph are Domain = [-4, 2] and Range = [-8, -2]

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

The graph

The points on the graph can be represented as a list of ordered pairs

The rule of a graph is that

Using the above as a guide, we have the following:

Domain = [-4, 2]

Range = [-8, -2]

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Answer:

The perimeter formula for a rectangle is P = (L + W) × 2, and area is L x W

Step-by-step explanation:

The margin of error at 95% confidence is approximately 2.16.

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 find the margin of error at 95% confidence, we need to use the following formula:

Margin of error = z * (σ/√n)

where:

z = the z-score associated with the desired level of confidence (in this case, 95% confidence corresponds to a z-score of 1.96)

σ = the population standard deviation

n = the sample size

Given that the population variance is 441, the population standard deviation is the square root of 441, which is 21.

So, the margin of error is:

Margin of error = 1.96 * (21/√361)

= 1.96 * (21/19)

= 2.16 (rounded to two decimal places)

Therefore, the margin of error at 95% confidence is approximately 2.16.

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The decimal form of the given number which is 5 3/4 is 5.75.

Given number = 5 3/4.

The given number is a fractional number, which is looking like a mixed fraction.

To write the mixed fraction into decimal form first, we have to write it into normal fraction, later we divide it to get the required decimal form.

To convert mixed fraction into normal fraction,

5 3/4 = ((4*5) + 3) / 4 = 23/4

So, the fraction is 23/4.

To convert the fraction into a decimal, we have to divide the numerator by the denominator as shown below,

23/4 = 5.75

From the above analysis, we can conclude that the decimal form of 5 3/4 is 5.75.

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Answer:

length = 2

width = 2

height = 3

Step-by-step explanation:

The volume of the ice sculpture pyramid is given as 4 cubic feet.

We can solve for the pyramid's dimensions by solving for x, and we can solve for x by plugging it into the pyramid volume formula:

[tex]V = \dfrac{1}{3} b h[/tex]

where [tex]V[/tex] is volume, [tex]b[/tex] is the area of the pyramid's base, and [tex]h[/tex] is height.

We can input the following values for base and height from the information given in the diagram:

[tex]b = x \cdot x = x^2[/tex]

[tex]h = x + 1[/tex]

Solving for x using the formula:

[tex]4 = \dfrac{1}{3} \cdot x^2 \cdot (x + 1)[/tex]

↓ multiplying both sides by 3

[tex]12 = x^2 \cdot (x + 1)[/tex]

[tex]12 = x^3 + x^2[/tex]

↓ subtracting 12 from both sides

[tex]0 = x^3 + x^2 - 12[/tex]

↓ factoring the cubic

[tex]0 = \left(x-2\right)\left(x^2+3x+6\right)[/tex]

↓ finding the real solution ... if [tex]AB = 0[/tex], then [tex]A = 0[/tex]  or  [tex]B=0[/tex]

[tex]x-2=0[/tex]

[tex]x=2[/tex]

Using this x-value, we can solve for the dimensions:

[tex]\boxed{\text{base length} = x = 2}[/tex]

[tex]\boxed{\text{base width} = x = 2}[/tex]

[tex]\boxed{\text{height} = x + 1 = 2 + 1 = 3}[/tex]

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The equation that best represents the phone company's monthly charges would be c = 1 / 4 m + 15 , 0 ≤ m ≤ 44, 640.

The equation would take the form of :

Total monthly charges = Slope x Number of minutes + y - intercept

The y - intercept is the point on the graph for 0 minutes which is shown to be $ 15 on the graph.

The slope would be with points ( 0, 15 ) and ( 40, 25 ):

= ( 25 - 15 ) / ( 40 - 0 )

= 10 / 40

= 1 / 4

The equation is then :

= c = 1 / 4 m + 15 , 0 ≤ m ≤ 44, 640

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The question is:

If there are a maximum of 44740 minutes in a month, which equation best represents the phone company’s charges?

In sigma notation, the sum is represented as follows: ∑ (k^2 + 1), k = 1 to 2.

The given sum is: 12 + 22 + 32 + 132.

To write this sum using sigma notation, we can observe the pattern in the terms. The first term is 12, the second term is 22 (which is 12 + 1), the third term is 32 (which is 22 + 1), and the fourth term is 132 (which is 32 + 1 + 2).

We can see that each term is obtained by adding the square of the position number (k^2) to the previous term, along with an additional constant value of 1 or 2 depending on the position.

So, let's write the sum using sigma notation:

∑ [(k^2 + c(k-1))], where k starts from 1 and goes up to 4.

In this notation, k represents the position of the term, k^2 represents the square of the position number, and c represents the constant value added to the previous term.

For the given sum, the constant value c changes depending on the position of the term:

For the first term (k = 1), c is 1.

For the second term (k = 2), c is 1.

For the third term (k = 3), c is 1.

For the fourth term (k = 4), c is 2.

So, the corrected sigma notation for the given sum is:

∑ [(k^2 + c(k-1))], k = 1 to 4.

This indicates that we sum the terms (k^2 + c(k-1)) as k takes values from 1 to 4, where c changes based on the position of the term.

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Answer:

Since the cost of producing one cell phone is $46, the cost of producing 10 cell phones is 10 times the cost of producing one, which is:

10 x $46 = $460Similarly, the cost of producing 20 cell phones is 20 times the cost of producing one, which is:

20 x $46 = $920Therefore, the cost to produce y cell phones is:

y x $46 = $46yTherefore, the correct answer is A. 46y.

Answer:

Vertical shrink by 2

Step-by-step explanation:

Multiplying by 2 stretches the function. It does not shrink it.

Answer: Vertical shrink by 2

In a Cartesian join, also known as a cross join, each row from the first table is combined with each row from the second table.

If the first table has 5 rows and the second table has 3 rows, the result of the Cartesian join will consist of 5 * 3 = 15 rows.

The appropriate technique for this study would be regression analysis. So, correct option is 2.

Regression analysis is a statistical tool that is used to determine the relationship between a dependent variable and one or more independent variables. In this case, the dependent variable is the house value, and the independent variables are the size of the house, whether it has a pool, the material with which it is built, and the location of the house.

The purpose of regression analysis is to estimate the values of the dependent variable based on the values of the independent variables. By using regression analysis, the researcher can determine the degree to which each independent variable contributes to the variation in house value.

This information can be used to determine which factors are the most important in determining the value of a house.

Therefore, regression analysis would be the appropriate technique for this study because it allows the researcher to investigate the relationship between the dependent and independent variables and to determine the extent to which each independent variable affects the dependent variable.

So, correct option is 2.

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A. The approximate value of the y-intercept is 48.

B. The approximate slope of the line is 2.76.

C. The expected number of cones of ice cream sold when the temperature is 30 °C is approximately 83.

To determine the line of best fit for the given data, we can use linear regression analysis. Linear regression helps us find the equation of a line that best represents the relationship between the temperature and the cones of ice cream sold.

A. To find the approximate value of the y-intercept (the point where the line intersects the y-axis), we can use the linear regression equation. In this case, the y-intercept represents the expected number of cones of ice cream sold when the temperature is 0 °C. From the given data, we do not have a data point at 0 °C. However, we can still estimate the y-intercept using the regression line. The approximate value of the y-intercept is around 48 (rounded to the nearest whole number).

B. To find the approximate slope of the line, we can use the linear regression equation. The slope represents the change in the number of cones of ice cream sold for a one-unit increase in temperature. From the linear regression analysis, the approximate slope of the line is around 2.76 (rounded to two decimal places).

C. To find the expected number of cones of ice cream sold when the temperature is 30 °C, we can substitute the temperature value into the regression equation. Using the approximate slope and y-intercept values from above, we can calculate the expected number of cones sold:

Expected number of cones sold = (slope x temperature) + y-intercept

Expected number of cones sold = (2.76 * 30) + 48

Expected number of cones sold ≈ 82.8 (rounded to the nearest whole number).

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Thus, the angle between the vectors u and v is θ = 5/4 radians or approximately 1.107 radians.

To find the angle between two vectors u and v, we can use the dot product formula:

u · v = |u| |v| cos(θ)

Where u · v is the dot product of u and v, |u| and |v| are the magnitudes of u and v, respectively, and θ is the angle between them.

Given u = (cos(3), sin(3)) and v = (cos(5/4), sin(5/4)), we can calculate the dot product as follows:

u · v = (cos(3))(cos(5/4)) + (sin(3))(sin(5/4))

Using the identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b), we can simplify the dot product:

u · v = cos(3 - 5/4)

Now, let's calculate the angle θ using the inverse cosine function:

θ = cos^(-1)(u · v / (|u| |v|))

To find the magnitudes of u and v, we can use the Pythagorean theorem:

|u| = sqrt((cos(3))^2 + (sin(3))^2) = sqrt(1) = 1

|v| = sqrt((cos(5/4))^2 + (sin(5/4))^2) = sqrt(1) = 1

Substituting these values into the formula for θ:

θ = cos^(-1)(cos(3 - 5/4) / (1 * 1))

Simplifying further:

θ = cos^(-1)(cos(-5/4))

Since the cosine function is an even function, cos(-x) = cos(x). Therefore:

θ = cos^(-1)(cos(5/4))

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The probability that a random sample of 20 pies will have a mean baking time that exceeds 48 minutes is approximately 0.0037 or 0.37%

We can use the central limit theorem to approximate the distribution of the sample mean baking time. Since the sample size is large enough (20 pies) and the population standard deviation is known, we can use the normal distribution to approximate the distribution of the sample mean.

The mean of the sample mean baking time is the same as the population mean, which is 45 minutes.

To find the probability that a random sample of 20 pies will have a mean baking time that exceeds 48 minutes, we can standardize the sample mean using the formula:

[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

= (48-45)/(5/√20)

= 2.68

Using a standard normal distribution table or calculator, we can find that the probability of a standard normal random variable being greater than 2.68 is approximately 0.0037. Therefore, the probability that a random sample of 20 pies will have a mean baking time that exceeds 48 minutes is approximately 0.0037 or 0.37%

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Answer:

Step-by-step explanation:

To solve the expression (7.2×10^(-1))×(4×10^(-7)), you can multiply the numerical values and combine the exponents.

First, multiply the numerical values:

7.2 × 4 = 28.8

Next, add the exponents of 10:

10^(-1) × 10^(-7) = 10^(-1-7) = 10^(-8)

Putting it all together, the expression simplifies to:

28.8 × 10^(-8)

This is the final answer in scientific notation.

The value of x in the right triangles is 8.37

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

The right triangles

There are three right triangles in the figure

So, we start by using the ratio of corresponding sides to calculate the length of the triangle that has a leg of 7 units

Using the above as a guide, we have the following:

y² = 7 * 3

The value of x is calculated using the pythagoras theorem

So, we have

x² = y² + 7²

So, we have

x² = 7 * 3 + 7²

This gives

x² = 70

Take the square roots

x = 8.37

Hence, the value of x is 8.37

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A change in the price of chicken, the good's own price, will cause a movement along the demand curve for chicken, a normal good, resulting in an increase in the quantity demanded.

The demand curve for chicken represents the relationship between the price of chicken and the quantity of chicken demanded by consumers. The law of demand states that there is an inverse relationship between the price of a good and the quantity demanded, holding all other factors constant. In other words, as the price of chicken decreases, the quantity demanded of chicken increases, and vice versa.

A movement along the demand curve for chicken occurs when there is a change in the price of chicken. When the price of chicken decreases, ceteris paribus, consumers are willing to purchase more chicken at the lower price, resulting in an increase in the quantity demanded along the demand curve. Conversely, when the price of chicken increases, consumers are willing to purchase less chicken at the higher price, resulting in a decrease in the quantity demanded along the demand curve.

Other factors that can shift the demand curve for chicken include changes in consumer income, the prices of substitute or complementary goods, and changes in consumer preferences. However, these factors cause a shift in the entire demand curve, rather than a movement along the curve.

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Among the random variables you mentioned - z, t, chi-square, and F - the ones that have only nonnegative values are the chi-square and F distributions.

The chi-square (χ²) distribution is a special case of the gamma distribution, and it is used extensively in hypothesis testing and statistical modelling.

It is defined for nonnegative values, as it represents the sum of squared independent standard normal random variables.
The F-distribution, named after statistician Sir Ronald A. Fisher, is another continuous probability distribution that is defined only for nonnegative values. It is commonly used in the analysis of variance (ANOVA) to test the equality of multiple group means or in regression analysis to test the overall significance of a model.
In contrast, both the z (standard normal) and t (Student's t) distributions are defined for values across the entire real number line, including positive, negative, and zero values. The z-distribution is used for hypothesis testing and confidence intervals in situations where the population standard deviation is known, while the t-distribution is used when the population standard deviation is unknown and estimated from the sample data.

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The dimensions of the rectangular poster are:

width = 6 inches and length = 21 inches.

We have,

Let's assume that the width of the poster is "w" inches.

According to the problem, the length of the poster is 9 more inches than two times its width.

l = 2w + 9

Area of the poster = 45 square inches.

Area of a rectangle:

A = lw

Substitute the values of "l" and "w" from the above equations into the area equation:

45 = (2w + 9)w

Simplify and solve for "w":

45 = 2w^2 + 9w

0 = 2w^2 + 9w - 45

0 = w^2 + (9/2)w - 22.5

Solve for "w":

w = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 9/2, and c = -22.5

w = (-9/2 ± √((9/2)² - 4(1)(-22.5))) / 2(1)

w = (-9/2 ± √(441)) / 2

w = (-9/2 ± 21) / 2

So, the possible values for "w" are:

w = (-9/2 + 21) / 2 = 6

or

w = (-9/2 - 21) / 2 = -15/2

Since the width of the poster cannot be negative, we can discard the second solution.

The poster width is 6 inches.

We can use the equation for "l" to find the length of the poster:

l = 2w + 9 = 2(6) + 9 = 21

Therefore,

The dimensions of the rectangular poster are:

width = 6 inches and length = 21 inches.

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The least possible measure of ∠ADC is 1 degree, and the greatest possible measure of ∠ADC is 178 degrees.

To find the least possible measure of ∠ADC, we need to start with the smallest possible measure of ∠ADB and ∠BDC, which is 1 degree. In this case, the sum of the measures of ∠ADB and ∠BDC is 2 degrees, so the measure of ∠ADC must be 178 degrees.

To find the greatest possible measure of ∠ADC, we need to start with the largest possible measure of ∠ADB and ∠BDC, which is 89 degrees. In this case, the sum of the measures of ∠ADB and ∠BDC is 178 degrees, so the measure of ∠ADC must be 2 degrees.

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The even function in the context of this problem is given as follows:

A. [tex]f(x) = -x^4[/tex]

The fourth power function has the same output values for x and -x, meaning that:

[tex]-x^4 = -(-x)^4[/tex]

Hence option A gives the even function in the context of this problem.

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Thus, the slope of the tangent to the curve r = -7 - 2cosθ at θ = π/2 is 0.

To find the slope of the tangent to the curve r = -7 - 2cosθ at θ = π/2, we first need to find the rectangular coordinates (x, y) and then the derivative of y with respect to x.

1. Convert polar coordinates to rectangular coordinates:
x = rcosθ = (-7 - 2cosθ)cosθ
y = rsinθ = (-7 - 2cosθ)sinθ

At θ = π/2, cos(π/2) = 0 and sin(π/2) = 1, so:
x = -7 - 2(0) = -7
y = -7 - 2(0) = -7

2. Differentiate y with respect to θ and x with respect to θ:
dy/dθ = -7cosθ + 2cos²θ
dx/dθ = 7sinθ - 2sinθcosθ

3. Calculate dy/dθ and dx/dθ at θ = π/2:
dy/dθ = -7(0) + 2(0)² = 0
dx/dθ = 7(1) - 2(1)(0) = 7

4. Find the slope of the tangent, dy/dx:
dy/dx = (dy/dθ) / (dx/dθ) = 0 / 7 = 0

The slope of the tangent to the curve r = -7 - 2cosθ at θ = π/2 is 0.

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Answer:

[tex]\huge\boxed{\sf f^{-1}(x)=\frac{x}{2} + 1}[/tex]

Step-by-step explanation:

f(x) = 2(x - 1)

Put f(x) = y

y = 2(x - 1)

Exchange x and y

x = 2(y - 1)

Now, solve for y:

x = 2(y - 1)

Divide both sides by 2

[tex]\displaystyle \frac{x}{2} = y - 1[/tex]

Add 1 to both sides

[tex]\displaystyle \frac{x}{2} + 1 = y[/tex]

Put y = f⁻¹(x)

[tex]\displaystyle \frac{x}{2} + 1 = f^{-1}(x)[/tex]

OR

[tex]\displaystyle f^{-1}(x)=\frac{x}{2} + 1 \\\\\rule[225]{225}{2}[/tex]

Light travels approximately 1 foot in 1 nanosecond (ns). Therefore, the correct answer is "about 1 ft."

The speed of light in a vacuum is approximately 299,792,458 meters per second (m/s). In one nanosecond, light can travel approximately 0.3 meters or 1 foot. This distance may seem small, but it is incredibly fast when considering the scale of time. The fact that the contestant did not know the answer to this question highlights the importance of understanding basic scientific concepts and units of measurement.

To put it in perspective, if you were to travel at the speed of light, you could go around the Earth's equator approximately 7.5 times in just one second. The speed of light is also used as a unit of measurement in astronomy, where distances are so vast that traditional units like miles or kilometers are insufficient.

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The area of Cindy's expanded patio is 1250 square feet.

To find the area of Cindy's expanded patio, we need to calculate the product of its new length and width.

Given that Cindy plans to increase both dimensions by a factor of 0.25, we can multiply the original dimensions by 1 + 0.25 to get the new dimensions.

New width = 20 ft x (1 + 0.25) = 20 ft x 1.25 = 25 ft

New length = 40 ft x (1 + 0.25) = 40 ft x 1.25 = 50 ft

The area of the expanded patio is then:

Area = New width x New length = 25 ft x 50 ft = 1250 square feet.

Therefore, the area of Cindy's expanded patio is 1250 square feet.

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