There were six people in a sample of 100 adults (ages 16-64) who had a
sensory disability. And, there were 55 people in a sample of 400 seniors
(ages 65 and over) with a sensory disability. Let Populations 1 and 2 be
adults and seniors, respectively. Construct a 95% confidence interval for P1-
P2.

Answer:

\(\dfrac{3x^4}{2y^4}\)

Step-by-step explanation:

\(\dfrac{21x^6y^5}{14x^2y^9}= \\\\\\\dfrac{21}{14}\cdot \dfrac{x^6}{x^2} \cdot \dfrac{y^5}{y^9}= \\\\\\\dfrac{3x^4}{2y^4}\)

Hope this helps!

The required simplified solution is given as 3/2x⁴y⁻⁴.

Given that,
To determine the quotient of the division, 21x⁶y⁵ divided by 14xy⁹.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

here,
Accoding to the question,
=  21x⁶y⁵/ 14xy⁹
= 3/2 [x⁶⁻¹][y⁵⁻⁹]
= 3/2 [x⁴][y⁻⁴]

Thus, the required simplified solution is given as 3/2x⁴y⁻⁴.

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Answer:

l=√261 in

Step-by-step explanation:

l²=(12/2)²+15²

l²=6²+15²

l²=36+225

l²=261

l=√261 in ≈ 16.1555 in

The angle of elevation is the angle an observer forms when looking at an object above the horizontal plane. Therefore, the distance from the marker to the building is 247.5 m.

The angle of elevation is the angle an observer forms when looking at an object above the horizontal plane. It is always measured in reference to the horizontal plane.

The given question forms a right-angled triangle, thus the trigonometric function should be applied. Let the distance from the marker to the building be represented by d, so that;

Tan θ = \(\frac{opposite}{adjacent}\)

Tan 22 = \(\frac{100}{d}\)

So that,

d = \(\frac{100}{Tan 22}\)

  = \(\frac{100}{0.4040}\)

d = 247.52

Therefore, the distance from the marker to the building is 247.5 m.

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\(\text{Solve:}\\\\1 < x + 3 < 4\\\\\text{Subtract 3 from all 3 sides}\\\\-2<x<1\\\\\boxed{-2<x<1}\)

Answer:

y= 3x

Step-by-step explanation:

Because between each point your going up by 3

Hope this helps you

Answer:

y = 3x

Step-by-step explanation:

This is dealing with slope so think of it as rise over run

\(\frac{Rise}{Run}\)

The y intercept is a 0 so you don't have to worry about adding a number after the plus symbol. You can if you want but that's not an option. You go up 3 over 1 and then you get to your next point.

Step-by-step explanation:

b)

make it braintliest please

Answer:

YOU ARE ONE OF THESE NUMBERS 1,3,5,7,9 etc i hope this helps if it didnt im sorry

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

The solution to the equations is at the point of intersection of the 2 lines.

If the system has no solution, this indicates the lines do not intersect and therefore must be parallel.

The transformation of the coordinate (-8, -3)  R 270° and T-2,-1 is (-5, -9)

Transformation is the change of the coordinates of a shape either by rotation, reflection or translation.

Analysis:

When coordinates (x, y) rotate 270° the resulting coordinates become (-y, x)

so coordinates (-8, -3) after 270° rotation becomes ( 3, -8)

When it is translated 2 units to the left and 1 unit down, that is -3 + -2 = -5 and -8 + -1 = -9

Therefore the transformed coordinate becomes (-5, -9)

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Answer:

This question is unsolvable because:

1) Volume can't be measured in cm (think you mean cm^3)

2) Volume of the cylinder is calculated with its height and bottom area.

   We can calculate its bottom area like this: (4/2)^2*pi

   But since we do not know the cylinder nor the cones' height then we can't

   calculate their volume.

Please correct me if im wrong

The value of the chi-square test statistic is 24.375.

To calculate the chi-square test statistic, we need to follow these steps:

State the null and alternative hypotheses.

Determine the expected values.

Calculate the chi-square test statistic.

Determine the degrees of freedom.

Find the p-value and compare it with the significance level.

State the null and alternative hypotheses:

Null hypothesis: The proportions of the five choices are equal.

Alternative hypothesis: The proportions of the five choices are not equal.

Determine the expected values:

Since there are 200 students and 5 possible choices, we would expect each choice to be marked 40 times if the proportions were equal. Thus, the expected values for each choice are:

Expected value for a: 40

Expected value for b: 40

Expected value for c: 40

Expected value for d: 40

Expected value for e: 40

Calculate the chi-square test statistic:

The formula for the chi-square test statistic is:

chi-square = sum((observed - expected)^2 / expected)

Using the given data and the expected values, we get:

chi-square = [(60-40)^2/40] + [(35-40)^2/40] + [(20-40)^2/40] + [(25-40)^2/40] + [(60-40)^2/40]

= 5 + 1.25 + 10 + 3.125 + 5

= 24.375

Determine the degrees of freedom:

The degrees of freedom for a chi-square test of independence with r rows and c columns is (r-1)(c-1). In this case, there are 5 choices, so c = 5. Therefore, the degrees of freedom are (5-1)(5-1) = 16.

Find the p-value and compare it with the significance level:

Using a chi-square distribution table with 16 degrees of freedom, we find the p-value to be less than 0.01. Since the significance level is 10%, we reject the null hypothesis if the p-value is less than 0.10. Since the p-value is less than 0.10, we reject the null hypothesis.

Therefore, the value of the chi-square test statistic is 24.375.

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Answer:

Pythagorean identity sin²θ+cos²θ = 1 is true for the angle θ = \(\frac{5\pi }{3}\)

Step-by-step explanation:

At first, let us simplify the left side of the identity

∵ The left side is sin²Ф + cos²Ф

∵ Ф = \(\frac{5\pi }{3}\) ⇒ lies in the 4th quadrant

∴ The left side is sin²(\(\frac{5\pi }{3}\)) + cos²(\(\frac{5\pi }{3}\))

→ Let us write the values of sin(\(\frac{5\pi }{3}\)) and cos(\(\frac{5\pi }{3}\))

∵ sin(\(\frac{5\pi }{3}\)) = \(\frac{-\sqrt{3}}{2}\) ⇒ sine an angle in the 4th quadrant is -ve

∵ cos(\(\frac{5\pi }{3}\)) = \(\frac{1}{2}\) ⇒ cosine an angle in the 4th quadrant is +ve

→ Substitute them in the left side

∵ sin²(\(\frac{5\pi }{3}\)) + cos²(\(\frac{5\pi }{3}\)) = [ \(\frac{-\sqrt{3}}{2}\)]² + [\(\frac{1}{2}\)]²

∴ sin²(\(\frac{5\pi }{3}\)) + cos²(\(\frac{5\pi }{3}\)) = [\(\frac{3}{4}\)] + [\(\frac{1}{4}\)]

∴ sin²(\(\frac{5\pi }{3}\)) + cos²(\(\frac{5\pi }{3}\)) = [\(\frac{4}{4}\)]

∴ sin²(\(\frac{5\pi }{3}\)) + cos²(\(\frac{5\pi }{3}\)) = 1

∵ The right side = 1

∴ Left side = Right side

∴ sin²(\(\frac{5\pi }{3}\)) + cos²(\(\frac{5\pi }{3}\)) = 1 ⇒ proved

∴ Pythagorean identity sin²θ+cos²θ = 1 is true for the angle θ = \(\frac{5\pi }{3}\)

Answer:

1 7/12

Step-by-step explanation:

The answer is 1/3+1 1/4 and if you make them common fractions it is 4/12+1 3/12=1 7/12

Answer:37/12

Step-by-step explanation:

1/3+11/4=37/12

Hi!

We can use point-slope form to solve this.

\(y-y_{1} =m(x -x_{1})\)

\(y_{1}\) and \(x_{1}\) will be from one of the points.

First, we have to find \(m\), the slope. We can use the slope equation to get this.

\(\frac{y_{1} -y_{2} }{x_{1} -x_{2} }\)

Plug in your points:

\(\frac{4-0}{8-(-8)} =\frac{4-0}{8+8} =\frac{4}{16} =\frac{1}{4}\)

Your slope is \(\frac{1}{4}\)

Now plug points and slope into point-slope equation. We will use (8, 4).

\(y-4=\frac{1}{4} (x-8)\)

Now, if you want to get it into y = mx + b form, you have to solve for y:

\(y-4=\frac{1}{4} (x-8)\)

\(y-4=\frac{1}{4} x-2\)

\(y=\frac{1}{4} +2\)

Your equation is \(y=\frac{1}{4} +2\)

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Answer:

\(t=3c-8\)

Step-by-step explanation:

It seems like your question is incomplete, so I will assume it is asking for an expression that represents how many cookies Anna has left.

Let t represent the total number of cookies left. Let's build this expression. If each batch contains c cookies, and there are 3 batches, the total number of cookies baked is 3 times c. Since she ate 8 cookies, 8 must be subtracted from that total. Therefore:

\(t=3c-8\)

Hope this helps!

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

Answer:

Hi

Step-by-step explanation:

The expression was reduced to it's lowest expression or term or we say we found the common factor amongst them

Answer:

200 inches

Step-by-step explanation:

divide 400 by 2

Answer:

I graphed it for you in the image below.

Step-by-step explanation:

Graph the logarithmic function f(x) = log2(x - 1) + 2 is attached below.

The function is referred to as a particular kind of relationship, every value in the domain is associated with exactly one value in the range. They have a set perimeter and territory.

It is given that the logarithmic function is, f(x) = log2(x - 1) + 2.

The first step in graphing a logarithmic function is to locate some points on the exponential f. (x). The graph will look better as we plot more points, and we can flip the x and y values to get points on the opposite axis. locate the asymptote. The following logarithmic functions can be graphed. Specify the domain and the range.

Thus, the graph is attached below.

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In the worst case, a linear search locates a value in an array of length n in O(n) steps.

A linear search is a basic search algorithm that sequentially checks each element in an array until it finds the target value or reaches the end of the array.

In the worst case scenario, the target value is not present in the array, and the linear search needs to iterate through all n elements of the array.

Since the linear search algorithm checks each element one by one, its time complexity is directly proportional to the size of the array. This means that as the array length (n) increases, the number of steps required by the linear search also increases linearly.

Therefore, the worst-case time complexity of a linear search is O(n), indicating that the number of steps grows in proportion to the size of the array.

It is important to note that other search algorithms, such as binary search, can achieve faster search times (e.g., O(log n)) in sorted arrays.

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Step-by-step explanation:

40% increase => 1.4 * Original price.

Therefore the new price of the TV

= 1.4 * $499 = $698.6.

Answer:

the answer new answer is 1567

Answer:

7/20

0.35

35%

Step-by-step explanation:

12 year olds: 40%

12 year olds: 25%

11 year olds: 100% - 40% - 25% = 35%

35% = 35/100 = 7/20

35% = 0.35

35% = 35%

Answer:

all 4 meals equal $20.95

Step-by-step explanation:

4 sandwiches = $2.59 each

4 hashbrowns = $1.10 each

4 orange juice = $1.25 each

sales tax = 6%

now you have two options you could either add all of the one meal prices together or you could do how much it would cost for the each individually

adding one meal

2.59 + 1.10 + 1.25 = 4.94

4.94 x 4 = 19.76

adding all the items individually

2.59 x 4 = 10.36

1.10 x 4 = 4.40

1.25 x 4 = 5.00

10.36 + 4.40 + 5.00 = 19.76

now if the sales taxes

19.76 x 0.06 = 1.19

now sales taxes plus all the items

19.76 + 1.19 = 20.95

Hence, Susan got a 35% discount on the shirt.

The discount equal to the difference between the price paid for and it is par value. Discount is a type of deduction or reduction  in the cost price of a product. It is more used in consumer transactions, where people are provided with discounts on various products. The discount rate is given in percentage.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, although the abbreviations pct., pct, and sometimes pc are also used. A percentage is a dimensionless number; it has no unit of measurement.

To calculate the percentage of  discount Susan got on the  shirt, we need to calculate the  difference between the  original price and the  discounted price and express it as a percentage of the original price:

We know that,

Discount = Original price - Discounted price

According to question,   Original price =  $32.50 and Discounted price = $21.13

Discount = $32.50- $21.13

Discount = $11.37

therefore , discount of Susan got on the  shirt is $11.37.

Now ,we calculate the percentage of discount

Percentage of discount = \(\frac{Discount}{Original price}\)x 100%

Percentage of discount = \(\frac{11.37}{32.50}\)x 100%

Percentage of discount = 35%

Therefore, Susan got a 35% discount on the shirt.

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Step-by-step explanation:

percent change = (new value - old value) / old value x 100%

Where the old value is Vera's final average in seventh grade and the new value is her final average in eighth grade.

percent change = (91 - 96) / 96 x 100%

percent change = -0.052 x 100%

percent change = -5.2%

Therefore, the percent of change in Vera's final average from seventh grade to eighth grade is a decrease of 5.2%.

Answer: To find the percent of change from seventh grade to eighth grade, we can use the formula:

percent change = (new value - old value) / old value * 100%

where "old value" is the value in seventh grade and "new value" is the value in eighth grade.

In this case, the old value is 96 and the new value is 91. Substituting into the formula, we get:

percent change = (91 - 96) / 96 * 100%

Simplifying, we get:

percent change = -5.21%

Therefore, the percent of change in Vera's final average from seventh grade to eighth grade is approximately 5.21% decrease.

Step-by-step explanation:

Answer:

15/19

Step-by-step explanation:

Nesta pergunta, queremos calcular a probabilidade de que uma bola retirada da urna não seja preta.

Existem três cores, uma vez que a bola removida não é preta, então é uma das outras duas cores.

Isso significa que a bola é branca ou vermelha. Observe que a probabilidade de a bola não ser preta é 1 menos a probabilidade de a bola ser preta Vamos descobrir a probabilidade de que a bola seja preta;

Matematicamente, isso seria;

número de bolas pretas / número total de bolas.

O número total de bolas é; 10 + 5 + 4 = 19 número de bolas pretas = 4

A probabilidade de a bola ser preta é de 4/19

Portanto, a probabilidade de que a bola não seja uma bola preta é

1 - 4/19 = 15/19

Answer:

f(6)=5+2(x)

f(6)=5+2(6)

f(6)=5+12

Step-by-step explanation:

Answer: 4,700

Step-by-step explanation: 678 is above 650, meaning it is closer to 700 than it is 600

so rounding this makes it 4,700

unless you meant it as a decimal which 4.678 would result in 4.68 since the 8 before 7 would round up the 7 to an 8 making it 4.68

Hope this helps ^_^

Answer:

It's 4,700.

Step-by-step explanation:

When rounding to the nearest hundred, we use the following rules:

1) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

2) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.

3) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.