Determine whether each sequence is geometric. If so, identify the common ratio and find the next two terms. 3,3 . . . . 6,4 . . . 32,5 . . . 184, . . . .

(a) Construct confidence intervals are : 90%: [428.95, 444.05], 95%: [427.13, 445.87], 99%: [423.67, 449.33].

(b) The 99% confidence interval has the widest interval.

(a) To construct confidence intervals for the mean breaking strength of the wool fibers, we shall use the given formula:

Confidence interval = sample mean ± (critical value * standard error)

The critical value here will depends on the level of confidence. For a 90% confidence level, the critical value is 1.645 (from the standard normal distribution). For a 95% confidence level, the critical value is 1.96, and for a 99% confidence level, the critical value is 2.576.

Standard error is obtained by dividing the sample standard deviation by the square root of the sample size.

Plugging in the values, we can calculate the confidence intervals:

90% confidence interval:

Lower bound = 436.5 - (1.645 * (11.9 / √20))

Upper bound = 436.5 + (1.645 * (11.9 / √20))

95% confidence interval:

Lower bound = 436.5 - (1.96 * (11.9 / √20))

Upper bound = 436.5 + (1.96 * (11.9 / √20))

99% confidence interval:

Lower bound = 436.5 - (2.576 * (11.9 / √20))

Upper bound = 436.5 + (2.576 * (11.9 / √20))

(b) The width of a confidence interval depends on both the critical value and the standard error. When aiming for a higher level of confidence, the interval becomes wider as it requires a larger critical value. Consequently, it can be concluded that among the given confidence intervals, the one with a 99% confidence level will have the broadest range.

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The exact length of the curve y=sqrt(x-x^2)+sin^-1(sqrt(x)) is 2.527.

The exact length of the curve y=sqrt(x-x^2)+sin^-1(sqrt(x)) can be calculated using the formula for arc length.

This formula states that the length of a parametric curve from t=a to t=b is equal to the integral of the square root of the sum of the squares of the respective derivatives of x and y, evaluated from a to b.

Using this formula, the length of the curve y=sqrt(x-x^2)+sin^-1(sqrt(x)) can be calculated by integrating the square root of (1-2x)^2 + (1/sqrt(x))^2 from 0 to 1. This yields a length of approximately 2.527.

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Answer:

y = 1.44x⁴

Step-by-step explanation:

From the question,

Y∝d²

To remove the proportionality sign we introduce a constant.

Y = kd²............... Equation 1

make k the subject of the equation

k = Y/d²............. Equation 2

Given: Y = 4, d = 10

Substitute these values into equation 2

k = 4/10²

k = 4/100

k = 0.04

Substitute these value of k in equation 1

Y = 0.04d²................ Equation 3

Similarly,

d∝x²,

d = Cx²

make C the subject of the equation

C = d/x²................... Equation 4

Given:  d = 24, x = 2

Substitute into equation 4

C = 24/2²

C = 24/4

C = 6

Hence,

d = 6x²................... Equation 5

Substitute the value of d in equation 5 into equation 3

y = 0.04(6x²)²

y = 0.04(36x⁴)

y = 1.44x⁴

Hence the formula for y in terms of x is y = 1.44x⁴

The area is 364 because the perimeter is 84 feet, the sides are 28 times two witch it 56 and 84-56 is 26 so the other sides are 13 and 13 times 28 is 364

Answer:-3

Step-by-step explanation:

If 3 =h and z=9 you just substitute them into the places of h and z

So 3(8) - 3(9) so 24-27

Step-by-step explanation:

the correct answer is exponent because 6 is its power.

hope this answer will help u.

have a great time.

Answer:

y= x-9

Step-by-step explanation:

Plug the values into the slope intercept equation:

y-y1 = m (x - x1)

where:

m is the slope

y1 is the y value from the given point

x1 is the x value from the given point

Step-by-step explanation:

so here the domain is the abstract background function so here the domain remains 45 and the angle preparing range is 18

The value of 'x' is 1. The height of the wall is 24 feet and the width of the wall is 15 feet.

To find the dimensions of the wall find the dimensions of the rectangles given in the figure. Calculate the area of the rectangle and factorize the resultant equation for the value of 'x'. Calculate the dimensions of the wall by using the number of panels along the height and top.

Here we have  

A wall has paneling made up of rectangles

Area of the rectangle = 30 square feet  

Given that the edge of each rectangle in the paneling is (2x+3) feet in width and (4x+2) feet in height.  

Area of the rectangle = (2x + 3)(4x +2) = [ 8x²+ 16x + 6 ]  

Given that area of the rectangle = 30 ft²  

=> 8x²+ 16x + 6 = 30

=> 8x²+ 16x - 24 = 0  

=> x² + 2x - 3 = 0

=> x² + 3x - x - 3 = 0

=> x(x + 3) - (x + 3) = 0

=> (x + 3)  (x - 1) = 0

=> x = -3 and  x = 1  

We need to x = 1  [ since height can't be taken in negative ]

Dimensions of the rectangle,

Width, 2x + 3 = 2(1) + 3 = 5 feet

Height, 4x + 2 = 4(1) + 2 = 6 feet

Given that there are 4 rectangles along the height

Height of the wall = 4 × 6 = 24 feet

There are 3 rectangles along the top.

Width of the wall = 3 × 5 = 15 feet

Therefore,

The value of 'x' is 1. The height of the wall is 24 feet and the width of the wall is 15 feet.

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Answer:

why can't you write the questions on brainly?

Answer:

y = -4x - 2

Step-by-step explanation:

y = mx + b where

m = slope, and b = y-intercept

slope = -4 = m

y-intercept = -2 = b

y = mx + b

y = -4x - 2

Answer: y = -4x - 2

Answer:

s = 10k + 30

Step-by-step explanation:

Cost of Adults ticket = $10 per adult

Cost of Ticket = $6 per child

Number of adults = k

Number of Children = 5

s = Total cost

Total cost = (Cost per adult * number of adults) + (Cost per child * Number of children)

s = ($10 * k) + ($6 * 5)

s = $10k + $30

s = 10k + 30

Answer: 1.8 units

Step-by-step explanation:

The type of sampling that relies upon knowledge of the distribution or proportion of population characteristics in order to choose a sample that assures representativeness of these characteristics is called stratified sampling.

In stratified sampling, the population is divided into different subgroups or strata based on specific characteristics or variables. The proportion of each subgroup in the population is known, and a sample is then selected from each stratum. This ensures that the sample is representative of the population in terms of the specific characteristics being studied.

To perform stratified sampling, follow these steps:
1. Identify the relevant characteristics or variables that you want to study.
2. Divide the population into distinct strata based on these characteristics.
3. Determine the proportion or distribution of each stratum in the population.
4. Select a random sample from each stratum, ensuring that the sample size is proportional to the size of the stratum in the population.
5. Combine the samples from each stratum to create the overall representative sample.

In conclusion, stratified sampling is a type of sampling method that ensures representativeness of population characteristics by dividing the population into subgroups and selecting samples from each stratum based on their proportion in the population.

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Answer:

Original price = $60

Step-by-step explanation:

Given:

Sales price of shoes = $45

Discount rate = 25%

Find:

Original price

Computation:

Original price = Sales price of shoes[1/(1-Discount rate)]

Original price = 45[1/(1-25%)]

Original price = 45[1/(1-0.25)]

Original price = 45[1/(0.75)]

Original price = $60

Answer:

Step-by-step explanation:

$60

Answer:

=15p+60-24q-48=15p-24q+12

it's the first one

The equivalent form of the given expression will be 15p - 24q +8. Hence, the first option is correct.

In mathematics, expressions are assertions that must contain at least two words with variables or terms with numbers in them, or both, and connect them with an operator. It is possible for the mathematical operators to be addition, subtraction, multiplication, or division.

For instance, the equation (x+y) has the terms x and y with an addition operator in between. Numerical expressions, which just contain numbers, and algebraic expressions, which also include variables, are the two types of expressions used in mathematics.

The given expression in the question,

15(p + 4) - 12(2q + 4)

15p + 60 - 24q - 48

15p - 24q + 12.

Hence, it is proved that the equivalent form of the expression is 15p - 24q + 12.

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\({ \begin{array} {l}\\ \quad \qquad \huge\color{green}{\boxed{ \colorbox{black}{ \color{green}{ \tt {Answer}}} }} \\ \\ \dashrightarrow \sf5(9 - x) + 2 {}^{2} \div 2 \\ \\ \dashrightarrow \sf45 - 5x+ (4 \div 2) \\ \\ \dashrightarrow \sf45 - 5x + 2\\ \\ \dashrightarrow\sf47 - 5x\\ \\ \texttt{hence, the equivalent expression is : -5x + 47 }\end{array}} \)

Answer:

I'm not sure if transformation is the same as transposition but if it's the same, then the rows will become columns and the columns will become rows.

Therefore: [5 -3]

The height of the tree is approximately 156.7 feet.

What is Trigonometry?

Trigonometry is the study of angles and the angular relationships of planar and three-dimensional shapes. Trigonometry is made up of trigonometric functions (also known as circle functions) such as cosecant, cosine, cotangent, secant, sine, and tangent.

The height of the tree can be calculated using trigonometry.

Let's call the height of the tree "h".

Then, using the right triangle formed by the height of the tree, the distance from the base of the tree to where Jerome is standing, and the angle between the ground and the top of the tree, we can set up the following equation:

tan(33°) = h / 90

Solving for h, we get:

h = 90 * tan(33°)

Using a calculator to find the value of tan(33°), we get:

h = 90 * 1.730

h ≈ 156.7 feet

So, The height of the tree is approximately 156.7 feet.

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Answer:

Cada ángulo igual es recto, es decir, mide 90°

Step-by-step explanation:

Intersección de dos rectas

Cuando dos rectas no paralelas se intersectan, forman en el punto de corte 4 ángulos iguales de a pares, es decir, dos pares de ángulos congruentes.

La suma de todos los ángulos formados es invariablemente 360°.

En general, siendo a y b dos ángulos adyacentes formados por el cruce, se cumple que:

a + b = 180°

Y la suma de todos los ángulos es el doble de lo anterior:

2a + 2b = 360°

Si todos los ángulos son iguales, a=b, entonces:

4a = 360°

a = 90°

Cada ángulo igual es recto, es decir, mide 90°

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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The graph of y = 1/2x is as shown below.

In this question, we need to graph an equation y = 1/2 x on the coordinate plane.

First we find the the coordinates of points passing through y = 1/2 x

The function is undefined at x =0 .

For x = 1,

y = 1/2

For x = -1

y = -1/2

For x = 2,

y = 1/4

So, we get coordinates (1, 1/2), (-1, -1/2), (2, 1/4)

We plot these points on the coordinate plane.

Therefore, the graph of y = 1/2x is as shown below.

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Using the given differential equation with the solution \(x^4\) and reduction order, we can substitute \(y^2 = ux^4\) to obtain the new equation \(2x^2u'' + 12xu' - 16u = 0\).

Given the differential equation \(x^2(d^2y/dx^2) - 7x(dy/dx) + 16y = 0\), with \(x^4\) as a solution, we can apply reduction order to obtain a simpler differential equation.

Reduction order involves substituting \(y^n = ux^i\), where i is the lowest positive integer for which the equation becomes simpler.

We can substitute \(y^n = ux^4\) into the given equation, which yields:

\(y^2 = ux^4\)

⇒\(2y(dy/dx) = 4x^3u + x^4u'\)

⇒\((d/dx)(y^2) = (d/dx)(x^4u)\)

⇒\(2y(dy/dx) + y^2(d^2y/dx^2) = 4x^3u' + 4x^4u''\)

Substituting this into the original equation and simplifying gives:

\(2x^2u'' + 12xu' - 16u = 0\), which is a second-order linear homogeneous differential equation that can be solved by substitution or other methods.

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Answer:

- 1

Step-by-step explanation:

5 - 2(12-3)/2+1 = - 18/3 + 5

= - 18/3 + 15/3

= - 3/3

= - 1

As angle OAB =40-degree, angle AOB is 100 degrees according to the properties of circle and triangle.

Some Properties of circle are distance from center of the circle to each point on the circumstances are equal. hence, OA=OB

Diameter is twice of radius.

The triangle having two equal side length is called isosceles triangle. In the figure, triangle OAB is an isosceles as OA=OB=radius

According to the criteria of isosceles triangle angle OAB =OBA =40°

hence, angle AOB= 180 degrees - (40°+40°) [angle sum of triangle =180°]

                  angle AOB= 100 degrees.

We get, AOB = 100 degrees

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Answer:

no solution

Step-by-step explanation:

Your question is in the form:

absval of something

= a NEGATIVE number



The absolute value is always positive. So it can never be negative.

There are no values that x can be that will make this math sentence true.

It's not really a trick question, but the course/teacher/book/program just wants you to recognize that an absolute value CANNOT be negative.

Answer:

32

Step-by-step explanation:

Absolute value is always positive.

Answer: -3

Step-by-step explanation:

The set of integers is a set of numbers that includes all negative numbers, all positive numbers, and zero.

Examples of integers are -4, 7, 0, -17.

Note that 1/2 is not an integer, but rather a rational number.

So now that we know what integers are, we will answer our question.

Which number is an integer? -3, -4, 1, -5, 2, 4, 2/3

In fact, all of these are integers, except 2/3.