Complete the inequality.


1/4 ___ 3/16


>

=

The surface area of the two solids are listed below:

Case 1 - 232 square centimeters

Case 2 - 240 square centimeters

The surface area of a solid is the sum of the areas of all its faces. There are two cases of solids whose surface areas must be determined. The area formulas for triangle and rectangle are, respectively:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Case 1

A = (6 cm) · (8 cm) + 2 · 0.5 · (6 cm) · (12 cm) + 2 · 0.5 · (8 cm) · (14 cm)

A = 232 cm²

Case 2

A = 2 · 0.5 · (8 cm) · (3 cm) + (8 cm) · (12 cm) + 2 · (5 cm) · (12 cm)

A = 24 cm² + 96 cm² + 120 cm²

A = 240 cm²

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Some possible prices for the socks that would meet this condition are $2.99, $2.50, $3.00, $2.95, etc.

A rate is a measure of the amount of change of one quantity with respect to another quantity. It expresses how much one quantity changes in relation to another quantity over a given time or distance.

If Diego has budgeted $35 for 5 pairs of socks and a pair of shorts, we can subtract the cost of the shorts from the total budget to find the amount he has left for the socks:

$35 - $19.95 = $15.05

To find the possible prices for the socks, we can divide the amount Diego has left by the number of pairs of socks he needs:

$15.05 / 5 pairs = $3.01 per pair

Therefore, Diego would be able to stay within his budget if he finds socks that cost $3.01 or less per pair. Some possible prices for the socks that would meet this condition are $2.99, $2.50, $3.00, $2.95, etc.

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Answer:

  48

Step-by-step explanation:

You want to know the number of cans 4 inches tall with a volume of 50.24 in³ that will fit on a shelf with a height and depth of 10 inches and a length of 50 inches.

The diameter of the can will be found from the volume formula:

  V = (π/4)d²h

  d = √(4V/(πh)) = √(4·50.24/(4·3.14)) = √16 = 4 . . . inches

The cans are 4 inches in diameter.

The number of cans that will fit in each dimension will be the integer part of the dimension divided by the size of the can in that dimension.

  Height: (10 in)/(4 in/can) = 2.5 cans . . . . cans will fit 2 cans high

  Depth: (10 in)/(4 in/can) = 2.5 cans . . . . cans will fit 2 cans deep

  Length: (50 in/4 in/can) = 12.5 cans . . . . cans will fit 12 cans long

A total of 2 × 2 × 12 = 48 cans will fit on the shelf.

__

Additional comment

There will be 2 inches of empty space in each direction.

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The surface area of the actual ramp, including the underside, is approximately 15.38 yd².

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

To find the surface area of the actual ramp, we need to first find the dimensions of the ramp.

We are given that the scale model of the ramp is a right triangular prism with legs of 8 in, 5 in, and 5 in, and a height of 3 in. We can use these dimensions to find the dimensions of the actual ramp.

Since the ramp is a scale model, the ratio of the dimensions of the model to the actual ramp is the same for all corresponding dimensions. The height of the triangular base in the actual ramp is given as 0.6 yards, which is equal to 21.6 inches. So, we have:

height of actual ramp / height of model = 21.6 in / 3 in = 7.2

We can use this ratio to find the dimensions of the actual ramp:

height of actual ramp = 7.2 * 3 in = 21.6 in

length of actual ramp = 7.2 * 8 in = 57.6 in

width of actual ramp = 7.2 * 5 in = 36 in

Now we can find the surface area of the actual ramp. The surface area of the top and bottom of the ramp is the area of the triangular base plus the area of the rectangle formed by the length and width of the ramp:

Area of triangular base = (1/2) * base * height = (1/2) * 5 in * 5 in = 12.5 in²

Area of rectangular top and bottom = length * width = 57.6 in * 36 in = 2073.6 in²

Total surface area of top and bottom = 2 * (Area of triangular base + Area of rectangular top and bottom) = 2 * (12.5 in² + 2073.6 in²) = 4153.2 in²

The surface area of the sides of the ramp is the area of the three rectangles formed by the height and width of the ramp:

Area of one side rectangle = height * width = 21.6 in * 36 in = 777.6 in²

Total surface area of sides = 3 * Area of one side rectangle = 3 * 777.6 in² = 2332.8 in²

Finally, we add the surface area of the top and bottom to the surface area of the sides to get the total surface area of the ramp:

Total surface area of ramp = Surface area of top and bottom + Surface area of sides = 4153.2 in² + 2332.8 in² = 6486 in²

Converting to yards and rounding to two decimal places, we get:

Total surface area of ramp = 6486 in² / (36 in/yd)² = 15.38 yd² (rounded to two decimal places)

Therefore, the surface area of the actual ramp, including the underside, is approximately 15.38 yd².

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According to the algebraic expressions, the sum of four smaller rectangles is 96.

First, let's consider the figure as one large rectangle. To find the area of a rectangle, we multiply its length by its width. In this case, the length of the rectangle is 8 and the width is 6 + 2 + 4 = 12. Therefore, the expression for the area of the rectangle can be written as:

Area = length x width

Area = 8 x 12

Area = 96

So the area of the figure as one large rectangle is 96 square units.

To find the area of each rectangle, we'll use the formula for the area of a rectangle, which is length x width. We can see from the figure that:

Rectangle A has a length of 8 and a width of 6

Rectangle B has a length of 8 and a width of 2

Rectangle C has a length of 4 and a width of 6

Rectangle D has a length of 4 and a width of 2

Therefore, the expressions for the area of each rectangle can be written as:

Area_A = length x width

Area_A = 8 x 6

Area_A = 48

Area_B = length x width

Area_B = 8 x 2

Area_B = 16

Area_C = length x width

Area_C = 4 x 6

Area_C = 24

Area_D = length x width

Area_D = 4 x 2

Area_D = 8

To find the total area of the figure, we simply add up the areas of the four rectangles. Therefore, the expression for the area of the figure as a sum of four smaller rectangles can be written as:

Area = Area_A + Area_B + Area_C + Area_D

Area = 48 + 16 + 24 + 8

Area = 96

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The general solution of the given higher-order differential equation is y(x) = c1e[tex].^{x/2}[/tex]cos((1/2)√5x) + c2e[tex].^{x/2}[/tex]sin((1/2)√5x) + c3eˣ + c4e⁻ˣ.

The given higher-order differential equation is:

16(d⁴y/dx⁴) + 40(d²y/dx²) + 25y = 0

To find the general solution of this differential equation, we can assume that y(x) has the form:

y(x) = e[tex].^{rx}[/tex]

where r is a constant to be determined.

Differentiating y(x) four times with respect to x, we get:

d⁴y/dx⁴ = r⁴e[tex].^{rx}[/tex]

Differentiating y(x) two times with respect to x, we get:

d²y/dx² = r²e[tex].^{rx}[/tex]

Substituting these derivatives and y(x) into the differential equation, we get:

16(r⁴e[tex].^{rx}[/tex]) + 40(r²e[tex].^{rx}[/tex]) + 25e[tex].^{rx}[/tex] = 0

Simplifying this equation by dividing through by e[tex].^{rx}[/tex], we get:

16r⁴ + 40r² + 25 = 0

This is a quadratic equation in r². Solving for r² using the quadratic formula, we get:

r² = [-40 ± √(40² - 4(16)(25))] / 2(16)

r² = [-40 ± √(3600)] / 32

r² = [-40 ± 60] / 32

We get two possible values for r²:

r² = 5/4 or r² = 1

Taking the square root of each value, we get:

r = ±(1/2)i√5 or r = ±1

Thus, the general solution of the given higher-order differential equation is:

y(x) = c1e[tex].^{x/2}[/tex]cos((1/2)√5x) + c2e[tex].^{x/2}[/tex]sin((1/2)√5x) + c3eˣ + c4e⁻ˣ

where c1, c2, c3, and c4 are constants determined by the initial or boundary conditions of the specific problem.

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The complete question is :

find the general solution of the given higher-order differential equation : 16(d⁴y/dx⁴) + 40(d²y/dx²) + 25y = 0

a) Positive correlation, b) No correlation, c) Negative correlation

a) Positive correlation - as the hours of lacrosse practice increase, the number of goals scored in a lacrosse game is likely to increase as well.

b) No correlation - there is no obvious relationship between a student's average marks and the number of siblings in their family.

c) Negative correlation - as the distance from a student's home to their school increases, the time they spend on the school bus each day is likely to decrease.

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The appropriate statement for the null hypothesis is "the depression status and caffeinated coffee consumptions are independent."

The statement that is not appropriate for the null hypothesis according to hypothesis testing is "the levels of depression status and caffeinated coffee consumptions are equally likely."

This statement implies that there is an equal chance of having different levels of depression status and different levels of caffeinated coffee consumption, which is not a suitable assumption for the null hypothesis.

The null hypothesis should state that there is no significant relationship between the two variables, and the distribution of one variable does not depend on the distribution of the other variable.

Therefore, the appropriate statement for the null hypothesis is "the depression status and caffeinated coffee consumptions are independent."

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The graphical representation that would be the best for this data would be a circle graph. That is option C.

A circle graph, which is also called a pie chart, is defined as a type of data representation where by the information concerning a data set is displayed in a circular form and in a way that the various information displayed is a percentage of the total data set involved.

Now, the number of students that were surveyed = 100 students.

The number of subjects that are preferred by the students would be represented as x,y,z.

Therefore to represent the number of students that preferred a particular subject on the circle graph the following is carried out;

For subject x = Number of X/100 × 360/1

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The missing angles in the given pair of lines AB and CD with transversals EF & GH intersecting at O & missing sides on the basis of similarity of triangles are:

∠IKF=w°=109°

JO=z=2.7 units

∠JLO=x°=39°

∠DLO=y°=141°

What is similarity?

If two forms or figures have an equal number of comparable sides and angles, they are said to be similar. Similar figures are those when two or more figures share the same shape but have varied sizes.

Given that

∠KIO=39°

∠IKO=71°

∠IOK=70°

IO=12 units

KO=8 units

LO=4 units

a)We know that ∠KIO=∠OLJ  {alternate interior angles}

∠KIO=∠OLJ=39°

∴x° = 39°

b)We know that ∠OLJ+∠OLD=180° {linear pair}

x°+y°=180°

39°+y°=180°

y°=180-39

y°=141°

c)We know that ∠IKO+∠IKF=180° {angles on straight line}

71°+w°=180°

w°=180-71

w°=109°

d)In ΔOKI and ΔOJL, we can see that

∠OIK=∠OLJ=39°

∠OKI=∠OJL=71°

∠KOI=∠JOL=70°

as the angles are congruent, we can say that ΔOKI and ΔOJL are similar.

∴Sides will be in same ratio

[tex]\frac{OI}{OL}[/tex]  = [tex]\frac{OK}{OJ}[/tex]  = [tex]\frac{KI}{JL}[/tex]

Taking [tex]\frac{OI}{OL}[/tex]  = [tex]\frac{OK}{OJ}[/tex]

[tex]\frac{12}{4} = \frac{8}{z}[/tex]

3z = 8

z =2.667

z≈2.7 units

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The required sample size is  8.90400.

Given a student wants to make a guess within 0.03 of the true ratio with a 90% confidence level.

Margin of Error, E = 0.03

significance level α=0.10  {90% confidence}

A given estimate of the percentage of population p is p = 0.79.

The critical value for the significance level α = 0.10 is Zc = 1.645. This can be determined using either Excel or a normal probability table.

Use the following formula to calculate the minimum sample size required to estimate the percentage of population p within the required margin of error.

n≥p(1-p)(Zc÷E)²

n = 0.796×(1-0.796)(1.645÷0.03)²

n = 0.796 x 0.204 x 54.833

n = 8.90400

Therefore, the resample size required to meet the condition is n ≥  8.90400 and must be an integer. From this, we conclude that the minimum sample size required is n =  8.90400

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An inequality for this situation "A cruise ship can carry at most 3500 passengers." is x ≤ 3,500.

A graph of the inequality x ≤ 3,500 is shown in the image attached below.

What is an inequality?

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Note: At most simply refers to less than or equal to (≤) in Mathematics.

Since the cruise ship can only carry at most 3500 passengers, an inequality that models this situation is given by;

x ≤ 3,500

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Answer:

m = 6

Step-by-step explanation:

We have the proportion:

12/m = 18/9

To solve for m, we can cross-multiply the terms in the proportion:

12 × 9 = 18 × m

Simplifying both sides of the equation, we get:

108 = 18m

Dividing both sides by 18, we get:m = 6

Therefore, the solution to the proportion 12/m = 18/9 is m = 6.

Answer: m = 6

Step-by-step explanation:

First, we will rewrite this proportion:

     [tex]\displaystyle \frac{12}{m} =\frac{18}{9}[/tex]

Next, we will cross-multiply:

     12 * 9 = 18 * m

     108 = 18m

Lastly, we will divide both sides of the equation by 18:

     m = 6

We can also solve this proportion another way.

     We know that 18/9 = 2, so 12/m must equal 2 as well.

     12/6 = 2, so m = 6.

The given expression in the form ax + b will be (B) 1.8x + 4.1.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

An example is the expression x + y, which combines the terms x and y with an addition operator.

In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers.

So, we have the expression:

(3.6x-1.4) - (1.8x-5.5)

First, solve it in the form of ax + b as follows:

(3.6x-1.4) - (1.8x-5.5)

3.6x-1.4 - 1.8x+5.5

1.8x + 4.1

So, we have the expression: 1.8x + 4.1

Then, the coefficient and content will be (B) and the correct expression would be 1.8x + 4.1.

Therefore, the given expression in the form ax + b will be (B) 1.8x + 4.1.

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Answer: To find the point on the line 3x + y = 8 that is closest to the point (-3,2), we need to minimize the distance between the line and the point.

Let (x, y) be the point on the line that is closest to (-3, 2). Then the vector from the point (-3, 2) to (x, y) is orthogonal (perpendicular) to the line. The direction vector of the line is <3, 1>, so the direction vector of the orthogonal vector is <-1/3, 1>.

Now we can write an equation for the line passing through (-3, 2) with the direction vector <-1/3, 1>:

(x - (-3))/(-1/3) = (y - 2)/1

Simplifying, we get:

3x + y = 11

This is the line passing through (-3, 2) that is orthogonal to the original line 3x + y = 8.

To find the intersection of these two lines, we can solve the system of equations:

3x + y = 8

3x + y = 11

Subtracting the first equation from the second, we get:

0 = 3

This is a contradiction, which means the two lines do not intersect. Therefore, the point on the line 3x + y = 8 that is closest to (-3, 2) does not exist.

However, we can still find the closest point to (-3, 2) on the line 3x + y = 8. This point will be the intersection of the line passing through (-3, 2) with the direction vector <-1/3, 1> and the line 3x + y = 8.

The equation of the line passing through (-3, 2) with the direction vector <-1/3, 1> is:

(x - (-3))/(-1/3) = (y - 2)/1

Simplifying, we get:

3x + y = 11

To find the intersection point with the line 3x + y = 8, we can solve the system of equations:

3x + y = 8

3x + y = 11

Subtracting the first equation from the second, we get:

0 = 3

This is a contradiction, which means the two lines do not intersect. Therefore, the point on the line 3x + y = 8 that is closest to (-3, 2) does not exist.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

to find the missing side x , subtract the sum of the 5 given sides from the given perimeter.

x = 137 - (39 + 37 + 12 + 10 + 13) = 137 - 111 = 26 m

Answer: The angle between line AB and the axis of the cylinder is 60 degrees.

Step-by-step explanation:

Let's draw a cross-sectional diagram of the cylinder to help visualize the problem.

Label the center of the top circle as O and the center of the bottom circle as O'.

Label the midpoint of line AB as M.

Draw a line from M to the center of the cylinder, which intersects the axis of the cylinder at point C.

Because line AB is perpendicular to the axis of the cylinder, line MC is also perpendicular to line AB.

Label the length of line MC as h, and the distance between point M and the axis of the cylinder as x.

By the Pythagorean theorem, we know that OM^2 + h^2 = R^2 (the radius of the cylinder)

Similarly, O'M^2 + h^2 = R^2

Subtracting these two equations, we get OM^2 - O'M^2 = 0, which means that OM = O'M = R.

Therefore, triangle MOC is an isosceles triangle with MO and O'M both equal to R.

Because x is the distance between line AB and the axis of the cylinder, we know that x = MC - (R√3)÷2.

We also know that h = R - x (because OM = R).

Using the Pythagorean theorem, we can solve for MC: (R^2 - h^2)^0.5 = MC

Substituting h = R - x, we get MC = (2Rx - x^2)^0.5

Setting MC = (R√3)÷2 (from the problem statement), we can solve for x: x = R(3 - 3^0.5)^0.5

Finally, using the tangent function, we can solve for the angle between line AB and the axis of the cylinder: tanθ = (R√3)÷2 / x, where θ is the angle we are looking for.

Substituting x from step 15, we get tanθ = 1 / (3 - 3^0.5)

Using a calculator, we can solve for θ: θ = 60 degrees.

In the given problem, the surface area of the triangular prism is 65 square centimeters. The answer is not listed among the options provided

We need to find the surface area of the triangular prism, which is the sum of the areas of all its faces.

The triangular faces of the prism are congruent triangles, so we can find their area by multiplying the base and height and dividing by 2. The dimensions of the triangular faces are 5 cm (base) and 4 cm (height).

Area of each triangular face = (5 cm x 4 cm)/2 = 10 cm²

The rectangular faces are congruent rectangles, so we can find their area by multiplying the length and width. The dimensions of the rectangular faces are 5 cm x 3 cm and 3 cm x 4 cm.

Area of each rectangular face = (5 cm x 3 cm) = 15 cm²

Total surface area of the prism = 2 x Area of triangular face + 3 x Area of rectangular face

= 2 x 10 cm² + 3 x 15 cm²

= 20 cm² + 45 cm²

= 65 cm²

Therefore, the surface area of the triangular prism is 65 square centimeters. The answer is not listed among the options provided, so there might be a mistake in the question or answer choices.

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The power of a statistical test of hypotheses is the probability that the test will reject the null hypothesis when a particular alternative value of the parameter is true.

It is the ability of the statistical test to detect a true difference between groups, or a true relationship between variables, when it exists. A high power indicates that the test has a low probability of making a type II error (failing to reject a false null hypothesis).

The power of a test is affected by various factors such as the sample size, level of significance, effect size, and variability of the data.

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It is not equal to 1 - (P-value), nor is it the smallest significance level at which the data will allow you to reject the null hypothesis or the probability that the test will reject both one-sided and two-sided hypotheses.

The correct answer is: The power of a statistical test of hypotheses is the probability that a significance test will reject the null hypothesis when a particular alternative value of the parameter is true. It is the ability of the test to detect a true difference or effect between two groups or conditions. The power is influenced by factors such as the sample size, effect size, and significance level, and is usually calculated before conducting a study to ensure that it has sufficient power to detect meaningful differences. It is not equal to 1 - (P-value), nor is it the smallest significance level at which the data will allow you to reject the null hypothesis or the probability that the test will reject both one-sided and two-sided hypotheses.

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The value of the digit 5 in 24,513 is 1,000 times the value of the digit 5 in 357.

In the number 357, the digit 5 is in the ones area, which means that its value is just 5. We can write this number as 5 x 10^0, where 10 is the base of our number system, and the exponent 0 represents the ones area.

Now, to find out how many times the value of the digit 5 in 357 is compared to the value of the digit 5 in 24,513, we need to divide the value of the digit 5 in 24,513 by the value of the digit 5 in 357.

We have:

Value of 5 in 24,513 = 5 x 10³

Value of 5 in 357 = 5 x 10⁰

So,

Value of 5 in 24,513 ÷ Value of 5 in 357 = (5 x 10³) ÷ (5 x 10⁰)

We can simplify this expression by dividing 5 by 5, which gives us:

(5 x 10³) ÷ (5 x 10⁰) = 10³ = 1000

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Answer:

Image

Step-by-step explanation:

After performing long division on (x3+3x2-x+2)/(x-1) we get x² + 4x +3 leaving a remainder of 5.

Long division refers to the method of performing a division of two numbers or polynomials by hand. Furthermore, it involves several steps to evaluate in order to find a quotient and a remainder. It is considered an important and crucial form of practice in the branch of mathematics.                  

In the subject of dividing a polynomial, first, we divide the highest degree term of the dividend by the highest degree term of the divisor, and the remaining result is subtracted from the dividend. The calculation is as follows in the picture

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Testing is only one part of the overall assessment process.

What is evaluation in education?

Assessment is an ongoing process of gathering evidence of what each student actually knows, understands, and can do. A comprehensive evaluation approach includes a combination of formal and informal evaluation (formative, preliminary, and summative).

What is an assessment? Also what does it mean?

At the course level, assessments provide important data on the breadth and depth of student learning. Evaluation is more than scoring. It's about measuring student learning progress. Assessment is therefore defined as “the process of data gathering to better understand the strengths and weaknesses of a student's learning”. 

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The number of poetry books at the library that are for children is 510

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

Books = 600

If 8.5/10 of the poetry books are for children, we can calculate the number of poetry books for children as follows:

Number of poetry books for children = (8.5/10) x 600

Number of poetry books for children = 510

Therefore, there are 510 poetry books at the library for children.

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The value of 5 pints is equal to 10 cups.

A liquid measurement with a capacity of 1/8 of a gallon.  If we recall, 8 ounces equals 1 cup and 2 cups (or 16 ounces) equals 1 pint. One pint is made up of 16 fluid ounces, which is also equivalent to 2 cups, 1/4 quart, and 1/8 gallon. Normally, there are 2 cups in 1 pint, however this might vary depending on the ingredients. A pint has two cups in it.

Two cups equal one pint. You must multiply the volume in pints by a factor of two to convert from pt to c.

Hence, 1 pt = 2c

Substitute the values;

Multiple both the sides by 5

5 * 1pt = 5* 2c

5pt = 10c

Therefore, The value of 5 pints is equal to 10 cups.

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We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752.

The correct practical interpretation is: "We are 95% confident that the proportion of all central Florida reefers who use led lighting falls between .648 and .752."

This means that if we were to take multiple random samples of 700 experienced central Florida reefers, 95% of the intervals created would contain the true population proportion of reefers who use LED lighting.

So, based on this sample, we can say with 95% confidence that the true proportion of all central Florida reefers who use LED lighting is somewhere between .648 and .752.

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We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752 from mean.

The correct practical interpretation is: "We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752." This means that based on the sample of 700 experienced reefers, we can estimate with 95% confidence that the true proportion of all reefers in central Florida who use LED lighting is likely to be between .648 and .752.

This confidence interval was constructed using sampling techniques, and in repeated sampling, 95% of the intervals created would contain the population mean.
We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752.

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Answer:

$525

Step-by-step explanation:

Jackie starts with $500, and the interest rate is 5% per year.

This means that, after one year, Jackie will have accumulated 5% interest with the $500 she put into the savings account.

Now, we can find 5% of $500 by converting 5% to its fraction form, which is 5/100. 5% of a value means that you need to multiply the fraction (or decimal) by the said value. So, we have:

[tex]\frac{5}{100}[/tex] · 500 =

[tex]\frac{2500}{100}[/tex] =

25

Therefore, the amount of interest she has accumulated in one year is $25. Combined with the money in her savings account, she has $525, since $500 + $25 = $525.

Answer:

Step-by-step explanation:

domain is -infinity to positive infinity range is -3 to infinity. Increasing from -3 to infinity and decreasing from - infinity to -3 and it’s minimum