The first, second and third terms of a geometric progression are the first, fourth and tenth terms, respectively,
of an arithmetic progression. Given that the first term in each progression is 12 and the common ratio of the geometric progression is r, where r # 1, find:
a) the value of r
b) the sixth term of each progression

There are 20 ways to choose 2 letters from the set A, B, C, D, and E if the order of the choices is relevant

If the order of the choices is relevant, we are looking for the number of permutations of 2 letters chosen from a set of 5 letters. We can use the permutation formula to calculate this:

nPr = n! / (n - r)!

where n is the total number of items in the set (5 letters in this case), and r is the number of items we want to choose (2 letters in this case).

nPr = 5! / (5 - 2)!

nPr = 5! / 3!

nPr = 5 x 4 x 3 x 2 x 1 / (3 x 2 x 1)

Divide the numbers

nPr = 20

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Answer: this is true

Step-by-step explanation:

The value of y is 9

Perimeter is the distance around the edge of a shape. Learn how to find the perimeter by adding up the side lengths of various shapes.

Therefore, the perimeter of a rectangle can be expressed as:

P = 2(l+b)

l = 4y

b = 3y+3

132 = 2(4y+3y+3)

132 = 2( 7y+3)

132 = 14y +6

14y = 132 -6

14y = 126

divide both sides by 14

y = 126/14

y = 9

therefore the value of y is 9

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The value of y in the rectangle shown is: y = 7.

The perimeter of a rectangle = 2(length + width)

Given the following as shown in the image attached below:

Length of rectangle = 5y + 3

Width of rectangle = 4y

Perimeter = 132 units

Plug in the values:

132 = 2(5y + 3 + 4y)

Solve for y:

132 = 2(9y + 3)

132 = 18y + 6

132 - 6 = 18y

126 = 18y

126/18 = y

7 = y

y = 7

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A chi-square distribution table is a table that lists critical values for the chi-square distribution.

The chi-square distribution is a probability distribution that is used in statistical hypothesis testing to test whether a set of observed data is consistent with a specified theoretical distribution.

The table is used to find the probability that the chi-square statistic computed from the data is greater than or equal to a given critical value. The critical values depend on the degrees of freedom (df), which are determined by the number of categories in the data.

The chi-square distribution table lists the critical values for various degrees of freedom and levels of significance. For each level of significance (e.g., 0.05 or 0.01),

The table provides the critical value for each degree of freedom. To use the table, you need to determine the degrees of freedom for your data and then find the appropriate critical value for the desired level of significance.

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The value of measuring mass 145 kilograms to pounds after conversion as per standard measurements  is equal to kilograms  319.7 pounds ( round off to one decimal )

Kilograms and pounds are related in standard form as given below :

1 kilograms = 2.20462 pounds ___(1)

Substitute the value 145 kilograms in (1) for the conversion into pounds form we have :

⇒ (  145 ) kilograms = ( 145 multiply to 2.20462 ) pounds

⇒ 145 kilograms = 319.67 pounds

Finally ,

145 kilograms = 319.7 pounds ( round off to one decimal )

Therefore, after conversion the given unit of mass kilograms into pounds is  145 kilograms = 319.7 pounds ( round off to one decimal ).

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There are 2 tablespoons in 1 fluid ounce. This conversion is often used in cooking and baking recipes, where ingredients are measured in ounces or tablespoons.

Fluid ounces and tablespoons are both units of volume used to measure liquids in cooking and baking recipes. One fluid ounce is equal to 29.5735 milliliters or approximately 2 tablespoons, which is equivalent to 6 teaspoons. Therefore, there are 2 tablespoons in 1 fluid ounce.

This conversion is important to know when following recipes that call for ingredients in fluid ounces or tablespoons. It allows for accurate measurement of ingredients, which is crucial for successful cooking and baking. Other common units of volume used in the kitchen include teaspoons, cups, and quarts, among others.

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MN = 17.09 cm

NMV = 16.31°

A cuboid is a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces. Cuboid is short for "like a cube." A cuboid is similar to a cube in that a cuboid can become a cube by varying the lengths of the edges or the angles between the faces.

MV = 1/2 VS = 6cm (midpoint)

NV= 1/2YV = 5cm (midpoint)

MV = [tex]\sqrt{MV^2 + UV^2} = \sqrt{6^2 + 16^2} = 17.09cm[/tex]

MN = [tex]\sqrt{MU^2 + NU^2} = \sqrt{6^2 + 16^2 + 5^2} = 17.80cm[/tex]

tanNMV= 5/17.09

= 16.31°

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The binomial probability distribution is a discrete probability distribution that describes the probabilities of two independent outcomes in an experiment. A Poisson probability distribution is a discrete distribution whereby the stochastic process x makes a difference the number of occasions that an event occurs in a given interval.

Is the result of such a laboratory activity a probability distribution?

A probability distribution consists of a table or an equation that associates each output of a random experiment with the likelihood of its event occurring. Consider the following simple experiment: we toss a coin twice. The experiment could result in the head count being equal in 2 different coin flips.

What are the two binomial distribution outcomes?

Binary Distribution

Each trial yields one of two outcomes: success or failure. The success probability, denoted by p, remains constant from trial to trial. The n trials are autonomous.

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Answer:

Step-by-step explanation:

as the driver makes 12 delivery in 3 hrs so the driver makes 12/3 delivery in 1 hr that is 4 delivery in 1 hour so he makes 5*4= 20 delivery in 5 hours

The density of water is 1 gram per milliliter, which means that 1 milliliter of water weighs 1000 milligrams (1 gram).

Milligrams (mg) and milliliters (ml) are two different units of measurement used for different purposes. Milligrams are used to measure mass or weight, while milliliters are used to measure volume or capacity.

The conversion between milligrams and milliliters depends on the density of the substance being measured. The density is a measure of the amount of mass per unit of volume.

In general, the conversion between milligrams and milliliters is not straightforward and requires knowing the density of the substance being measured. However, for liquids with a density of approximately 1 gram per milliliter, 1 milliliter is equivalent to 1000 milligrams.

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Answer: 40

Step-by-step explanation:

20% = 0.2

0.2 x 200 = 40

The volume of the composite figure would be 120 m³.

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is the composite figure as shown in the image.

We can write the volume of the image as -

V = {6 x 5 x 2} + {1/2 x 5 x 4 x 6}

V = {60 + 60}

V = 120 m³

Therefore, the volume of the composite figure would be 120 m³.

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Try using Socratic and it may help

The critical value, zα/2, that corresponds to a 87% confidence level is approximately 1.514.

The critical value, zα/2, is the z-score that cuts off an area of α/2 in the tails of the standard normal distribution. In other words, it represents the number of standard deviations away from the mean that corresponds to a particular level of confidence.

To find the critical value for a 87% confidence level, we first need to determine the area that is left in the tails of the distribution. Since the confidence level is 87%, the area in the middle of the distribution is (1 - 0.87) = 0.13. We then divide this area in half to get the area in each tail, which is 0.065.

Using a standard normal distribution table or a calculator, we can find that the z-score that cuts off an area of 0.065 in one tail is approximately 1.514. Therefore, the critical value, zα/2, is:

zα/2 = ±1.514

However, since we want to find the z-score that corresponds to the middle 87% of the distribution, we need to add the absolute value of this number to the mean of the distribution, which is 0. This gives us:

zα/2 = |1.514| = 1.514

Therefore, the critical value, zα/2, that corresponds to a 87% confidence level is approximately 1.514

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--The question is incomplete, answering to the question below--

"Find the critical value, zα/2 that corresponds to the given confidence level 87​%"

You kayak 140 feet further in 5 minutes going downstream than you do in 5 minutes going upstream.

Speed is determined by dividing the distance traveled by the time taken to travel it. It gives the distance traveled and the amount of time it took to travel that distance.

Speed is directly Proportional to Distance and Inversely proportional to Time. Hence,

Distance = Speed X Time.

Given: You paddle a kayak 168 feet up a river every two minutes.

Hence, 168/2 = 84 feet per minute.

Therefore you go up  84 feet in one minute.

You reach 84*5 = 420 feet in 5 minutes.

Given: As you paddle back down the river, you cover 56 feet every 30 seconds.

Speed is determined by distance traveled divided by time, therefore when traveling downward, 56/0.5 equals 112 feet per minute.

In one minute, you descend by 112 feet.

You descend 560 feet in 5 minutes, or 5*(112) feet.

As a result, you will move on 140 feet (560 - 420)=140 feet further .

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The number 5/8 as a decimal is 0.625

As we divide a whole into smaller parts, we get decimals. Hence, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. After the decimal point, however, when we proceed to the right, we obtain the fractional portion of the decimal number.   

An informal way to read a decimal is to first read the whole number as you would any whole number, then the decimal point as "point," and finally each individual digit of the rational part.

the decimal of 5/8 is

5÷8 = 0.625

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The expansion of (2x+3y) ∧ 6 will contain 7 terms.

The expansion of [tex](2x+3y)^6[/tex] will contain 7 terms.

To see why, consider the binomial theorem, which tells us that the expansion of [tex](a + b) ^n[/tex] will have (n+1) terms, where the first term has coefficient 1 and the last term has coefficient 1.

In the case of [tex](2x+3y)^ 6[/tex], we can think of this as the expansion of [tex](2x + 3y) ^6 as (2x) ^ 6 + 6(2x) ^ 5(3y) + 15(2x) ^ 4(3y) ^ 2 + 20(2x) ^ 3(3y) ^3 + 15(2x) ^2(3y) ^ 4 + 6(2x)(3y) ^5 + (3y) ^6.[/tex]

As we can see, there are seven terms in this expansion, each with a different combination of powers of 2x and 3y. Therefore, the expansion of [tex](2x+3y)^ 6[/tex] will have 7 terms.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or roots.

Expressions are used to represent numerical or algebraic quantities, and they can be as simple as a single number or variable, or as complex as a polynomial or rational function.

For example, the expression 2 + 3 represents the sum of 2 and 3, and the expression 3x - 7 represents the result of multiplying x by 3 and then subtracting 7.Expressions can be evaluated by following the order of operations, which tells us to perform operations in a specific order (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).

Expressions can also be simplified or manipulated using algebraic rules and properties to make them easier to work with or to solve equations involving them.

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The slope and y - intercept of the line of best fit are 1.22 and -0.09 respectively.

a.

To fill the table of the residuals, we can approach it as;

residual = food waste - number of people.

3.2 - 2 = 1.4

2.5 - 3 = -0.5

8.9 - 4 = 49

4.7 - 4 = 0.7

3.5 - 4 = -0.5

4 - 4 = 0

5.3 - 5 = 0.3

4.6 - 5 = -0.4

7.8 - 5 = 2.8

3.2 - 6 = -2.8

12 - 8 = 4

b.

The equation is given as;

y = 1.22x - 0.09

The slope of the line of best fit is 1.22

c.

The y - intercept is given as -0.99

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Answer: I’m pretty sure it’s c

Step-by-step explanation:

It should be noted that the value of the angles will be m<2= 101; m<1=79°.

It should be noted that if parallel lines are intersected by a transversal, the correspondng angles are congruent

Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°.

In this case, m2 = 180 - 79

= 101°

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To find the equation of the tangent plane to the parametric surface, we need to find the partial derivatives of x, y, and z with respect to u and v, evaluate them at the point (u, v) = (2, 1), and use them to construct the equation of the tangent plane.

The partial derivatives of x, y, and z with respect to u and v are:

∂x/∂u = 1, ∂x/∂v = 1

∂y/∂u = 10u, ∂y/∂v = 0

∂z/∂u = 1, ∂z/∂v = -1

Evaluating these partial derivatives at (u, v) = (2, 1), we get:

∂x/∂u = 1, ∂x/∂v = 1

∂y/∂u = 20, ∂y/∂v = 0

∂z/∂u = 1, ∂z/∂v = -1

So the normal vector to the tangent plane is:

N = <1, 20, 1> × <1, 0, -1> = <-20, 0, -20>

This normal vector is perpendicular to the tangent plane, so the equation of the tangent plane can be written as:

-20(x - 2) + 0(y - 5) - 20(z - 0) = 0

Simplifying this equation, we get:

-20x + 20z = -40

Dividing both sides by -20, we get:

x - z = 2

Therefore, the equation of the tangent plane to the given parametric surface at the point (2, 5, 0) is x - z = 2.

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If the boat needed to travel 15 miles there and back, while the stream only moves 5 miles per hour, it would take 3 hours to travel there and back. This means that in still water, the boat would take 6 hours to move 15 miles upstream and back.

There will be approx four teaspoons of US measurement system in 20 ml. That is the unit conversion of 20 mililitre is equals to four teaspoons.

A milliliter is a unit of volume equal to 1/1000 of a liter. It is the same as a cubic centimeter. A US teaspoon is a unit of volume in the cooking system that is equal to 1/3 of a tablespoon or 1/48 of a US cup. To calculate the value in milliliters to the corresponding value in teaspoons [US], multiply the amount in milliliters by 0.2028841362 (conversion factor). Here is the formula: Value in teaspoons [US]

= value in milliliters × 0.2028841362

Now we need to convert 20 ml to teaspoons. So using the above formula we can write the number of teaspoons in 20 ml is Value in teaspoons [US]

= value in milliliters × 0.2028841362

= 20 ml × 0.2028841362

= 4.057682724 ~ 4

Hence required value is 4 teaspoons.

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The area of the figure composed of the square and four semicircles is approximately 242.4 square units.

A semicircle is a two-dimensional geometric shape that is half of a circle. It is formed by drawing a diameter of a circle and then drawing the arc that connects the two endpoints of the diameter. The diameter divides the circle into two equal parts, each of which is a semicircle.

A semicircle has several important properties, including:

It has one straight side, which is the diameter of the circle.

The other side is curved, and it is a half-circle.

The radius of the semicircle is equal to half the diameter of the circle.

The circumference of a semicircle is half the circumference of the circle.

The area of a semicircle is half the area of the circle.

Semicircles are used in many applications of geometry and trigonometry, including in the study of angles, arcs, and circles. They are also used in architecture and engineering to design buildings, bridges, and other structures that have semicircular features.

In addition to being a geometric shape, a semicircle can also refer to a half-circle that is used as a decorative element or design motif. Semicircles are often used in art, architecture, and graphic design to create visually interesting patterns and compositions.

To find the area of the figure composed of a square and four semicircles, we need to first find the area of the square and the area of the four semicircles. Then, we can subtract the area of the four semicircles from the area of the square to get the total area of the figure.

The area of the square is simply the side length squared, so in this case it is:

Area of square = (22)^2 = 484 square units

The diameter of each semicircle is equal to the side length of the square, so the radius is half of that or 11 units. Therefore, the area of each semicircle is:

Area of semicircle = (1/2) * π * r^2 = (1/2) * π * 11^2 = 60.4 square units

Since there are four semicircles, the total area of the four semicircles is:

Total area of semicircles = 4 * Area of semicircle = 4 * 60.4 = 241.6 square units

To get the area of the entire figure, we need to subtract the area of the four semicircles from the area of the square:

Area of figure = Area of square - Total area of semicircles

Area of figure = 484 - 241.6 = 242.4 square units

Rounding this to the nearest tenth gives:

Area of figure = 242.4 (rounded to the nearest tenth)

Therefore, the area of the figure composed of the square and four semicircles is approximately 242.4 square units.

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The example of histogram is dataset of exam scores of 100 students, with scores ranging from 50 to 100

A histogram is a graphical representation of the distribution of a dataset. It is a way to visualize the frequency distribution of a set of continuous or discrete data. Here's an example of a histogram:

Suppose we have a dataset of exam scores of 100 students, with scores ranging from 50 to 100. We can create a histogram to visualize the distribution of scores. The histogram will have a vertical axis representing the frequency of scores and a horizontal axis representing the range of scores. We can divide the horizontal axis into equal intervals, called bins, and count the number of scores falling into each bin.

The histogram is shown in the figure

In this example, the histogram shows that most students scored between 70 and 80, with a few students scoring below 60 and above 90.

The histogram also shows that the distribution of scores is roughly symmetrical, with no outliers.

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The length of the hypotenuse is 8√2 units.

According to the Pythagoras theorem, we can write -

        (hypotenuse)² = (base)² + (perpendicular)²

        (h)² = (b)² + (p)²

Given is a 45 - 45 - 90 triangle with a leg length of 8.

Equal Opp. Angles Theorem -

We can write using the Pythagoras theorem as -

x² = 8² + 8²

x² = 64 + 64

x² = 128

x = √(2 x 2 x 2 x 2 x 2 x 2 x 2)

x = √(2² x 2² x 2² x 2 )

x = 8√2

Therefore, the length of the hypotenuse is 8√2 units.

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Answer:

The correct graph is D

The conversion of 26 Celsius to Fahrenheit is 78.8.

Celsius and Fahrenheit are two scales used to measure temperature.

Celsius, also known as the centigrade scale, is a temperature scale where the freezing point of water is 0 degrees Celsius and the boiling point of water is 100 degrees Celsius at standard atmospheric pressure.

To convert Celsius to Fahrenheit, you can use the following formula:

°F = (°C x 9/5) + 32

where °C is the temperature in Celsius and °F is the temperature in Fahrenheit.

Substituting the value of 26 °C in the formula, we get:

°F = (26 x 9/5) + 32

°F = (46.8) + 32

°F = 78.8

Therefore, 26°C is equivalent to 78.8°F in Fahrenheit.

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Correct Question :

What is the conversion of 26 Celsius to Fahrenheit ?

A heart-shaped mathematical curve is a cardioid (picture is attached below).

In the mathematical branch of geometry, we can use certain equations, etc. to create a heart-shaped mathematical curve which is called a cardioid. Its name has been derived from the greek word kardiá which literally translates to heart.

It can be described as a plane curve that is drawn by a point on the perimeter of a circle and this circle is rolling around a fixed circle that has a similar radius. It is also described as an epicycloid having a single cusp. The equation (a+x)^(a-x) can be used to make a cardioid.

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