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Isolde is stacking books. The stack of books forms a rectangular prism.



Each book is the same size. Isolde knows the area of the base of one book is 22 1/2 square inches and each book is 3/4 inch thick.

The volume of a stack of 9 books is cubic inches.

The number of outcomes that are in the sample space = 20

The number of outcomes that are in the event = 5

To calculate the probability of an event, the formula that should be used is given as follows;

Probability = possible event/sample space.

possible outcome = 5

sample space = 20

Probability = 5/20 = 1/4

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From the given dimensions, area of the figure is approximately equal to 75.8 cm².

A regular polygon is a closed shape with straight sides and equal-length edges, as well as equal angles between those sides. Examples of regular polygons include equilateral triangles, squares, and hexagons. The number of sides a regular polygon has is referred to as its order, while the measure of each interior angle of a regular polygon can be calculated using the formula (n-2) x 180/n, where n represents the number of sides.

From the image we can see that, ABHI is a square with sides 6 cm, BCDGH is a regular pentagon with sides 6 cm (BH = AI = 6 cm) and DEFG is a rectangle with length 11 cm and breadth 6 cm ( DG = AI = 6 cm).

To find the area of the figure we have to find the area of each shape and add it together.

Area of square = side × side = 6 × 6 = 36 cm²

Area of regular pentagon = [tex]\frac{1}{4} \sqrt{5(5+25)a^{2} }[/tex]

= [tex]\frac{1}{4} \sqrt{5(5+25)6^{2} }[/tex]

= [tex]\frac{1}{4} \sqrt{25 + 10*1.41*36}[/tex]

= [tex]\frac{1}{4} \sqrt{532.6 }[/tex]

≈ 5.77 cm²

Area of rectangle = 2(l + b) = 2(11 + 6) = 34 cm²

Therefore area of the figure = 36 cm² + 5.77 cm² + 34 cm² ≈ 75.8 cm².

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Answer:

3 cm

Step-by-step explanation:

because the correct answer is 3cm

Answer:

32m

Step-by-step explanation:

area= L×B

L= 10m ×2 =20m

B= 6m×2 =12m

Area= 20m + 12m = 32m

Answer:

20 3/5

Step-by-step explanation:

this is the correct result when 30 9/10 is multipled by 2/3

Answer:

141 degrees

Step-by-step explanation:

First find the value of the other interior angle that is not shown. To find it u add 108 n 33 which gives you 141

Then subtract 141 from 180 which gives u 39 degrees

After subtract 39 from 180 which gives you 141 degrees

The correct list of functions ordered from 0 ≤ x ≤ 3 is:

h(x) = sin(x) < f(x) = x^2 < g(x) = 2x + 1 < k(x) = e^x

Line connecting the interval's endpoints in order to compute the average rate of change for each function over range 0 x 3.

For f(x) = x^2, the slope between x = 0 and x = 3 is:

[tex](f(3) - f(0)) / (3 - 0) = (9 - 0) / 3 = 3[/tex]

For g(x) = 2x + 1:

[tex](g(3) - g(0)) / (3 - 0) = (7 - 1) / 3 = 2[/tex]

For h(x) = sin(x):

[tex](h(3) - h(0)) / (3 - 0) = (sin(3) - sin(0)) / 3[/tex] ≈ 0.279

For k(x) = e^x, the slope between x = 0 and x = 3 is:

[tex](k(3) - k(0)) / (3 - 0) = (e^3 - 1) / 3[/tex] ≈ 6.076

Therefore, correct list of functions ordered from least to greatest by average rate of change over the interval 0 ≤ x ≤ 3 is:

[tex]h(x) = sin(x) < f(x) = x^2 < g(x) = 2x + 1 < k(x) = e^x[/tex]

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--The complete Question is, Consider the following four functions:

f(x) = x^2

g(x) = 2x + 1

h(x) = sin(x)

k(x) = e^x

What is the correct list of functions ordered from least to greatest by average rate of change over the interval 0 ≤ x ≤ 3? --

The confidence interval for the difference in average lifespan between the two groups of children (-43, 9) years includes 0, which means that we cannot conclude with confidence that there is a significant difference between the two groups.

Since the confidence interval includes negative values, we cannot even conclude that the garlic pills were beneficial in prolonging the life of the children. It is possible that the garlic pills had no effect or even a harmful effect on the lifespan of the children.

Therefore, based on this information, we cannot conclude that garlic pills are effective in prolonging the life of children with deliops disease. Further research would be needed to determine whether garlic pills have any beneficial effects on the lifespan of these children.

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The missing angles are sides are;

We can see that we would have to first apply the cosine rule here;

[tex]a^2 = b^2 + c^2 - 2abCos A\\a^2 = (17)^2 + (19.6)^2 - 2(17 * 19.6)Cos 30\\a^2 = 673.16 - 666.4Cos 30[/tex]

a = 9.8

We can now apply the sine rule to obtain the angle B

[tex]a/Sin A = b/Sin B\\SinB = bSin A/a\\B = Sin-1 ( bSin A/a)\\B = Sin-1(17 * Sin 30/9.8)[/tex]

B = 60

Then;

C = 180 - (30 + 60)

C = 90 degrees

Thus the triangle in the problem have been solved.

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Answer:

f(x) = 2(x + 1)² + 1

Step-by-step explanation:

the equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

given

f(x) = 2x² + 4x + 3 ← factor out 2 from the first two terms

    = 2(x² + 2x) + 3

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² + 2x

f(x) = 2(x² + 2(1)x + 1 - 1) + 3

     = 2(x + 1)² - 2(1) + 3

     = 2(x + 1)² - 2 + 3

    = 2(x + 1)² + 1 ← in vertex form

To discover the t-value for testing a person parameter at the 1% level, we ought to isolate the coefficient appraise by its standard deviation and compare it to the t-distribution with suitable degrees of flexibility.

For case, to test the parameter gauge for x1, we would calculate the t-value as: t = (-3.682) / 2.630 ≈ -1.4

At that point compare this t-value to the t-distribution with 485 degrees of flexibility (which compares to the leftover degrees of opportunity), and decide on the off chance that it surpasses the basic esteem at the 1% level (which is around 2.977).

In any case, the given yield does not demonstrate which parameter appraise is being tried, so we cannot decide the comparing t-value. Hence, none of the reply choices are rectified.

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The probability that Ann picked a ball from the second box given that she selected an orange ball is 0.56 or 56% (rounded to two decimal places).

We can use Bayes' theorem to calculate the probability that Ann picked a ball from the second box given that she selected an orange ball.

Let A be the event that Ann selected an orange ball, and B be the event that Ann picked a ball from the second box. We want to find P(B|A), the probability that Ann picked a ball from the second box given that she selected an orange ball.

We know that there are two boxes, each with a probability of 1/2 of being selected. The probability of selecting an orange ball from the first box is 3/7, and the probability of selecting an orange ball from the second box is 7/11. Therefore, the probability of selecting an orange ball overall is:

P(A) = P(A|B)P(B) + P(A|B')P(B')

= (7/11)(1/2) + (3/7)(1/2)

= 25/42

Now we can use Bayes' theorem:

P(B|A) = P(A|B)P(B)/P(A)

= (7/11)(1/2)/(25/42)

= 14/25

Therefore, the probability that Ann picked a ball from the second box given that she selected an orange ball is 0.56 or 56% (rounded to two decimal places).

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Answer:

Less

Step-by-step explanation:

Look at the hundreds number in set L the numbers are greater in Set L than Set K.

The type of error that could have occurred in this scenario is a Type II error. A Type II error occurs when the null hypothesis is not rejected, even though it is false.

In this case, the null hypothesis is that the proportion of defective bulbs in the shipment is greater than or equal to 5%. By not rejecting this null hypothesis, the company is accepting the possibility that the shipment has a high proportion of defective bulbs, when in reality it does not. This can lead to significant costs for the company, such as the cost of returning the shipment or the cost of replacing defective bulbs in the future.

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A. a prism with a height of x cm and a square base with side length of x cm = option 2

B. a cylinder with a radius of x and height of cm= option 6

C. a pyramid with a height of x cm and a square base with a side length of x cm = option 3.

For statement A=

The formula for a square based prism= a²h

where a= X

h = X

Vol = x³

For statement B;

The formula for a cylinder=πr²h

where r= X, h= X

Vol= π×x³

For statement C;

The formula for a square based pyramid= 1/3a²h

a = X

H = X

Vol = 1/3 * x³

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The graph that correctly displays the data is this: C. bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44.

A graph plots values to show the relationship between two variables often depicted by the x and y axes. The correct graph to display this data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students."

The first bar should be labeled "Basketball" and go to a value of 17, the second bar should be labeled "Baseball" and go to a value of 12, the third bar should be labeled "Soccer" and go to a value of 27, and the fourth bar should be labeled "Tennis" and go to a value of 44.

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Understanding the meaning of addition and subtraction will allows us to make predictions about how changing the value of a variable will affect the value of an expression.

In mathematics, integers are a set of whole numbers that include both positive and negative numbers, as well as zero. The set of integers is denoted by the symbol Z, and it includes all the natural numbers (1, 2, 3,...), their negatives (-1, -2, -3,...), and zero (0). Integers are used in a variety of mathematical contexts, including algebra, number theory, and geometry. Integers can be used to represent many real-world situations, such as temperatures above or below zero, changes in altitude, gains or losses in money, and more. They are also used extensively in computer programming and other fields that rely heavily on mathematics.

Knowing what addition and subtraction mean allows you to understand how changing the value of a variable can affect the value of an expression.

For example, consider the expression x + 2. If x has a value of 3, then the value of the expression is 5. However, if x increases to 4, then the value of the expression increases to 6. This is because we are adding 2 to the value of x.

On the other hand, if we have the expression x - 2 and x has a value of 3, then the value of the expression is 1. If x increases to 4, then the value of the expression decreases to 2. This is because we are subtracting 2 from the value of x, so as x increases, the value of the expression decreases.

Understanding the meaning of addition and subtraction is essential to be able to manipulate expressions and variables, and it allows us to make predictions about how changing the value of a variable will affect the value of an expression.

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For a 10,000 linear feet of fencing and wants to enclose a rectangular field, the maximum area of each pasture is equals to the 2,083,333.33 square feet .

A rancher wants to enclose about 10,000 linear feet of fencing in a rectangular field. There are two equal pastures. Let, W the Width and L the Length with 3 pieces. The total length will be equal to 2W + 3L. As we know, the Area of rectangle, A = L×W ---(1)

Perimeter of rectangle = 10,000 feet, so sum of all sides of rectangle, 2W + 3L = 10000

Solve for determining value of L, 3L

= 10000 - 2W

[tex]L = \frac{ 10000 - 2W }{3}[/tex]

Substitutes for L into the first equation, A = L×W

[tex]A = W(\frac{ 10000 - 2W }{3})[/tex]

For maximum area, set the 1st derivative = 0.

differentiating above Area equation w.r.t W,[tex] A = \frac{(10000 \: W - 2W^2)}{3}[/tex]

[tex] \frac{dA}{dW} = \frac{d(\frac{10000 \: W - 2W^2}{3})}{dW}[/tex]

=> [tex]\frac { 1}{3}(10000 - 4W) = 0 [/tex]

=> W = 2500 meters

Now, using above relation, 2W + 3L= 10000

=> 5000 + 3L = 10000

=> 3L = 5000

=> L = 1667 meters

Area = 2500× 5000/3 = 4,166,666.67 sq feet. Now, maximum area of each pasture

= 4,166,666.67/2 = 2,083,333.33333 sq. feet. Hence, required value is 2,083,333.33 sq. feet.

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Based on the information, the y-intercept is (0, 6.5).

The function is increasing.

Based on the information, we can use the variable x. This will be:

0 = 6.5 + 5.25%x

-6.5 = 5.25%x

x = -6.5 / 5.25% ≈ -123.81

There's no x intercept due to the negative value which doesn't make sense in this scenario.

In order to find the y-intercept, we set x = 0 and evaluate b(x):

b(0) = 6.5 + 5.25% × 0 = 6.5

Therefore, the y-intercept is (0, 6.5).

The function b(x) is increasing since the coefficient of x is positive (5.25%). This means that as the number of engines produced (x) increases, the time it takes to manufacture the engines also increases.

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Answer:

2x²- 10x + 8

3x² - x - 4

Step-by-step explanation:

Answer:

hope this helps..........

The coordinates of the point which is an outlier would be ( 14, 13).

The correlation between the 13 British towns is Linear.

The number of hours of sunshine for the British town with the maximum of 17.4 degrees Celsius is 13 hours of sunshine.

The coordinates of the outlier would be ( 14, 13). This is because, that point on the graph is far from the other points and does not follow their correlation.

The rest of the towns seem to be increasing in the same direction so they are linear.

The number of hours of sunshine in the British town with the maximum temperature of 17.4 degrees Celsius, based on the line of best fit drawn, would be 13 hours of sunshine.

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Full question is:

The scatter graph shows the maximum temperature and the numbers of hours of sunshine in 13 British towns in one day.

A line of best fit has also been drawn.

One of the points in an outliner.

a) Write down the coordinates of this point. (1)

b) For all the other points write down the type of correlation in just one word. (1)

On the same day, in another British town, the maximum temperature was 17.4C.

c) Estimate the number of hours of sunshine in this town on this day. (2)

Answer:

The radius of the circle is 3, so

Circumference = 2(3)π = 6π = 18.84

Area = π(3^2) = 9π = 28.26

55/63 is already in its simplified form.

To simplify 55/63, we can divide both the numerator and denominator by their greatest common factor (GCF). To find the GCF of 55 and 63, we can use prime factorization:

55 = 5 × 11

63 = 3 × 3 × 7

The common factors of 55 and 63 are 1, so the GCF is 1. We can divide both the numerator and denominator by 1:

55/1/63/1

Therefore, 55/63 in simplest form is 55/63.

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Answer:

Step-by-step explanation:

36

The equation of the circle is (x - 2)²+ (y - 3)² = 169

A circle is a two-dimensional form that may be described as a collection of points that are equally spaced apart from a central fixed point. The radius of a circle is the separation between its centre and any other point on the circle. Another way to think of a circle is as the collection of all points at a certain radius from the centre.

The following is the equation for a circle with centres (a, b) and radius r:

(x - a)² + (y - b)² = r²

In this case, the center of the circle is A(2,3), and a point on the circle is B(7,15). The radius of the circle may be calculated using the distance formula:

r = √((7 - 2)² + (15 - 3)²) = √(5² + 12²) = 13

So the equation of the circle is:

(x - 2)² + (y - 3)² = 13²

(x - 2)²+ (y - 3)² = 169

Therefore, the equation of the circle is (x - 2)²+ (y - 3)² = 169

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The requried side length of the square is approximately 9.695 units.

To find the side length of a square with an area of 94 square units, we need to take the square root of the area.

a² = 94
a = √94

a ≈ 9.695

Therefore, the side length of the square is approximately 9.695 units.

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The new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:

|-3 -2 1 |

| 7 0 7 |

| 1 1 1 |

In mathematics, a translation refers to a geometric transformation that moves every point in a figure or a space by the same distance in a given direction. In other words, it involves sliding a figure or a point to a new location without changing its size, shape, or orientation.

To translate the triangle by a vector (x, y), we use the following transformation matrix:

|1 0 x|

|0 1 y|

|0 0 1|

For the given triangle with vertices at A(-1, 3), B(0, -4), and C(3, 3), let's assume we want to translate it by a vector (−2, 4). Then the transformation matrix for translation is:

|1 0 -2|

|0 1 4 |

|0 0 1 |

To apply this transformation matrix to each vertex of the triangle, we represent the vertices as column vectors and multiply them by the matrix:

| -1 | | 1 0 -2 | | -3 |

| 3 | -> | 0 1 4 | = | 7 |

| 1 | | 0 0 1 | | 1 |

| 0 | | 1 0 -2 | | -2 |

| -4 | -> | 0 1 4 | = | 0 |

| 1 | | 0 0 1 | | 1 |

| 3 | | 1 0 -2 | | 1 |

| 3 | -> | 0 1 4 | = | 7 |

| 1 | | 0 0 1 | | 1 |

So, the new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:

|-3 -2 1 |

| 7 0 7 |

| 1 1 1 |

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A function can have zero to many parameters, and it can return only one (option c).

In mathematics, a function is a rule that maps each element from one set, called the domain, to a unique element in another set, called the range.

The number of parameters a function can take determines the number of arguments required to call the function.

For instance, a function f(x) takes one parameter, and it requires one argument to be called.

On the other hand, a function g(x,y,z) takes three parameters, and it requires three arguments to be called. However, a function h() takes no parameters and does not require any argument to be called.

Hence the correct option is (c).

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