Geometric probability

1. x < 20

x - 7 < 13

x < 20

2. x > -7

-3(x + 4) < 9

-3x - 12 < 9

-3x < 21

x > -7

Hope this helps!

A geometric sequence goes from one term to the next by always multiplying or dividing by the constant value except 0. The constant number multiplied (or divided) at each stage of a geometric sequence is called the common ratio (r).

We have:

[tex]a_1=\dfrac{1}{2}\\\\a_2=2\\\\a_3=8\\\\a_4=32\\\vdots[/tex]

Find the common ratio:

[tex]\boxed{r=\dfrac{a_n}{a_{n-1}}}\Rightarrow r=\dfrac{2}{\frac{1}{2}}=\dfrac{8}{2}=\dfrac{32}{8}=...\\\\\boxed{r=4}[/tex]

[tex]\boxed{a_n=a_1\cdot r^{n-1}}[/tex]

Substitute:

[tex]a_1=\dfrac{1}{2},\ r=4,\ n=8\\\\a_8=\dfrac{1}{2}\cdot4^{8-1}=\dfrac{1}{2}\cdot4^7=\dfrac{1}{2}\cdot16384\\\\\huge\boxed{a_8=8192}[/tex]

[tex]a_4=32,\ r=4\\\\a_5=a_4\cdot r\Rightarrow a_5=32\cdot4=128\\\\a_6=a_5\cdot r\Rightarrow a_6=128\cdot4=512\\\\a_7=a_6\cdot r\Rightarrow a_7=512\cdot4=2048\\\\a_8=a_7\cdot r\Rightarrow a_8=2048\cdot4=8192[/tex]

The expected value of y when x-value is 45 is 35.06

Any equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables. For example, y = 2x+3 and 2y = 4x + 9 are two-variable linear equations.

In the given question value of x is given and value of y is asked.

The given equation : y = -2.61x+152.51 Such questions can be solved by substituting the given value of variable in the equation which will help us find the unknown.

Substituting x = 45 in the given equation , we get

y = -2.61 x 45 + 152.51

y =  -117.45 + 152.51

y = 35.06

Thus the expected value of y when x-value is 45 is 35.06

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Circumference of a circle: }[/tex]

[tex]\bullet\ \large\boxed{\mathsf{2\pi r}}}\\\rightarrow\large\boxed{\textsf{Whereas, } \pi \large\textsf{ is your pi and it is approximately equal to 3.14}}\\\rightarrow\large\boxed{\textsf{ And \underline{r} is the radius of the circle.}}[/tex][tex]\huge\textbf{Area of a triangle:}[/tex]

[tex]\bullet\ \large\boxed{\mathsf{\dfrac{1}{2}bh}}\\\\\rightarrow\large\boxed{\textsf{Whereas, }\mathsf{\dfrac{1}{2}} \large\textsf{ is half your triangle, \underline{b} is your \underline{b}ase, and b is your \underline{h}eight}}[/tex]

[tex]\huge\textbf{Surface area of a rectangular prism: }[/tex]

[tex]\bullet \ \large\boxed{\textsf{2(wl + hl + hw)}}\\\rightarrow\large\boxed{\textsf{Whereas, l is your \underline{l}ength, h is your \underline{h}eight, and w is your \underline{w}idth.}}[/tex]

[tex]\huge\textbf{Volume of a rectangular prism:}[/tex]

[tex]\bullet\ \large\boxed{\textsf{whl = v}}\\\rightarrow\boxed{\large\textsf{Whereas, v is your \underline{v}olume, w is your \underline{w}idth, h is your \underline{h}eight, l is}}\\ \ \large\boxed{\textsf{your \underline{l}ength}}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

False, An exponential growth function represents a quantity that has a constant doubling time.

What does an exponential growth function represent?

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Answer: 30 cm

Step-by-step explanation:

The volume of the composite solid is 17000 cm³. To find h, we must first subtract the volume of the half cylinder from the composite volume.

From the figure, AE = MK, and so the radius of the half cylinder is 10cm. The volume of the half cylinder is thus [tex]\frac{1}{2}[/tex] the volume of a cylinder. The volume of a cylinder is πr²h. So a half cylinder is 1/2 πr²h. This gives us a volume of  [tex]\frac{1}{2} (\frac{22}{7})(10 cm)^2(28 cm) = 4400 cm^3[/tex].

Thus, the volume of the right prism is 17000cm³ - 4400cm³ = 12600cm³. Consider the cross-section ABKJ. If we multiply this by AE, we'll have the volume of the right prism.

The ABKJ is a trapezoid so it's area is [tex]\frac{1}{2}(AJ + BK) \cdot AB[/tex]. Thus the volume of the right prism is [tex]\frac{1}{2}(AJ + BK) \cdot AB \cdot AE[/tex]. This gives us [tex]\frac{1}{2}(28 + 14) \cdot h \cdot 20 = 12600[/tex], and thus h = 30 cm.

Answer:

3rd graph from the top.

Step-by-step explanation:

It can't be the top one because the kids shoulder doesn't start at the ground.

It can't be the second or fourth because it shows him not waiting in line.

Therefore it must be the 3rd!

Answer: 3rd option

Step-by-step explanation:

Because the description says that it starts not at 0(from the kid's shoulder), the 1st and 4th options are out.

2nd option is incorrect because the kid had to stand in line so the shoulder height doesn't change(unless he was picking stuff up or something)

That leaves the 3rd option.

This exercise refers to the identification of statistics that is misleading or erroneous. In this case, a circle graph and a table are involved.

A circle graph is simply a pie chart. It is used to depict information in percentages. An example is attached.

Although charts and tables are very useful descriptive and or illustrative statistics, they can be misleading.

This can happen when:

This answer is general in nature due to the limited information provided.

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Answer:

C

Step-by-step explanation:

The amount remaining out the money earned is $37.5

Given the following parameters

Amount earned by kevin = $80

If he spent $68/5 on shopping, $51/2 on food, and $22/5 for taxi, the total money spent is given as;

Total money spent = 51/2 + 68/5 + 22/5

Total money spent = 51/2 + 90/5

Total money spent = 25.5 + 18

Total money spent = 43.5

Amount remaining = 80. - 43.5

Amount remaining = 37.5

Hence the amount remaining out the money earned is $37.5

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The domain and the range of f(x) = -25x + 50 are the set of all real numbers

The function is given as:

f(x) = -25x + 50

The above function is a linear function.

All linear functions have their domain and range to be the set of all real numbers

Hence, the domain and the range of f(x) = -25x + 50 are the set of all real numbers

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Answer:

Circumference = 18.84 ft

Area = 28.26 ft squared

Step-by-step explanation:

C(circumference) = 2 x [tex]\pi[/tex] x r(radius)

radius = 1/2 circumference

1. divide circumference by two to get the radius, which would be three ft.

2. multiply the radius by pie (3.14) and then multiply that by two and you have your circumference, which is 18.84 ft

area = [tex]\pi[/tex] x r(radius)^2

1. find the radius squared, which would be 9 because 3^2 = 3 x 3 which = 9

2. multiply 9 by pie (3.14) and you get the area which =  28.26

Answer:

2,000

Step-by-step explanation:

⇒ 200/8 = 25

⇒ 25 * 80 = 2,000

Answer:

2000.

Step-by-step explanation:

8 * x = 200

x = 200/8

80x = 80 * 200/8

       = 10 *200

       = 2000.

Based on the matrices given, the true statement on matrices AB = BA is A. A⁻¹ = ¹/₃B.

If:

AB = BA = [3    0]

                 [0    3]

Then:

AB = BA = 3 [1    0]

                    [0    1]

This can be further written as:

AB = BA = 3I₂

And again as:
A (¹/₃ B) = I

This then allows us to either write this as:

A⁻¹ = ¹/₃ B

Or:

B⁻¹ = ¹/₃ A

In conclusion, option A is correct.

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The pattern {1, 3, 5, ...} is an arithmetic sequence with the following rule:

[tex]a_n = 1 + 2(n - 1)[/tex].

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

The pattern {1, 3, 5, ...} has first term and common difference given, respectively, by:

[tex]a_1 = 1, d = 2[/tex]

Hence the rule for the pattern is given by:

[tex]a_n = 1 + 2(n - 1)[/tex].

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Answer: Option (1)

Step-by-step explanation:

The slope of the line is

[tex]\frac{9-6}{4-(-4)}=\frac{3}{8}[/tex]

This eliminates all the options except for (1).

Answer:

12

Step-by-step explanation:

Diagonals of a rhombus bisect each other at right angles, so in triangle JNK, we have JK=20 and JN=16.

Using the Pythagorean theorem, it follows that KN = 12.

Answer:

xyucyxxhc9gohjpbkvicucucuc7vucuc7cucuc7cuvuv8v8

Step-by-step explanation:

q+++

The probability that he rolls a 4 and flips a head is 1/12

Probability determines odds that a random event would happen. The odds of the random event happening lie between 0 and 1.

The probability that he rolls a 4 and flips a head = (number of sides that is a 4 / total number of sides) x (number of sides that is a head / total number of sides)

(1/6) x (1/2) = 1/12

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Answer: 1/12

Step-by-step explanation:

just say the answer

The triangle congruence postulate is illustrated below

It should be noted that two triangles are congruent if they have the same shape and size.

AAS: The angle-angle-side theorem illustrates that two triangles are congruent if the two angles and a side note between the two angles are identical to that of another triangle.

SSS: This illustrates that the three sides of a triangle are congruent to the corresponding three sides of the other triangle.

ASA: This illustrates that the triangles are congruent when the two angles and the side are the same as the corresponding angles and sides of the other triangle.

SAS: When two sides and the included angle of a triangle are congruent to the corresponding sides and the included angle if a second triangle then it follows the side-angle-side theorem.

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Acceptance sampling is a statistical method used to monitor the quality of purchased parts and components. To ensure the quality of incoming parts, a purchaser or manufacturer normally samples 20 parts and allows one defect.

a) Concerned with inspection of products

b) Concerned with decision making regarding products

c) One of the oldest aspects of quality assurance

The Acceptance sampling procedure is necessarily a lot sentencing procedure. It cannot be used to estimate the lot quality or lot conformity to the standard specifications.

The acceptance sampling is used when the test is destructive, or the cost of 100% inspection is quite high, or when we need a continuously monitoring program

The Acceptance sampling procedure is used for decision making of either acceptation or rejection of a lot. It can’t be used as a lot quality estimator

As Acceptance sampling is just a lot sentencing process, it can’t estimate the quality of products in the lot. But designed experiments ensure good quality of the process output before even production

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Answer:

The second choice.

Step-by-step explanation:

The length of AC must be equal to 5, since it is horizontally five units. We can rule out the first option.

Length BC cannot be the square root of 16, since that would be exactly 4 units. BC is slanted and does not represent a completely vertical line, so it is not a whole number. We can rule out the fourth option.

Length AB cannot be a whole number, being a slanted line that crosses a total of more than four units. Option three can be ruled out.

Therefore, we are left with the second option.

Answer:

AC = 5, BC = √17, AB = √32

Explanation:

Given points: A(-3, -2), B(1, 2), C(2, -2)

Use distance between two points formula:

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

AC length:

[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2-(-3))^2 + (-2-(-2))^2} = \sqrt{25+ 0} = 5[/tex]

BC length:

[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2-1)^2 + (-2-2)^2} = \sqrt{1 + 16} = \sqrt{17}[/tex]

AB length:

[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(-3-1)^2 + (-2-2)^2} = \sqrt{16 + 16} = \sqrt{32}[/tex]

m∠X + m∠Y < 90° is true.

XYZ is a triangle.

We have to find the option that is true about △XYZ.

By angle sum property of a triangle,

The sum of all the interior angles of a triangle is always equal to 180°.

So, ∠X + ∠Y + ∠Z = 180°

Given, m∠Z > m∠X + m∠Y.

This implies that ∠Z is greater than the sum of the angles ∠X and ∠Y.

so, ∠X + ∠Y must be less than 90°.

Hence, we can say that ∠X + ∠Y < 90°

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Answer: Option 4 or D. m∠x + m∠y∠90°

Step-by-step explanation: Trust Me! It is correct on Edge!

Q: In triangle xyz, m∠z > m∠x m∠y. which must be true about △xyz?

A: D. m∠x + m∠y∠90°

By applying the concept of discriminant, the discriminant of the quadratic equation 2 · x² - 9 · x + 2 = - 1 is equal to  57.

For a quadratic equation of the form a · x² + b · x + c = 0, the discriminant is equal to d = b² - 4 · a · c. In this problem we must transform the polynomial into the canonical form and calculate the discriminant:

2 · x² - 9 · x + 2 = - 1

2 · x² - 9 · x + 3 = 0

d = (-9)² - 4 · (2) · (3)

d = 81 - 24

d = 57

By applying the concept of discriminant, the discriminant of the quadratic equation 2 · x² - 9 · x + 2 = - 1 is equal to  57.

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Considering the expression of a line, the equation for the function that is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9 is y= -58x +17.3.

A linear equation o line can be expressed in the form y = mx + b.

where

Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

In this case, the function f(x) is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9. This is:

So, the slope m can be calculated as:

[tex]m=\frac{-5.9-11.5}{0.4-0.1}[/tex]

Solving:

m= -58

Considering point 1 and the slope m, you obtain:

11.5= -58×0.1 +b

11.5= -5.8 + b

11.5 + 5.8= b

17.3= b

Finally, the equation for the function that is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9 is y= -58x +17.3.

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Answer:

38,710.

Step-by-step explanation:

This is an arithmetic series  with common difference  8 , first term a = 7 and last term L = 783.

The number of terms n = (783 - 7) / 8 + 1 = 98

Sum of 98 terms = (n/2)[a + L)

= (98/2)(7 + 783)

= 49 * 790

= 38,710.

Answer:

False.

These are not simultaneous equations.

Step-by-step explanation:

Simultaneous equations are equations involving two or more unknowns that are to have the same values in each equation. In the equations given there is only one unknown value.

Answer:

3 2/3

Step-by-step explanation:

To do this question, you would need to multiply 7 1/3 with 1/2. The answer is 3 2/3.

Answer:

3 2/3 albums

Step-by-step explanation:

Let's say that the stamp album has 12 stamps (12 is just an arbitrary number used to make calculation easier). If Linda collects half of the album, it means she has 6 stamps. If that is the case, Becky has 6 * 7 1/3 stamps. Since 7 1/3 is equivalent to 22/3, we can determine that Becky has collected 44 stamps (6*22/3). There are 12 stamps in one album, which means there are 44 stamps in 3 2/3 (11/3) albums:

[tex]\frac{12}{1}=\frac{44}{y} \\12y=44\\y=11/3[/tex]

Since the ratio of stamps to albums is constant, the calculation above demonstrates that the number of albums it takes to have 44 stamps is 3 2/3. Please note that the numbers I used are arbitrary. If you substitute 12 for a variable x, you will get the same result.

The expression is -1/6 x (-1/5) = 1/30.

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given:

negative 1 over 6 multiplied by negative 1 over 5.

As per the data,

if -1/6 is multiplied with -1/5 then the resultant value will be

=-1/6 * -1/5

= 1/5*6

=1/30

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Answer:

Answer:

1/6

Step-by-step explanation:

Solution:

The given equation is:y=x/6 -5

arranging the equation :x/6-y=5

Given,

Coefficient of x=1/6

coefficient of y=-1

So,

Slope(m)=-(Coefficient of x/coefficient of y))

= -(1/6 / -1) {minus divided by - becomes plus }

1 by 6 whole divide by 1

= 1/6 ans✓