Answers
The function [tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.
The given table is
Days After Number of
Release Date Games sold
0 1024
1 512
2 256
3 128
Here, the common ratio = 512/1024
= 1/2
The formula to find nth term of the geometric sequence is aₙ=arⁿ⁻¹. Where, a = first term of the sequence, r= common ratio and n = number of terms.
Here, [tex]G(t)= 1024(0.5)^{t-1[/tex]
Therefore, the function [tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.
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Related Questions
From the observation deck of a skyscraper, Morgan measures a 67^{\circ}
∘
angle of depression to a ship in the harbor below. If the observation deck is 955 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.
Answers
The Horizontal distance from the base of the skyscraper to the ship is approximately 403.81 feet.
We can use trigonometry and the concept of angles of depression. We can consider the height of the observation deck as the opposite side and the horizontal distance to the ship as the adjacent side of a right triangle.
Given that the angle of depression is 67 degrees and the height of the observation deck is 955 feet, we want to find the horizontal distance (adjacent side).
Using the trigonometric function tangent, we can set up the following equation:
tan(67°) = opposite/adjacent
tan(67°) = 955/adjacent
To find the value of the adjacent side (horizontal distance), we can rearrange the equation:
adjacent = 955/tan(67°)
Using a calculator, we can evaluate the tangent of 67 degrees:
tan(67°) ≈ 2.3693
Now we can substitute this value into the equation:
adjacent = 955/2.3693
adjacent ≈ 403.81
Therefore, the horizontal distance from the base of the skyscraper to the ship is approximately 403.81 feet.
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I need help bro how do you find the median, perp bisector, altitude, and angle bisector of a triangle? I need to know this for my final
Answers
You can determine the median of a triangle by looking out for the point that is 2/3 of the distance tht connects from the vertices, to midpoint and oposite sides.
The perpendicular bisector is determined by measuring the point that is equidistant from the segment.
How to find the altitude and angle bisectorThe altitude of a triangle can be found by measiring the height of the triangle's extension that could be inside or outside the triangle. In obtsue triangles, this altitude is commonly found outside the triangle.
Also, the angle bisector of a triangle is the point that is equidistant from the angles sides. These descriptions can help in analyzing a trinagle.
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An ethical hacker, also referred to as a white hat hacker, is an information security expert who systematically attempts to penetrate a computer system, network, application or other computing resource on behalf of its owners. The purpose of ethical hacking is to evaluate the security of and identify vulnerabilities in systems, networks or system infrastructure. It includes finding and attempting to exploit any vulnerabilities to determine whether unauthorized access or other malicious activities are possible.
An ethical hacker is required to randomly guess the correct pin code that consists of the number 0 through 9 that must be entered in the correct order to access a company system.
1. What is the probability that the ethical hacker will guess the pin code correctly on the first try?
2. There are many variations of this guess. Assuming the primary variation allows the ethical hacker to guess correctly if the four-digit in the number are selected in any order as long as they are the same four digits as set by the IT security of the company.
For example, if the ethical hacker picks four digits making the number 2376, then the he will guest it right if 2376, 3726, 6327, 7632, and so forth, are entered. Consider the following four different versions of his presumptions.
(a) All four digits are unique (e.g. 1234)
(b) Exactly one of the digits appears twice (e.g. 2334, 8185)
(c) Two digits each appear twice (e.g. 1212, 8855)
(d) One digit appears three times (e.g. 2226, 8188)
Find the probability that the ethical hacker will successfully guess the accurate pin code in the first try for each of these four situations.
Show the necessary steps and explanation for the four presumptions stated above.
Answers
Answer: What is the probability that the ethical hacker will guess the pin code correctly on the first try?
Since the pin code consists of 10 possible digits (0 through 9), the probability of guessing the correct pin code on the first try is 1 in 10. This is because there is only one correct pin code out of the 10 possible options.
Therefore, the probability is 1/10 or 0.1 (or 10%).
Calculating the probability for each of the four situations:
(a) All four digits are unique (e.g., 1234):
In this case, there are 10 options for the first digit, 9 options for the second digit (since it can't be the same as the first), 8 options for the third digit, and 7 options for the fourth digit. The total number of possible combinations is given by:
10 × 9 × 8 × 7 = 5040
So, there are 5040 possible four-digit combinations when all digits are unique.
The probability of guessing the correct pin code on the first try in this situation is 1 in 5040, or 1/5040.
(b) Exactly one of the digits appears twice (e.g., 2334, 8185):
In this case, we have two scenarios to consider:
Scenario 1: The repeated digit is the first digit:
The first digit can be chosen in 10 ways, the second digit (repeated) can be chosen in 9 ways, and the remaining two distinct digits can be chosen in 8 and 7 ways, respectively. So, the total number of possible combinations is:
10 × 9 × 8 × 7 = 5040
Scenario 2: The repeated digit is not the first digit:
The first digit can be chosen in 9 ways (excluding the repeated digit), the repeated digit can be chosen in 10 ways, and the remaining two distinct digits can be chosen in 8 and 7 ways, respectively. So, the total number of possible combinations is:
9 × 10 × 8 × 7 = 5040
Combining both scenarios, we get a total of 2 × 5040 = 10080 possible combinations when exactly one of the digits appears twice.
The probability of guessing the correct pin code on the first try in this situation is 1 in 10080, or 1/10080.
(c) Two digits each appear twice (e.g., 1212, 8855):
In this case, there are two scenarios to consider:
Scenario 1: The two pairs of digits are different:
The first pair of digits can be chosen in 10 ways, the second pair of digits can be chosen in 9 ways, and the order of the pairs can be switched. So, the total number of possible combinations is:
10 × 9 × 2 = 180
Scenario 2: The two pairs of digits are the same:
The pair of digits can be chosen in 10 ways, and the order of the digits can be switched. So, the total number of possible combinations is:
10 × 1 = 10
Combining both scenarios, we get a total of 180 + 10 = 190 possible combinations when two digits each appear twice.
The probability of guessing the correct pin code on the first try in this situation is 1 in 190, or 1/190.
(d) One digit appears three times (e.g., 2226, 8188):
In this case, there are two scenarios to consider:
Scenario 1: The repeated digit is the first digit:
The first digit can be chosen in 10 ways, and the remaining two distinct digits can be chosen in 9 and 8 ways, respectively. So, the total number of possible combinations is:
10 × 9 × 8 = 720
Scenario 2: The repeated digit is not the first digit:
The first digit can be chosen in 9 ways (excluding the repeated digit), and the repeated digit can be chosen in 10 ways. The remaining distinct digit can be chosen in 8 ways. So, the total number of possible combinations is:
9 × 10 × 8 = 720
Combining both scenarios, we get a total of 2 × 720 = 1440 possible combinations when one digit appears three times.
The probability of guessing the correct pin code on the first try in this situation is 1 in 1440, or 1/1440.
To summarize, the probabilities for each of the four situations are:
(a) All four digits are unique: 1/5040
(b) Exactly one of the digits appears twice: 1/10080
(c) Two digits each appear twice: 1/190
(d) One digit appears three times: 1/1440
Which graph represents the solution set to the system of inequalities?
{ Y ≤ 1/4X-2
Y ≥ −54X+2
ANSWER Down Below
Answers
The graph of the system of inequalities:
y ≤ (1/4)*x - 2
y ≥ −(5/4)x +2
Is in the image at the end.
Which is the graph of the system of inequalities?Here we have the system of inequalities:
y ≤ (1/4)*x - 2
y ≥ −(5/4)x +2
To graph this, we just need to graph both of the linear equations, and we need to shade the region below the first line (the one with positive slope) and the region above the second line, the one with negative slope.
Then the graph of the system of inequalities is the graph you can see in the image at the end of the answer.
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Multiplying polynomials (7x - 5)(6x - 4)
Answers
The product of (7x - 5)(6x - 4) is 42x^2 - 58x + 20.
First, distribute the first term of the first polynomial (7x) to each term in the second polynomial (6x - 4):
7x × 6x = 42x²
7x × (-4) = -28x
Next, distribute the second term of the first polynomial (-5) to each term in the second polynomial (6x - 4):
-5 × 6x = -30x
-5 × (-4) = 20
Now, combine the like terms:
42x² - 28x - 30x + 20
Simplify the expression:
42x² - 58x + 20
Therefore, the product of (7x - 5)(6x - 4) is 42x^2 - 58x + 20.
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Describe the transformations of each equation
Answers
The required answer are :
6. The transformation from the graph of f to the graph of r in equation (6) involves compressing the graph horizontally by a factor of 5/2.
7. The transformation from the graph of f to the graph of r in equation (7) involves stretching the graph vertically by a factor of 6.
8. The transformation from the graph of f to the graph of r in equation (8) involves shifting the graph horizontally to the right by 3 units.
9. The transformation from the graph of f to the graph of r in equation (9) involves compressing the graph horizontally by a factor of 4/3.
10. The transformation from the graph of f to the graph of r in equation (10) involves shrinking the graph vertically by a factor of 1/2.
11. The transformation from the graph of f to the graph of r in equation (11) involves shifting the graph vertically upward by 3 units.
In formula form: r(x) = f(2/5x)
This transformation causes the graph of r to become narrower compared to the graph of f, as it is compressed horizontally. The rate at which x-values change is increased, resulting in a steeper slope. The overall shape and direction of the graph remain the same, but it is narrower and more compact.
Therefore, the transformation from the graph of f to the graph of r in equation (6) involves compressing the graph horizontally by a factor of 5/2. This means that every x-coordinate in the graph of f is multiplied by 2/5 to obtain the corresponding x-coordinate in the graph of r. The vertical positioning of the graph remains unchanged.
In formula form: r(x) = 6f(x)
This transformation causes the graph of r to become taller compared to the graph of f, as it is stretched vertically. The rate at which y-values change is increased, resulting in a steeper slope. The overall shape and direction of the graph remain the same, but it is taller and more elongated.
Therefore, the transformation from the graph of f to the graph of r in equation (7) involves stretching the graph vertically by a factor of 6. This means that every y-coordinate in the graph of f is multiplied by 6 to obtain the corresponding y-coordinate in the graph of r. The horizontal positioning of the graph remains unchanged.
In formula form: g(x) = f(x - 3)
This transformation causes the entire graph of f to shift to the right by 3 units. Every point on the graph of f moves horizontally to the right, maintaining the same vertical position. The overall shape and slope of the graph remain the same, but it is shifted to the right.
Therefore, the transformation from the graph of f to the graph of r in equation (8) involves shifting the graph horizontally to the right by 3 units. This means that each x-coordinate in the graph of f is increased by 3 to obtain the corresponding x-coordinate in the graph of r. The vertical positioning of the graph remains unchanged.
In formula form: g(x) = f(4/3x)
This transformation causes the graph of r to become narrower compared to the graph of f, as it is compressed horizontally. The rate at which x-values change is increased, resulting in a steeper slope. The overall shape and direction of the graph remain the same, but it is narrower and more compact.
Therefore, the transformation from the graph of f to the graph of r in equation (9) involves compressing the graph horizontally by a factor of 4/3. This means that every x-coordinate in the graph of f is multiplied by 4/3 to obtain the corresponding x-coordinate in the graph of r. The vertical positioning of the graph remains unchanged.
In formula form: g(x) = 1/2 f(x)
This transformation causes the graph of r to become shorter compared to the graph of f, as it is vertically shrunk. The rate at which y-values change is decreased, resulting in a flatter slope. The overall shape and direction of the graph remain the same, but it is shorter and more compact.
The transformation from the graph of f to the graph of r in equation (10) involves shrinking the graph vertically by a factor of 1/2. This means that every y-coordinate in the graph of f is multiplied by 1/2 to obtain the corresponding y-coordinate in the graph of r. The horizontal positioning of the graph remains unchanged.
In formula form: g(x) = f(x) + 3
This transformation causes the entire graph of f to shift upward by 3 units. Every point on the graph of f moves vertically upward, maintaining the same horizontal position. The overall shape and slope of the graph remain the same, but it is shifted upward.
The transformation from the graph of f to the graph of r in equation (11) involves shifting the graph vertically upward by 3 units. This means that every y-coordinate in the graph of f is increased by 3 to obtain the corresponding y-coordinate in the graph of r. The horizontal positioning of the graph remains unchanged.
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Find the values of x and y with the answers in simplest radical form
Answers
The values of x and y in simplest radical form are :
5) x = 3 and y = 3√3
6) x = 5√3 and y = 10√3
7) x = 21 and y = 14√3
Given are three right angled triangles, whose angles are 30° - 60° - 90°.
The measures of sides for a 30° - 60° - 90° triangle is in the ratio 1 :√3 :2.
That is if length of the shorter leg which is the side opposite to 30° is k, then the length of the longer leg, which is the side opposite 60° will be √3k and the length of the hypotenuse, which is the side opposite to 90° will be 2k.
5) Using the above fact, here,
2k = 6
⇒ k = 6/2 = 3
So, x = 3 and y = 3√3
6) √3 k = 15
k = 15 /√3 = 5√3
So, x = 5√3 and y = 2 × 5√3 = 10√3
7) k = 7√3
So, x = √3 × 7√3 = 21
y = 2 × 7√3 = 14√3
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Two car services charge different rates. A charges .60 per mile plus 3.00initial charge B charges .75 per mile mile traveled . the situation is modeled bu this system where x is the number of miles traveled and y is the charge for that distance ,in cents. How many miles must each car travel for the charges to be equal and ehat is the charge for that distance
Answers
The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.
To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.
Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:
For car service A: y_A = 0.60x + 300 (in cents)
For car service B: y_B = 0.75x (in cents)
To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:
0.60x + 300 = 0.75x
Subtracting 0.60x from both sides:
300 = 0.15x
Dividing both sides by 0.15:
x = 300 / 0.15
x = 2000
Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:
y_A = 0.60(2000) + 300
y_A = 1200 + 300
y_A = 1500 cents or $15.00
So, when each car travels 2000 miles, the charges will be equal at $15.00.
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Copy the axes below.
By first filling the table for y=x+4, draw the graph on your axes.
Answers
The complete table for the function are
x -2 -1 1 3
y 2 3 5 7
The graph is added as an attachment
How to complete the missing parts of the table for the function.From the question, we have the following parameters that can be used in our computation:
The function equation and the incomplete table of values
This is given as
y = x + 4
From the table, the missing values are at
x = -2, x = -1, 1 and x = 3
So, we have
y = -2 + 4 = 2
y = -1 + 4 = 3
y = 1 + 4 = 5
y = 3 + 4 = 7
The graph is added as an attachment
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If you spin the spinner 90 times, what is the best prediction possible for the number of times
it will not land on yellow?
times
Submit
Answers
Answer:
Assuming the spinner has 6 equal sectors of different colors, and yellow is only one of those colors, we can say that the probability of the spinner not landing on yellow is 5/6 or approximately 0.8333.
To predict the number of times the spinner will not land on yellow out of 90 spins, we can multiply the probability by the total number of spins:
0.8333 x 90 = 74.997 or approximately 75
Therefore, the best prediction possible for the number of times the spinner will not land on yellow out of 90 spins is 75 times.
Find the value of the permutation.
P(5,0)
P(5,0)= (Simplify your answer.)
www
Answers
The value of the permutation P(5,0) is 1.
To find the value of the permutation P(5,0), we can use the formula:
P(n, r) = n! / (n - r)!
In this case, we have n = 5 and r = 0.
Substituting these values into the formula, we get:
P(5,0) = 5! / (5 - 0)!
Since any number factorial is equal to 1, we have:
P(5,0) = 5! / 5!
Simplifying further:
P(5,0) = 1
Therefore, the value of the permutation P(5,0) is 1.
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What is the volume of a square pyramid with base edges of 18 cm and a slant height of 15 cm?
Answers
Answer:
the volume of the square pyramid is 2430 cubic cm
Answer:
1296 cm³
Step-by-step explanation:
V = a² x [√s²- (a/2)²] / 3
a = 18 cm
s = 15 cm
V = 18² x [√15²-(18/2)²] / 3 = 18² x [√225-81] / 3
V = 324 x (√144/3) = 1296 cm³
Cylindrical solid has a circumference of 132cm,height is 30cm.what is the area of the solid
Answers
Step-by-step explanation:
Cylinder LATERAL S.A. = circ X Height = 132 cm X 30 cm = 3960 cm^2
PLUS the two ends = two X pi r^2
the circumference = pi * d = 132 cm
then diameter = 132 / pi then radius = 1/2 132 / pi = 66/ pi
so end areas : two * pi (66/ pi)^2 = 2773.1
TOTAL = 3960 + 2773.1 = 6733.1 cm^2
Given below are lease terms at the local dealership. What is the total cash due at signing?
Terms:
Length of lease: 30 months
MSRP of the car $15,500
• Purchase value of the car after lease: $9900
Down payment $2500
Monthly payment $425
-Security deposit $375
Acustion fee $500
A. 375
B. 3375
C. 3800 (✅️)
D. 3400
Answers
Given:
Down payment: $2500
Security deposit: $375
Acquisition fee: $500
Total cash due at signing:
$2500 + $375 + $500 = $3375
Therefore, the correct answer is B. $3375.
Help with this question pls?
Answers
The image of point A after the reflection is A'(3, -4).
The image of point B after the reflection is B'(2, -3).
To reflect a point in the x-axis, we keep the y-coordinate the same and change the sign of the x-coordinate.
For point A(3, 4):
After reflecting point A in the x-axis, the y-coordinate remains the same (4), and the sign of the x-coordinate changes.
Therefore, the image of point A after the reflection is A'(3, -4).
To reflect a point in the y-axis, we keep the x-coordinate the same and change the sign of the y-coordinate.
For point B(-2, -3):
After reflecting point B in the y-axis, the x-coordinate remains the same (-2), and the sign of the y-coordinate changes.
Therefore, the image of point B after the reflection is B'(2, -3).
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A five question multiple choice quiz has five choices for each answer. Use the random number table provided, with 0’s representing incorrect answers, and 1’s representing correct answers to answer the following question: What is the experimental probability of correctly guessing at random exactly one correct answer?
Answers
The total number of possible outcomes is the number of rows in the table, which depends on the size of the table.
To determine the experimental probability of correctly guessing exactly one correct answer out of five choices, we can utilize the random number table provided, where 0's represent incorrect answers and 1's represent correct answers.
Since we have five choices for each answer, we will focus on a single row of the random number table, considering five consecutive values.
Let's assume we have randomly selected a row from the table, and the numbers in that row are as follows:
0 1 0 1 0
In this case, the second and fourth answers are correct (represented by 1's), while the remaining three choices are incorrect (represented by 0's).
To calculate the experimental probability of exactly one correct answer, we need to determine the number of favorable outcomes (i.e., rows with exactly one 1) and divide it by the total number of possible outcomes (which is equal to the number of rows in the table).
Looking at the table, we can see that there are several possible rows with exactly one 1, such as:
0 1 0 0 0
0 0 0 1 0
0 0 0 0 1
Let's assume there are 'n' favorable outcomes. In this case, 'n' is equal to 3.
The total number of possible outcomes is the number of rows in the table, which depends on the size of the table. Without the specific size of the table, we cannot provide an accurate value.
To calculate the experimental probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Experimental probability = n / Total number of possible outcomes
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The average fourth grader is about three times as tall as the average newborn baby. If babies are on average 45cm 7mm when they are born, What is the height of the average fourth grader?
Answers
The height of the average fourth grader is 135 cm 21 mm
How to determine the height of the average fourth grader?From the question, we have the following parameters that can be used in our computation:
Birth age = 45 cm 7 mm
Average fourth grader = three times as tall
using the above as a guide, we have the following:
Average fourth grader = 3 * Birth age
So, we have
Average fourth grader = 3 * 45 cm 7 mm
Evaluate
Average fourth grader = 135 cm 21 mm
Hence, the height of the average fourth grader is 135 cm 21 mm
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100 Points! Geometry question. Photo attached. Determine whether each pair or figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning. Please show as much work as possible. Thank you!
Answers
The pair of figures are similar because:
• Both figures are parallelograms
• All sides are congruent.
• Scale factor 1: 2.5
How to identify the similarity statement?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The pair of figures are similar because:
• Both figures are parallelograms
• All sides are congruent
• Angles W and Y are congruent with angles P and R
• Angles X and Z are congruent with angles S and Q
• Scale factor 1 : 2.5
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The equation T^2=A^3 shows the relationship between a planets orbital period, T, and the planets mean distance from the sun, A in astronomical units, AU. If planet y is twice the mean distance from the sun as planet x. by what fsctor is the orbital period increased?
Answers
Answer:
2 * A^(3/2).
Step-by-step explanation:
Given that planet y is twice the mean distance from the sun as planet x, we can denote the mean distance of planet x as "A" and the mean distance of planet y as "2A".
The equation T^2 = A^3 represents the relationship between the orbital period (T) and the mean distance from the sun (A) for a planet.
Let's compare the orbital periods of planet x and planet y using the equation:
For planet x:
T_x^2 = A^3
For planet y:
T_y^2 = (2A)^3 = 8A^3
To find the factor by which the orbital period is increased from planet x to planet y, we can take the square root of both sides of the equation for planet y:
T_y = √(8A^3)
Simplifying the square root:
T_y = √(2^3 * A^3)
= √(2^3) * √(A^3)
= 2 * A^(3/2)
Now, we can express the ratio of the orbital periods as:
T_y / T_x = (2 * A^(3/2)) / T_x
As we can see, the orbital period of planet y is increased by a factor of 2 * A^(3/2) compared to the orbital period of planet x.
Therefore, the factor by which the orbital period is increased from planet x to planet y depends on the value of A (the mean distance from the sun of planet x), specifically, it is 2 * A^(3/2).
Write the quadratic equation in standard form that corresponds to the graph shown below.
Answers
The quadratic equation shown in the graph is:
y = x² + 2x - 8
How to write the quadratic equation?Here we want to find the graph of the given quadratic equation, where we only know the zeros of it.
Remember that if a quadratic equation has the zeros:
x = a
x = b
Then we can write it as:
y = (x - a)*(x - b)
Here the zeros are:
x = -4
x = 2
Then we can write:
y = (x + 4)*(x - 2)
Expanding that we will get the standard form:
y = x² + 4x - 2x - 8
y = x² + 2x - 8
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A presidential candidate plans to begin her campaign by visiting the capitals and three of 43 states. What is the probability that she selects the route of three specific capitals
Answers
The probability that she selects the route of three specific capitals is 3/43
What is the probability that she selects the route of three specific capitalsFrom the question, we have the following parameters that can be used in our computation:
States = 43
Capitals = 3
The probability is then calculated as
P = Capitals/States
substitute the known values in the above equation, so, we have the following representation
P = 3/43
Hence, the probability is 3/43
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helppp!! someone help me asappp
Answers
Answer:
[(5 ± √(29)) ÷ 2]
Step-by-step explanation:
x = [(-b ± √(b² - 4ac)) ÷ 2a]
= [(-(-5) ± √((-5)² - 4(1)(-1))) ÷ 2(1)]
= [(5 ± √(25 + 4)) ÷ 2]
= [(5 ± √(29)) ÷ 2]
please answer asap!!!!!!!!
Answers
hope this helps :)
After lunch, you and your friends decide to head to a local theme park for some afternoon fun in the sun. You must choose between the three theme parks shown below! Use the table, graphs, and equation to answer the questions that follow.
Answers
Based on the data, we can infer that the park with the highest fee is Coaster City.
How to find the value of each park?To find the value of each park we must take into account the different tables that show the value of each park. In this case we must find the unit value of each park as follows:
Park 1:
10 / 2 = $5Park 2:
y = 5(1) + 7.50and = $12.5Park 3:
40 / 10 = $4In accordance with the above, we can infer that the 2 Coaster City park is the one with the highest rate.
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A pencil box has dimensions of 6 1/2 in 3 1/2 in and one one over 2 in respectively approximately how many cubes with the side length of 1/2 inches will be needed to fill the prism
Answers
Approximately 273 cubes with a side length of 1/2 inch will be needed to fill the prism.
To determine the number of cubes with a side length of 1/2 inch needed to fill the prism, we need to calculate the volume of the prism and divide it by the volume of a single cube.
The given dimensions of the pencil box are:
Length: 6 1/2 inches
Width: 3 1/2 inches
Height: 1 1/2 inches
To find the volume of the prism, we multiply the length, width, and height:
Volume of the prism = Length [tex]\times[/tex] Width [tex]\times[/tex] Height
[tex]= (6 1/2) \times (3 1/2) \times (1 1/2)[/tex]
First, we convert the mixed numbers to improper fractions:
[tex]6 1/2 = (2 \times 6 + 1) / 2 = 13/2[/tex]
[tex]3 1/2 = (2 \times 3 + 1) / 2 = 7/2[/tex]
[tex]1 1/2 = (2 \times 1 + 1) / 2 = 3/2[/tex]
Now we substitute the values into the formula:
Volume of the prism [tex]= (13/2) \times (7/2) \times (3/2)[/tex]
[tex]= (13 \times 7 \times 3) / (2 \times 2 \times 2)[/tex]
= 273 / 8
≈ 34.125 cubic inches.
Next, we calculate the volume of a single cube with a side length of 1/2 inch:
Volume of a cube = Side length [tex]\times[/tex] Side length [tex]\times[/tex] Side length
[tex]= (1/2) \times (1/2) \times (1/2)[/tex]
= 1/8
To find the number of cubes needed to fill the prism, we divide the volume of the prism by the volume of a single cube:
Number of cubes = Volume of the prism / Volume of a single cube
= (273 / 8) / (1/8)
= 273
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PLEASE HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The distance across the stream is 198 m.
We have,
ΔABC and ΔEBD are similar.
This means,
Corresponding sides ratios are the same.
Now,
AC/ED = AB/BE
Substituting the values.
x/360 = 220/400
x = 220/400 x 360
x = 22/40 x 360
x = 22 x 9
x = 198
Thus,
The distance across the stream is 198 m.
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Triangle ABC, with vertices A(-9,-8), B(-2,-9), and C(-8,-5), is drawn inside a rectangle. What is the area, in square units, of triangle ABC?
Answers
The area of triangle ABC is 19 square units.
To find the area of a triangle, we can use different formulas depending on the information available. Since we have the coordinates of the vertices A(-9, -8), B(-2, -9), and C(-8, -5), we can use the Shoelace Formula (also known as the Gauss's area formula) to calculate the area of the triangle.
The Shoelace Formula states that if the coordinates of the vertices of a triangle are (x1, y1), (x2, y2), and (x3, y3), then the area (A) of the triangle can be calculated as:
Area = 0.5 * |(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))|
Using the coordinates of the vertices A(-9, -8), B(-2, -9), and C(-8, -5), we can substitute these values into the formula to calculate the area.
Let's calculate step by step:
x1 = -9
y1 = -8
x2 = -2
y2 = -9
x3 = -8
y3 = -5
Area = 0.5 * |(-9 * (-9 - (-5)) + (-2) * (-5 - (-8)) + (-8) * ((-8) - (-9)))|
Area = 0.5 * |(-9 * (-4) + (-2) * (3) + (-8) * (-1))|
Area = 0.5 * |(36 + (-6) + 8)|
Area = 0.5 * |(38)|
Area = 0.5 * 38
Area = 19
Therefore, the area of triangle ABC is 19 square units.
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Find the maximum for the profit function,
P = 2x+10y
subject to the following constraints.
4x + 2y ≤ 5
-3x+y 2-2
X>0
(y ≥0
4x + 2y ≤ 5
-3x + y 2 -2
Round your answer to the nearest cent (hundredth).
Answers
Answer:
The maximum value of the profit function occurs at the corner point with the highest value, which is P2 = 25.
Therefore, the maximum profit is $25.
Step-by-step explanation:
Please answer the attached question
Answers
Answer:
∠ DFG = 48°
Step-by-step explanation:
the central angle is equal to the measure of the arc that subtends it.
since EOG is the diameter of the circle with central angle of 180° , then
arc EG = 180°
the inscribed angle EGD is half the measure of the arc ED that subtends it, so
arc ED = 2 × ∠ EGD = 2 × 42° = 84° , then
ED + DG = EG , that is
84° + DG = 180° ( subtract 84° from both sides )
DG = 96°
Then
∠ DFG = [tex]\frac{1}{2}[/tex] × EG = [tex]\frac{1}{2}[/tex] × 96° = 48°
In the figure below, S is the center of the circle. Suppose that JK = 20, LM = 3x + 2, SN = 12, and SP = 12. Find the
following.
Answers
The values from figure is,
x = 2
NS = 3.5
We have to given that,
In the figure below, S is the center of the circle.
And, Suppose that JK = 16, MP = 8, LP = 2x + 4, and SP = 3.5.
Now, We know that,
By figure,
MP = LP
Substitute the given values,
8 = 2x + 4
8 - 4 = 2x
4 = 2x
x = 4/2
x = 2
Hence, We get;
LM = MP + LP
LM = 8 + (2x + 4)
LM = 8 + 2 x 2 + 4
LM = 8 + 4 + 4
LM = 16
Since, We have JK = 16
Hence, We get;
NS = SP
This gives,
NS = 3.5
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