The probability that the 4th or 5th student you stop is the first to have the jumper cables is 0.2417 or about 24.17%.
how to find probability of 4th or 5th student?This is an example of a negative binomial probability problem, where we want to know the probability of obtaining a certain number of failures before obtaining a certain number of successes in a series of independent trials. In this case, the "success" is finding a student with jumper cables, and the "failure" is finding a student without jumper cables.
Let p be the probability of success (finding a student with jumper cables) on any given trial, which is 0.18 according to the problem. Let k be the number of successes we want to obtain, which is 1 in this case (since we only need to find one student with jumper cables). Let x be the number of trials it takes to obtain k successes, which is either 4 or 5 in this case.
Then, the probability of finding the first student with jumper cables on the 4th or 5th stop is:
P(X = 4 or X = 5) = P(X = 4) + P(X = 5)
We can calculate these probabilities using the negative binomial distribution formula:
[tex]P(X = x) = (x-1) choose (k-1) * p^k * (1-p)^{x-k}[/tex]
For x = 4:
[tex]P(X = 4) = (4-1) choose (1-1) * 0.18^1 * (1-0.18)^{4-1} = 0.1778[/tex]
For x = 5:
[tex]P(X = 5) = (5-1) choose (1-1) * 0.18^1 *(1-0.18)^{5-1} = 0.0639[/tex]
So, the probability of finding the first student with jumper cables on the 4th or 5th stop is:
P(X = 4 or X = 5) = 0.1778 + 0.0639 = 0.2417
Therefore, the probability that the 4th or 5th student you stop is the first to have the jumper cables is 0.2417 or about 24.17%.
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You have $20 to spend on taxi fare. The ride costs $5 plus $2.50 per
kilometer.
Write an inequality to determine the distance in kilometers, d, you can
ride for $20.
What is the maximum distance, in kilometers, you can ride for $20?
kilometers
Answer:
To determine the distance in kilometers, d, you can ride for $20, we can use the following inequality: 5 + 2.5d ≤ 20 Simplifying the inequality, we get: 2.5d ≤ 15 d ≤ 6 Therefore, the maximum distance you can ride for $20 is 6 kilometers.
In total you have $20.
Base fare of taxi is $5.
Per mile cost is $2.50.
Your total cost is where x is the number of miles. Since you're on a budget of maximum $20, the cost should be less than or equal to $20. We can write:
[tex]5+2.5x\leq 20[/tex]
To find how many miles we can write, let's solve the inequality:
[tex]5+2.5x\leq 20[/tex]
[tex]2.5x\leq 20-5[/tex]
[tex]2.5x\leq 15[/tex]
[tex]x\leq \dfrac{15}{2.5}[/tex]
[tex]x\leq 6[/tex]
This means 6 is the maximum number of miles you can ride with $20.
ANSWER: Maximum 6 miles
PLEASE ANSWER ASAP WILL MARK BRAINLIST
in the circle below what is the measure of angle ABC
Answer:
AngleABC = 30°
Step-by-step explanation:
In the diagram, the important measure you need to know to find the answer is the measure of Arc AC
Arc AC = 60°
Then you need to see where the vertex (point, corner) of the Angle ABC is. Since the vertex is ON the circle, the angle is HALF the arc.
(if the vertex was at the center, the angle and arc would be the SAME)
Since arc AC = 60°, angleABC = 30°
How much would you be willing to pay today for an investment that would return $800 each year at the end of each of the next 6 years? Assume a discount rate of 4 percent.
Answer: Approximately $4,176.19 today for an investment that returns $800 each year for 6 years
Step-by-step explanation:
To calculate the present value of an investment that returns $800 each year for 6 years at a discount rate of 4 percent, we can use the formula for the present value of an annuity:
PV = C x [(1 - (1 / (1 + r)^n)) / r]
where PV is the present value, C is the annual cash flow, r is the discount rate, and n is the number of years.
Plugging in the given values, we get:
PV = 800 x [(1 - (1 / (1 + 0.04)^6)) / 0.04]
PV = $4,176.19 (rounded to the nearest cent)
Therefore, if the discount rate is 4 percent, you would be willing to pay approximately $4,176.19 today for an investment that returns $800 each year for 6 years
100 points!!! Algebra graphing question. Describe the end behavior of the graph in each function. Photo attached. Thank you!
Answer: your originally supposed to use arrows to show end behaviors
graph one down /up
graph two down/ down
graph three up/ down
Step-by-step explanation:
pretty sure this is the answer if your asking for the end behaviors
How do you solve this?
A hemisphere over the cone with a radius of 10 cm and a height of 15 cm.
a) volume of the cone: V = 1570.8 cm³
b) volume of the hemisphere: V = 2093.33 cm³
c) voume of the entire figure : V= 3664.13 cm³
a) The formula V = (1/3)r2h, where r is the cone's radius and h is its height, determines the volume of the cone.
Substituting r = 10 cm and h = 15 cm, we get:
V = (1/3)π(10 cm)²(15 cm)
V ≈ 1570.8 cm³
The volume of the cone is approximately 1570.8 cm³.
b) The volume of the hemisphere is given by the formula V = (2/3)πr³, where r is the radius of the hemisphere. Since the hemisphere has the same radius as the cone, i.e., r = 10 cm, we get:
V = (2/3)π(10 cm)³
V = 2093.33 cm³
The volume of the hemisphere is approximately 2093.33 cm³.
c) The volume of the entire figure is the sum of the volume of the cone and the volume of the hemisphere. Adding the volumes of the two shapes, we get:
V = 1570.8 cm³ + 2093.33 cm³
V = 3664.13 cm³
The volume of the entire figure is approximately 5759.6 cm³.
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X FINANCIAL LITERACY - FIND YOUR LEVEL!
Newrow Tech Check
Donovan has a Bachelor's degree and earns an annual salary
of $55,000. He works 40 hours per week for 48 weeks per year.
His brother has a Associate degree and earns an average
salary of $43,000. He works 40 hours a week for 52 weeks.
How much greater is Donovan's hourly wage than his brother's
hourly wage? Round your answer to the nearest whole dollar.
Dοnοvan's hοurly wage than his brοther's hοurly wag wοuld be, $7.98/hοur
What is Average salary ?Average salary is the average amοunt οf mοney earned by wοrkers in a particular industry, ecοnοmy, area, etc.
Tοtal hοurs wοrked by Dοnοvan = 40 hοurs/week x 48 weeks/year = 1,920 hοurs/year
Next, we can calculate Dοnοvan's hοurly wage:
Hοurly wage οf Dοnοvan = Annual salary οf Dοnοvan / Tοtal hοurs wοrked by Dοnοvan
= $55,000 / 1,920 hοurs/year
= $28.65/hοur
Similarly, we can find the tοtal number οf hοurs that his brοther wοrks in a year:
Tοtal hοurs wοrked by Dοnοvan's brοther = 40 hοurs/week x 52 weeks/year = 2,080 hοurs/year
Hοurly wage οf Dοnοvan's brοther = Annual salary οf Dοnοvan's brοther / Tοtal hοurs wοrked by Dοnοvan's brοther
= $43,000 / 2,080 hοurs/year
= $20.67/hοur
Difference in hοurly wages = Hοurly wage οf Dοnοvan - Hοurly wage οf Dοnοvan's brοther
= $28.65/hοur - $20.67/hοur
= $7.98/hοur
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Suppose that Mars rotates on its axis once every hours. The equator lies on a circle with a diameter of miles.
(a) Find the angular speed of a point on its equator in radians per day ( hours).
(b) Find the linear speed of a point on the equator in miles per day.
Do not round any intermediate computations, and round your answer to the nearest whole number.
a) the angular speed of a point on its equator in radians per day is 6 rad/day.
b) the linear speed of a point on the equator in miles per day is 2 ×10² m.
What is angular speed?
Angular speed is defined as the rate of change of angular displacement, and it is expressed as follows: ω = θ t. where θ is the angular displacement, t is the time and ω is the angular speed.
Here, we have
Given: Suppose that Mars rotates on its axis once every hour. The equator lies on a circle with a diameter of miles.
a) The angular velocity is
W = θ / t
t = 1 day (24 h / 1 day) (3600s / 1 h) = 86400 s
w = 2π / 86400
w = 7.27 10⁻⁵ rad / s
Reduce to rad/day
w = 7.27 rad / s (3600s / 1 h) (24 h / 1 day)
w = 6.28 rad/day
w= 6 rad/day
Hence, the angular speed of a point on its equator in radians per day is 6 rad/day.
b) the linear velocity is
v = w r
Mercury radius is
r = 2.43 106 m
v = 7.27 10⁻⁵ 2.43 10⁶
v = 1.76661 10² m / s
v = 2 ×10² m
Hence, the linear speed of a point on the equator in miles per day is 2 ×10² m.
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help I can't clarify it
A young executive is going to purchase a vacation property for investment purposes. She needs to borrow $128,000.00 for 25 years at a 5.3% annual interest rate, with interest compounded monthly, and will make monthly payments of $770.82. (Round all answers to 2 decimal places.)
Create an amortization table to answer the following:
a) What is the unpaid balance after 9 months? $
b) Over the 9 months in part (a), how much total interest did she pay?
Answer:
(a) After 9 months, the unpaid balance is $125,874.09.
(b) Over the 9 months, she paid a total of $4,918.56 in interest.
To create the amortization table, we can use the formula for calculating the monthly payment of a loan:
P = (r * A) / (1 - (1 + r)^(-n))
where:
P = monthly payment
r = monthly interest rate
A = loan amount
n = total number of payments
In this case, we have:
A = $128,000.00
n = 25 years * 12 months/year = 300 months
r = 5.3% / 12 = 0.00441666667
Using the formula, we can calculate the monthly payment:
P = (0.00441666667 * $128,000.00) / (1 - (1 + 0.00441666667)^(-300))
P = $770.82
Now, we can create the amortization table:
triangle congruence maze (50 points. will report if just saying anything)
Answer:
Step-by-step explanation:
please help me i need to get these right
The length of side AC of right triangle ABC is 13. So,the option A is correct
What do you mean by term Triangle ?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted Δ triangle ABC.
We can use the trigonometric ratios of right triangle ABC to find the value of y.
We label the sides of the triangle as follows:
Side AB (opposite angle C) is the hypotenuse.
The length of side BC (opposite angle A) is 13.
Side AC (opposite angle B) is the unknown side called y.
Since angl
e A is 45 degrees, we know that the sine and cosine of angle A are equal:
sin(A) = cos(A) = 1/√2
Using the Pythagorean theorem, we can relate the lengths of the sides of a triangle:
AB² = AC² BC²
Substituting the known values, we get:
AB² = y² 169
Taking the square root of both sides gives us:
AB = √(y² 169)
Now we can use the sine ratio to relate the length of the sides:
sin(A) = opposite/hypotenuse
Substituting the known values, we get:
1/√2 = and/√(y² 169)
By cross linking and simplifying, we get:
y√2 = √(y² 169)
Squaring both sides we get:
2y² = y² 169
Subtracting y² from both sides, we get:
y² = 169/1
Taking the square root of both sides gives us:
y = ±13
Since y represents length, we can reject the negative solution and the value of y is:
y = 13
Therefore, the length of side AC of right triangle ABC is 13.
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Consider the following hypothesis test.
H0: = 20
Ha: μ ≠ 20
A sample of 167 items will be taken and the population standard deviation is 9.31.
Compute the p-value for the following if the sample means.
mean is:
a. 18.0
b. 21.8
c. 21.3
According to given information the p-value for each sample mean is:
a. 0.001 b. 0.001 c. 0.074
What is meant by p-value?
In statistics, the p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. It is used in hypothesis testing to determine the statistical significance of the results.
To compute the p-value for each sample mean, we need to first calculate the corresponding z-score using the formula:
z = (x - μ) / (σ / [tex]\sqrt{(n)[/tex])
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
a. For x = 18.0, the z-score is:
z = (18.0 - 20) / (9.31 / [tex]\sqrt{(167)[/tex]) = -3.28
Using a standard normal distribution table or calculator, we can find that the corresponding p-value is approximately 0.001.
b. For x = 21.8, the z-score is:
z = (21.8 - 20) / (9.31 / [tex]\sqrt{(167)[/tex]) = 3.28
Using a standard normal distribution table or calculator, we can find that the corresponding p-value is approximately 0.001.
c. For x = 21.3, the z-score is:
z = (21.3 - 20) / (9.31 / sqrt(167)) = 1.79
Using a standard normal distribution table or calculator, we can find that the corresponding p-value is approximately 0.074.
Therefore, sample of 167 items will be taken and the population standard deviation is 9.31 has the p-value for each sample mean is:
a. 0.001
b. 0.001
c. 0.074
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Central Park is a rectangular park in New York City. Use the provided ruler to answer the following questions. a. Find the perimeter and the area of Central Park in the scale drawing. Round your measurements for the length and the width to the nearest half centimeter to calculate your answers. The perimeter in the scale drawing is centimeters. The area in the scale drawing is square centimeters. b. Find the actual perimeter and area of Central Park. The actual perimeter is meters. The actual area is square meters.
The perimeter of scale drawing of Central Park is 30 centimeter.
The area of scale drawing of Central Park is 31.25 square centimeters.
What is perimeter?
The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter.
Given that Central Park is a rectangular park in New York City
The measured length is 12.5 centimeters
The measured width is 2.5 centimeters
The perimeter of scale drawing of Central Park is given as:
Given is a rectangular park
perimeter of rectangular = 2(length + width)
perimeter of rectangular = 2(12.5 + 2.5)
perimeter of rectangular = 2(15) = 30
Thus perimeter is 30 centimeter
The area of scale drawing of Central Park is given as:
area = length x width
area = 12.5 x 2.5 = 31.25 cm²
Thus area of rectangular park is 31.25 square centimeters
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The rectangular rug is similar to the rectangular floor. If the floor of the room measures 32 feet in length and 26 feet in width, what is the width of the rug?
The width of the rectangular rug is 13 feet and the length of the rectangular rug is 26 feet.
What is the step to calculate the area of the rectangle?Area of a rectangle formula: A = L * W. A
rectangle's length and width are multiplied to produce its area.
A is the area, L is the length, and W is the width or girth, where
A = L * W.
The corresponding sides of the rectangular rug and the rectangular floor must be proportional if they are alike.
Let's use "x" to represent the rug's width. The floor measures 32 feet in length and 26 feet in width, and the length of the rug is 16 feet according to the details provided. Since the rug and the surface are comparable, we can establish the following ratio:
Rug width/floor width = rug length/floor length
x / 26 = rug's length / 32
We can cross-multiply and then solve for "x" to find the answer:
32x = 26 * Rug's length
x = (26 * Rug Length) / 32
[tex]= \frac{26 * 16}{32} \\= \frac{26}{2} \\= 13[/tex]
Therefore x ( the width of the rug) is = 13 feet.
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Complete question:
The rectangular rug is similar to the rectangular floor. If the floor of the room measures 32 feet in length and 26 feet in width, and the length of the rug is 16 feet, what is the width of the rug?
If the spinner does not land on yellow, what is the probability it will land on blue?
1/6
3/8
1/8
1/4
Answer-
1/8 because their are 8 peices and 1 of them are blue and 2 of them are yellow so it become 1/8
Answer:
ans is 1/6
because its sure spinner not land on the yelow so two pieces neglect
so prob =favourable cases/total cases
blue has one piece only
1/6
|||
9
C
Erica has $120. If sweatshirts cost $28.99, estimate the maximum number of
shirts she can buy by rounding the price to the nearest ten.
sweatshirts
If sweatshirts cost $28.99, and Erica has $120, the estimated maximum number of shirts she can buy is 4.
How is the number determined?The unit cost is approximated to $30 and used as the divisor of $120.
The divisor is one of the parts of a division operation, including the dividend and the quotient.
The total amount that Erica has = $120
The unit cost of sweatshirts =- $28.99 ≈ $30)
The estimated maximum number of shirts she can buy = 4 ($120 ÷ $30)
Thus, to estimate the maximum number of sweatshirts Erica can buy with her $120, the unit cost is approximated to $30 and used to divide the dividend.
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When rolling a fair, eight-sided number cube, determine P(number greater than 5).
0.125
0.375
0.17
0.25
State the dimensions of the matrix. Identify the indicated element.
2
1-3
0
a.
2x3; 1
b. 3x2; 2
OA
OB
OC
OD
a12
c.
d.
3x1;2
1x 3; 1
Please select the best answer from the choices provided
The number of rows and columns in the specified matrix and the matrix element are; 2 rows and 3 columns, the correct option is therefore;
a. 2 × 3; 1, which is option A
How are the elements in a matrix denoted?The common form of denoting the elements in a matrix is by using a letter and two subscripts in the form; A[tex]_{ij}[/tex].
The specified matrix can be presented as follows;
[tex]\begin{bmatrix}-4 &1 &-3 \\ 2& 1& 0 \\\end{bmatrix}, a_{12}[/tex]
The size of a matrix is indicated by the number of rows and columns in the matrix. The size of a matrix is usually indicated as m × n where;
m × n = Number of rows × Number of columns
Where;
m = The number of rows
n = The number of columns
The number of rows in the specified matrix are two rows
The number of columns in the matrix are three columns
The size of the specified matrix therefore is; 2 × 3
The position of a matrix element is similarly indicated by two subscripts, the first indicating the row number of the element and the second indicating the column number of the matrix.
Therefore;
a₁₂ is the element in the first row and in the second column, which is the number 1
The correct option is therefore;
a. 2 × 3; 1
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A Pail holds 6 3/4 of water How much is this in cups write your answer as a whole number or a mixed number
Volume of 6 3/4 cups of water is equal to 54 cups of water.
What is Volume?
One cup is equal to 8 fluid ounces. Therefore, to convert 6 3/4 cups to fluid ounces, we can multiply by 8:
6 3/4 cups = (6 x 8) + (3/4 x 8) cups = 48 + 6 = 54 cups
So, 6 3/4 cups of water is equal to 54 cups of water.
What is fluid?
A fluid is a substance that has the ability to flow and take the shape of its container. Fluids include liquids, gases, and plasmas.
Liquids are a common type of fluid that can flow and take the shape of their container, but have a definite volume. Some examples of liquids include water, oil, and milk.
Gases are another type of fluid that can flow and fill the entire volume of their container, taking on the shape of the container. Some examples of gases include air, oxygen, and nitrogen.
Plasmas are a unique type of fluid that occurs at very high temperatures, in which some or all of the atoms or molecules have been ionized, resulting in the presence of free electrons and positive ions. Some examples of plasmas include lightning, the sun, and neon lights.
Fluids are important in many fields, including physics, engineering, and biology. They play a critical role in many processes, such as the circulation of blood in the body, the flow of water in a river, and the movement of air in the atmosphere.
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Answer:
The following statements about Josiah's solution are true:
1. He predicted the number of rock songs on his MP3 player to be 300 songs. (This is stated in the problem description.)
2. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. (This is true, as he should have divided both the numerator and denominator of the first fraction by 2 to simplify it.)
3. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500. (This is true, as he needed to find a common multiple of 20 and 1,500 to set up the proportion correctly.)
Use identities to write the expression as a single function of x or θ cos (θ+pi/2)
Math write your answer step by step
The area of the shaded parts are:
1. Area of shaded part = 165.76 cm²
2. Area of shaded part = 736 cm²
3. Area of shaded part = 155.52 cm²
4. Area of shaded part = 169 cm²
Calculating the area of the shaded partsFrom the question, we are to determine the area of the shaded parts
1.
Area of shaded part = Area of triangle - Area of circle
Area of shaded part = (1/2 × base × height) - (πr²)
Area of shaded part = (1/2 × 18 × 24) - (3.14 × 4²)
Area of shaded part = 216 cm² - 50.24 cm²
Area of shaded part = 165.76 cm²
2. Area of shaded part = = (32 × 24) - (8 × 4)
Area of shaded part = = 768 - 32
Area of shaded part = 736 cm²
3.
Area of shaded part = Area of square - Area of semicircle
Area of shaded part = (length)² - (1/2πr²)
Area of shaded part = 16² - (1/2 × 3.14 × 8²)
Area of shaded part = 256 - 100.48
Area of shaded part = 155.52 cm²
4.
Area of shaded part = (1/2 × 26 × 13)
Area of shaded part = 169 cm²
Hence, the area of the shaded part is 169 cm²
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24
Find the median of the given data.
3 5 78 81 90
Median =
=
The median of the given data is 78.
What is median?
The median is a measure of central tendency that represents the middle value in a set of data when the data is arranged in order from smallest to largest. It is the value that separates the upper half of the data from the lower half.
To calculate the median, the data must first be ordered. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values.
The median of the given data can be found by first arranging the data in order from smallest to largest:
3, 5, 78, 81, 90
In this case, there are five values, so the median is the middle value, which is 78.
Therefore, the median of the given data is 78.
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Find the missing side lengths. Leave your answers as radicals in simplest form
Answer:
u = 2√3;
v = 2
Step-by-step explanation:
Use trigonometry:
[tex] \cos(60°) = \frac{v}{4} [/tex]
Cross-multiply to find v:
[tex]v = 4 \times \cos(60°) = 4 \times 0.5 = 2[/tex]
Use the Pythagorean theorem to find u:
[tex] {u}^{2} = {4}^{2} - {v}^{2} [/tex]
[tex] {u}^{2} = {4}^{2} - {2}^{2} = 16 - 4 = 12[/tex]
[tex]u > 0[/tex]
[tex]u = \sqrt{12} = \sqrt{4 \times 3} = 2 \sqrt{3} [/tex]
the mean of 6, 29, 3, 14, q, (q+8), Q^2 and (q-10) is 20. find the possible values of q
We can start by finding the sum of the given numbers and equating it to the product of 20 and 8 (the number of elements):
6 + 29 + 3 + 14 + q + (q+8) + Q^2 + (q-10) = 20 * 8
Simplifying the left side by combining like terms, we get:
2q^2 + 20q - 100 = 124
Bringing everything to one side, we get:
2q^2 + 20q - 224 = 0
Dividing both sides by 2, we get:
q^2 + 10q - 112 = 0
Now, we can use the quadratic formula to solve for q:
q = (-10 ± √(10^2 - 4(1)(-112))) / (2(1))
q = (-10 ± 18) / 2
So the possible values of q are:
q = 4 or q = -14
To verify, we can substitute these values back into the original equation and see if the mean is indeed 20:
For q = 4:
(6 + 29 + 3 + 14 + 4 + 12 + 16 + -6) / 8 = 20 (checks out)
For q = -14:
(6 + 29 + 3 + 14 - 14 - 6 + 196 + -24) / 8 = 20 (checks out)
Therefore, the possible values of q are 4 and -14.
ALG 2 imaginary numbers (EVEN ONLY)
Imaginary Numbers are 21. (5+2i)/ 4i is -(5/4) + (1/2)i, 22. 3i/(-2+i) is -1.5i + 0.75. 23. (3-2i)/(4-3i) is 4/5 + (1/25)i, 24. 7/(5-2i) is (14/29) + (7/29)i.
Describe Imaginary Numbers?In mathematics, imaginary numbers are a type of complex number that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.
Imaginary numbers were first introduced in the 16th century as a solution to certain polynomial equations that did not have real solutions. They were initially met with skepticism and derision, but eventually became widely accepted as a fundamental part of complex analysis and number theory.
One of the key properties of imaginary numbers is that when they are multiplied by themselves, the result is always a negative real number. For example, i * i = -1. This property is what makes imaginary numbers useful for representing certain physical quantities, such as the amplitude and phase of an oscillating system.
21. (5+2i)/ 4i = -(5/4) + (1/2)i
To divide complex numbers, we can multiply the numerator and denominator by the conjugate of the denominator. Here, the conjugate of 4i is -4i.
(5+2i)/ 4i = (5+2i)/4i * (-4i/-4i)
= -(20i - 8)/(-16)
= -(20i - 8)/16
= -(5/4) + (1/2)i
Therefore, (5+2i)/ 4i = -(5/4) + (1/2)i.
22. 3i/(-2+i) = -1.5i + 0.75
We can again use the conjugate to simplify the division of complex numbers.
3i/(-2+i) = 3i/(-2+i) * (-2-i)/(-2-i)
= (-6i -3)/(-5)
= 3/5 + 1.5i
Therefore, 3i/(-2+i) = -1.5i + 0.75.
23. (3- 2i)/(4-3i) = (18+5i)/25
Using the conjugate:
(3-2i)/(4-3i) = (3-2i)/(4-3i) * (4+3i)/(4+3i)
= (12+9i-8i-6i²)/(16+12i+12i-9i²)
= (20+i)/25
= 20/25 + (1/25)i
= 4/5 + (1/25)i
Therefore, (3-2i)/(4-3i) = (18+5i)/25 = 4/5 + (1/25)i.
24. 7/(5-2i) = (14/29) + (7/29)i
Using the conjugate:
7/(5-2i) = 7/(5-2i) * (5+2i)/(5+2i)
= (35+14i)/(29)
= (14/29) + (7/29)i
Therefore, 7/(5-2i) = (14/29) + (7/29)i.
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What’s is 100/58 in the simplest form
Answer:
1 21/29
Step-by-step explanation:
Complete this proof using SAS.
Given: AC || DF; BC ≅ DE
Prove: ∆DBE ≅ ∆BEC
STATEMENTS
1. ___
2. <CBE ≅ <DEB
3. BE ≅ BE
4. ∆DBE ≅ ∆BEC
REASONS
1. Given
2. __ (Hint: AC || DF)
3. __
4. __
1) AC || DF; BC ≅ DE , 2) )Alternate interior angles formed by transversal BC and parallel lines AC and DF are congruent 3) Identity Property of Congruence (Any segment is congruent to itself)
what is Congruence?
In mathematics, congruence is a term used to describe the relationship between two geometric figures that have the same shape and size. Two objects are said to be congruent if they are identical in shape and size.
In the given question,
STATEMENTS
AC || DF; BC ≅ DE
<CBE ≅ <DEB
BE ≅ BE
∆DBE ≅ ∆BEC
REASONS
1)Given
2)Alternate interior angles formed by transversal BC and parallel lines AC and DF are congruent
3) Identity Property of Congruence (Any segment is congruent to itself)
4) SAS (Side-Angle-Side) Congruence Postulate (Since BC and BE are congruent and <DBE and <BEC are congruent, and BE is common to both triangles)
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two supplementary angles are such that the measure of one is twice the measure of the other find the angles
Answer:
60°
120°
Step-by-step explanation:
Supplementary angle are those that sum up to a total of 180 degrees.
So, let's have 2 angles, angle A and angle B.
Angle A's measure is α so the measure of angle B is 2α.
The sum of these two angles sum up to 180 degrees, so we can say that:
α + 2α = 180°
3α = 180°
α = 60°
So, one of our angles is 60° and the other is (2*60)° which is 120°.
Which rectangle has the greater area, a rectangle with length 12 1 foot and width foot or a rectangle with length 16 foot and width foot?
Therefore, the second rectangle has a greater area than the first rectangle.
RectangleA rectangle is a quadrilateral geometric shape that has four sides and four right angles (90-degree angles). It is characterized by having opposite sides that are equal in length and parallel to each other. The rectangle's other two sides are also equal in length and parallel to each other but different in length than the opposite sides.
The area of a rectangle is calculated by multiplying its length by its width, which gives the total amount of space inside the shape. The perimeter of a rectangle is the sum of all its sides.
To find the area of a rectangle, we multiply its length by its width. Therefore, the area of the first rectangle is:
Area of first rectangle = 12 ft × 1 ft = 12 sq ft
And the area of the second rectangle is:
Area of second rectangle = 16 ft × 1 ft = 16 sq ft
Therefore, the second rectangle has a greater area than the first rectangle.
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