Answer:
1. With the height and base of a triangle given, we can use the Pythagorean Theorem to find the length of the hypotenuse (the third side) of the right triangle.
Given:
Height (a) = 6
Base (b) = 8
We can plug these values into the Pythagorean Theorem formula:
a^2 + b^2 = c^2
Substituting the values:
6^2 + 8^2 = c^2
Simplifying:
36 + 64 = c^2
100 = c^2
Now, we can take the square root of both sides to solve for c:
√100 = √c^2
10 = c
So, the length of the hypotenuse (c) of the right triangle is 10 units.
2.
Given:
Base (b) = 8
One side (a or c) = 12
We can use the Pythagorean Theorem to find the length of the remaining side (either a or c) of the right triangle.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Using the formula:
a^2 + b^2 = c^2
Substituting the values:
a^2 + 8^2 = 12^2
Simplifying:
a^2 + 64 = 144
Next, we can isolate a^2 by subtracting 64 from both sides of the equation:
a^2 = 144 - 64
a^2 = 80
Finally, we can take the square root of both sides to solve for a:
√(a^2) = √80
a ≈ 8.94 (rounded to two decimal places)
So, the length of the remaining side (either a or c) of the right triangle is approximately 8.94 units. Please note that depending on the context of the problem, you may need to use the positive square root value for a or c, depending on which side is relevant in the specific scenario.
Answer:
X = 10^2
Y = /80
Step-by-step explanation:
Pythagorean theorem = A^2 +B^2= C^2
Fist triangle
6^2+8^2
36 + 64= 100
/100 = 10^2
X= 10^2
Second triangle
Pythagorean theorem = C^2 - A^2= B^2
12^2 - 8^2
144 - 64= 80
/80 = /80
X = /80
Chad drinks 64. 88 fluid ounces of water per day. How much water does he drink in 6 days
Chad drinks 389.28 fluid ounces of water in 6 days.
What is ounces?A unit of weight equal to ¹/₁₂ troy pound see Weights and Measures Table. : a unit of weight equal to ¹/₁₆ avoirdupois pound. : a small amount. an ounce of sense.
An ounce (oz) is a unit of weight that is equal to one-sixteenth of a pound. Items that weigh approximately one ounce include a slice of bread and a pencil. A fluid ounce is a unit of liquid volume that is equal to one-eighth of a cup. A medicine cup has a volume of approximately one fluid ounce.
given that,
chad drinks 64.88 fluid ounces of water per day,
so in 6 days
he will drink = 6 x water drink per day
= 6 x 64.88
= 389.28
Learn more about ounces here :-
https://brainly.com/question/29374025
#SPJ4
I need help ASAP mean absolute deviation (mad)
The absolute deviation for the observation of 16 in the data-set is given as follows:
5.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
Hence the mean of the data-set in this problem is given as follows:
(19 + 16 + 4 + 9 + 7)/5 = 11.
The absolute deviation of 16 is given by the difference between 16 and the mean of 11, hence:
16 - 11 = 5.
More can be learned about the mean of a data-set at https://brainly.com/question/1136789
#SPJ1
ladder 13 feet long is leaning against a wall. if the foot of the ladder is pulled away from the wall at the rate of 0.5 feet per second, how fast will the top of the ladder be dropping when the base is 5 feet from the wall?
The top of the ladder is dropping at a rate of -5/24 ft/s (approximately -0.208 ft/s) when the base is 5 feet from the wall.To answer your question, we'll use the Pythagorean theorem for the right triangle formed by the ladder, wall, and ground.
Let x be the distance from the base of the ladder to the wall, and y be the distance from the top of the ladder to the ground. The ladder's length (13 ft) is the hypotenuse of the triangle.
According to the Pythagorean theorem:
x² + y² = 13²
When the base is 5 feet from the wall:
5² + y² = 13²
y² = 144
y = 12 ft
Now, we'll differentiate the equation with respect to time (t):
2x(dx/dt) + 2y(dy/dt) = 0
Given that the base is being pulled away at 0.5 ft/s (dx/dt = 0.5 ft/s), we can find the rate at which the top of the ladder is dropping (dy/dt) when x = 5 ft and y = 12 ft:
2(5)(0.5) + 2(12)(dy/dt) = 0
5 + 24(dy/dt) = 0
dy/dt = -5/24
Learn about more Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ11
The top of the ladder is dropping at a rate of [tex]5/\sqrt(119)[/tex]feet per second.
Let's begin by drawing a diagram of the situation:
|\
| \
| \ <-- ladder
| \
| \
| \
| \
|______\
wall
A right triangle formed by the ladder, the wall, and the ground.
Let's call the distance from the foot of the ladder to the wall "x" and the height of the ladder "y".
The ladder is 13 feet long and that the foot of the ladder is being pulled away from the wall at a rate of 0.5 feet per second.
The height of the ladder is changing when the foot of the ladder is 5 feet from the wall.
Using the Pythagorean theorem,
the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation
[tex]{\displaystyle a^{2}+b^{2}=c^{2}.}[/tex]
The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.
The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem.
The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.
[tex]x^2 + y^2 = 13^2[/tex]
Differentiating both sides with respect to time t, we get:
[tex]2x dx/dt + 2y dy/dt = 0[/tex]
We want to find. [tex]dy/dt[/tex] when [tex]x = 5[/tex], so, we need to substitute. [tex]x = 5[/tex] and [tex]dx/dt = 0.5[/tex] into the equation above:
[tex]2(5)(0.5) + 2y dy/dt = 0[/tex]
[tex]y dy/dt = -5[/tex]
[tex]dy/dt = -5/y[/tex]
Pythagorean theorem to solve for y when. [tex]x = 5[/tex]:
[tex]5^2 + y^2 = 13^2[/tex]
[tex]y^2 = 144 - 25[/tex]
[tex]y^2 = 119[/tex]
[tex]y = \sqrt(119)[/tex]
The foot of the ladder is 5 feet from the wall, the height of the ladder is:
[tex]y = \sqrt(119) feet[/tex]
And the rate of change of the height of the ladder is:
[tex]dy/dt = -5/y = -5/\sqrt(119) feet per second[/tex]
For similar questions on Ladder
https://brainly.com/question/11002157
#SPJ11
20 POINTS!!!!!!
4. Find the value of x and y.
3y - 5
x =
y =
y+1
2x+6
II
work:
Answer:
x = 8, y = 3
Step-by-step explanation:
Assuming the figure is a parallelogram, opposite sides on a parallelogram are equal.
This means that 3x-2 = 2x+6 and 3y-5 = y+1.
To solve these equations:
3x-2 = 2x+6 (collect like terms)
3x-2x = 6+2
x = 8
3y-5 = y+1 (collect like terms)
3y-y = 1+5
2y = 6 (divide both sides by 2)
y = 3
∴ x = 8, y = 3
5x(x - 4) = 3x + 4 someone help me pls
Answer: x=23±√609/10
Step-by-step explanation:
math please. its for a quiz
The quotient function of f(x) and g(x) is given as follows:
(f/g)(x) = 3x^(3/4).
How to obtain the quotient function?The functions in the context of this problem are defined as follows:
f(x) = 3x.g(x) = x^(1/4).When we want to divide two functions, we just divide each other, hence:
(f/g)(x) = f(x)/g(x) = 3x/x^(1/4).
When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence:
x/x^(1/4) = x^(1 - 1/4) = x^(3/4).
Hence the function is:
(f/g)(x) = 3x^(3/4).
More can be learned about quotient of functions at https://brainly.com/question/23520000
#SPJ1
what is the proportional relationship between x 2 6 8 10 and y 6 18 24 30
The proportional relationship is y = 3x.
What is the proportional relationship?
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
Here, we have
Given:
x: 2, 6, 8, 10
y: 6, 18, 24, 30
We have to find the proportional relationship between x and y.
So, we can see from inspection and visual observation that there is a proportional relationship between x and y.
6 = 3 2, 18 = 3 6, 24 = 3 8, 30 = 3 10.
Hence, The proportional relationship is y = 3x.
To learn more about the proportional relationship from the given link
https://brainly.com/question/2143065
#SPJ1
Joel wants to fence off a triangle portion of his yard for his chickens. The three pieces of fencing he has measured 8 ft, 15 ft, and 20 ft. will Joel be able to make a right triangle with the current lengths of fencing? why or why not?
Joel cannot make a right triangle with the current lengths of fencing.
What is right triangle?A right triangle is a triangle that has one angle that measures exactly 90 degrees (a right angle). This means that the other two angles of the triangle are acute (measuring less than 90 degrees). The side opposite the right angle is called the hypotenuse, and it is always the longest side of the triangle. The other two sides are called the legs of the triangle.
To check if Joel can make a right triangle with the current lengths of fencing, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).
So, let's check if the measurements satisfy the Pythagorean theorem:
8² + 15² = 64 + 225 = 289
20² = 400
According to the Pythagorean theorem, a triangle with sides of length 8 ft, 15 ft, and 20 ft would be a right triangle if it satisfies the equation a² + b² = c² , where a and b are the shorter sides (legs) and c is the longest side (hypotenuse). However, in this case, we can see that the sum of the squares of the shorter sides (8² + 15² ) is not equal to the square of the longest side (20² ), so the measurements cannot form a right triangle.
Therefore, Joel cannot make a right triangle with the current lengths of fencing.
To know more about right triangle visit:
https://brainly.com/question/29869536
#SPJ1
Aniya got a 44 out of 40 points on her American Government quiz due to an extra credit question. What is Aniya's grade written as a percent?
Therefore , the solution of the given problem of unitary method comes out to be Aniya's final grade is 10%.
What is an unitary method?To complete the assignment, use the iii . -and-true core method, the real variables, and any pertinent information acquired through general and specific questions. In response, customers might be given another opportunity to sample expression the products. We will miss out on important developments in the comprehension of programmes if these changes don't take place.
Here,
Aniya obtained additional credit worth a total of 4 points because she received 44 out of a possible 40 (44 - 40 = 4). We can use the following equation to represent her grade as a percentage:
=> (Points Earned / Total Points) x 100 = percentage.
Inserting the values:
=> Percentage = (4/40) * 100.
=> Ratio = 0.1 x 100
=> percent = 10.
With the extra credit, Aniya's final grade is 10%.
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1
Questions seven and eight please
The results are:
7a) Explicit = h(n) = [tex]0.87^{n-1}[/tex] * 200.
Recursive = h(0) = 200 and h(n) = 0.87 * h(n-1)
7b) Rebound height = 99.76 cm (rounded to the nearest hundredth).
8a) Explicit formula: A(n) = 575 + 47.50n
Recursive formula: A(0) = 575, A(n) = A(n-1) + 47.50
8b) 30 weeks to save $2000'
Step by step explanation:7a) Explicit: h(n) = [tex]0.87^{n-1}[/tex] * 200 (
where h(n) = height of the golf ball after n bounces,
0.87 is the rebound factor,
200 is the initial height)
h(n) = [tex]0.87^{n-1}[/tex] * 200
Recursive: h(0) = 200
h(n) = 0.87 * h(n-1)
where h(n) = the height after n bounces,
h(n-1) = height after (n-1) bounces,
0.87 = rebound factor.
Apply given values:
h(0) = 200
h(n) = 0.87 * h(n-1)
7b) Rebound height, using recursive formula:
h(0) = 200
h(1) = 0.87 * 200 = 174
h(2) = 0.87 * 174 = 151.38
h(3) = 0.87 * 151.38 = 131.70
h(4) = 0.87 * 131.70 = 114.71
h(5) = 0.87 * 114.71 = 99.76 (rounded to the nearest hundredth)
8a)Explicit: A(n) = 575 + 47.50n,
where A(n) = amount of money Jessica has after n weeks,
575 = initial amount given by grandfather,
47.50 = amount Jessica adds each week.
Recursive: A(0) = 575, A(n) = A(n-1) + 47.50,
where A(n) = the amount of money Jessica has after n weeks,
A(n-1) = amount Jessica has after (n-1) weeks
47.50 = amount Jessica adds each week.
8b) Weeks to save $2000:
A(n) = 575 + 47.50n = 2000
Solving for n:
575 + 47.50n = 2000
47.50n = 2000 - 575
47.50n = 1425
n = 1425 / 47.50
= 30 weeks.
Learn more about explicit formula at brainly.com/question/24198356
#SPJ1
There are four times as many cows as horses on a farm. There are twice as many horses as pigs on the farm. Which list shows the number of each type of animal on this farm?
As per the unitary method, the list shows the number of each type of animal on this farm is
Number of pigs = x
Number of horses = 2x
Number of cows = 8x
Let us start by assigning variables to each type of animal on the farm. Let's say the number of pigs is "x".
From the problem statement, we know that there are twice as many horses as pigs. Therefore, the number of horses would be 2x.
Further, we know that there are four times as many cows as horses. So, the number of cows would be 4 times the number of horses. Mathematically, we can represent it as:
Number of cows = 4 * Number of horses
Or, Number of cows = 4 * (2x) = 8x
Therefore, we have the number of each type of animal on the farm as follows:
Number of pigs = x
Number of horses = 2x
Number of cows = 8x
This is the same ratio as we found using the unitary method.
Therefore, our solution is correct.
To know more abut unitary method here
https://brainly.com/question/28276953
#SPJ4
a production process produces 2.5% defective parts. a sample of five parts from the production process is selected. what is the probability that the sample contains exactly two defective parts? group of answer choices 0.2637 0.0058 0.0000 0.0250
The probability that the sample contains exactly two defective parts is 0.0058.
We may utilize the binomial probability formula to resolve this issue:
P(X = k) is equal to (n pick k) * p * k * (1-p) (n-k)
where n is the sample size, k denotes the number of successes, p denotes the likelihood that a success will occur, and (n pick k) denotes the binomial coefficient, which indicates the number of possible ways to select item k from n.
Here, n = 5, k = 2, and p = 0.025 (due to the fact that 2.5% of the pieces are flawed).
P(X = 2) therefore equals (5 pick 2)*0.025*2*(1 - 0.025)*3
We calculate P(X = 2) = 0.0058 using a calculator.
As a result, there is a 0.0058 percent chance that the sample has exactly two defective components.
Learn more about probability :
https://brainly.com/question/14210034
Find the circumference of each circle with a diameter of 20.2 in. Use 3.14 for the value of Pi. Round your answer to the nearest tenth. IM IN 7TH
Answer:
3.14×10.1×10.1
3.14×102.01
320.311
=320.300
Madison is reading a book that is 860 pages long. She reads 25 pages in 0.5 hours. At that rate, how long will it take for her to read the entire book
Answer:
17.2 hours, or 17 hours and 12 minutes
Step-by-step explanation:
If she reads 50 pages per hour, then 860/50 = 17.2
Ages of 12 players on a basketball team: {11,10,11,11,8,11,12,11,9,10,11,12}
Best Center:
Why?:
The best center is the mean because there are no outliers
To determine the best center, we need to examing the ages of the player withing the range of age.
The ages of the players are: 11, 10, 11, 11, 8, 11, 12, 11, 9, 10, 11, 12
In the above list of age, we can seee that there are no outliers are
When there are no outliers in a dataset, the best center to use is the mean
Hence, the best center is the mean
Read more about mean at
https://brainly.com/question/548811
#SPJ1
I need some help please
what time does a 12-hour clock read a) 80 hours after it reads 11:00? b) 40 hours before it reads 12:00? c) 100 hours after it reads 6:00?
a) 80 hours after 11:00 on a 12-hour clock would be 7:00.
b) 40 hours before 12:00 on a 12-hour clock would be 4:00.
c) 100 hours after 6:00 on a 12-hour clock would be 10:00.
a, To find this, we need to divide 80 by 12 (the number of hours on the clock), which gives us a quotient of 6 and a remainder of 8. We then add the remainder to the starting time of 11:00, giving us 7:00.
b, To find this, we need to subtract 40 from 12 (the number of hours on the clock), which gives us 8. We then subtract 8 from the starting time of 12:00, giving us 4:00.
c, To find this, we need to divide 100 by 12 (the number of hours on the clock), which gives us a quotient of 8 and a remainder of 4. We then add the quotient (which represents a full cycle of 12 hours) to the starting time of 6:00, giving us 6+8=14:00, which is equivalent to 2:00 on a 12-hour clock. Finally, we add the remainder of 4 to 2:00, giving us 10:00.
Learn more about clock
https://brainly.com/question/24051741
#SPJ4
Construct a two-way frequency table for the data. Include row and column totals. Hint: Let column categories be labeled by after school activity.
Every student at Georgia Southern Middle School participates in exactly one after school activity. The school activities coordinator recorded data on after extracurricular activity
and grade for all 254 students in 7th grade and 8th grade.
The counselor's findings for the 254 students are the following:
• Of the 80 students enrolled in music, 42 are in 7th grade.
.
. Of the 21 students enrolled in student government, 9 are in 8th grade.
.
Of the 65 students enrolled in theatre, 20 are in 7th grade.
. Of the 88 students enrolled in sports, 30 are in 8th grade.
Answer:
[tex]\begin{array}{|c|c|c|c|c|c|} \cline{1-6} & \text{Music} & \text{Gov} & \text{Theater} & \text{Sports} & \text{Total}\\\cline{1-6}\text{7th grade} & 42 & 12 & 20 & 58 & 132\\\cline{1-6}\text{8th grade} & 38 & 9 & 45 & 30 & 122\\\cline{1-6}\text{Total} & 80 & 21 & 65 & 88 & 254\\\cline{1-6}\end{array}[/tex]
"Gov" refers to "Student Government".
==================================================
Explanation:
The rows are labeled "7th grade", "8th grade" and "Total".
The columns are labeled "Music", "Student Government", "Theater", "Sports", and "Total".
I'll abbreviate "Student Government" to "Gov" so that the table doesn't get too wide.
There are 254 students total. This value goes in the bottom right corner of the table. This is the grand total.
----------
We have 80 students in music. This value goes at the bottom of the "music" column since we're in a "total" row. Basically it's the total of all the music students regardless of grade.
Of those 80 students in music, 42 are in seventh grade. Write 42 in the first row of this column and 38 just underneath it (because 80-42 = 38). The two values 42 and 38 should add to the 80 mentioned.
----------
There are 21 students in student government. This value goes at the bottom of the "student government" column.
9 of these students are in eighth grade, so the remaining 21-9 = 12 must be in seventh grade.
----------
There are 65 students in theater. This value goes at the bottom of the "theater" column.
There are 20 such students in 7th grade and 45 in 8th grade (because 65-20 = 45).
----------
There are 88 students in sports.
30 are in 8th grade, so 88-30 = 58 must be in 7th.
----------
At this point, you should have these values along the bottom row:
80, 21, 65, 88, 254
The first four values (80, 21, 65, 88) should add to the grand total 254.
Along each row, add up the values to get the row total.
7th grade: 42 + 12 + 20 + 58 = 132
8th grade: 38 + 9 + 45 + 30 = 122
There are 132 seventh graders and 122 eighth graders.
Those subtotals add to 132+122 = 254 total students, which helps confirm we did things correctly.
What does the correspondence of angles mean
Answer:
the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line
If a monopolistic firm takes over a perfectly competitive market, we would expect to see market price of the good to rise and the quantity sold to increase. Fall as the monopolist tries to increase sales. Fall because demand is perfectly elastic. Rise and quantity sold to fall
In the event that a monopolistic firm takes over superbly competitive advertising, we would anticipate seeing the advertising cost of the great rise and the amount sold drop.
Be that as it may, when a monopolistic firm takes over the showcase, it picks up showcase control and the capacity to impact the cost. The monopolist can charge a better cost than the competitive advertising cost since there are no near substitutes for its item. As the monopolist raises the cost, the amount requested will drop, as customers switch to substitutes or decrease their utilization of the item.
we would anticipate seeing the advertising cost of the great rise and the amount sold fall as the monopolist tries to extend benefits by raising costs. This is often in differentiating from impeccably competitive advertising.
To learn about monopolistic firms visit:
https://brainly.com/question/13806356
#SPJ4
hel me please please
The incorrect expressions are given as follows:
h^9/h³ = h^6 -> keep the base and subtract the exponents.9b^7/3b² = 3b^5 -> we have to divide the bases.d^5 x d²/d³ = d^4 -> add the exponents in the numerator, then subtract the exponent with the denominator.How to simplify the exponential expressions?When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents.
When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents.
More can be learned about exponent rules at https://brainly.com/question/11975096
#SPJ1
Emilio has a bag of dog food. The bag contains 24 3/4cups of dog food. Emilio feeds his dog 2 3/4 cups of dog food each day.
What is the total number of days Emilio can feed his dog from this bag of dog food?
a student takes an exam containing 11 true or false questions. if a student randomly guesses on the entire exam, what is the standard deviation of the number of incorrect answers? round your answer to two decimal places.
The first step is to find the mean number of incorrect answers. Since there are 11 questions, and each question has a 50/50 chance of being answered incorrectly, we can expect the student to get 5.5 questions wrong on average.
Next, we need to calculate the variance. To do this, we can use the formula:
Variance = p(1-p)n
Where p is the probability of getting a question wrong (0.5), and n is the number of questions (11).
Variance = 0.5(1-0.5)11 = 1.375
Finally, we can find the standard deviation by taking the square root of the variance:
Standard deviation = sqrt(1.375) = 1.17 (rounded to two decimal places)
Therefore, the standard deviation of the number of incorrect answers on the exam is 1.17.
Learn more about deviation:
https://brainly.com/question/475676
#SPJ11
PLEASE HELP DUE TODAY!!!!!!!
Consider the functions g(x) = 2x + 1 and h(x) = 2x + 2 for the domain 0 < x < 5
a. Without evaluating or graphing the functions, how do the ranges compare?
b. graph the 2 functions and describe each range over the given interval
a. The ranges of g(x) and h(x) differ by a constant value of 1, since h(x) is simply g(x) shifted upward by 1 unit. Therefore, the range unit.
b.
Graph of g(x) = 2x + 1 and h(x) = 2x + 2 over the interval 0 < x < 5:
![Graph of g(x) over the interval 0 < x < 5 is (1, 11), while the range of h(x) is (2, 12). This confirms that the range of h(x) is equal to the range of g(x) shifted upward by 1 unit.
g(x) = 2x+1 h(x) = 2x + 2
for the domain 0 < x < 5.
These are two parallel lines where h(x) is 1 unit above g(x) Then, the range of h(x) over the given domain will have endpoints 1 unit greater.
b. Evaluating g(x) when x = 0 :g(0) = 2(0) + 1 g(0) = 0 + 1 g(0) = 1
Evaluating g(x) when x = 5 :
g(5) = 2(5) + 1
g(5) = 10 + 1
g(5) = 11
Then, we can graph g(x) by connecting the points (0, 1) and (5, 11).
Evaluating h(x) when x = 0 :
h(0) = 2(0) + 2 h(0) = 0 + 2 h(0) = 2
Evaluating h(x) when x = 5 :
h(5) = 2(5) + 2
h(5) = 10 + 2
h(5) = 12
Then, we can graph h(x) by connecting the points (0, 2) and (5, 12).
See GraphFrom the graph, the range of g(x) over the given domain is (1, 11) and of h(x) is (2,12)
please help !!!!!!
MULTIPLY (3x + 4)(4x + 5)
Answer:
B. 12x^2 + 31x + 20
Step-by-step explanation:
Use FOIL (First, Outer, Inner, Last)
(3x + 4)(4x + 5)
12x^2 + 15x +16x + 20
12x^2 + 31x + 20
Answer:
B
Step-by-step explanation:
You are going to want to use the FOIL method. First outer inner last. Multiply 3x*4x to get 12x^2 then multiply 3x*5 to get 15x then multiply 4*4x to get 16x and last multiply 4*5 to get 20. Since 15x and 16x are like terms we add them together to get 31x
the number of square feet per house are normally distributed with a population standard deviation of 154 square feet and an unknown population mean. a random sample of 16 houses is taken and results in a sample mean of 1550 square feet. what is the correct interpretation of the 80% confidence interval? select the correct answer below: we estimate that 80% of the number of square feet per house are between 1501 and 1599 square feet. we estimate with 80% confidence that the sample mean is between 1501 and 1599 square feet. we estimate with 80% confidence that the true population mean is between 1501 and 1599 square feet.
The 80% confidence interval is 1501 to 1599 square feet, indicating with 80% confidence that the true population mean of square feet per house falls within this range based on the sample data.
How to find correct interpretation of the 80% confidence interval?Based on the given information, we can calculate the 80% confidence interval for the true population mean of the number of square feet per house using the sample mean of 1550 square feet and the population standard deviation of 154 square feet. The interval is 1501 to 1599 square feet. This means that if we were to repeat the sampling process and construct confidence intervals in the same way for an infinite number of times, approximately 80% of these intervals would contain the true population mean. Therefore, we can estimate with 80% confidence that the true population mean falls within the range of 1501 to 1599 square feet.
Learn more about Population standard deviation
https://brainly.com/question/14747159?referrer=searchResults
#SPJ11
If 2 inches represents 75 miles on a map, then how many inches will represent 11 miles?
We can use proportions to solve this problem. If 2 inches represent 75 miles, then we can set up a proportion:
2 inches / 75 miles = x inches / 11 miles
To solve for x, we can cross-multiply:
2 inches * 11 miles = 75 miles * x inches
22 inches = 75 miles * x inches
Divide both sides by 75 miles:
22 inches / 75 miles = x inches
Simplify:
0.2933 inches = x inches
Therefore, 11 miles on the map would be represented by approximately 0.2933 inches.
What is the value of the y-coordinate of the ordered pair that reflects (2-12) over the x-axis?
what is the probability that a five-card poker hand contains a straight, that is, five cards that have consecutive kinds? (note that an ace can be considered either the lowest card of an a-2-3-4-5 straight or the highest card of a 10-j-q-k-a straight.)
The probability of getting a straight in a five-card poker hand is 0.0019, which is calculated by dividing the total number of possible straights by the total number of possible five-card hands.
How to find probability that a five-card poker hand contains a straight?To calculate the probability of getting a straight in a five-card poker hand, we need to first understand the concept of a straight. A straight is a combination of five cards that are in consecutive ranks, such as 6-7-8-9-10 or 10-J-Q-K-A.
The total number of possible five-card hands is given by the mathematical formula 52 choose 5, which is equal to 2,598,960. To calculate the number of possible straights, we need to consider the number of ways that we can choose five consecutive ranks out of the thirteen ranks available in a standard deck of cards. There are 10 ways to do this, since we can start with each of the 10 possible ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10) and have one unique straight for each.
However, there are different ways to arrange the cards in a straight. For example, the straight 10-J-Q-K-A can be arranged in five different ways (10-J-Q-K-A, A-10-J-Q-K, K-A-10-J-Q, Q-K-A-10-J, J-Q-K-A-10). Therefore, the total number of possible straights is 10 * 5 = 50.
To calculate the probability of getting a straight, we divide the number of possible straights by the total number of possible five-card hands. Thus, the probability of getting a straight in a five-card poker hand is 50/2,598,960, or approximately 0.0019. Therefore, the chances of getting a straight are relatively low, but not impossible.
Learn more about Probability
brainly.com/question/30034780
#SPJ11
Steven has a bag of 20 pieces of candy. Five are bubble gum, 8 are chocolates, 5 are fruit chews, and the rest are peppermints. If he randomly draws one piece of candy what is the probability that it will be chocolate?
A. 0. 4
B. 0. 45
C. 0. 2
D. 0. 8
The opportunity of drawing a chocolate from the bag is 0.4, therefore, the answer is A. 0.4.
Steven has a bag of 20 pieces of candy, out of which 8 are chocolates. If he draws one piece of sweet at random, the opportunity of it being a chocolate may be calculated through dividing the wide variety of chocolates in the bag with the aid of the full quantity of chocolates inside the bag. In this situation, there are 8 chocolates out of 20 total candies.
The formulation to calculate the opportunity is:
P(chocolate) = number of candies / total range of candies
Substituting the given values, we get:
P(chocolate) = 8 / 20
Simplifying this fraction, we get:
P(chocolate) = 0.4
Consequently, the opportunity of drawing a chocolate from the bag is 0.4
Learn more about Probability:-
https://brainly.com/question/13604758
https://brainly.com/question/24756209
#SPJ4