4. A function f:x→ b/x-a, a>0, is such that f(b) = b and f(2a) = 2a find the value of a and of b. If ff(x) = x, show that x^2-x-2 = 0.
A committee of size 5 is to be chosen from a group of 7 men and 8 women. The 5 names are to be chosen randomly "out of a hat".
(a) Describe the sample space for this situation and calculate the probability of selecting any given committee.
The number of ways to choose 5 people from a total of 15 people is given by 15C5. This can be calculated as follows:15C5 = (15!)/((15-5)! * 5!) = (15 * 14 * 13 * 12 * 11)/(5 * 4 * 3 * 2 * 1) = 3003Therefore, there are 3003 ways to select a committee of 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003.
There are a total of 15 people in the group. A committee of size 5 is to be chosen from a group of 7 men and 8 women randomly. Therefore, the sample space for this situation is 15C5 ways to choose 5 people from a total of 15 people. 15C5 = 3003 ways. That means there are 3003 ways to select 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003. That means the probability of selecting any one committee out of 3003 committees is 1/3003.To compute the probability of selecting any given committee, we first need to determine how many possible committees can be formed from the group of 15 people. The number of ways to choose 5 people from a total of 15 people is given by 15C5. This can be calculated as follows:15C5 = (15!)/((15-5)! * 5!) = (15 * 14 * 13 * 12 * 11)/(5 * 4 * 3 * 2 * 1) = 3003Therefore, there are 3003 ways to select a committee of 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003.
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Please help!!! i'll give brainliest and offering 20 pts each!!!
write each trinomial in the form a(x+b)^2 or a(x-b)^2
please answer all questions correctly! please no spam :-(
5x^2 + 15x + 11.25
10x^2 +20x +10
1/4x^2 + x + 1
3x^2 + 5x + 25/12
explanation isn't necessary, but i will give brainliest to the person with an explanation/best explanation
Answer:
5(x +1.5)^210(x +1)^21/4(x +2)^23(x +5/6)^2Step-by-step explanation:
When your desired form is expanded, it becomes ...
a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2
This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.
a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2
b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2
c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2
d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2
_____
Additional comment
If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.
En una clase de matemáticas hay 3 niñas y 3 niños del séptimo grado y 7 niñas y 5 niños del octavo grado. La maestra elige al azar un estudiante del
séptimo grado y un estudiante del octavo grado en la clase para una competencia. Cuál es la probabilidad de que los estudiantes que ella seleccione sean
Escribir la respuesta como una fracción en forma reducida.
ninas?
Answer:
No comprendo espanol. Yo se un muy poco.
Step-by-step explanation:
suppose we want to test whether there is a difference between the room rates of luxury hotels in new york versus los angeles. we collect data from 20 random luxury hotels in new york and 30 random luxury hotels in l.a. what are the degrees of freedom associated with a pooled-variance two-sample t-test or confidence interval? type your answer here
The degrees of freedom associated with a pooled-variance two-sample t-test or confidence interval in the given case would be 48.
When a pooled-variance two-sample t-test or confidence interval is to be conducted on two groups, the degrees of freedom is calculated using the following formula: df = n1 + n2 - 2, where n1 and n2 are the sample sizes of the two groups being compared.
In the given scenario, data is collected from 20 random luxury hotels in New York and 30 random luxury hotels in Los Angeles. Therefore, the degrees of freedom for a pooled-variance two-sample t-test or confidence interval would be:df = 20 + 30 - 2df = 48. Hence, the degrees of freedom associated with a pooled-variance two-sample t-test or confidence interval are 48.
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Which of the following situations or activities involve permutation?
a. matching shirts and pants
b. forming different triangles out of 5 points on a plane, no three of which are collinear
c. assigning telephone numbers to subscribers
d. forming a committee from members of a club
The carbon cycle is nature's way of reusing carbon atoms, which travel from the atmosphere into organisms in the earth and then back into the atmosphere over and over again. most carbon is stored in rocks and sediments, while the rest is stored in the ocean, atmosphere, and living organisms. evaluate the carbon cycle model. predict the changes that would occur within the carbon cycle as a result of deforestation. choose all that apply.
The carbon cycle is a natural process that involves the movement of carbon atoms between the atmosphere, organisms, rocks, sediments, and the ocean.
The carbon cycle is a crucial process for maintaining the balance of carbon in the Earth's ecosystems. Carbon dioxide (CO2) is taken up by plants during photosynthesis, converting it into organic carbon compounds that are stored in plant tissues. When plants die and decompose, or when animals respire or decompose, carbon is released back into the atmosphere as CO2. Additionally, carbon can be stored in rocks and sediments over long periods of time.
Deforestation, the clearing of forests on a large scale, can significantly disrupt the carbon cycle. When forests are cut down, the stored carbon in trees and vegetation is released into the atmosphere as CO2 through the process of decomposition or burning. This contributes to increased greenhouse gas emissions and can contribute to climate change.
Furthermore, deforestation reduces the number of trees available to absorb CO2 through photosynthesis, leading to decreased carbon uptake from the atmosphere. The loss of forests also means the loss of carbon sinks, as trees are natural carbon storage systems. Without these sinks, more carbon remains in the atmosphere, further exacerbating the greenhouse effect.
In addition to these changes, deforestation can also impact the water cycle, which in turn affects the carbon cycle. Trees play a vital role in regulating water flow and moisture levels in ecosystems. When forests are removed, there is a higher risk of soil erosion and decreased water retention. These changes can affect the growth and survival of plants, ultimately impacting carbon uptake and storage.
In summary, deforestation disrupts the carbon cycle by releasing stored carbon into the atmosphere, reducing carbon uptake, and altering carbon storage patterns. These changes contribute to increased greenhouse gas emissions, climate change, and overall environmental imbalance.
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Needed help with this part of the homework. Am i headed in the right direction? Having trouble finding the range as well
Given -
Where b>1
To Find -
a. Which is the graph of f(x) = -bˣ
b. Which is the graph of f(x) = b-ˣ
c. For which graph(s) is the range (-∞, 0)
Step-by-Step Explanation -
a. Since b > 1
So, bˣ will be positive
f(x) = -bˣ will be negative.
So,
The correct Option is B.
b. f(x) = b-ˣ
So, b-ˣ will be positive
Also, in -x will tends to 1
So,
The correct Option is A
c. Range of (-∞, 0)
So,
we can observe the value of y tending to -∞ in graphs B and D.
Final Answer -
a. Option B
b. Option A
c. Options B and D
Assume boolean[][] x = new boolean[5][7], what is the index variable for the element at the last row and last column in array x?
a. x[4][5]
b. x[4][6]
c. x[5][6]
d. x[5][7]
The index variable for the element at the last row and last column in the array x is B. x[4][6].
In Java, arrays are zero-indexed, which means the first element of an array is at index 0. The given array x is a 2D boolean array with dimensions 5x7 (5 rows and 7 columns). To access the last row and last column, we need to subtract 1 from each dimension:
- For the last row, the index is 5 - 1 = 4.
- For the last column, the index is 7 - 1 = 6.
So, the correct index variable to access the last row and last column is x[4][6]. The other options provided are incorrect as they do not accurately represent the index of the last element:
- a. x[4][5] refers to the second to last element in the last row.
- c. x[5][6] would be out of bounds, as the maximum row index is 4.
- d. x[5][7] would also be out of bounds, as both the row and column indices are too large.
Therefore, the correct option is B.
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-6x - 42= –10x + 62
X =
\( - 6x - 42 = - 10x + 62\)
Add sides 42
\( - 6x - 42 + 42 = - 10x + 62 + 42 \\ \)
\( - 6x = - 10x + 104\)
Add sides 10x
\( 10x - 6x =10x - 10x + 104 \)
\(4x = 104\)
Divided sides by 4
\( \frac{4}{4}x = \frac{104}{4} \\ \)
\(x = 26\)
_________________________________
Done ♥️♥️♥️♥️♥️
tom can type a report in 3 hours and nelson takes 5 hours. how long will it take the two of them typing together?
It will take Tom and Nelson 1.875 hours, or 1 hour and 52.5 minutes, to complete the report working together.
How to know work done together?To solve this problem, we can use the concept of work done. Let's assume that a report is a unit of work, and Tom and Nelson each do a fraction of the work in one hour.
Tom can do the entire report in 3 hours, which means he can do 1/3 of the report in one hour. Similarly, Nelson can do 1/5 of the report in one hour.
If they work together, the fraction of the report they can do in one hour is the sum of their individual fractions:
1/3 + 1/5 = 8/15
So, together they can do 8/15 of the report in one hour. To find out how long it will take them to do the entire report working together, we can use the formula:
time = work ÷ rate
where work is 1 (the whole report) and rate is 8/15 (the fraction of the report they can do in one hour).
time = 1 ÷ (8/15)
time = 1.875 hours
Therefore, it will take Tom and Nelson 1.875 hours, or 1 hour and 52.5 minutes, to complete the report working together.
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PLEASE HELP WILL GIVE BRAINLY AND 5.0 RATING
Answer:
(-1,5)Step-by-step explanation:
(-3,5)
-2 in the x-axis
(-5,5)
+4 in the x-axis
(-1,5)
two hundred five thousandths in decimal numbers
The required decimal form of two hundred five thousandths is 0.205.
When we write a decimal number, each digit represents a different power of 10, with the digit to the left of the decimal point representing the one place, and the digits to the right of the decimal point representing fractions of a whole.
So, to represent two hundred five thousandths in decimal form, we need to write 2 in the thousandth place, which is three digits to the right of the decimal point. This gives us the number 0.205.
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A friend of yours was interested in determining whether the news media noticed campus events. Your friend decided to do a content analysis of the local paper.Your friend counted each story that mentioned his university's name. At the end of two months, 136 events had been counted. Your friend asked for your comments on his research. You told your friend:
The inference is that the person will tell the friend that he did manifest coding and he should have recorded the base.
What is an inference?The options are:
He did manifest coding.
He did latent coding.
He should have recorded the base.
He did manifest coding and he should have recorded the base.
It should be noted that an inference simply means the conclusion that can be deduced based on the information given.
In this case, the friend was interested in determining whether the news media noticed campus events and decided to do a content analysis of the local paper.
Therefore, the the person will tell the friend that he did manifest coding and he should have recorded the base.
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You told your friend: d. he did manifest coding and he should have recorded the base.
How to determine the true statement?The missing options are:
a. he did manifest coding. b. he did latent coding.
c. he should have recorded the base.
d. he did manifest coding and he should have recorded the base.
e. he did latent coding and he should have recorded the base.
From the question, we understand that:
Each story is counted136 events were counted after 2 monthsAs a general rule, manifest coding include making use of the contents at the surface gotten from available data and questionnaires.
Because the stories that mentioned the university name can be gotten from publications, it means that your friend used manifest coding
Hence, the true statement is (d) he did manifest coding and he should have recorded the base.
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Finding the initial amount and rate of change given a table for a linear function
Answer:
What the heII happened? aight nvm It's function
Step-by-step explanation:
my old answer got deleted ;(
Evaluate the following integral using integration by parts. 4 sin-1 4 sin - ¹2x dx [4 sin -¹2x dx =
The complete solution is:
∫4\(sin^{-1}(2x) dx = sin^{-1}(2x)\) x 4x + √(1 - (2x)²) + C, where C is the constant of integration.
We have,
\(u = sin^{-1)}(2x)\)
dv = 4 dx
Taking the derivative of u, we get:
du/dx = 1 / √(1 - (2x)²)
Integrating dv, we get:
v = ∫4 dx = 4x
Now, applying the integration by parts formula:
∫4 \(sin^{-1}(2x) dx\) = uv - ∫vdu
Plugging in the values, we have:
∫4 \(sin^{-})(2x) dx = sin^{-1}(2x) \times\) 4x - ∫(4x / √(1 - (2x)²)) dx
At this point, we need to evaluate the integral on the right side.
Let's perform a substitution to simplify it:
Let u = 1 - (2x)²
Differentiating u with respect to x, we get:
du/dx = -4(2x) = -8x
Solving for dx, we have:
dx = -du / (8x)
Substituting these values, the integral becomes:
∫(4x / √(1 - (2x)²)) dx = ∫(-4x / (8x x √u)) (-du / (8x))
Simplifying, we get:
∫(4x / √(1 - (2x)²)) dx = ∫(-1 / (2√u)) du
= -∫(1 / (2√u)) du
= -√u + C
Substituting back the value of u, we have:
∫(4x / √(1 - (2x)²)) dx = -√(1 - (2x)²) + C
Therefore,
The complete solution is:
∫4\(sin^{-1}(2x) dx = sin^{-1}(2x)\) x 4x + √(1 - (2x)²) + C, where C is the constant of integration.
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The complete question:
a) Evaluate the integral ∫4 sin^(-1)(2x) dx using integration by parts.
At best buy you are planning on buying a new phone for x dollars. You also want to buya new phone case that costs $10. 99. If there is a 15% discount, write an expression for the total that you will pay for the phone and phone case.
Answer:
C = 0.85x
Step-by-step explanation:
Total Cost = (phone + phone case) - .15(phone + phone case)
C = (x+10.99) - .15(x+10.99)
C = 1x + 10.99 - 0.15x - 10.99
combine 'like terms' to get:
C = 0.85x
PLEASE HELP ME! Sally is paid a fixed amount of money to walk her neighbor's dog every day after school. When she is paid each month, she puts aside $20 to spend and saves the remaining amount. Write an expression that represents the amount Sally will save in 6 months if she earns m dollars each month.
Answer: 6($m - $20)
Step-by-step explanation:
From the question, we are told that Sally earns m dollars each month to walk her neighbor's dog every day after school and that when she is paid each month, she puts aside $20 to spend and saves the remaining amount. This means that Sally saves:
$m - $20.
The expression that represents the amount Sally will save in 6 months will be so multiplied by the amount saved every month. This will be:
= 6($m - $20)
Answer:
Ok first of all. You cant be in highschool with this question. because this is a 6th grade question. Second that person who gave you that asnwer is wrong because thats not even the answer now I advise you to listen for future refrences.
Step-by-step explanation:
she is paid $65 and she saves $20 so subtract those numbers then you get $45 so that means she saves $20 and had $45 to spend. that means 20 times 6(months) is... $120 so $120 is your answer. But, to be more professional "Sally has saved $120 in 6 (Months.)
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a=3 inches and c=7 inches, what is the perimeter? If necessary, round to the nearest tenth.
Answer: 16.325 in
Step-by-step explanation:
First, we will find b. We will use the Pythagorean theorem to do this.
a² + b² = c²
3² + b² = 7²
9 + c² = 49
c² = 40
c = \(\sqrt{40}\) ≈ 6.324555 ≈ 6.325 in
Now, we will add all the sides together to find the perimeter.
3 in + 7 in + 6.325 in = 16.325 in
Endpoint: (-4, 8), midpoint: (3,-4)
Find the other endpoint
Explain please
Answer: (10,-16)
Step-by-step explanation:
\(A(-4,8)\ \ \ \ C(3,-4)\ \ \ \ \ B(x_B,y_B)=?\\\)
See the graph below.
\(\displaystyle\\\boxed {x_C=\frac{x_A+x_B}{2} }\\\\\)
Multiply both parts of the equation by 2:
\(2x_C=x_A+x_B\\2x_C-x_A=x_A+x_B-x_A\\2x_C-x_A=x_B\)
Hence,
\(x_B=2*3-(-4)\\x_B=6+4\\x_B=10\)
\(\displaystyle\\\boxed {y_C=\frac{y_A+y_B}{2} }\)
Multiply both parts of the equation by 2:
\(2y_C=y_A+y_B\\2y_C-y_A=y_A+y_B-y_A\\2y_C-y_A=y_B\)
Hence,
\(y_B=2*(-4)-8\\y_B=-8-8\\y_B=-16\\Thus,\ B(10,-16)\)
Fild the slope of the line.( in the picture)
Answer:
m = 3/1
Hope that helps!
Answer:
-12/4 or -3Step-by-step explanation:
I can give you step by step if u want, just ask, but if you want the answer fast: its -3
A bag contains 3 blue marbles, 2
green marbles and 1 red marble.
What is the probability of pulling a
red marble from the bag?
a) 12
b) 1/3
c) 1/5
d) 1/6
Help ASAP
Answer:
D 1/6
Step-by-step explanation:
There are 6 total marbles and only one of them is red so
1=red
6=total
1/6
PLZ MARK ME BRAINLIEST
When csc(0)sin(0) is simplified, what is the result?
Answer:
csc θ * sin θ
Simplified using trig identities:
csc (x) = 1/sin(x)
so, csc (0) = 1/sin(0)
1/sin(0) * sin (0), the result will be sin(0) / sin (0) which is equal to 1.
Therefore, the answer is 1.
Step-by-step explanation:
Expression in sin θ and cos θ below
4cos ec^2 2θ as 2 / 2 (4 sin θ cos θ )^2
or
cos ec^2 θ as 1 / sin ^2 θ
. Accept terms like
cos ec^2 θ = 1 +cot^2 θ =1 + cot^2 θ /sin^2 θ
Find an equivalent statement for the following absolute value equation |x - 5] = 1x +6
ANSWER:
STEP-BY-STEP EXPLANATION:
chregg Find the dimensions of a rectangle (in m) with perimeter 92 m whose area is as large as possible. (Enter the dimensions as a comma-separated list.)
The dimensions of a recatngle with perimeter 92m whose area is as large as possible or maximum area are 23 meters and 23 meters.
Let the dimensions of the rectangle be x and y meters.
According to th egiven question.
The perimeter of the rectangle is 92 m.
⇒ 92 = 2(x + y)
⇒ 46 = x + y
⇒ x = 46 - y
Now, the area of the rectangle is given by
Area of recatnagle, A = xy
⇒ A = ( y - 46)y
For the large possible area or maximum area
dA/dy = 0
⇒ d(y - 46)y/dy = 0
⇒ d(y^2 - 46y)/dy = 0
⇒ 2y - 46 = 0
⇒ y - 23 = 0
⇒ y = 23
Therefore,
x = 46 - 23
⇒ x = 23
Hence, the dimensions of a recatngle with perimeter 92m whose area is as large as possible or maximum area are 23 meters and 23 meters.
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If Mary and Jane walks around her garden twice per day what is the total
distance she walks around the garden per day rounded off to the nearest
tens place.
A.40
B.80 m
C.80
D.41 m
Answer:
Step-by-step explanation:
A,B or C, depends on the garden length.
Which equation represents the situation below?
After a 20% discount, the cost of a pair of headphones was $260. How much did the headphones cost before the discount?
Let h = original cost of headphones
Answer:
Para calcular el precio original de los auriculares antes del descuento, podemos usar la fórmula:
Precio original = Precio después del descuento / (1 - Porcentaje de descuento)
Donde "Precio después del descuento" es el costo de los auriculares después del descuento, y "Porcentaje de descuento" es el porcentaje aplicado como descuento. En este caso, el porcentaje de descuento es del 20%, es decir, 0.2 en términos decimales.
Sustituyendo los valores conocidos, obtenemos:
Precio original = 260 / (1 - 0.2)
Precio original = 260 / 0.8
Precio original = 325
Por lo tanto, el costo original de los auriculares antes del descuento era de $325.:
Answer:
The answer is D. (1-0.2)h=260
Step-by-step explanation:
5(10k + 1) + 2(2+8k)
Answer:
5(10k + 1) + 2(2+8k)
Use distributive property
5(10k)+5(1)+2(2)+2(8k)
50k+5+4+16k
combine like terms (50k and 16k are alike as well as 5 and 4)
50k+16k and 5+4
66k+9 is the answer
1.) Shown is Equilateral triangle ABC.
AB = 6 cm.
BC
11
CA E
В
Answer: All answers are 6.
Step-by-step explanation: Equilateral triangles have equal side lengths and angle measures.
Answer:
Step-by-step explanation:
All sides of an equilateral triangle is equal.so,
length BC=6 cm
length CA=6 cm
A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 47 states. What is the probability that she selects the route of three specific capitals? P(she selects the route of three specific capitals) 97290 (Type an integer or a simplified fraction:)
The probability that she selects the route of three specific capitals is 97290/1.
The probability that she selects the route of three specific capitals can be calculated by taking the total number of possible routes and dividing it by the total number of routes that involve the three specific capitals. To calculate the total number of possible routes, multiply the number of states (47) by the number of routes that could be selected from each state (2). This gives 94 total possible routes.
47 x 46 x 45 ways = 97290 ways
= 1/97290
Now, calculate the number of routes that involve the three specific capitals. Since the president is selecting three states, the total number of routes will be 3. Therefore, the probability that she selects the route of three specific capitals is 3/94, which can be simplified to 97290/1.
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