According to the informations, there are 7 different ways a committee of six people can be selected from a group of seven candidates.
How can we find this number?In this case, we must use the combination formula, which is expressed by:
nCr = n! / r!(n-r)!Where n is the total number of items in the set, r is the number of items being selected, and ! denotes the factorial function, which means multiplying a number by all the positive integers less than it.
Therefore, from a group of 7 candidates, a committee of 6 people can be selected in 7 different ways using the combination formula. The formula for the combination of n objects taken r at a time is C(n,r) = n!/r!(n-r)!, where n is the total number of objects and r is the number of objects to be chosen. In this case, we have n = 7 and r = 6, so the formula gives us C(7,6) = 7!/6!(7-6)! = 7 ways.
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A digital thermometer in Olivia's car says the temperature outside is –5°C. Which statement BEST describes the meaning of the value –5 in this context?
The value -5°C represents the temperature outside as measured by the digital thermometer in Olivia's car.
Which statement describes the meaning of the valueIn this context, the value -5 represents the temperature outside in Celsius degrees.
The minus sign indicates that the temperature is below freezing point. The Celsius scale is a temperature scale that uses the freezing point of water (0°C) and the boiling point of water (100°C) at standard atmospheric pressure as its reference points.
Thus, a temperature of -5°C means that it is five degrees Celsius below the freezing point of water.
The negative sign indicates that the temperature is below zero degrees Celsius, which is the freezing point of water.
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A surge function is a function of the form
f (t) = Atne(−bt)
The values A, n, and b are the parameters of the function.
This function accurately represents the way a drug interacts in the bloodstream. Studying
this function is essential to doctors and pharmacists because it allows them to administer
dosages of medicine correctly.1
A drug dose is being designed for a 90kg male patient. The amount of the drug in the
patient’s bloodstream after t hours, measured in nanograms per milliliter (ng/ml) is given
by a surge function.
Any positive value of A can be achieved by increasing or decreasing the amount of
medicine given. However, depending on the type of delayed release mechanism selected
there are choices possible for the value of the pair (n,b): The achievable pairs are listed in
the table below.
Delay Type n value b value
Extended 2 0.3
Medium 3 0.5
Rapid 3 0.7
The medical requirements for the treatment are:
• The dose (in ng/ml) may not exceed 100 at any time.
• The dose must fall to be at or below 20 ng/ml by 24 hours.
Within these parameters, the treatment effect will be measured in ng/ml-hours. (1
ng/ml concentration for 1 hour is 1 ng/ml-hour of treatment). The objective is to obtain
the maximum possible treatment effect while ensuring the requirements are met.
1Tarko, Olta (2021) ”Surge Functions and Drug Interactions,” Undergraduate Journal of Mathematical
Modeling: One + Two: Vol. 12: Iss. 1, Article 7
The top three prices for works of art sold at auction in 2013 totaled $308.0 million. These three works of art were a sculpture, a painting, and a photograph. The selling price of the painting was $49.4 million more than that of the photograph. Together, the painting and the photograph sold for $24.4 million more than the sculpture. What was the selling price of each work?
The selling prices of the sculpture, painting, and photograph were 166.5 million, 107.0 million, and 57.6 million respectively.
How to Determine the Selling Price?Let's call the selling prices of the sculpture, painting, and photograph as S, P, and Ph respectively.
From the first sentence, we know that:
S + P + Ph = 308.0 million
From the second sentence, we know that:
P = Ph + 49.4 million
And from the third sentence, we know that:
P + Ph = S + 24.4 million
Now we can substitute the second equation into the third equation:
(Ph + 49.4 million) + Ph = S + 24.4 million
Simplifying:
2Ph + 49.4 million = S + 24.4 million
2Ph = S - 25 million
Substituting this into the first equation:
S + P + Ph = 308.0 million
S + (Ph + 49.4 million) + Ph = 308.0 million
2Ph + S = 258.6 million
Now we can substitute the equation we derived earlier:
S + 2Ph - 49.4 million = 258.6 million
S + 2Ph = 308.0 million
Substituting 2Ph = S - 25 million:
S + S - 25 million = 308.0 million
2S = 333.0 million
S = 166.5 million
Now we can use this value to find P and Ph:
P = Ph + 49.4 million
P + Ph = S + 24.4 million
Substituting S = 166.5 million in both equations:
P + Ph = 190.9 million
P = Ph + 49.4 million
Solving these two equations simultaneously:
Ph = 57.6 million
P = 107.0 million
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Help me Help me Help me
Answer:
F
Step-by-step explanation:
First, find the answer to (180 /5 + 4 x 12 - 10) which is 74.
Next, start with solving the possible answers.
Lastly, once you have solves determine which answer is the same, which is F.
How many significant digits are there in the number 9.15 x 10000
There are four significant digits in the number 9.15 x 10⁴.
The digits that provide the number with useful information are known as the important digits.
As they add to the value of the number in this instance, the numbers 9, 1, and 5 are all important.
The exponent, 4, just instructs us on how many places to relocate the decimal point, therefore it has no bearing on the number of significant digits.
Therefore, the number 9.15 x 10⁴ has four significant digits.
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Use w for the unknown.
"A number split into 3 equal parts"
Answer:
[tex] \frac{w}{3} [/tex]
What is the work done on an object if a force of 4 x − x 2 is applied from x = 0 to 3?
The work done on an object if a force of 4 x − x^2 is applied from x = 0 to 3 is 9J
What is the workdone?Work Done serves as the quantity of energy which is been moved by the force so that a particular energy can move howver the relation between Work and Energy can be seen as a direct one.
Give that force= 4 x − x^2 from x = 0 to 3
Work done by force , F= ∫(4 x − x^2 )dx (0-3)
F= (4x^2/2 - x^3/3)
=[2x^2 -x^3/3]
= [2*3^2 -3^3/3 - 2*0^2 -0^3/3]
18 -9= 9
9J
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The owners of Applewood Farmstead tracked their fruit sales over the weekend. The graph below shows the relative frequencies of the sales of each fruit. Applewood Farmstand sold a total of 320 pieces of fruit over the weekend. How many of those were apples?
Applewood Farmstand sold 102 pieces of apples over the weekend.
What is graph?Graph is a data structure which consists of nodes (vertices) that are connected with each other. Graphs are used to represent relationships between different objects, such as networks, social connections, and pathways. Graphs are useful for representing data as they can provide a visual representation that is easy to interpret, and can be used to analyse patterns in the data. Graphs can also be used to represent problems such as shortest path problems, and can be used to solve problems such as finding the most efficient route between two points.
The graph shows that apples accounted for 32% of the total fruit sales. To find the exact number of apples sold, we can calculate the following:
Apples = (320 pieces of fruit) x (0.32)
Apples = 102 pieces
Therefore, Applewood Farmstand sold 102 pieces of apples over the weekend.
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a rectangular prism is 12 units high and 5 units wide an 10 units long
Answer:
To find the surface area of a rectangular prism, we can use the formula:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism, respectively.
Given that the rectangular prism is 12 units high, 5 units wide, and 10 units long, we can substitute these values into the formula:
Surface Area = 2(10)(5) + 2(10)(12) + 2(5)(12)
Surface Area = 100 + 240 + 120
Surface Area = 460 square units
Therefore, the surface area of the rectangular prism is 460 square units
How much property tax must be paid
each month when the property tax is
$1,176 a year?
Answer:
$98 a month
Step-by-step explanation:
1,176 divided by 12
A 2-pound package of hamburger costs $7.00, and you pay $10.50 for a 3-pound package of hamburger.
A 2-pound package of hamburger costs $7.00, and you pay $10.50 for a 3-pound package of hamburger.
To find the cost per pound of hamburger, we need to divide the total cost by the weight in pounds.
For the 2-pound package
Cost per pound = Total cost / Weight in pounds
Cost per pound = $7.00 / 2 lbs
Cost per pound = $3.50 per pound
For the 3-pound package
Cost per pound = Total cost / Weight in pounds
Cost per pound = $10.50 / 3 lbs
Cost per pound = $3.50 per pound
Therefore, the cost per pound of hamburger is the same for both packages, at $3.50 per pound.
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Use the functions [tex]f(x)[/tex] and [tex]g(x)[/tex] to find the domain of the indicated functions, and simplify the expressions for the domain in question.
FUNCTIONS:
[tex]f(x) = x^4[/tex]
[tex]g(x)=\sqrt{x+7}[/tex]
1) [tex](f+g)(x)[/tex] = [tex]f(x)+g(x)[/tex]
2) [tex](f-g)(x)[/tex] = [tex]f(x)-g(x)[/tex]
3) [tex](fg)(x)[/tex] -> [tex](f(g(x))[/tex]
POSSIBLE ANSWERS:
A) The domain of all three pairs is -∞ ≤ [tex]x[/tex] ≤ ∞.
B) The domain for #1 and #2 is [tex]x[/tex] ≥ -7 and the domain for #3 is -∞ ≤ [tex]x[/tex] ≤ ∞.
C) The domain of every pair is [tex]x[/tex] ≥ -7.
D) A through C are partially true.
E) None of the above OR the domain is undefined.
B) The domain for #1 and #2 is ≥ -7 and the domain for #3 is -∞ ≤ ≤ ∞.
Explanation:1. [tex](f + g)(x) = f(x) + g(x)[/tex]
The domain of [tex](f + g)(x)[/tex] is the intersection of the domains of [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since [tex]f(x) = x^4[/tex] is defined for all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for [tex]x > = -7[/tex] (since we can't take the square root of a negative number), the domain of [tex](f + g)(x)[/tex] is [tex]x > = -7[/tex].
2. [tex](f - g)(x) = f(x) - g(x)[/tex]
The domain of [tex](f - g)(x)[/tex] is also the intersection of the domains of [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since [tex]f(x) = x^4[/tex] is defined for all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for[tex]x > = -7[/tex], the domain of [tex](f - g)(x)[/tex] is also [tex]x > = -7[/tex].
3. [tex](fg)(x) - > (f(g(x))[/tex]
The domain of [tex]f(g(x))[/tex] is the set of all values of [tex]x[/tex] such that [tex]g(x)[/tex] is in the domain of [tex]f[/tex]. Since the domain of [tex]f[/tex] is all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for [tex]x > = -7[/tex], the domain of [tex]f(g(x))[/tex] is [tex]x > = -7[/tex].
Therefore, the correct answer is option:
B) The domain for 1) and 2) is [tex]> = -7[/tex] and the domain for 3) is -∞ ≤ [tex]x[/tex] ≤ ∞.
< ^2 − 3
^2 ≥ x^2/2 -12
Is this a system of linear inequalities?
The linear inequalities in the given graph is y ≥ x/2 -1 and y< -1/2x -3.
What is Linear inequalities ?Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These quantities may be numerical, algebraic, or a combination of the two.
Here, we have,
The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality has the same appearance as a linear equation, but uses a different symbol to link the two expressions.
we have,
In the given graph, the area above solid line,
points, (-2 , -2) , (0 , -1)
slope = 1/2
so, y ≥ x/2 -1
The area below dashed line ,
points, (-2 ,-2) , (0 ,-3)
slope= -1/2
so, y< -1/2x -3.
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5 pts
It's time to remodel your home! You'd like to replace the tile in your kitchen. The room is 12'x20' with
8' ceilings. The tile costs $4.75 per square foot. How much will it cost?
If the room is 12'x20' with 8' ceilings and the tile costs $4.75 per square foot, the total cost is $1140.
To calculate the cost of replacing the tile in the kitchen, we need to first calculate the total area of the floor.
Area of the floor = Length x Width = 12 ft x 20 ft = 240 sq ft
Since we know the cost per square foot of tile, we can now multiply the total area of the floor by the cost per square foot to find the total cost:
Total cost = Area of the floor x Cost per square foot
Total cost = 240 sq ft x $4.75/sq ft
Total cost = $1140
Therefore, it will cost $1140 to replace the tile in the kitchen, assuming there are no additional costs such as labor or materials for removing the old tile.
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What part of the proof uses the justification that angles with a combined degree measure of 90⁰ are complementary?
The justification of the angles with a combined degree measure of 90⁰ are complementary angles is proved by part 3. ∠1 is complementary to ∠2.
In the figure,
Measure of angle 1 = 40 degrees.
Measure of angle 2 = 50 degrees
Angle 2 is complementary to angle 3.
Proof of the result,
Measure of ∠1 = 40 degrees ( given )
Measure of ∠2 = 50 degrees ( given )
Measure of ∠1 + measure of ∠2 = 40° + 50°
⇒ Measure of ∠1 + measure of ∠2 = 90°
⇒ Angle 1 and angle 2 are complementary to each other.
Complementary angles are such pairs of angles whose sum is equal to 90°.
It is given that
Angle 2 is complementary to angle 3.
This implies ,
m ∠1 + m ∠2 = m ∠2 + m ∠3
⇒ m ∠1 = m ∠3
⇒ m ∠1 ≅ m ∠3
Therefore, the part 3 . ∠1 is complementary to ∠2 gives the justification for the proof of complementary angles.
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The perimeter of a rectangle is 42.4 inches. The length of the rectangle is three times its
width. What is the length of the rectangle?
The length of the rectangle is 15.9 inches. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
The four fundamental operations, often known as "arithmetic operations," can be used to explain any real number. Operations like quotient, product, sum, and difference come after operations like division, multiplication, addition, and subtraction in mathematics.
We are given that the perimeter of a rectangle is 42.4 inches and the length is three times its width.
Let the width be 'x'.
So, length will be 3x.
From this, we get
⇒ Perimeter = 2 (length + width)
⇒ 42.4 = 2 (3x + x)
⇒ 42.4 = 2 (4x) (Using addition operation)
⇒ 42.4 = 8x (Using multiplication operation)
⇒ x = 5.3 (Using division operation)
So,
⇒ Length = 3 * 5.3
⇒ Length = 15.9 inches
Hence, the length of the rectangle is 15.9 inches.
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The area of this rhombus is 20 square miles. One of its diagonals is 10 miles. What is the length of the missing diagonal?
========================================================
Work Shown:
[tex]d_1 = \text{ one of the diagonals} = 10\\\\d_2 = \text{ the other diagonal}= \text{x}\\\\A = \text{ area of the rhombus} = 20\\\\A = \frac{d_1*d_2}{2}\\\\20 = \frac{10\text{x}}{2}\\\\20*2 = 10\text{x}\\\\40 = 10\text{x}\\\\\text{x} = 40/10\\\\\text{x} = 4[/tex]
The other diagonal is 4 miles long.
Find the percent of increase. Round to the nearest tenth.
125 to 240
A. 104.0%
B. 92.0%
C. 115.0%
D. 143.8%
Please what is the answer?
Answer:
When we have a set of points, we can find the distance between them using the formula:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex], where d is the distance, x1 and x2 are one point and y1 and y2 are another point.
OB:
Thus, for OB, we can allow O(6, 6) to be our x1 and x2 point and we can allow B(9, 6) to be our y1 and y2 point:
[tex]d=\sqrt{(6-9)^2+(6-6)^2} \\d=\sqrt{(-3)^2+(0)^2} \\d=\sqrt{(-9)} \\d=3[/tex]
Thus, the first part/step in the equation is your subtraction expression to find the length of OB.
AB:
For AB, we can allow A(9, 10) to be our x1 and x2 point and we can allow B (9, 6) to be our y1 and y2 point:
[tex]d=\sqrt{(9-9)^2+(10-6)^2}\\ d=\sqrt{(0)^2+(4)^2}\\ d=\sqrt{16}\\ d=4[/tex]
The first part/step is your subtraction expression for the length of AB.
(2a² b c³) (-a² b⁵)
pls help asap!
Answer:
-2a⁴ b⁶ c³
Step-by-step explanation:
2a² b c³ (-a² b⁵)
determine the signs for multiplication or division
-2a²bc³a²b⁵
multiply the monomials
-2a⁴b⁶c³
(then done)
1) You're traveling to Spain this
summer. You'll have $200 to spend on
memorabilia items. How much euros
do you have to spend on memorabilia
items? Note: $1=0.84 E
Using the conversion factor we know that we will spend 180.69€ on memorabilia items.
What is the conversion factor?A conversion factor is a number that is used to multiply or divide one set of units into another.
If a conversion is required, it must be done using the correct conversion factor to get an identical value.
A fraction that is equal to "1" is a conversion factor.
The numerator and denominator are the same amounts, but they are expressed in different units. It is used to change a number's unit of measurement.
By multiplying the initial number by the fraction that is equal to "1," you can change the units without changing the original number's value.
So, in the given situation:
$200 = euros?
We know that:
$1 = 0.90€
Then,
$200 = 180.69€
Therefore, using the conversion factor we know that we will spend 180.69€ on memorabilia items.
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A laptop has a listed price of 639.99 before tax. If the sales tax rate is 9.75%, find the total cost of the laptop with sales tax included. Round your answer to the nearest cent, if necessary.
Answer: $702.39
Step-by-step explanation: To find the total cost of the laptop with sales tax included, we need to add the sales tax to the listed price.
First, we need to calculate the amount of sales tax.
Sales tax = 9.75% of 639.99
Sales tax = 0.0975 x 639.99
Sales tax = 62.40
Now we can find the total cost of the laptop with sales tax included:
Total cost = listed price + sales tax
Total cost = 639.99 + 62.40
Total cost = 702.39
Therefore, the total cost of the laptop with sales tax included is $702.39.
100 Points!!! Determine if the equation (2x²+y²)²=(2x²-y²)²+(2xy√2)² is a polynomial identity. Photo attached. Please show as much work as possible. Thank you!
Answer:
Yes, it is a polynomial identity (work below).
Step-by-step explanation:
Let's start by expanding the left side of the equation.
[tex](2x^2+y^2)^2=\\4x^4+y^4+4x^2y^2[/tex]
Now, let's expand the second side.
[tex](2x^2-y^2)^2+(2xy\sqrt{2} )^2=\\4x^4+y^4-4x^2y^2+4x^2y^2(2)=\\4x^4+y^4-4x^2y^2+8x^2y^2[/tex]
There are no like terms on the left side, so let's combine the like terms on the right side.
[tex]4x^4+y^4-4x^2y^2+8x^2y^2=\\4x^4+y^4+4x^2y^2[/tex]
Now, let's check if the left and right sides are equal:
[tex]4x^4+y^4+4x^2y^2= 4x^2+y^4+4x^2y^2[/tex]
Both sides are the same. Thus, the equation is a polynomial identity.
Find the value of x
The value of 'x' in the given figure is 14.73.
The given figure is a Right-angled triangle.
According to the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of squares of the adjacent side and the opposite side.
In the given figure,
Hypotenuse is 19.
The adjacent side is 12.
The opposite side is x.
Now, we have to find the value of x.
According to the theorem,
19² = 12²+x²
361 = 144+x²
x² = 361 - 144
x² = 217
x = √217
x = 14.73
Therefore, the value of 'x' in the given figure is 14.73.
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please help me
a!!!!!!!!
Answer:
Step-by-step explanation:
Hopefully this is right.
Area = r²
Which is pi times the the radius squared
The radius is 2, so 2² is 4, So we multiply 3.14, which is pi, by 4.
Multiply 3.14 by 4, and the answer is 12.56, the question says round to the nearest tenth, so the final answer will be 12.6
My math teacher back in 7th grade gave us this sentence to help us memorize the equations.
Cherry Pie Delicious (C=d), Apple Pie Are Too (A=r²)
Do the same with the other two questions, and the answer for question two will be 3.14, rounded to the nearest tenth will be 3.1
Hope this helps!
For a circle with a radius of 2, the area can be calculated using the formula:
Area = π x r^2
where π is approximately 3.14 and r is the radius.
Plugging in the values, we get:
Area = 3.14 x 2^2
Area = 3.14 x 4
Area = 12.56
Rounding to the nearest tenth, we get:
Area ≈ 12.6
Therefore, the area of the circle with radius 2 is approximately 12.6.
For a circle with a radius of 1, the area can be calculated using the same formula:
Area = π x r^2
Plugging in the values, we get:
Area = 3.14 x 1^2
Area = 3.14
Rounding to the nearest tenth, we get:
Area ≈ 3.1
Therefore, the area of the circle with radius 1 is approximately 3.1.
Barry buys a plot of land that measures 1/4 acre. He divides the plot into 3 equal pieces
The calculated area of each piece is 1/12 acre
Calculating the area of each pieceIf Barry buys a plot of land that measures 1/4 acre, then the total area of the land is 1/4 acre.
If he divides the land into 3 equal pieces, then each piece will have 1/3 of the total area.
So the area of each piece will be:
Area of each piece = (1/3) x (1/4) acre
Multiplying the fractions, we get:
Area of each piece = 1/12 acre
Therefore, each piece of land will have an area of 1/12 acre.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
g°f = -9 So, the correct answer is (B) -9.To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.
what is function ?
In mathematics, a function is a relation between two sets, called the domain and the range, that assigns to each element of the domain exactly one element of the range.
In the given question,
To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.
Step 1: Apply f to -3
f(x) = 3x + 7
f(-3) = 3(-3) + 7 = -2
Step 2: Apply g to the result of f(-3)
g(x) = 2x - 5
g(-2) = 2(-2) - 5 = -9
Therefore, g°f = -9.
So, the correct answer is (B) -9.
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Breck has 22 dimes and nickels. The total value of the coins is $1.45.
How many dimes and how many nickels does Breck have?
Answer:
11 dimes and nickels.
Step-by-step explanation:
22 total coins divided by 2 equals 11 for each.
the number 2 represents the dimes and nickels, 22 for the total amount of coins, and 11 for the answer.
Answer:15 nickels and 7 dimes.
Step-by-step explanation:
7x³+5x² - 2 = [?]
X = -1
What is the numerical coefficient in the expression 2x³y?
Answer:
2
Step-by-step explanation:
The numerical coefficient is the number that is multiplied to a variable.
Example.
2x^2 + 7y^3
The numerical coefficients would be 2 and 7.
So for your problem it would be 2 since 2 is the number being multiplied to x and y.