In this case, we have 6 places to fill from a pool of 22 candidates. There is no difference in the places: they are all commissioners, so if candidate A is selected, the order does not matter, but there is only one candidate, so there is no repetition.
Then, this is a combination (as the order does not matter) with no repetition of 22 elements in 6 places.
We can calculate this as:
[tex]\begin{gathered} C(n,r)=\frac{n!}{r!(n-r)!} \\ C(22,6)=\frac{22!}{6!(22-6)!}=\frac{22!}{6!\cdot14!}=\frac{22\cdot21\cdot20\cdot19\cdot18\cdot17\cdot16\cdot15}{6\cdot5\cdot4\cdot3\cdot2\cdot1}=17907120 \end{gathered}[/tex]Answer: there are 17,907,120 ways this can be done.
The Gift Basket Store had the following premade gift baskets containing the following combinations in stock.CookiesMugsCandyTotalCoffee57820Tea73313TOTAL12101133Choose 1 basket at random. Find the probability that it contains cookies given that it contains coffee (to three places after the decimal point).
We are asked to find the probability that it contains cookies given that it contains coffee.
This is called conditional probability and is given by
[tex]P(A|B)=\frac{P(A\: and\: B)}{P(B)}[/tex]This means that the probability of event A given that event B has occurred.
For the given case, it becomes
[tex]P(Cookies|Coffee)=\frac{P(Cookies\: \: and\: \: Coffee)}{P(Coffee)}[/tex]The probability P(Cookies and Coffee) is the intersection of the column "Cookies" and the row "Coffee" divided by the grand total.
[tex]P(Cookies\: \: and\: \: Coffee)=\frac{5}{33}[/tex]The probability P(Coffee) is the row total of the row "Coffee" divided by the grand total.
[tex]P(Coffee)=\frac{20}{33}[/tex]Finally, the conditional probability is
[tex]P(Cookies|Coffee)=\frac{P(Cookies\: \: and\: \: Coffee)}{P(Coffee)}=\frac{\frac{5}{33}}{\frac{20}{33}}=\frac{5}{33}\cdot\frac{33}{20}=\frac{5}{20}=\frac{1}{4}=0.25[/tex]Therefore, the probability that it contains cookies given that it contains coffee is 0.25
Please help me I was sick today and missed out on class and I don’t understand this question
I hope this is clear enough , although I did not arrive at the same answer using x in both equation .
Drum Tight Containers is designing an open-top, square-based, rectangular box that will have a volume of 171.5 in.³.
What dimensions will minimize surface area?
The length of one side of the base is?
The height of the box is?
What is the minimum surface area?
The length of one side of the base is 7 inches.
The height of the box is 3.5 inches.
The minimum surface area of the box is 147 inch².
Let the length of the box be "l".Let the height of the box be "h".The volume of the box is given to be 171.5 inch³.171.5 = l²hh = 171.5/l²The surface area of the box is "A".The surface is made up of the base and the four sides of the box.A = l² + 4*h*lA = l² + 4*(171.5/l²)*lA = l² + 686/lWe need to minimize the surface area.Differentiate the equation with respect to "l".dA/dl = 2l - 686/(l²)To get the minima, put dA/dl = 0.2l - 686/(l²) = 02l = 686/(l²)l³ = 343l = 7 inchesh = 171.5/l²h = 3.5 inchesA = l² + 686/lA = 49 + (686/7)A = 147 inch²To learn more about minima, visit :
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What are some advantages of writing the polynomial I factored form when interpreting this situation
Answer: what
Step-by-step explanation:bye
Given: x ∥ y
w is a transversal of x and y.
Prove: ∠4 ≅ ∠5
Parallel lines x and y are cut by transversal w. On line x where it intersects line w, 4 angles are created. Labeled clockwise, from the uppercase left: angle 2, angle 1, angle 3, angle 4. On line y where it intersects line w, 4 angles are created. Labeled clockwise, from uppercase left: angle 6, angle 5, angle 8, angle 7.
A 2-column table with 5 rows. Column 1 is labeled statements with the entries x is parallel to y, w is a transversal, angle 4 is congruent to angle 1, angle 1 is congruent to angle 5, angle 4 is congruent to angle 5. Column 2 is labeled reasons with the entries given, given, A, B, C.
Complete the two-column proof.
A
B
C
∠4 ≅ ∠5 Alternate internal angles
Applying the description we have the table is completed as follows
Statement Reasons
x is parallel to y Given
w is a transversal Given
angle 4 is congruent to angle 1 Vertical opposite angle
angle 1 is congruent to angle 5 Corresponding angle
angle 4 is congruent to angle 5 Alternate internal angles
How to find angle 4 is congruent to angle 5 ( ∠4 ≅ ∠5 )
The prove ∠4 ≅ ∠5 is done by the Alternate angle theorem
∠4 ≅ ∠ 1 vertical opposite angles
∠ 1 ≅ ∠5 Corresponding angle
then we can say that
∠ 1 ≅ ∠4 ≅ ∠5
hence: ∠4 ≅ ∠5 Alternate internal angles
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Answer:
A ✔ vertical angles
B ✔ corresponding angles theorem
C ✔ transitive property
Step-by-step explanation: i hope this helps :)
A baking scale measures mass to the tenth of a gram, up to 650 grams. Which of the following measurements is possible using this scale?
742.5 grams
300.0 grams
85.25 grams
370 milligrams
The possible measures using this scale are 742.5 grams and 300.0 grams.
What is a scale?The link between a measurement on a model and the corresponding measurement on the real item is represented by scale.
Note that a tenth of a gram is 0.1 grams, therefore, the precision of the scale is 0.1 grams.
Note that 370 milligrams are equivalent to 0.370 grams.
Since the measures on the scale increase by 0.1 units, 0.25 and 0.370 are not possible on this scale.
Hence, the possible measures using this scale are 742.5 grams and 300.0 grams.
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Can you please solve this.
⇒I will use the laws of exponents. When you multiply powers of the same base you keep one base and add the exponents.
Below are all the steps in details
[tex]=9^{-8+(-2)} \\=9^{-8-2} \\=9^{-10} \\=\frac{1}{9^{10} } \\=\frac{1}{3486784401}[/tex]
11. A 20 foot ladder is leaned against a wall. The base of the ladder is 10 feet from the wall. How much longer is the ladder than the height of the wall? Round to the nearest hundredth. You may use a calculator. Hint: draw a right triangle, label the sides appropriately, and use the pythagorean theorem.
Okay so draw a diagram with a ladder leaning against a wall and draw the ground now label the diagram take the hypotenuse is ladder and the base is distance between the ladder and the wall while the perpendicular is the wall
As we know hypo=√perpendicular^2+base^2 if we want to finder the p(perpendicular) the formula changes to p=√hypo^2-base^2 put the no in the places of the equation It should look something like this p=√20^2-10^2 use calculate to solve the answer should be 17. 32
Data
Given;
Hypo(h)= 20
Base(b)= 10
Required;
Perpendicular (p)=
Solution
As we know
hypo=√perpendicular^2+base^2
by changing the formula to find p
p=√hypo^2-b^2 -----eqi
by putting the values in eq i
p=√20^2-10^2
p=17.32
Suppose that the relation H is defined as follows.
H={(6, q), (7, p), (0, 6), (7, n)}
Give the domain and range of H.
Write your answers using set notation.
domain =
range =
Answer:
Domain = {0, 6, 7}Range = {6, n, p, q}Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
In a running competition, a bronze, silver and gold medal must be given to the top
three girls and top three boys. If 15 boys and 11 girls are competing, how many
different ways could the six medals possibly be given out?
Answer:
2702700
Step-by-step explanation:
Hi there ,
Given:
In a running competition, a bronze, silver and gold medal must be given to the top three girls and three boys. If 15 boys and 11 girls are competing.
To find:
How many different ways could the six medals possible be given out?
Explanation:
As given,
The number of boys competing in a competition = 15
The number of girls competing in a competition = 11
Three medals are given to top three girls and three medals are given to top three boys.
(I have given the rest of the answer in the images below :-)
If this helped you out do mark me as brainliest and stay positive :)
A fellow mate
Cheers !
an employer pays 22 for 2 hours. use the ratio table to determine how much she chargesfor 5 hours
The employer will charge $55 for 5 hours
How to calculate the amount charged for 5 hours ?The first step is to calculate the amount charged for an hour
22= 2
x= 1
cross multiply
2x= 22
x= 22/2
x= 11
The amount charged for 5 hours can be calculated as follows
11= 1
y= 5
cross multiply
y= 55
Hence $55 will be charged for 5 hours
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Please answer the question in the picture, I will mark brainliest
A two-variable linear equation is one with the formula ax + by + c = 0.
The solution of the system exists (1, 1) and (2, 4).
What is meant by linear equations?A linear equation is an algebraic equation of the form y = mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it exists occasionally directed to as a "linear equation of two variables."A two-variable linear equation is one with the formula ax + by + c = 0, where a, b, c R, a, and b 0. An inconsistent pair of linear equations is a system of linear equations that cannot be solved.Let the system of Equations be
y = 3x - 2 and y = x²
From these Equations:
x² = 3x - 2,
simplifying the above equation, we get
⇒ x² - 3x + 2 = 0
⇒ x = 1, 2.
Therefore, the value of x exists x = 1, 2.
Therefore, the solution of the system exists (1, 1) and (2, 4).
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answer this question please
The step function and its graph that represents the relationship between the number x of days and the total cost y of renting the chipper are present in the first option.
What is a step function?A function on the real numbers is referred to as a step function in mathematics if it can be expressed as a finite linear combination of interval indicator functions. A step function is, informally speaking, a piecewise constant function with a finite number of pieces.Given:
Charge for 1 day = $100
Charge for each additional day = $50
Let's assume
The cost of rent is y.
The number of days is x.
The total cost, y according to the data provided can be calculated by the equation,
y = 100 + 50x
Using y = mx+c, when graphing a step function that represents the relationship between the number of days and the total cost,
The gradient or slope will be always 50 for the graph.
So, when x = 0, y = 100 + 0 = 100
When x = 1, y = 100 + 50 = 150
When x = 2, y = 100 + 50 × 2 = 200
When x = 3, y = 100 + 50 × 3 = 250
Thus the step function is,
f(x) = 100 , if 0 < x ≤ 1
f(x) = 150 , if 1 < x ≤ 2
f(x) = 200 , if 2 < x ≤ 3
f(x) = 250 , if 3 < x ≤ 4
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Victor found 12 sand dollars and 20 starfish at the beach cheyenne found 8 sand dollars and 16 starfish at the beach collection has a higher ratio of sand dollars to starfish
Using proportions, it is found that Victor has a higher ratio of of sand dollars to starfish.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using multiplications such as division or multiplication.
One example of proportions is for ratio problems, as:
The ratio between two amounts a and b is given by the division of a by b, that is, a/b.The ratio between two amounts b and a is given by the division of b by a, that is, b/a.Hence the ratios of sand dollars to starfish for Victor and Cheyenne are given as follows:
Victor: 12/20 = 0.6.Cheyenne: 8/16 = 0.5.0.6 > 0.5, hence Victor has the higher ratio.
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2. Find two ordered pairs that make the equation – 2x + y = 8 true. Show all work.
Answer:
(0, 8) and (-4, 0)
Step-by-step explanation:
Equation is -2x + y = 8
Manipulate this equation so that it becomes a slope-intercept form of equation
To do this:
Add 2x on both sides
-2x + 2x + y = 2x + 8
y = 2x + 8
Once we have this, 2 points which definitely lie on the line are its x and y intercepts
This is the equation of a line with slope = 2 and x-intercept = 8
x-intercept is y-value when x = 0
We can check by plugging in 0 for x in y = 2x + 8
=> y = 2(0) + 8 = 8
=> Point(0, 8) is one of the ordered pairs
Similarly we can find the x-intercept by setting y = 0 and solving for x
Setting y = 0 in y = 2x + 8
=> 0 = 2x + 8
Switch sides
2x + 8 = 0
Subtract 8 from both sides
2x + 8 - 8 = 0 - 8
2x = -8
Divide both sides by 2
=> 2x/2 = -8/2
x = -4
So (-4, 0) is another point on the line
Two ordered pairs are therefore
(0, 8) and (-4, 0)
The attached graph shows you that it is indeed so
A coach has 12 jerseys. He buys 2 sets of jerseys. Each has 10 jerseys. How many jerseys does he have now?
Total number of jerseys he have now is 32 jerseys.
A coach has 12 jerseys in beginning. Now, he buys 2 sets of jerseys.
Each set of jerseys have 10 jerseys.
2 set of jerseys have 20 jerseys.
Using unitary method this can also be written as,
1 set ----------------> 10 jerseys
2set ----------------> 20 jerseys
So, total of 20 jerseys are present in 2 sets of jerseys.
Total number of jerseys he have now = 12 jerseys + jerseys in two sets
Total number of jerseys he have now = 12 jerseys + 20 jerseys = 32 jerseys
So we can write, he have total of 32 jerseys now.
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Find the constant of variation and the degree. Is it a power function? (See pictures)
Answer:
The given function is a power function.
[tex]\textsf{The constant of variation is $\sqrt[3]{\dfrac{7}{5}}$}.[/tex]
[tex]\textsf{The power is $\dfrac{1}{3}$}.[/tex]
Step-by-step explanation:
Power function
Any function that can be written in the form:
[tex]\boxed{f(x)=k \cdot x^a}[/tex]
where:
a is the power.k is the constant of variation.Given function:
[tex]f(x)=\sqrt[3]{\dfrac{7x}{5}}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}:[/tex]
[tex]f(x)=\sqrt[3]{\dfrac{7}{5}\cdot x}[/tex]
[tex]\implies f(x)=\sqrt[3]{\dfrac{7}{5}} \cdot \sqrt[3]{x}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies f(x)=\sqrt[3]{\dfrac{7}{5}} \cdot x^{\frac{1}{3}}[/tex]
Therefore, the given function is a power function.
[tex]\textsf{The constant of variation is $\sqrt[3]{\dfrac{7}{5}}$}.[/tex]
[tex]\textsf{The power is $\dfrac{1}{3}$}.[/tex]
Given f(x) = 6x and g(x) = 9x² +5, find the following expressions (a) (fog)(4) (b) (gof)(2) (c) (fof)(1) (d) (gog)(0)
The functions are solved below
What is a function?
A function from either a given Set X to a set Y allocates exactly one item of Y to each member of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.
The functions are solved as follows
(a) f(4) = 6x4 = 24
(b) g(2) = 9x2² + 5 = 36 + 5 = 41
(c) f(1) = 6x1 = 6
(d) g(0) = 9x0² + 5 = 0 + 5 = 5
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please help 4. What is the loan payment on a fixed-rate/fixed-term mortgage loan of $100,000 at 8% for 30 years? (LO 7-3).
the loan payment on a fixed term mortgage loan of $100,000 at 8% for 30 years will be $ 340,000.
Principal amount = $ 100,000
Interest rate = 8 %
Time period = 30 years.
Now, the interest is simple interest as it is a fixed rate/ fixed term mortgage.
So, the interest will be:
Simple interest = p r t / 100
SI = 100,000 × 8 × 30 / 100
SI = $ 240,000
Amount will be:
A = $100,000 + $ 240,000
A = $ 340,000
Therefore, we get that, the loan payment on a fixed term mortgage loan of $100,000 at 8% for 30 years will be $ 340,000.
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Hello! I need some help with this homework question posted below. Q17
To solve an inequality, we need to isolate the value of x, and to do so we will perform a series of calculations in such a way that it remains the inequality unchanged, or at least still true.
To do so, we will perform first a sum of 2x to both sides of it, as follows:
[tex]\begin{gathered} 7-2x+2x\ge3+2x \\ 7\ge3+2x \end{gathered}[/tex]Now, we subtract 3 from both sides:
[tex]\begin{gathered} 7-3\ge3+2x-3 \\ 4\ge2x \end{gathered}[/tex]To finish it, we divide both sides by 2:
[tex]\begin{gathered} \frac{4}{2}\ge\frac{2x}{2} \\ \\ 2\ge x \end{gathered}[/tex]In another way, we can express the following:
[tex]\mleft\lbrace x|x\le2\mright\rbrace or(-\infty,2\rbrack[/tex]It means that the solution is option B.
To solve the second part, we need a filled line that comes from the negative infinity and goes until 2, but it must be including the number 2, and for this reason, the correct answer in the second part is:
D.
Which equation represents a line parallel to the line of the one shown on the graph
Line goes through -2,0 and 0,-4
Answer:
A
Step-by-step explanation:
Sets B and G are defined as follows. B=(-2, 2, 3, 5) G=(-1,0,2,4,7) - Answer each part below. Write your answer in roster form or as (a) Find the intersection of B and G. B n G=0 (b) Find the union of Band G. BU G=0 X
Answer
B n G = {2}
B u G = {-2, -1 , 0 , 2, 3, 4, 5, 7)
Step-by-step explanation:
Given the following two sets
B = { -2, 2, 3, 5}
G = { -1, 0, 2, 4, 7}
Part A
Find the intersection of B and G
The intersection of two sets is defined as the set of all the elements in set A that is also present in set G
Hence, the set of elements that is present in set B and set G is 2
Mathematically, B n G = {2}
Part B
Find the union of set B and set G
The union of two sets is a set containing all elements that are in both sets B and G
B u G = {-2, -1 , 0 , 2, 3, 4, 5, 7)
jjjjjjjjjjjjjjjjjjjjjjjjj
To solve this problem we will use the following property of triangles:
So if we are given the angles a and b of a triangle, the third side c, must be:1) The angles are a =
[tex]\begin{gathered} a+b+c=180^{\circ}, \\ c=180^{\circ}-a-b\text{.} \end{gathered}[/tex][tex]c=180^{\circ}-48^{\circ}-62^{\circ}=70^{\circ}\text{.}[/tex]
i. 70°
2) a = 48° and b = 62°, so we have:
[tex]c=180^{\circ}-71^{\circ}-36^{\circ}=73^{\circ}.[/tex]h. 73°
3) a = 41° and b = 86°, so we have:
[tex]c=180^{\circ}-41^{\circ}-86^{\circ}=53^{\circ}.[/tex]j. 53°
4) a = 61° and b = 88°, so we have:
[tex]c=180^{\circ}-61^{\circ}-88^{\circ}=31^{\circ}.[/tex]d. 31°
5) a = 55° and b = 92°, so we have:
[tex]c=180^{\circ}-55^{\circ}-92^{\circ}=33^{\circ}.[/tex]b. 33°
Answers
0. j. 70°
,1. h. 73°
,2. j. 53°
,3. d. 31°
,4. b. 33°
Need help graphing some problem.
INFORMATION:
Using the graph of f(x) = x^2, we must describe transformations for the function g(x)=-8x^2
STEP BY STEP EXPLANATION:
First, we need to use the graph of f(x) = x^2 which is
Then, if analyze difference between f(x) and g(x), we can see that g(x) = -1*8*f(x)
So, to graph g(x) we have two transformations:
- Multiply f(x) by -1: When we multiply by -1 we obtain the parabola opening down
- Multiply f(x) by 8: When we multiply by 8 we obtain a more closed parabola
Finally, the final graph would be
ANSWER:
Given the following vector u and v, compute the linear combination below: Please provide a step by step solution ty :))
The linear combination of the given vector is computed to be:
[tex]-4u+v=\left[\begin{array}{ccc}23\\-28\\\end{array}\right][/tex]
How to find -4u + vgiven data
[tex]u=\left[\begin{array}{ccc}-6\\6\\\end{array}\right][/tex]
[tex]v=\left[\begin{array}{ccc}-1\\-4\\\end{array}\right][/tex]
Required to compute the linear combination in the form -4u + v
solving for -4u
[tex]-4u=\left[\begin{array}{ccc}-6*-4\\6*-4\\\end{array}\right][/tex]
[tex]-4u=\left[\begin{array}{ccc}24\\-24\\\end{array}\right][/tex]
solving for -4u + v
[tex]-4u+v=\left[\begin{array}{ccc}24+-1\\-24+-4\\\end{array}\right][/tex]
[tex]-4u+v=\left[\begin{array}{ccc}24-1\\-24-4\\\end{array}\right][/tex]
[tex]-4u+v=\left[\begin{array}{ccc}23\\-28\\\end{array}\right][/tex]
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question will be in picture
Step 1: Write the given expression
[tex](2y-3)^2[/tex][tex](2y-3)^2=(2y-3)(2y-3)[/tex]Step2: Expand the expression
[tex]\begin{gathered} 2y(2y-3)-3(2y-3) \\ =4y^2-6y-6y+9 \\ =4y^2-12y+9 \end{gathered}[/tex]Hence
[tex](2y-3)^2=4y^2-12y+9[/tex]hence the righ
On January 1, a company purchased new furniture ata cost of $26,000. The furniture is estimated to have a useful life of 5 years and a salvage value of $3200
If on January 1, a company purchased new furniture at a cost of $26,000. The furniture is estimated to have a useful life of 5 years and a salvage value of $3200. The book value of the furniture on December 31 of the first year is: $21,440.
Book valueGiven data:
Cost = $26,000
Useful life = 5 years
Salvage value = $3,200
First step is to calculate the depreciation expenses:
Particular Amount
Cost $26,000
Less: Salvage value ($3,200)
Net cost (a) $22,800
Useful life (b) 5
Depreciation expenses (a/b) $4,560
($22,800 / 5 years)
Second step is to compute the book value of furniture on 31 Dec of first year:
To determine the book value we would have to deduct the depreciation expenses from the cost.
Particular Amount
Cost of an furniture $26,000
Less: Depreciation ($4,560)
Book value $21,440
Therefore we can conclude that the book value is the amount of $21,440.
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The complete question is:
On January 1, a company purchased new furniture ata cost of $26,000. The furniture is estimated to have a useful life of 5 years and a salvage value of $3200The company uses the straight-line method of depreciation. What is the book value of the furniture on December 31 of the first year?
Question
Solve: 9(x - 1) - 13x = -3(x + 5).
Provide your answer below:
X =
Answer:
x=6
Step-by-step explanation:
[tex]9(x - 1) - 13x = - 3(x + 5)[/tex]
[tex]9x - 9 - 13x = - 3x - 15[/tex]
[tex]9x - 13x + 3x = - 15 + 9[/tex]
[tex] - x = - 6[/tex]
[tex] \frac{ - \times }{ -1 } = \frac{ - 6}{ - 1} [/tex]
[tex]x = 6[/tex]
The table shows the distance a small
motor scooter can travel using one gallon
of gasoline. Complete the table to find the
number of miles the scooter can travel for
other amounts of gasoline.
Answer:
0.1 gallons = 11.8 miles
10 gallons - 1,180 miles
Step-by-step explanation:
Grant orders a $55 bouquet of flowers to be delivered to his sister. He pays the bill plus a 6.5% sales tax and a 15% tip on the total cost including tax. He also pays a $10 delivery fee that is charged after the tax and tip. How much change does he receive to the nearest cent, if he pays the delivery driver with a $100 bill?
The change that Grant received to the nearest cent after giving the delivery driver with a $100 bill is $ 32.6.
This is a question of percentages.
Given that:-
Price of bouquet of flowers = $ 55
Sales tax % = 6.5 %
Tip % = 15 %
Delivery fee= $10
We have to find the change that Grant received to the nearest cent after giving the delivery driver with a $100 bill.
Sales tax = (6.5/100)*55 = $3.575
$55 + $3.575 = $58.575
Tip = (15/100)*58.575 = $ 8.78625
Total money paid by Grant = 55 + 3.575 + 8.78625 = $ 67.36125 ≈ $ 67.4
Hence,
Change received by Grant = 100 - 67.4 = $ 32.6
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