The number of ways the first group of three wolves (necessary to include the male wolf) is given by: Option A: 28
What is the rule of product in combinatorics?If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in [tex]p \times q[/tex] ways.
Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.
Thus, doing A then B is considered same as doing B then A
For the considered case, we have:
There are 3 wolves to be included in first group.There are 8 female wolves, and 1 male wolf.1 male wolf is sure to be in the first group.So 2 spaces are remaining and are to be filled by 2 of 8 wolves.
Assuming that all 8 of them are distinguishable, choosing 2 of them is done in [tex]^8C_2 = 28[/tex] ways.
The first process of choosing male wolf for first place is done in 1 way only.
And the second process of choosing 2 female wolves can be done in 28 ways(ordering doesn't matter),
and since first and second process have no necessary order, using product rule, we get;
Number of ways of forming first group of wolves = [tex]1 \times 28 = 28[/tex] ways.
Thus, the number of ways the first group of three wolves (necessary to include the male wolf) is given by: Option A: 28
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Answer:
The above answer is correct! The right answer is option A. 28 :)
Hope this helped! Brainliest would be greatly appreciated :D
Step-by-step explanation:
The length of a rectangular frame is represented by the expression 2x 10, and the width of the rectangular frame is represented by the expression 2x 6. Write an equation to solve for the width of a rectangular frame that has a total area of 140 square inches. 4x2 32x − 80 = 0 4x2 32x 60 = 0 2x2 32x − 80 = 0 x2 16x 60 = 0.
The equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.
What is the area of the rectangle?The area of the rectangle is the product of its length and its breadth.
As it is given that the length of the rectangular frame is (2x+10), while the width of the rectangular frame is (2x+6). Also, it is mentioned that the area of the rectangular frame is 140 in².
Now we know the area is the product of length and breadth, therefore,
[tex]\rm \text{Area of rectangle} = length \times breadth[/tex]
[tex]140 = (2x+10)(2x+6)\\\\140 = 4x^2 + 12x + 20x + 60\\\\0=-140+4x^2 + 12x + 20x + 60\\\\4x^2 + 32 x -80=0[/tex]
Hence, the equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.
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Answer:
A.) 4x2 + 32x − 80 = 0
Step-by-step explanation:
Just took the test
Can i get some help With This Please
Step-by-step explanation:
See the solution for each part
1)
f(-2) = - 3(-2) - 6 = 6 - 6 = 02)
g(3) = 3² + 4 = 9 + 4 = 133)
f(g(x)) = -3(x² + 4) - 6 = - 3x² - 12 - 6 = - 3x² - 184)
f(g(3)) = f(13) = - 3(13) - 6 = - 39 - 6 = - 455)
x = - 3f⁻¹(x) - 63f⁻¹(x) = - x - 63f⁻¹(x) = -(x + 6)f⁻¹(x) = - (x + 6)/3Now
f(-2)=-3(-2)-6=6-6=0g(3)=3²+4=9+4=13f(g(x))=-3(x²+4)-6=-3x²-12-6=-3x²-18f(g(3))=-3(3)^2-18=-27-18=-45A circular counter top has a radius of 5 feet.
Enter the area, in square feet, of the counter top. Round your answer to the nearest tenth.
Answer:78.6[tex]ft^{2}[/tex]
Step-by-step explanation:
Area=π[tex]r^{2}[/tex]
Area=[tex]\frac{22}{7}[/tex] x [tex]5^{2}[/tex]
=[tex]\frac{22}{7}[/tex] x 25
=78.6[tex]ft^{2}[/tex]
Draw and label a triangle with a base that is 3 times its height and has an area that is less than 50 square inches.
Answer: i dont knpw how to do tht can u tell me where to draw im just getting points
Step-by-step explanation:
In which of the following situations should a debit card be used? A Eugene is at a cash-only restaurant, and needs to use the ATM. B Eugene is going to buy a guitar, but he does not have the money for it. с Eugene is not sure how much money is in his account and does not want an overdraft fee. D Eugene was in a car crash, and now he has a lot of expensive medical bills to pay.
Answer:
the answer is A
Step-by-step explanation:
If Eugene is at a cash-only restaurant he must withdraw cash out of his bank account (linked to debit card.)
Can someone help me?
Answer:
Min = 4
Q1 = 9.5
Median = 13
Q3 = 16
Max = 19
Step-by-step explanation:
4, 6, 9, 10, 11, 12, 13, 13, 14, 15, 17, 17, 19
Q1 Q2 Q3
Min (minimum value) = 4
Q1 (middle value of values before Q2) = (9 + 10) / 2 = 9.5
Median (middle value) = 13
Q3 (middle value of values after Q2) = (15 + 17) / 2 = 16
Max (maximum value) = 19
What is the volume of a sphere with a radius of 3 m, rounded to the nearest tenth
[tex]\rightarrow[/tex]Radius(r) of sphere = 3m
To Find:-[tex]\rightarrow[/tex] Volume of the sphere.
Formula Used:-[tex]\rightarrow[/tex]Volume of sphere = [tex]\sf{\frac{4}{3}πr^3}[/tex]
Solution:-[tex]\rightarrow[/tex]Volume of sphere = [tex]\sf{\frac{4}{3}πr^3}[/tex](putting the value of r(radius) from the above given and pie(π) = [tex]\sf{\frac{22}{7}}[/tex])
[tex]\rightarrow[/tex][tex]\sf{=\frac{4}{3}×\frac{22}{7}×3^3}[/tex]
[tex]\rightarrow[/tex][tex]\sf{=\frac{4}{3}×\frac{22}{7}×27}[/tex]
[tex]\rightarrow[/tex][tex]\sf{=\frac{2,376}{21}}[/tex]
[tex]\rightarrow[/tex][tex]\sf{=113.14m^3}[/tex]
Therefore, the volume of the sphere [tex]\sf{=113.14m^3}[/tex], which can be rounded off to it's nearest tenth as [tex]\sf{113.1m^3}[/tex]
____________________________________
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Question 4(Multiple Choice Worth 1 points)
(03.01 MC)
Simplify 972-317 + V8 - 28
011/2-5/7
0 1184 – 5/14
065
be
C 6/9
Question 5 Multiple Choice Worth 1 points)
(03.01 LC
Answer:
The choice A.
Step-by-step explanation:
[tex]9 \sqrt{2} - 3 \sqrt{7} + \sqrt{8} - \sqrt{28} \\ \\ 9 \sqrt{2} - 3 \sqrt{7} + ( \sqrt{2} \sqrt{4} ) - ( \sqrt{4} \sqrt{7} ) \\ 9 \sqrt{2} - 3 \sqrt{7} + (2 \sqrt{2} ) - (2 \sqrt{7} ) \\ 9 \sqrt{2} - 3 \sqrt{7} + 2 \sqrt{2} - 2 \sqrt{7} \\ (9 \sqrt{2} + 2 \sqrt{2} ) + ( - 3 \sqrt{7} - 2 \sqrt{7} ) \\ 11 \sqrt{2} - 5 \sqrt{7} [/tex]
The simplified value of in radical form is 11√2 - 5√7.
What is Radical?In mathematics, a radical is the inverse of an exponent, which is represented by the symbol '√' , also known as root. It can be a square root or a cube root, and the number preceding the symbol or radical is known as an index number or degree. This is a whole integer with an exponent that cancels out the radical.
We have 9√2 - 3√7 + √8 - √28
First, solve the radical as possible
√8= 2√2
and, √28= 2√7
So, 9√2 - 3√7 + √8 - √28
= 9√2 - 3√7 + 2√2- 2√7
= 9√2 + 2√2- 3√7- 2√7
= 11√2 - 5√7
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Given the function h of x equals negative 2 times the square root of x, which statement is true about h(x)?
The function is decreasing on the interval (0, ∞).
The function is decreasing on the interval (–∞, 0).
The function is increasing on the interval (0, ∞).
The function is increasing on the interval (–∞, 0).
Using translation concepts, it is found that the correct statement about h(x) is:
The function is decreasing on the interval (0, ∞).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent function is:
[tex]f(x) = \sqrt{x}[/tex]
Which is increasing on (0, ∞).
After the translation, the function is:
[tex]h(x) = -2\sqrt{x}[/tex]
It was multiplied by a negative number, which means that it was reflected over the x-axis, and it will be decreasing on the interval (0, ∞).
More can be learned about translation concepts at https://brainly.com/question/4521517
Ella traveled by train to visit her friend.
• It took 3 hours for Ella to reach her destination.
• The train averaged a speed of 100 miles per hour.
Enter an equation to express the distance, d, Ella traveled.
Answer:
d = st, d = 100 x 3
Step-by-step explanation:
distance = speed x time
distance = 100 x 3, therefore, distance = 300, but if you just want the equation, it is d = 100 x 3 or d = st
Step-by-step explanation:
d = 100 x 3.
d= 100n
where n = time the journey took.
this is due today! please help and i will give 50 points
Answer:
D) 154 ft²
Step-by-step explanation:
Formula
Area of a rectangle = width x length
We only need to calculate the area of the walls.
There are two pairs of walls with the following dimensions:
5 ft x 7 ft6 ft x 7 ftTherefore, area to paint = 2(5 x 7) + 2(6 x 7)
= 70 + 84
= 154 ft²
Bottom cube 's LSA need to be counted
H=7ftL=6B=5LSA:
2H(L+B)2(7)(5+6)14(11)154ft²Question 9 (Mandatory) (1 point)
A bakery sells hollow chocolate spheres. Each chocolate sphere contains
about 19.4 cubic inches of chocolate.
The bakery packages 8 of them into a box. If the density of the chocolate is
1.308 g/cm3, determine and state, to the nearest gram, the total mass of the
chocolate in the box.
a) 198
b) 203g
C) 25g
d) 150g
Answer:
B) 203 grams
Step-by-step explanation:
19.4 * 1.308 = 25.3752
25.3752 * 8 = 203.0016
A scale model of a ramp is a right triangular prism as given in this figure. in the actual ramp, the triangular base has a height of 0.5 yards. what is the surface area of the actual ramp, including the underside? enter your answer as a decimal in the box.
The surface area of the actual ramp including the underside is 16.8 ft²
The height of the actual ramp = 1.2 feet
The height of the model = 6 cm
What is the surface area of a right triangular prism?A right triangular prism is a 3-dimensional triangle with two congruent triangular faces and 3 rectangular faces that connect the triangular.
The surface area of a right triangular prism
= (Perimeter of the base × Length of the prism) + (2 × Base Area)
Scale factor = 1.2 feet / 6 cm = 0.2 ft/cm
Actual base = 16 cm × 0.2 ft/cm = 3.2 ft
convert the units
9 cm = 9 cm × 0.2 ft/cm = 1.8 ft
10 cm = 10 cm × 0.2 ft/cm = 2 ft
The surface area of a right triangular prism
= (Perimeter of the base × Length of the prism) + (2 × Base Area)
Surface area of actual ramp = 2(0.5 × 3.2 ft × 1.2 ft) + 2(2 ft × 1.8 ft) + (1.8 ft × 3.2 ft)
= 16.8 ft²
Hence, the surface area of the actual ramp including the underside is 16.8 ft²
Learn more about the area here:
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Answer:
7.2 yd² for K12
Using the Linear equation 4x-3y=12, express each of the following.
y in terms of x. y=
Using the Linear equation 4x-3y=12, express each of the following.
x in terms of y. x=
Using the given linear function, it is found that the expressions are given by:
[tex]y = \frac{4x}{3} - 4[/tex].[tex]x = \frac{3y}{4} + 3[/tex].What is the given linear function?It is:
4x - 3y = 12.
To find y in terms of x, we isolate y, hence the expression is given by:
[tex]3y = 4x - 12[/tex]
[tex]y = \frac{4x}{3} - 4[/tex]
To find x in terms of y, we isolate x, hence the expression is given by:
[tex]4x = 12 + 3y[/tex]
[tex]x = \frac{3y}{4} + 3[/tex]
More can be learned about linear functions at https://brainly.com/question/24808124
Is 1,-9 a solution to y=-9
Answer:
yes
Step-by-step explanation:
(x,y) -> (1,-9) y=-9
A rectangular bathroom mirror is 4
feet tall and 7 feet wide. What is its
area?
square feet
Given -
A rectangular bathroom mirror is 4 feet tall and 7 feet wide.ie, length of the mirror, L = 4 feet and breadth of the mirror, B = 7 feet .
To find -
the area of the mirrorSolution -
As we know to find the area of rectangle we use the formula, Area = L × B
Hence, we will be doing the same.
Area = 4 × 7
Area = 28 square feet
Answer:
28 sq. feet
Step-by-step explanation:
Given:-
The length of bathroom mirror :- 4 feetWidth :- 7 feetTo find:-
The area of the rectangular bathroom mirrorSolution:-
Area of rectangular bathroom mirror:- L × B
putting the values ,
Area :- 4 × 7 sq. feet
Area:- 28 sq. feet
If $1209 is deposited in an account that pays 8. 2% interest compounded monthly, what is the balance after 26 years? Use: A=P(1+r)t
Round to the nearest cent
Answer:
Step-by-step explanation:
We can use the interest equation (mind you it is the same thing as said in the problem) to solve this:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where A is the resulting amount, r is the interest rate, n is the number of times compounded per year and t is the time.
[tex]A=1209(1+\frac{.082}{12} )^{12*26}[/tex]
A = $10,120.29
The numbers in any column row or diagonal in the gird below multiply to give an answer of 1 complete the grid
Step-by-step explanation:
Let’s just start with rows. I’m going to use a, b, and c for the missing numbers (a in the first row, b in the second, c in the third).
Row 1 — 5 × 4 × a = 1
20 × a = 1 → a = 1/20
Row 2 — b × 1 × 100 = 1
b × 100 = 1 → b = 1/100
Row 3 — 20 × 1/4 × c = 1
5 × c = 1 → c = 1/5
—
Check Columns:
5×1/100×20 = 5(20)/100 = 100/100 = 1 ✓
4 × 1 × 1/4 = 1 ✓
1/20×100×1/5 = 100/(20*5) = 100/100 = 1 ✓
Check Diagonals:
5 × 1 × 1/5 = 5/5 = 1 ✓
20 × 1 × 1/20 = 20/20 = 1 ✓
Suppose $500 is divided into two bank accounts. One account pays 15% simple interest per year and the other pays 10%. After three years there is a total of $200 in interest between the two accounts. How much was invested into the bank account that pays 15% simple interest (rounded to the nearest cent)?
Answer:
x = amount invested in the 15% account
x*.15*3 + (500-x)*.1*3 = 200
x = 333.33
so, 500-333.33 = 166.67 at 10%
Step-by-step explanation:
Answer:
x = amount invested in the 15% account
x*.15*3 + (500-x)*.1*3 = 200
x = 333.33
so, 500-333.33 = 166.67 at 10%
Step-by-step explanation:
sorry if i did it wrong
n expression is shown below. -x + 1 + 4x - 3
Answer:
3x - 2
Step-by-step explanation:
Collect like timers. -x + 4x = 3x and -3 + 1 = -2, 3x - 2
Hey there!
-x + 1 + 4x - 3
= -1x + 1 + 4x - 3
COMBINE the LIKE TERMS
= (-1x + 4x) + (1 - 3)
= -1x + 4x + 1 - 3
= 3x - 2
Therefore, your answer is: 3x - 2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A. where will vertex A be located after a rotation of -90°
B. where will vertex B be located after a rotation of 90°
C. where will vertex C be located after a -180° rotation
D. where will vertex D be located after a 270° rotation?
Answer:
this image should help a lot:
vertex b: (-5,3)
vertex a: (0,-1)
vertex c: (-6,-7)
vertex d: (-4,-1)
Step-by-step explanation:
Gobe weighs 53.6 kg. he wears shoes which weigh 450 gm and carries a school bag weighing 4.5 kg. if he stands on the scales in his shoes and carrying the school bag. what weight will be recorded?
Answer:
The key to this question is converting all the mass units to the same unit and adding them all up.
The only value that isn't consistent with the other units is 450 gm or grams.
Recall that 1 gram is equal to 0.001 kilo grams. So if you want to convert grams to kilograms you would multiply that amount by 0.001 or 1/1000
[tex]450gm * \frac{1}{1000} = 0.45kg[/tex]
Now let's add up all the masses.
[tex]53.6kg + 0.45kg + 4.5kg = 58.55 kg\\[/tex]
(Now a few footnotes here, that I considered but wasn't sure about. The answer asks for weight, but you're only given mass to work with. That would be fine, if the question asked you to convert it to SI weight units like Newtons, but there's no mention of that. And also I'm not sure if the question requires significant digits. But I'll continue the answer if you think so)
To convert this into weight in Newtons, multiply by 9.81 m/s^2
[tex]58.55kg*9.81m/s^2 = 574.3755 N\\\\= 5.7 * 10^2 N[/tex]
What are the solutions to the equation x^2 - 8x= 24
Answer:
Step-by-step explanation:
Try to get all the numbers and variables on one side of the =
X^2 - 8x - 24 = 0
I think solving this equation via factorisation would be difficult so you should use the quadratic formula which I have attached.
what is a solution in 6th-grade math?
Answer:
A solution means any variable that makes the equation true
surface area of prisms: find it and. fix it
Answer:
Step-by-step explanation:
i can't solve without seeing the prism
The carson family pays $3,252 a year for their cell phones is $3,252 a reasonable answer?
Answer:
Here we will show you how to calculate how much you will make in a year if you make $3252 an hour. Our calculations are based on the following information, but you can change the numbers further down on this page to make it better reflect your situation.
Hourly Pay: $3252
Work hours per week: 40
Work weeks per year: 52
Income Tax Rate: 12%
To calculate how much $3252 an hour is per year, we first calculate weekly pay by multiplying $3252 by 40 hours per week, and then we multiply the product by 52 weeks, like this:
$3252 × 40 hours
= $130,080.00 per week
$130,080.00 × 52 weeks
= $6,764,160.00 per yearNow you know that your gross income per year (income before tax) is $6,764,160.00 if you make $3252 per hour. However, you have to deduct taxes to find your net yearly income (income after tax).
Everyone has to pay 6.2% Social Security Tax and 1.45% Medicare Tax. Furthermore, we assume you will pay about 12% in Federal, State, and Local income taxes. Here is how to calculate your net income (the actual amount you will receive per year):
Social Security Tax
($6,764,160.00 × 6.2)/100
= $419,377.92
Medicare Tax
($6,764,160.00 × 1.45)/100
= $98,080.32
Income Taxes
($6,764,160.00 × 12)/100
= $811,699.20
+ $6,764,160.00 Gross Income
- $419,377.92 Social Security Tax
- $98,080.32 Medicare Tax
- $811,699.20 Federal/State/Local Taxes
= $5,435,002.56 Net IncomeThere you have it. Now you have the answer to "$3252 an hour is how much a year?" If you make $3252 per hour, then your yearly income before taxes is $6,764,160.00 and your yearly income after taxes is $5,435,002.56
We made some assumptions about how much you work and how much taxes you have to pay. You can adjust these assumptions below to match your situation to get the exact amount for your situation.
Step-by-step explanation:
Which ordered pair is a solution to the system of inequalities {y <3x-1
y>|x-2|
Answer:
(4, 4)
Explanation:
I have solved it using graph.(4, 4) is the only point which lies inside both of the inequalities.
An equation is shown below:
4(2x - 5) + 15 = 11
Write the steps you will use to solve the equation and explain each step.
Answer:
Step-by-step explanation:
Swimming Pool On a certain hot summer's day, 163 people used
the public swimming pool. The daily prices are $1.25 for children
and $2.00 for adults. The receipts for admission totaled $257.00.
How many children and how many adults swam at the public pool
that day?
There were
children at the public pool.
x=15 in the form of |x-b|=c
(where b is a number and c can be either number or an expression)
Step-by-step explanation:
don't mind with my hand writting