Answer:
(a) 56 ways
(b) 6 ways
(c) 56 ways
Step-by-step explanation:
Given:
candidates: 6 mail, 1 female
number to hire : 3
a) In how many different ways can choose new employees?
use the combination formula to choose r to hire out of n candidates
C(n,r) = C(8,3) = 8! / (3! (8-3)! ) = 40320 / (120*6) = 56 ways
b) In how many different ways can choose a single male candidate?
6 ways to choose a male, one way to choose two female, so 6*1 = 6 ways
c) In how many different ways can choose at least one male candidate?
To choose at least 1 male candidate, we subtract the ways to choose no male candidates out of 56.
Since there are only two females, there is no way to choose 3 female candidates.
In other words, there are 56-0 = 56 ways (as in part (a) ) to hire 3 employees with at least one male candidate.
what is the product number of 88 and 26?
Answer:
2288
Step-by-step explanation:
∫1/(1+sinx^2 +2cos^2x)
Answer:
Im not sure, is this correct?
Pleas answer this question now
Answer:
[tex]x = 17[/tex]
Step-by-step explanation:
According to the two tangent theory, tangent MN and tangent NP, which are both from point N, are congruent.
That is, [tex]x + 4 = 21[/tex]
Solve for x
[tex]x + 4 = 21[/tex]
Subtract 4 from both sides
[tex]x + 4 - 4 = 21 - 4[/tex]
[tex]x = 17[/tex]
Show that: (sec theta - cosec theta) (1 + tan theta + cot theta) = sec theta tan theta - cosec theta cot theta)
Answer:
see derivation below
Step-by-step explanation:
Show that:
( sec(t) - cosec(t) ) ( 1 + tan(t) + cot(t) ) =
sec(t) tan(t) - cosec(t) cot(t)
Some trigonometric definitions used:
tan(t) = sin(t)/cos(t)
cot(t) = cos(t)/sin(t)
sec(t) = 1/cos(t)
csc(t) = 1/sin(t)
some trigonometric identities used:
sin^2(t) + cos^2(t) = 1 ......................(1)
rewrite left-hand side in terms of sine and cosine
(1/cos(t) - 1/sin(t) ) ( 1 + sin(t)/cos(t) + cos(t)/sin(t) )
Simplify using common denominator sin(t)cos(t)
= ( (sin(t) - cos(t))/(sin(t)*cos(t)) ) * ( ( sin(t)cos(t) + sin^2(t) + cos^2(t)) / ( sin(t)cos(t) ) )
= ( sin(t) -cos(t) ) * (1 + sin(t)cos(t) ) / ( sin^2(t) cos^2(t) ) ...... using (1)
Expand by multiplication
= ( sin(t) -cos(t) + sin^2(t)cos(t) - sin(t)cos^2(t) ) / ( sin^2(t) cos^2(t) )
Rearrange by factoring out sin(t) and cos(t) in numerator
= ( sin(t) (1-cos^2(t) - cos(t)(1-sin^2(t) ) / ( sin^2(t) cos^2(t) )
= ( sin^3(t) - cos^3(t) ) /( sin^2(t) cos^2(t) ) .........................using (1)
Cancel common factors
= sin(t)/(cos^2(t)) - cos(t)/(sin^2(t))
Rewrite using trigonometric definitions
= sec(t)tan(t) - csc(t)cot(t) as in Right-Hand Side
|6–x|=5 plzzzzzzzzz help
Answer: x = 1, 11
Step-by-step explanation:
When answering a problem like this, normally, you first isolate the absolute value. As it is already isolated, the next thing you do is split the equation into 6–x=5 and 6–x=-5, because the contents of the absolute value could be negative or positive, and simplifying both into x = 1, and x = 11.
Hope it helps <3
Which of the following is a factor of x3+ 6x2 + 5x – 12?
A.X + 1
B. x - 3
C. x + 2
D. x + 4
1,3,4 that is the answer
Answer:
The answer is option D.Step-by-step explanation:
x³ + 6x² + 5x - 12
A factor of the polynomial is the value of x when substituted into the expression will make it zero
Choosing x + 4
x = - 4
We have
(- 4)³ + 6(- 4)² + 5(- 4) - 12
-64 + 96 - 20 - 12 = 0
Since the result is zero
x + 4 is a factor of the polynomial
Hope this helps you
√144² =
√9 + √16 =
√9 + √16 × √400 =
Answer:
Step-by-step explanation
√144²
12²
144
√9 + √16
3 + 4
7
√9 + √16 × √400 =
3 + 2^{4} x 5
3 + 80
83
Given the geometric sequence where a1 = −1 and the common ratio is 7, what is the domain for n? A. All integers B. All integers where n ≥ −1 C. All integers where n ≥ 0 D. All integers where n ≥ 1
Answer:
D
Step-by-step explanation:
Hello, This is a geometric sequence where the first term is [tex]a_1=-1[/tex].
It means that the sequence is [tex](a_n)_{n\geq 1}[/tex].
In other words, as the common ratio is 7 the sequence is defined by
[tex]a_1=-1[/tex]
[tex]a_{n+1}=a_n\cdot 7 \ \ \text{ for n }\geq 1[/tex]
For instance, we can estimate the first terms:
[tex]a_1=-1\\\\a_2=7a_1=-7\\\\a_3=7a_2=-49[/tex]
And we know that we can even find a formula for the [tex]n^{th}[/tex] term of the sequence by:
[tex]a_n=a_1\cdot 7^{n-1}=-7^{n-1}[/tex]
Now, to answer the question, the domain for n is all integers where [tex]n\geq 1[/tex].
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Please Help!!! Will get brainiest if answer correctly with an explanation. Name the postulate or theorem you can use to prove wzv=wzy. given:
Answer:
AAS
Step-by-step explanation:
Δwzy=Δwzv
to prove the equality:
1- wz is a common side
angle: wzv=wzy=90 degrees ( height of triangle)
angle v= angle y
Since WZ bisects W, it's good to say that vwz and zwy
prove one side is equal and two angles
so ASA or AAS is the answer
piece of wire 8 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much wire should be used for the square in order to maximize the total area
Answer:
piece of wire 8 m long
one piece is bent into square:
the square has four equal sides , so at least 4 m has to be cut from the wire to form a square with side=1 m.
the perimeter of the square =2L+2W=2(1)+2(1)=4 m
that is the max. amount can be cut from the wire, since the other part is bent into a circle.
( note if you cut more, the square will take the whole wire)
Perimeter=2L+2W=2(2)=2(2)=8 m and the area=2*2=4 m²)
Area and perimeter are two crucial characteristics of 2D shapes in mathematics.
The perimeter of the square exists 8 m and the area exists 4 m².
What is the perimeter and area of a square?Area and perimeter are two crucial characteristics of 2D shapes in mathematics. The area and perimeter both specify the shape's boundaries and the space they occupy, respectively. Area and perimeter are significant mathematical concepts that are used to daily life. All sizes and shapes, regular or unusual, are covered by this. Each shape's area and perimeter calculations are unique.
Piece of wire is 8 m long and one piece is bent into square:
The square has four equal sides , so at least 4 m has to be cut from the wire to form a square with side = 1 m.
The perimeter of the square = 2L + 2W = 2(1) + 2(1) = 4 m
Which exists the maximum amount that can be cut from the wire, since the other part is bent into a circle.
Perimeter = 2L + 2W =2(2) = 2(2) = 8 m and the area = 2 × 2= 4 m²
To learn more about perimeter and area, refer to:
brainly.com/question/19819849
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Given f(x) = 3x - 1 and g(x) = 2x + 1, find (f +g)(3)
Answer:
(f + g)(3) = 15Step-by-step explanation:
f(x) = 3x - 1
g(x) = 2x + 1
To find (f +g)(3) , first find (f + g)(x)
To find (f + g)(x) add g(x) to f(x)
That's
(f + g)(x) = 3x - 1 + 2x + 1
= 3x + 2x + 1 - 1
(f + g)(x) = 5x
Now to find (f + g)(3) substitute 3 into
(f + g)(x)
That's
(f +g)(3) = 5(3)
(f + g)(3) = 15Hope this helps you
Suppose you computed a 95% confidence interval for the difference in mean weight between two species of snakes in a large nature reserve (species #1 – species #2), and your interval is –3.6 to 61.6 ounces. What can you conclude?
Answer:
1. In a situation were we are willing to use 90% confidence, this means we could say that the observed difference that we have in the sample means tend to represents a real difference in the population means.
2. We cannot actually say because even with 95% confidence, that is the observed difference in sample means tend to as well represents a real difference in the population means.
3. Because the interval extends further in the positive direction than the negative direction this means that the evidence suggests that species #1 tend to weighs more than species #2 on average, but we can't actually say for sure.
Step-by-step explanation:
The following are what I will conclude about based on the information given in the question.
1. In a situation were we are willing to use 90% confidence, this means we could say that the observed difference that we have in the sample means tend to represents a real difference in the population means.
2. We cannot actually say because even with 95% confidence, that is the observed difference in sample means tend to as well represents a real difference in the population means.
3. Because the interval extends further in the positive direction than the negative direction this means that the evidence suggests that species #1 tend to weighs more than species #2 on average, but we can't actually say for sure.
Nicole has x marbles. Together we have 44 marbles. How many marbles will I have if I lose 1/4 of my marbles ?
Answer:
I have:
33 - 3N/44 marbles
N = marbles of Nicole
Step-by-step explanation:
Nicole + me = 44 marbles
m = 44 - N
m = me
N = Nicole
if i lose 1/4 of my marbles
4/4 - 1/4 = 3/4
i have left:
3/4 of my marbles
then:
m = 3(44-N)/4
m = 3*44/4 + 3*-N/44
m = 33 - 3N/44
I have finally:
33 - 3N/44
Need help!! Please if you know this go ahead and answer but if you don’t don’t bother!! Thanks
Work Shown:
area of base = 18*17 = 306 square yards
V = volume of pyramid
V = (1/3)*(area of base)*(height)
V = (1/3)*(306)*(15)
V = 1530 cubic yards
Answer:1530
Step-by-step explanation: length*width*height* divided by 3
HELP ME PLEASEEEE! Thank you
Answer:
A. Yes
B. Yes
C. No
Step-by-step explanation:
We can substitute each value in to the equation and see if the sides match up. Let's start with a.
[tex]4\cdot(2)-3 = -2\cdot(2)+9\\8-3 = -4+9\\5 = 5[/tex]
So, n = 2 works for equation a. Let's try B.
[tex]9\cdot(\frac{10}{3}) - 19 = 3\cdot(\frac{10}{3}) + 1\\\\\\\frac{90}{3} -19 = \frac{30}{3} + 1 \\ 30 - 19 = 10 + 1\\11 = 11[/tex]
So, m = [tex]\frac{10}{3}[/tex] works for B. Now let's try C.
[tex]3(30+8) = 2\cdot(30)-6\\3(38) = 60-6\\114 \neq 54[/tex]
So y = 30 doesn't work for C.
Hope this helped!
Which expression can be used to find the surface area of the following square pyramid?A 16+16+55+55+8816+16+55+55+8816, plus, 16, plus, 55, plus, 55, plus, 88 (Choice B) B 10+10+55+55+8810+10+55+55+8810, plus, 10, plus, 55, plus, 55, plus, 88 (Choice C) C 8 +8+55+55+888+8+55+55+888, plus, 8, plus, 55, plus, 55, plus, 88 (Choice D) D 16+8816+8816, plus, 88
Answer:
4 + 3+3+3+3
Step-by-step explanation:
We add up all the areas to find the surface area
The bottom is
2*2 = 4
The sides are all the same
The area of one side is
A = 1/2 bh = 1/2 (2*3) = 3
There are 4 triangular side
SA = 4 + 3+3+3+3
Answer:
4 + 3 + 3 + 3 + 3
Step-by-step explanation:
The base is a square.
Find area of a square.
2² = 4
Find the area of one triangle.
2 × 3 × 1/2 = 3
There are 4 triangles.
3 + 3 + 3 + 3
Add all the areas:
4 + 3 + 3 + 3 + 3
99 students choose to attend one of three after school activities: football, tennis or running.
There are 61 boys.
19 students choose football, of which 5 are girls.
31 students choose tennis.
28 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.
Answer: [tex]\dfrac{49}{99}[/tex]
Step-by-step explanation:
There are 61 boys --> 38 girls
A) 19 chose football: 5 are girls --> 14 are boys
B) 38 girls: 28 chose running, 5 chose football --> 5 girls chose tennis
C) 31 students chose tennis: 5 are girls --> 26 are boys.
D) 61 boys: 14 chose football, 26 chose tennis --> 21 boys chose running.
[tex]\large\boxed{\begin{array}{l|cc||c}&\underline{Boys}&\underline{Girls}&\underline{Total}\\Football&14&5&19\\Tennis&26&5&31\\\underline{Running}&\underline{\quad 21\quad}&\underline{\quad 28\quad}&\underline{\quad 29\quad}\\Total&61&38&99\end{array}}[/tex]
Total running = 21 boys + 28 girls = 49
Total students = 99
[tex]\dfrac{\text{Total running}}{\text{Total students}}=\large\boxed{\dfrac{49}{99}}[/tex]
. What is half the next number in the pattern 1, 3, 9, 27, 81
A. 234
B. 67
D c. 468
0 0.76
Answer:
A. 243
Step-by-step explanation:
just multiply the next number by 3
81*3= 243
Answer:
[tex]\boxed{243}[/tex]
Step-by-step explanation:
The ratio can be found by dividing a term in the sequence by the previous term.
[tex]\frac{27}{9} =3[/tex]
Each term gets multiplied by 3 to get the next term.
[tex]81 \times 3 = 243[/tex]
What is answer for 26/25 × -16/63 Step by step no explanation I will make you as brainlist Please find out Thanks
Answer:
[tex] - \frac{416}{1575} [/tex]Step-by-step explanation:
[tex] \frac{26}{25} \times ( - \frac{16}{63} )[/tex]
Multiplying a positive and a negative equals a negative[tex]( + ) \times ( - ) = ( - )[/tex]
[tex] = - \frac{26}{25} \times \frac{16}{63} [/tex]
Multiply the fractions:
[tex] = - \frac{416}{1575} [/tex]
Hope this helps..
Best regards!!
Can somebody plz help me 15-[7+(-6)+1]^3
Answer:
7.
Step-by-step explanation:
15 - [7 + (-6)+ 1]^3
Using PEMDAS:
= 15 - [ 7-6+1]^3
Next work out what is in the parentheses:
= 15 - 2*3
Now the exponential:
= 15 - 8
= 7.
Step-by-step explanation:
Hi,
I hope you are searching this, right.
=15[7+(-6)+1]^3
=15[7-6+1]^3
=15[2]^3
=15-8
=7...is answer.
Hope it helps..
The diameter of a circle is 3.5 inches. What is the circumference of the circle?
Answer:
About 11 (10.9955742876...)
Step-by-step explanation:
Circumference=(pi) (diameter) or C=πd
Hope this helps!
The circumference of the circle is about 11 inches.
We are given that the diameter of a circle is 3.5 inches.
Noted that the circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
Therefore circumference of the circle = 2πr
Circumference=(2πr)
The diameter or C = πd
diameter = 3.5 inches
Circumference=(3.5 x 3.14)
Circumference = (10.99) inches
Learn more about circumference here;
brainly.com/question/12512221
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a single carton of juice cost $4.20. A special offer pack of 3 cartons cost $9.45. Jace bought a special offer instead of 3 single cartons. Calculate his percent saving
The 3 pack cost $9.45
3 single cartons would have cost: 3 x 4.20 = $12.60
Difference in cost: 12.60 - 9.45 = $3.15
Percent savings : 3.15/ 9.45 = 0.3333
0.333 x 109 = 33.33%
Round the answer as needed
PLEASE HELP ME! Please do not comment nonsense, and actually comment the answer and the solution.
=================================================
Explanation:
For choice C, the x values are out of order, so it might be tricky at first. I recommend sorting the x values from smallest to largest to get -2, -1, 0, 1, 2. Do the same for the y values as well. Make sure the correct y values stay with their x value pairs. You should get the list of y values to be 4, 2, 1, 1/2, 1/4
Check out the attached image below for the sorted table I'm referring to
We can see the list of y values is going down as x increases. This is a good sign we have decay. Further proof is that we multiply each term by 1/2 to get the next one
4 times 1/2 = 2
2 times 1/2 = 1
1 times 1/2 = 1/2
1/2 times 1/2 = 1/4
and so on. Effectively we can say the decay rate is 50%
HELP!! Fiona races BMX around dirt course. If the radius of the course is 70 meters, what is the total distance Fiona covers in two laps of the race?
Answer:
879.64 (C)
Step-by-step explanation:
Answer:
879.2
Step-by-step explanation:
Given the coordinate points of the preimage, use the transformation given to provide the points of the image. E(−5,−1) D(−5,1) C(−1,0) B(−2,−3) Rotation: 180∘ about the origin
Answer:
The points of the image are;
E'(5, 1), D'(5, -1), C'(1, 0), E'(-2, -3)
Step-by-step explanation:
The coordinates of the preimage are E(-5, -1) D(-5, 1) C(-1, 0) B(-2, -3)
Rotation of a point 180° about the origin gives;
Coordinates of the point of the preimage before rotation = (x, y)
The coordinates of the image after rotation = (-x, -y)
Therefore, the coordinates of the points EDCB after 180° rotation about the origin are;
E(-5, -1) rotated 180° becomes E'(5, 1)
D(-5, 1) rotated 180° becomes D'(5, -1)
C(-1, 0) rotated 180° becomes C'(1, 0)
B(-2, -3) rotated 180° becomes E'(-2, -3).
Simplify the expression: 4(n-5)
Answer: 4n - 20
Step-by-step explanation: We can use the distributive property.
The distributive property tells us that if were given an expression
such as 4(n - 5), we can multiply the 4 by both the n and the -5.
So our answer is just 4n - 20.
need help asap use the screen shot
Answer:
7 and 37
Step-by-step explanation:
Imagine our 3rd side becoming smaller and smaller. In the ultimate case the triangle will be a flat line, and the two other lines overlap. The third line will have to be 7, to get from 15 to 22 (22-15=7).
Likewise, if the line increases and increases, again you'll endup with a flat line, but now the two otherlines will span the entire third line, so its length is the sum, i.e., 15+22 = 37
what is known as terms of ratio
Answer: The mathematics terms of ratio are the indicates many times one number contains to the another number.
Step-by-step explanation:Terms of ratio may be specified both constitution number or value to the equal correspond to the equal ratio.
"a to b"
"a:b"
There are Sixteen and eight apples and lemon in the table of fruit the ratio(that is 16:8 to the equivalent the ratio 8:4).
a:b=(a+b):a or ratio is equivalently a:b=(1+b/a):1.
The number in a terms ratio quantities of both numbers are to be positive
A farmer has a rectangular piece of land measuring 840 meters by 396 meters. He divides it into equal square plots of equal size. What is the maximum area of one square plot?.......PLLLZZZ HELP
Answer:
The maximum area of one square plot is 144 [tex]m^2[/tex]
Step-by-step explanation:
Start by looking at what are the greater common factor of both provided dimensions (840 and 396) to find what the numbers are they both can be divided by evenly:
[tex]840=2^3\,*\,3\,*\.5\,*\,7\\396=2^2\,*\,3^2\,*\,11[/tex]
therefore, both numbers can be divided by [tex]2^2\,*\,3=12[/tex]
Which then gives:
[tex]\frac{840}{12} =70\\\frac{396}{12} =33[/tex]
Then, one can divide the longest side (840 m) into 70 sections of 12 meters each, and the shortest side of the piece of land (396 m) into 33 sections of 12 meters each.
Then we can have a total of 33 * 70 = 2310 smaller lots of 12 m by 12 m
That is smaller plots of a total area 144 square meters
Can someone help me with this question (:
I’d appreciate it!
brainliest to the correct answer/explanation) ♀️
Answer:
bet whats the question
Step-by-step explanation:
