Answer:
The answer is below
Step-by-step explanation:
The possible ways of choosing r items from a total of n item is given as C(n,r) = [tex]\frac{n!}{(n-r)!r!}[/tex]
Suppose that 6 female and 6 male applicants have been successfully screened for 5 positions.
Since they are 12 finalists and only 5 positions, the total number of possible outcomes is:
[tex]Total\ number\ of \ outcome (n(s))=C(12,5)=\frac{12!}{(12-5)!5!} =792[/tex]
A) 3 females and 2 males
The possible ways of choosing 3 females and 2 males is given as:
[tex]n(e)=C(6,3)*C(6,2) = \frac{6!}{(6-3)!3!}* \frac{6!}{(6-2)!2!}=20*15=300[/tex]
probability of selecting 3 females and 2 males P(E) = [tex]\frac{n(e)}{n(s)}=\frac{300}{792}=0.379[/tex]
B) 4 females and 1 males
The possible ways of choosing 4 females and 1 males is given as:
[tex]n(e)=C(6,4)*C(6,1) = \frac{6!}{(6-4)!4!}* \frac{6!}{(6-1)!1!}=15*6=90[/tex]
probability of selecting 4 females and 1 males P(E) = [tex]\frac{n(e)}{n(s)}=\frac{90}{792}=0.1136[/tex]
C) 5 females
The possible ways of choosing 5 females is given as:
[tex]n(f)=C(6,5) = \frac{6!}{(6-5)!5!}=6[/tex]
probability of selecting 5 females = [tex]\frac{n(f)}{n(s)}=\frac{6}{792}[/tex]
(D) At least 4 females
This can be done by choosing 4 females out of 6 females i.e. C(6,4) , 5 females out of 6 females i.e C(6,5) and 1 male out of six male i.e (6,1)
The possible ways of choosing atleast 4 females is given as:
[tex]n(h)=C(6,5)*C(6,4)*C(6,1)= \frac{6!}{(6-5)!5!}* \frac{6!}{(6-4)!4!}* \frac{6!}{(6-1)!1!}=6*15*6=540[/tex]
probability of selecting atleast 4 females = [tex]\frac{n(h)}{n(s)}=\frac{540}{792}[/tex]
Write the expression in standard form. -3 + yi = x + 6i
Answer:
The expression in standard form is -3 + 6i
Step-by-step explanation:
Writing complex equation in standard form we have;
-3 + yi = x + 6i
We transfer the real and imaginary parts to be on different sides of the equation as follows;
yi - 6i = x + 3
We factorize the imaginary part;
i(y-6) = x + 3
We note that the real portion on the left hand side of the equation is zero, therefore, we have;
i(y-6) + 0= x + 3
x + 3 = 0
Therefore, x = -3
Substituting the value of x in the first equation, we have;
-3 + yi = -3 + 6i
Comparing gives;
y = 6
The expression in standard form is -3 + 6i.
What is an equation to a line parallel to the line on the graph that passes through (4,15)?
The equation to a line parallel to the line on the graph that passes through (4,15) is y = 3x + 3
How to find equation of a line?The equation of a line can be represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
parallel line have the same slope
(5, 35)(10, 50)
m = 50 - 35 / 10 - 5 = 15 / 5 = 3
Hence,
(4, 15)
y = 3x + b
15 = 3(4) + b
15 - 12 = b
b = 3
Therefore, the equation to a line parallel to the line on the graph that passes through (4,15) is y = 3x + 3
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The windows of a downtown office building are arranged so that each floor has 6 fewer windows than the floor below. If the ground floor has 52 windows, how many windows are on the 8th floor?
Answer:
10
Step-by-step explanation:
This is an arithmetic sequence. The common difference is -6, and the first term is 52.
a = 52 − 6(n − 1)
When n = 8:
a = 52 − 6(8 − 1)
a = 52 − 42
a = 10
Find the pattern and fill in the missing numbers: 0, …, 9, 18, 30, 45, ...
it is 9
and it is also 54
Answer:
3 and 63.
Step-by-step explanation:
The sequence formula is [tex]\frac{3n(n+1)}{2}[/tex].
Resulting in a sequence of 0, 3, 9, 18, 30, 45, 63.
A regular four-sided die and a regular eight-sided die are rolled to form a sum. a) Determine the probability distribution for the sum of the two dice. Show Steps b) Create a frequency histogram for the probability distribution. c) Determine the expected sum of the two dice.
Answer:
4+8=12 so,if its 12 so
Step-by-step explanation:
the some will be 12
12-8=4
12-4=8
Help me with 2a and 2b please
Answer:
Step-by-step explanation:
A∩B={x| x∈a and x∈B}
a) A∩B={4,6}
b) A∩B={ 4,9}
c) A∩B={yellow,green}
A can in the shape of a cylinder has a diameter of 6 centimeters and a height of 10 centimeters. Which measurement is closest to the total surface area of the can in square centimeters? 245.04 cm2 203.19 cm2 376.99 cm2 188.50 cm2
Answer:
245.04 cm²
Step-by-step explanation:
Use the formula for the surface area of a cylinder: 2[tex]\pi[/tex]r² + 2[tex]\pi[/tex]rh
Now, we can plug in the values:
2[tex]\pi[/tex](3)² + 2[tex]\pi[/tex](3)(10)
18[tex]\pi[/tex] + 60[tex]\pi[/tex] = 245.04
The total surface area of the can is 244.92 square centimeters which is closest to 245.04 square centimeters.
We have a can in the shape of a cylinder has a diameter of 6 centimeters and a height of 10 centimeters.
We have to determine total surface area of the can in square centimeters.
What is the formula to calculate the total surface area of a cylinder with radius 'r' and height 'h'.The total surface area of a cylinder with radius 'r' and height 'h' is given by -
A = 2πr(h + r)
According to the question, we have -
diameter of can = 6 cm
Then, the radius will be (r) = 6/2 = 3 cm
Height of can (h) = 10 cm
Substituting the values, we get -
A = 2 x 3.14 x 3 (10 + 3)
A = 2 x 3.14 x 3 x 13
A = 6 x 13 x 3.14
A = 78 x 3.14
A = 244.92 square centimeters.
Hence, the total surface area of the can is 244.92 square centimeters which is closest to 245.04 square centimeters.
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1. A car bought for $20,000. Its value depreciates by 10% each year for 3 years. What is the car's worth after3 years?
2. Find the perimeter of a circle whose radius is 3.5cm. (Take pi = 22/7)
3. The volume of a cone is 1540cm³. If its radius is 7cm, calculate the height of the cone. (Take pi = 22/7)
4. What is the coefficient of b in the expression b² - 5b +18
5. Expand (x +2) (9 - x)
7. Find x and y in the simultaneous equations. x + y = 4 3x + y = 8
8. Factorize a² +3ab - 5ab - 15b²
9. The bearing of a staff room from the assembly ground is 195degrees, what is the bearing of the assembly ground from the staff room?
Step-by-step explanation:
68$53++83(-$(7(3($++$
Which of these tables represents a function
Answer:
Z.
Step-by-step explanation:
A function must pass the Vertical Line Test. No 2 y-values can have the same x-values. Since the first 3 graphs fail to pass the vertical line test, our answer is Z.
Which choice is the most efficient first step to solve this set of equations?
Answer:
x + 2x = 30 is the correct answer.
Tom, Kristen, Kaley, and Bill bought 333 granola bars to share among themselves. They divided each granola bar into 444 equal portions. Kristen ate 111 portion from each granola bar.
Answer:
Kristen had (3/4) of a granola bar in total.
Then the three other people have 2.25 granola bars to share amongst themselves.
Step-by-step explanation:
Complete Question
Tom, Kristen, Kaley, and Bill bought 3 granola bars to share among themselves. They divided each granola bar into 4 equal portions. Kristen ate 1 portion from each granola bar.
How many granola bars did Kristen eat.
Solution
4 of them bought 3 granola bars.
Then they divide each granola bar into 4 equal portions.
Each of the 3 granola bars gets divided into 4 equal portions, where each granola bar now has (4 × 1/4) portions.
Each portion is (1/4) of a granola bar.
Kristen then takes 1 portion from the 3 granola bars.
This means she had 3 × (1/4) granola bars.
Kristen had (3/4) of a granola bar in total.
Then the other three people had [3 - (3/4)] of a granola bar to share amongst themselves. It means they had (9/4) or 2.25 granola bars to share amongst themselves.
Hope this Helps!!!
What are two integers whose sum is -2 and product is -80?
Answer:
We can write:
x + y = -2
xy = -80
We can rewrite the first equation as x = -y - 2 and then plug that into the second equation to get (-y-2) * y = -80 → -y² - 2y = -80 → y² + 2y - 80 = 0 → (y - 8)(y + 10) = 0 → y = 8, -10. Substituting these values into the first equation we get x = -10, 8 so the answer is (x₁, y₁) = (-10, 8) or (x₂, y₂) = (8, -10).
Is 540171 divisible by 9?
Image is attached below.
If the sum of the digits its divisible by 9,
then the original number is divisible by 9.
Since 18 (the sum of the digits) is divisible by 9,
the number 540,171 is also divisible by 9.
Answer:
Yes, The number is divisible by 9
Step-by-step explanation:
If you divide the number by 9 you will get 60019. Also if we add the numbers we will get 18 which is also divisible by 9.
Hope this helps.
The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x − 4)3 − 7. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?
Answer:
The point (0, 0) in the graph of f(x) corresponds to the point (4, -7) in the graph of g(x)
Step-by-step explanation:
Notice that when we start with the function [tex]f(x)=x^3[/tex], and then transform it into the function: [tex]g(x)=(x-4)^3-7[/tex]
what we have done is to translate the graph of the function horizontally 4 units to the right (via subtracting 4 from the variable x), and 7 units vertically down (via subtracting 7 to the full functional expression).
Therefore, the point (0, 0) in the first function, will now appeared translated 4 units to the right (from x = 0 to x = 4) and 7 units down (from y = 0 to y = -7).
then the point (0, 0) after the translation becomes: (4, -7)
Answer:4, -7
Step-by-step explanation:
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Answer:
Step-by-step explanation:
(0,5), (1,0)
(0-5)/(1-0)= -5/1= -5
y - 0 = -5(x - 1)
y = -5x + 5
Find the area of the composite figure in square mm. Round your
answer to the nearest square milimeter. (Enter only a number as
your answer.)
Answer:
521
Step-by-step explanation:
Composite figure.
Draw a straight down from C to line segment AB. This forms a triangle.
Now, the area of this figure=
Area of semicircle+area of rectangle+ area of triangle.
Rectangle area formula = l times w
Length - 20
Width =14
14 times 20 = 280
Area of rectangle = 280
Semicircle area = area of circle/2
Area of circle = π[tex]r^2[/tex]
Diameter =20= 2r
r=10
π[tex]r^2[/tex]= π 10^2 =100π
100 times 3.14 =314
314/2 = 157
Area of semicircle = 157
Area of triangle= bh/2
Triangle's base= 32-20=12
Triangles height = 14
14 times 12 = 168
168/2 = 84
Area of triangle: 84
Area of semicircle+area of rectangle+ area of triangle.
157+280+84 =521
Below is the work a student completed with an error. Identify the step where the error occurred and give the correct solution. Step 1:(12-20)-3(8-3)+13 Step 2:-8-24-9+13 Step 3:-32-9+13 Step 4:-41+13
Answer:
The error is in Step 2. The student distributed -3 incorrectly; it should have been 9, not -9. The correct solution is -8 - 24 + 9 + 13 = -32 + 9 + 13 = -32 + 22 = -10.
Which of the following expressions are equivalent to -9/6?
the correct answer is:
A. 9/-6
In a causal-comparative study, what is the difference between independent variables and dependent variables? independent variables cause the effect measured in the dependent variables dependent variables cause the effect measured in the independent variables dependent variables are those that affect each other; independent variables do not independent variables exist before the study; dependent variables do not
Answer: independent variables cause the effect measured in the dependent variables
Step-by-step explanation: In a causal - comparative study, the dependent variables refers to the variable whose changes is being measured or observed. The changes or alteration of the dependent variable is induced by the different values of the independent variable. In causal - comparative study, the different independent variables is assumed to have a direct impact on the output or values of the dependent variable which is measured by the experimenter. Therefore, the independent variable does not change, but causes the observed changes noticed in the dependent variable.
PLLLLLLLLLLLLLLLEEEEEEEEEAAAAAAAASSSSSSSE HEEEEEEEEELP As soon as a new car that costs $25,000 is driven off the lot, it begins to depreciate at a rate of 24.9% annually. About how much money is the car worth after the second year?
Answer:
The value of the car after two years is $14,100.025
Step-by-step explanation:
Here, we want to calculate the value of a car after its second year, given the depreciation percentage.
To get the value of the car year after year at the fixed percentage level, what we do is to set up an exponential equation;
V = I(1-r)^t
where V is the present value
I is the initial value = $25,000
r is the rate = 24.9% = 24.9/100 = 0.249
t is the number of years = 2 in this case
So we substitute these values in the depreciation case and have;
V = 25000(1-0.249)^2
V = 25000(0.751)^2
V = $14,100.025
What is the solution to this equation?
4x-3 + 2x= 33
O A. x= 15
B. x = 18
O c. x = 5
O D. x = 6
Answer:
4x – 3 + 2x = 33
6x = 36
x = 6
D. x = 6
what is this answer 4\5+2\10
Answer:
1
Step-by-step explanation:
To add fractions, we need to make the denominators the same. Luckily, we can simplify 2/10 to 1/5. Now that the denominators are both 5, we can add. When adding fractions, we only add the numerator, and the denominator remains the same, so we'd do 4+1/5, which equals 5/5, which simplifies to 1.
Answer:
1 or 10/10
Step-by-step explanation:
Step 1 make a common denominator
to make a common demoniator multiply the top and bottom number by the same number
so multiply the 4 and 5 by 2 to get 8/10
Step 2 now that you have 8/10 add it with 2/10
Step 3 solve to get 10/10 and then simplify it to 1
3) What is the difference? 7,840 - 4,971*
0 2,769
0 2,869
0 2,879
0 2,969
Answer:
2869
Step-by-step explanation:
7,840 - 4,971
Subtract.
= 2869
Answer:
0 2,869
hopefully this helped :3
A recipe calls for 3 cups of flour for every 8 ounces of water. How many cups of
flour are needed if the baker uses 96 ounces of water?
Answer:
you need 36cups of flour
Step-by-step explanation:
3 cups of flour = 8 ounces of water
x cups of flour = 96 ounces of water
96*3 =8x
288 =8x
288/8=36
x=36
Factor this trinomial.
x² + 2x-3
A. (x + 3)(x + 1)
B. (x + 3)(x - 1)
C. (x-3)(x - 1)
D. (x-3)(x + 1)
Answer:
the answer is (x+3)(x-1).
hope u get it....
Answer:
B
Step-by-step explanation:
x^2 +3x -x -3 = x(x+3) -(x+3)=(x-1)(x+3)
The cost of six hens and one duck at the university poultry farm is GH₵40. While four hens and three ducks cost GH₵36. What is the cost of each type of bird?
Answer:
Step-by-step explanation:
Let's call hens h and ducks d. The first algebraic equation says that 6 hens (6h) plus (+) 1 duck (1d) cost (=) 40.
The second algebraic equations says that 4 hens (4h) plus (+) 3 ducks (3d) cost (=) 36.
The system is
6h + 1d = 40
4h + 3d = 36
The best way to go about this is to solve it by substitution since we have a 1d in the first equation. We will solve that equation for d since that makes the most sense algebraically. Doing that,
1d = 40 - 6h.
Now that we know what d equals, we can sub it into the second equation where we see a d. In order,
4h + 3d = 36 becomes
4h + 3(40 - 6h) = 36 and then simplify. By substituting into the second equation we eliminated one of the variables. You can only have 1 unknown in a single equation, and now we do!
4h + 120 - 18h = 36 and
-14h = -84 so
h = 6.
That means that each hen costs $6. Since the cost of a duck is found in the bold print equation above, we will sub in a 6 for h to solve for d:
1d = 40 - 6(6) and
d = 40 - 36 so
d = 4.
That means that each duck costs $4.
A study of an association between which ear is used for cell phone calls and whether the subject is left-handed or right-handed began with a survey e-mailed to 5000 people belonging to an otology online group, and 717 surveys were returned. (Otology relates to the ear and hearing.) What percentage of the 5000 surveys were returned? Does that response rate appear to be low? In general, what is a problem with a very low response rate? Of the 5000 surveys, nothing% were returned. This response rate ▼ appears does not appear to be low.
Answer:
Of the 5000 surveys, 14% were returned. This response rate APPEARS to be low.
Step-by-step explanation:
Given:
Total sample collected = 5000
Survey returned = 700
i) What percentage of the 5000 surveys were returned?
To find percentage returned, we have:
[tex] = \frac{700}{5000} * 100 = 14 percent [/tex]
Percentage returned = 14%
ii) Does that response rate appear to be low?
Yes, the response is significantly low as only 14% is returned out of expected 100%
iii) In general, what is a problem with a very low response rate?
The problem with in low response rate in general is that it causes the result to be biased as biased samples of those interested in a particular aspect may have been gotten.
Therefore, of the 5000 surveys, 14% were returned. This response rate APPEARS to be low.
The Vance family is saving money to buy a new car that costs $12,000. They plan to save $715 per month (m), and they have already saved $645. Which of the following inequalities show the number of months (m) the Vance family could save in order to buy the new car? Select all that apply. A. 715m≥11,355 B. 715m≤11,355 C. 12,000≤715m+645 D. 12,645≤715m
Answer:
C. 12,000≤715m+645
Step-by-step explanation:
You want to have either equal to or more than 12,000
Answecr:
C
Step-by-step explanation:
△ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and AX. Triangle A Y X is shown. Line segment B C is drawn from side A Y to A X to form triangle A B C. The proof that △ABC ~ △AYX is shown. Statements Reasons 1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given 2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle 3. AB = AC and AY = AX 3. definition of congruency 4. AY • AC = AX • AC 4. multiplication property of equality 5. AY • AC = AX • AB 5. substitution property of equality 6. 6. division property of equality 7. 7. division property of equality 8. ? 8. ? 9. △ABC ~ △AYX 9. SAS similarity theorem Which statement and reason are missing in the proof?
Explanation:
Here is our take on the proof shown in the problem statement. The missing statements and reasons are shown in bold.
Statements Reasons
1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given
2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle
3. AB = AC and AY = AX 3. definition of congruency
4. AY • AC = AX • AC 4. multiplication property of equality
5. AY • AC = AX • AB 5. substitution property of equality
6. AY • AC/AX = AB 6. division property of equality
7. AC/AX = AB/AY 7. division property of equality
8. Corresponding sides are proportional 8. Definition of proportional
9. △ABC ~ △AYX 9. SAS similarity theorem
_____
The reason given in statements 6 and 7 suggest you need to divide something. For SAS similarity, you need to show corresponding sides are proportional. The missing steps are to get to the point where you can say that.
Answer:
I think its A. ∠A ≅ ∠A; reflexive property
Step-by-step explanation:
FUNCTIONS HELP ME ASAP
Hey there! :)
Answer:
f(-2) = 2.
Step-by-step explanation:
To find f(-2), we simply need to look at the y value at x = -2.
At x = -2, the y value is equal to 2.
Therefore:
f(-2) = 2.
Answer: b)2
Step-by-step explanation:
Visually, when x = -2, y = 2